Title: A System Of Logic, Ratiocinative And Inductive
Author: Mill, John Stuart, 1806-1873
Language: English
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                            A SYSTEM OF LOGIC,

                       RATIOCINATIVE AND INDUCTIVE,

                      BEING A CONNECTED VIEW OF THE

                         PRINCIPLES OF EVIDENCE,

                                 AND THE

                   METHODS OF SCIENTIFIC INVESTIGATION.

                                    by

                            JOHN STUART MILL.

                             Eighth Edition.

                                New York:

                      Harper & Brothers, Publishers,

                             Franklin Square.

                                  1882.



CONTENTS


Preface To The First Edition.
Preface To The Third And Fourth Editions.
Introduction.
Book I. Of Names And Propositions.
   Chapter I. Of The Necessity Of Commencing With An Analysis Of Language.
   Chapter II. Of Names.
   Chapter III. Of The Things Denoted By Names.
   Chapter IV. Of Propositions.
   Chapter V. Of The Import Of Propositions.
   Chapter VI. Of Propositions Merely Verbal.
   Chapter VII. Of The Nature Of Classification, And The Five Predicables.
   Chapter VIII. Of Definition.
Book II. On Reasoning.
   Chapter I. Of Inference, Or Reasoning, In General.
   Chapter II. Of Ratiocination, Or Syllogism.
   Chapter III. Of The Functions And Logical Value Of The Syllogism.
   Chapter IV. Of Trains Of Reasoning, And Deductive Sciences.
   Chapter V. Of Demonstration, And Necessary Truths.
   Chapter VI. The Same Subject Continued.
   Chapter VII. Examination Of Some Opinions Opposed To The Preceding
   Doctrines.
Book III. Of Induction.
   Chapter I. Preliminary Observations On Induction In General.
   Chapter II. Of Inductions Improperly So Called.
   Chapter III. Of The Ground Of Induction.
   Chapter IV. Of Laws Of Nature.
   Chapter V. Of The Law Of Universal Causation.
   Chapter VI. On The Composition Of Causes.
   Chapter VII. On Observation And Experiment.
   Chapter VIII. Of The Four Methods Of Experimental Inquiry.
   Chapter IX. Miscellaneous Examples Of The Four Methods.
   Chapter X. Of Plurality Of Causes, And Of The Intermixture Of Effects.
   Chapter XI. Of The Deductive Method.
   Chapter XII. Of The Explanation Of Laws Of Nature.
   Chapter XIII. Miscellaneous Examples Of The Explanation Of Laws Of
   Nature.
   Chapter XIV. Of The Limits To The Explanation Of Laws Of Nature; And Of
   Hypotheses.
   Chapter XV. Of Progressive Effects; And Of The Continued Action Of
   Causes.
   Chapter XVI. Of Empirical Laws.
   Chapter XVII. Of Chance And Its Elimination.
   Chapter XVIII. Of The Calculation Of Chances.
   Chapter XIX. Of The Extension Of Derivative Laws To Adjacent Cases.
   Chapter XX. Of Analogy.
   Chapter XXI. Of The Evidence Of The Law Of Universal Causation.
   Chapter XXII. Of Uniformities Of Co-Existence Not Dependent On
   Causation.
   Chapter XXIV. Of The Remaining Laws Of Nature.
   Chapter XXV. Of The Grounds Of Disbelief.
Book IV. Of Operations Subsidiary To Induction.
   Chapter I. Of Observation And Description.
   Chapter II. Of Abstraction, Or The Formation Of Conceptions.
   Chapter III. Of Naming, As Subsidiary To Induction.
   Chapter IV. Of The Requisites Of A Philosophical Language, And The
   Principles Of Definition.
   Chapter V. On The Natural History Of The Variations In The Meaning Of
   Terms.
   Chapter VI. The Principles Of A Philosophical Language Further
   Considered.
   Chapter VII. Of Classification, As Subsidiary To Induction.
   Chapter VIII. Of Classification By Series.
Book V. On Fallacies.
   Chapter I. Of Fallacies In General.
   Chapter II. Classification Of Fallacies.
   Chapter III. Fallacies Of Simple Inspection; Or A Priori Fallacies.
   Chapter IV. Fallacies Of Observation.
   Chapter V. Fallacies Of Generalization.
   Chapter VI. Fallacies Of Ratiocination.
   Chapter VII. Fallacies Of Confusion.
Book VI. On The Logic Of The Moral Sciences.
   Chapter I. Introductory Remarks.
   Chapter II. Of Liberty And Necessity.
   Chapter III. That There Is, Or May Be, A Science Of Human Nature.
   Chapter IV. Of The Laws Of Mind.
   Chapter V. Of Ethology, Or The Science Of The Formation Of Character.
   Chapter VI. General Considerations On The Social Science.
   Chapter VII. Of The Chemical, Or Experimental, Method In The Social
   Science.
   Chapter VIII. Of The Geometrical, Or Abstract, Method.
   Chapter IX. Of The Physical, Or Concrete Deductive, Method.
   Chapter X. Of The Inverse Deductive, Or Historical, Method.
   Chapter XI. Additional Elucidations Of The Science Of History.
   Chapter XII. Of The Logic Of Practice, Or Art; Including Morality And
   Policy.
Footnotes



PREFACE TO THE FIRST EDITION.


This book makes no pretense of giving to the world a new theory of the
intellectual operations. Its claim to attention, if it possess any, is
grounded on the fact that it is an attempt, not to supersede, but to
embody and systematize, the best ideas which have been either promulgated
on its subject by speculative writers, or conformed to by accurate
thinkers in their scientific inquiries.

To cement together the detached fragments of a subject, never yet treated
as a whole; to harmonize the true portions of discordant theories, by
supplying the links of thought necessary to connect them, and by
disentangling them from the errors with which they are always more or less
interwoven, must necessarily require a considerable amount of original
speculation. To other originality than this, the present work lays no
claim. In the existing state of the cultivation of the sciences, there
would be a very strong presumption against any one who should imagine that
he had effected a revolution in the theory of the investigation of truth,
or added any fundamentally new process to the practice of it. The
improvement which remains to be effected in the methods of philosophizing
(and the author believes that they have much need of improvement) can only
consist in performing more systematically and accurately operations with
which, at least in their elementary form, the human intellect, in some one
or other of its employments, is already familiar.

In the portion of the work which treats of Ratiocination, the author has
not deemed it necessary to enter into technical details which may be
obtained in so perfect a shape from the existing treatises on what is
termed the Logic of the Schools. In the contempt entertained by many
modern philosophers for the syllogistic art, it will be seen that he by no
means participates; though the scientific theory on which its defense is
usually rested appears to him erroneous: and the view which he has
suggested of the nature and functions of the Syllogism may, perhaps,
afford the means of conciliating the principles of the art with as much as
is well grounded in the doctrines and objections of its assailants.

The same abstinence from details could not be observed in the First Book,
on Names and Propositions; because many useful principles and distinctions
which were contained in the old Logic have been gradually omitted from the
writings of its later teachers; and it appeared desirable both to revive
these, and to reform and rationalize the philosophical foundation on which
they stood. The earlier chapters of this preliminary Book will
consequently appear, to some readers, needlessly elementary and
scholastic. But those who know in what darkness the nature of our
knowledge, and of the processes by which it is obtained, is often involved
by a confused apprehension of the import of the different classes of Words
and Assertions, will not regard these discussions as either frivolous, or
irrelevant to the topics considered in the later Books.

On the subject of Induction, the task to be performed was that of
generalizing the modes of investigating truth and estimating evidence, by
which so many important and recondite laws of nature have, in the various
sciences, been aggregated to the stock of human knowledge. That this is
not a task free from difficulty may be presumed from the fact that even at
a very recent period, eminent writers (among whom it is sufficient to name
Archbishop Whately, and the author of a celebrated article on Bacon in the
_Edinburgh Review_) have not scrupled to pronounce it impossible.(1) The
author has endeavored to combat their theory in the manner in which
Diogenes confuted the skeptical reasonings against the possibility of
motion; remembering that Diogenes’s argument would have been equally
conclusive, though his individual perambulations might not have extended
beyond the circuit of his own tub.

Whatever may be the value of what the author has succeeded in effecting on
this branch of his subject, it is a duty to acknowledge that for much of
it he has been indebted to several important treatises, partly historical
and partly philosophical, on the generalities and processes of physical
science, which have been published within the last few years. To these
treatises, and to their authors, he has endeavored to do justice in the
body of the work. But as with one of these writers, Dr. Whewell, he has
occasion frequently to express differences of opinion, it is more
particularly incumbent on him in this place to declare, that without the
aid derived from the facts and ideas contained in that gentleman’s
“History of the Inductive Sciences,” the corresponding portion of this
work would probably not have been written.

The concluding Book is an attempt to contribute toward the solution of a
question which the decay of old opinions, and the agitation that disturbs
European society to its inmost depths, render as important in the present
day to the practical interests of human life, as it must at all times be
to the completeness of our speculative knowledge—viz.: Whether moral and
social phenomena are really exceptions to the general certainty and
uniformity of the course of nature; and how far the methods by which so
many of the laws of the physical world have been numbered among truths
irrevocably acquired and universally assented to, can be made instrumental
to the formation of a similar body of received doctrine in moral and
political science.



PREFACE TO THE THIRD AND FOURTH EDITIONS.


Several criticisms, of a more or less controversial character, on this
work, have appeared since the publication of the second edition; and Dr.
Whewell has lately published a reply to those parts of it in which some of
his opinions were controverted.(2)

I have carefully reconsidered all the points on which my conclusions have
been assailed. But I have not to announce a change of opinion on any
matter of importance. Such minor oversights as have been detected, either
by myself or by my critics, I have, in general silently, corrected: but it
is not to be inferred that I agree with the objections which have been
made to a passage, in every instance in which I have altered or canceled
it. I have often done so, merely that it might not remain a
stumbling-block, when the amount of discussion necessary to place the
matter in its true light would have exceeded what was suitable to the
occasion.

To several of the arguments which have been urged against me, I have
thought it useful to reply with some degree of minuteness; not from any
taste for controversy, but because the opportunity was favorable for
placing my own conclusions, and the grounds of them, more clearly and
completely before the reader. Truth on these subjects is militant, and can
only establish itself by means of conflict. The most opposite opinions can
make a plausible show of evidence while each has the statement of its own
case; and it is only possible to ascertain which of them is in the right,
after hearing and comparing what each can say against the other, and what
the other can urge in its defense.

Even the criticisms from which I most dissent have been of great service
to me, by showing in what places the exposition most needed to be
improved, or the argument strengthened. And I should have been well
pleased if the book had undergone a much greater amount of attack; as in
that case I should probably have been enabled to improve it still more
than I believe I have now done.

                  -------------------------------------

In the subsequent editions, the attempt to improve the work by additions
and corrections, suggested by criticism or by thought, has been continued.
The additions and corrections in the present (eighth) edition, which are
not very considerable, are chiefly such as have been suggested by
Professor Bain’s “Logic,” a book of great merit and value. Mr. Bain’s view
of the science is essentially the same with that taken in the present
treatise, the differences of opinion being few and unimportant compared
with the agreements; and he has not only enriched the exposition by many
applications and illustrative details, but has appended to it a minute and
very valuable discussion of the logical principles specially applicable to
each of the sciences—a task for which the encyclopedical character of his
knowledge peculiarly qualified him. I have in several instances made use
of his exposition to improve my own, by adopting, and occasionally by
controverting, matter contained in his treatise.

The longest of the additions belongs to the chapter on Causation, and is a
discussion of the question how far, if at all, the ordinary mode of
stating the law of Cause and Effect requires modification to adapt it to
the new doctrine of the Conservation of Force—a point still more fully and
elaborately treated in Mr. Bain’s work.



INTRODUCTION.


§ 1. There is as great diversity among authors in the modes which they
have adopted of defining logic, as in their treatment of the details of
it. This is what might naturally be expected on any subject on which
writers have availed themselves of the same language as a means of
delivering different ideas. Ethics and jurisprudence are liable to the
remark in common with logic. Almost every writer having taken a different
view of some of the particulars which these branches of knowledge are
usually understood to include; each has so framed his definition as to
indicate beforehand his own peculiar tenets, and sometimes to beg the
question in their favor.

This diversity is not so much an evil to be complained of, as an
inevitable and in some degree a proper result of the imperfect state of
those sciences. It is not to be expected that there should be agreement
about the definition of any thing, until there is agreement about the
thing itself. To define, is to select from among all the properties of a
thing, those which shall be understood to be designated and declared by
its name; and the properties must be well known to us before we can be
competent to determine which of them are fittest to be chosen for this
purpose. Accordingly, in the case of so complex an aggregation of
particulars as are comprehended in any thing which can be called a
science, the definition we set out with is seldom that which a more
extensive knowledge of the subject shows to be the most appropriate. Until
we know the particulars themselves, we can not fix upon the most correct
and compact mode of circumscribing them by a general description. It was
not until after an extensive and accurate acquaintance with the details of
chemical phenomena, that it was found possible to frame a rational
definition of chemistry; and the definition of the science of life and
organization is still a matter of dispute. So long as the sciences are
imperfect, the definitions must partake of their imperfection; and if the
former are progressive, the latter ought to be so too. As much, therefore,
as is to be expected from a definition placed at the commencement of a
subject, is that it should define the scope of our inquiries: and the
definition which I am about to offer of the science of logic, pretends to
nothing more than to be a statement of the question which I have put to
myself, and which this book is an attempt to resolve. The reader is at
liberty to object to it as a definition of logic; but it is at all events
a correct definition of the subject of this volume.

§ 2. Logic has often been called the Art of Reasoning. A writer(3) who has
done more than any other person to restore this study to the rank from
which it had fallen in the estimation of the cultivated class in our own
country, has adopted the above definition with an amendment; he has
defined Logic to be the Science, as well as the Art, of reasoning; meaning
by the former term, the analysis of the mental process which takes place
whenever we reason, and by the latter, the rules, grounded on that
analysis, for conducting the process correctly. There can be no doubt as
to the propriety of the emendation. A right understanding of the mental
process itself, of the conditions it depends on, and the steps of which it
consists, is the only basis on which a system of rules, fitted for the
direction of the process, can possibly be founded. Art necessarily
presupposes knowledge; art, in any but its infant state, presupposes
scientific knowledge: and if every art does not bear the name of a
science, it is only because several sciences are often necessary to form
the groundwork of a single art. So complicated are the conditions which
govern our practical agency, that to enable one thing to be _done_, it is
often requisite to _know_ the nature and properties of many things.

Logic, then, comprises the science of reasoning, as well as an art,
founded on that science. But the word Reasoning, again, like most other
scientific terms in popular use, abounds in ambiguities. In one of its
acceptations, it means syllogizing; or the mode of inference which may be
called (with sufficient accuracy for the present purpose) concluding from
generals to particulars. In another of its senses, to reason is simply to
infer any assertion, from assertions already admitted: and in this sense
induction is as much entitled to be called reasoning as the demonstrations
of geometry.

Writers on logic have generally preferred the former acceptation of the
term: the latter, and more extensive signification is that in which I mean
to use it. I do this by virtue of the right I claim for every author, to
give whatever provisional definition he pleases of his own subject. But
sufficient reasons will, I believe, unfold themselves as we advance, why
this should be not only the provisional but the final definition. It
involves, at all events, no arbitrary change in the meaning of the word;
for, with the general usage of the English language, the wider
signification, I believe, accords better than the more restricted one.

§ 3. But reasoning, even in the widest sense of which the word is
susceptible, does not seem to comprehend all that is included, either in
the best, or even in the most current, conception of the scope and
province of our science. The employment of the word Logic to denote the
theory of Argumentation, is derived from the Aristotelian, or, as they are
commonly termed, the scholastic, logicians. Yet even with them, in their
systematic treatises, Argumentation was the subject only of the third
part: the two former treated of Terms, and of Propositions; under one or
other of which heads were also included Definition and Division. By some,
indeed, these previous topics were professedly introduced only on account
of their connection with reasoning, and as a preparation for the doctrine
and rules of the syllogism. Yet they were treated with greater minuteness,
and dwelt on at greater length, than was required for that purpose alone.
More recent writers on logic have generally understood the term as it was
employed by the able author of the Port Royal Logic; viz., as equivalent
to the Art of Thinking. Nor is this acceptation confined to books, and
scientific inquiries. Even in ordinary conversation, the ideas connected
with the word Logic include at least precision of language, and accuracy
of classification: and we perhaps oftener hear persons speak of a logical
arrangement, or of expressions logically defined, than of conclusions
logically deduced from premises. Again, a man is often called a great
logician, or a man of powerful logic, not for the accuracy of his
deductions, but for the extent of his command over premises; because the
general propositions required for explaining a difficulty or refuting a
sophism, copiously and promptly occur to him: because, in short, his
knowledge, besides being ample, is well under his command for
argumentative use. Whether, therefore, we conform to the practice of those
who have made the subject their particular study, or to that of popular
writers and common discourse, the province of logic will include several
operations of the intellect not usually considered to fall within the
meaning of the terms Reasoning and Argumentation.

These various operations might be brought within the compass of the
science, and the additional advantage be obtained of a very simple
definition, if, by an extension of the term, sanctioned by high
authorities, we were to define logic as the science which treats of the
operations of the human understanding in the pursuit of truth. For to this
ultimate end, naming, classification, definition, and all other operations
over which logic has ever claimed jurisdiction, are essentially
subsidiary. They may all be regarded as contrivances for enabling a person
to know the truths which are needful to him, and to know them at the
precise moment at which they are needful. Other purposes, indeed, are also
served by these operations; for instance, that of imparting our knowledge
to others. But, viewed with regard to this purpose, they have never been
considered as within the province of the logician. The sole object of
Logic is the guidance of one’s own thoughts: the communication of those
thoughts to others falls under the consideration of Rhetoric, in the large
sense in which that art was conceived by the ancients; or of the still
more extensive art of Education. Logic takes cognizance of our
intellectual operations only as they conduce to our own knowledge, and to
our command over that knowledge for our own uses. If there were but one
rational being in the universe, that being might be a perfect logician;
and the science and art of logic would be the same for that one person as
for the whole human race.

§ 4. But, if the definition which we formerly examined included too
little, that which is now suggested has the opposite fault of including
too much.

Truths are known to us in two ways: some are known directly, and of
themselves; some through the medium of other truths. The former are the
subject of Intuition, or Consciousness;(4) the latter, of Inference. The
truths known by intuition are the original premises from which all others
are inferred. Our assent to the conclusion being grounded on the truth of
the premises, we never could arrive at any knowledge by reasoning, unless
something could be known antecedently to all reasoning.

Examples of truths known to us by immediate consciousness, are our own
bodily sensations and mental feelings. I know directly, and of my own
knowledge, that I was vexed yesterday, or that I am hungry to-day.
Examples of truths which we know only by way of inference, are occurrences
which took place while we were absent, the events recorded in history, or
the theorems of mathematics. The two former we infer from the testimony
adduced, or from the traces of those past occurrences which still exist;
the latter, from the premises laid down in books of geometry, under the
title of definitions and axioms. Whatever we are capable of knowing must
belong to the one class or to the other; must be in the number of the
primitive data, or of the conclusions which can be drawn from these.

With the original data, or ultimate premises of our knowledge; with their
number or nature, the mode in which they are obtained, or the tests by
which they may be distinguished; logic, in a direct way at least, has, in
the sense in which I conceive the science, nothing to do. These questions
are partly not a subject of science at all, partly that of a very
different science.

Whatever is known to us by consciousness is known beyond possibility of
question. What one sees or feels, whether bodily or mentally, one can not
but be sure that one sees or feels. No science is required for the purpose
of establishing such truths; no rules of art can render our knowledge of
them more certain than it is in itself. There is no logic for this portion
of our knowledge.

But we may fancy that we see or feel what we in reality infer. A truth, or
supposed truth, which is really the result of a very rapid inference, may
seem to be apprehended intuitively. It has long been agreed by thinkers of
the most opposite schools, that this mistake is actually made in so
familiar an instance as that of the eyesight. There is nothing of which we
appear to ourselves to be more directly conscious than the distance of an
object from us. Yet it has long been ascertained, that what is perceived
by the eye, is at most nothing more than a variously colored surface; that
when we fancy we see distance, all we really see is certain variations of
apparent size, and degrees of faintness of color; that our estimate of the
object’s distance from us is the result partly of a rapid inference from
the muscular sensations accompanying the adjustment of the focal distance
of the eye to objects unequally remote from us, and partly of a comparison
(made with so much rapidity that we are unconscious of making it) between
the size and color of the object as they appear at the time, and the size
and color of the same or of similar objects as they appeared when close at
hand, or when their degree of remoteness was known by other evidence. The
perception of distance by the eye, which seems so like intuition, is thus,
in reality, an inference grounded on experience; an inference, too, which
we learn to make; and which we make with more and more correctness as our
experience increases; though in familiar cases it takes place so rapidly
as to appear exactly on a par with those perceptions of sight which are
really intuitive, our perceptions of color.(5)

Of the science, therefore, which expounds the operations of the human
understanding in the pursuit of truth, one essential part is the inquiry:
What are the facts which are the objects of intuition or consciousness,
and what are those which we merely infer? But this inquiry has never been
considered a portion of logic. Its place is in another and a perfectly
distinct department of science, to which the name metaphysics more
particularly belongs: that portion of mental philosophy which attempts to
determine what part of the furniture of the mind belongs to it originally,
and what part is constructed out of materials furnished to it from
without. To this science appertain the great and much debated questions of
the existence of matter; the existence of spirit, and of a distinction
between it and matter; the reality of time and space, as things without
the mind, and distinguishable from the objects which are said to exist in
them. For in the present state of the discussion on these topics, it is
almost universally allowed that the existence of matter or of spirit, of
space or of time, is in its nature unsusceptible of being proved; and that
if any thing is known of them, it must be by immediate intuition. To the
same science belong the inquiries into the nature of Conception,
Perception, Memory, and Belief; all of which are operations of the
understanding in the pursuit of truth; but with which, as phenomena of the
mind, or with the possibility which may or may not exist of analyzing any
of them into simpler phenomena, the logician as such has no concern. To
this science must also be referred the following, and all analogous
questions: To what extent our intellectual faculties and our emotions are
innate—to what extent the result of association: Whether God and duty are
realities, the existence of which is manifest to us _a priori_ by the
constitution of our rational faculty; or whether our ideas of them are
acquired notions, the origin of which we are able to trace and explain;
and the reality of the objects themselves a question not of consciousness
or intuition, but of evidence and reasoning.

The province of logic must be restricted to that portion of our knowledge
which consists of inferences from truths previously known; whether those
antecedent data be general propositions, or particular observations and
perceptions. Logic is not the science of Belief, but the science of Proof,
or Evidence. In so far as belief professes to be founded on proof, the
office of logic is to supply a test for ascertaining whether or not the
belief is well grounded. With the claims which any proposition has to
belief on the evidence of consciousness—that is, without evidence in the
proper sense of the word—logic has nothing to do.

§ 5. By far the greatest portion of our knowledge, whether of general
truths or of particular facts, being avowedly matter of inference, nearly
the whole, not only of science, but of human conduct, is amenable to the
authority of logic. To draw inferences has been said to be the great
business of life. Every one has daily, hourly, and momentary need of
ascertaining facts which he has not directly observed; not from any
general purpose of adding to his stock of knowledge, but because the facts
themselves are of importance to his interests or to his occupations. The
business of the magistrate, of the military commander, of the navigator,
of the physician, of the agriculturist, is merely to judge of evidence,
and to act accordingly. They all have to ascertain certain facts, in order
that they may afterward apply certain rules, either devised by themselves
or prescribed for their guidance by others; and as they do this well or
ill, so they discharge well or ill the duties of their several callings.
It is the only occupation in which the mind never ceases to be engaged;
and is the subject, not of logic, but of knowledge in general.

Logic, however, is not the same thing with knowledge, though the field of
logic is co-extensive with the field of knowledge. Logic is the common
judge and arbiter of all particular investigations. It does not undertake
to find evidence, but to determine whether it has been found. Logic
neither observes, nor invents, nor discovers; but judges. It is no part of
the business of logic to inform the surgeon what appearances are found to
accompany a violent death. This he must learn from his own experience and
observation, or from that of others, his predecessors in his peculiar
pursuit. But logic sits in judgment on the sufficiency of that observation
and experience to justify his rules, and on the sufficiency of his rules
to justify his conduct. It does not give him proofs, but teaches him what
makes them proofs, and how he is to judge of them. It does not teach that
any particular fact proves any other, but points out to what conditions
all facts must conform, in order that they may prove other facts. To
decide whether any given fact fulfills these conditions, or whether facts
can be found which fulfill them in a given case, belongs exclusively to
the particular art or science, or to our knowledge of the particular
subject.

It is in this sense that logic is, what it was so expressively called by
the schoolmen and by Bacon, _ars artium_; the science of science itself.
All science consists of data and conclusions from those data, of proofs
and what they prove: now logic points out what relations must subsist
between data and whatever can be concluded from them, between proof and
every thing which it can prove. If there be any such indispensable
relations, and if these can be precisely determined, every particular
branch of science, as well as every individual in the guidance of his
conduct, is bound to conform to those relations, under the penalty of
making false inferences—of drawing conclusions which are not grounded in
the realities of things. Whatever has at any time been concluded justly,
whatever knowledge has been acquired otherwise than by immediate
intuition, depended on the observance of the laws which it is the province
of logic to investigate. If the conclusions are just, and the knowledge
real, those laws, whether known or not, have been observed.

§ 6. We need not, therefore, seek any further for a solution of the
question, so often agitated, respecting the utility of logic. If a science
of logic exists, or is capable of existing, it must be useful. If there be
rules to which every mind consciously or unconsciously conforms in every
instance in which it infers rightly, there seems little necessity for
discussing whether a person is more likely to observe those rules, when he
knows the rules, than when he is unacquainted with them.

A science may undoubtedly be brought to a certain, not inconsiderable,
stage of advancement, without the application of any other logic to it
than what all persons, who are said to have a sound understanding, acquire
empirically in the course of their studies. Mankind judged of evidence,
and often correctly, before logic was a science, or they never could have
made it one. And they executed great mechanical works before they
understood the laws of mechanics. But there are limits both to what
mechanicians can do without principles of mechanics, and to what thinkers
can do without principles of logic. A few individuals, by extraordinary
genius, or by the accidental acquisition of a good set of intellectual
habits, may work without principles in the same way, or nearly the same
way, in which they would have worked if they had been in possession of
principles. But the bulk of mankind require either to understand the
theory of what they are doing, or to have rules laid down for them by
those who have understood the theory. In the progress of science from its
easiest to its more difficult problems, each great step in advance has
usually had either as its precursor, or as its accompaniment and necessary
condition, a corresponding improvement in the notions and principles of
logic received among the most advanced thinkers. And if several of the
more difficult sciences are still in so defective a state; if not only so
little is proved, but disputation has not terminated even about the little
which seemed to be so; the reason perhaps is, that men’s logical notions
have not yet acquired the degree of extension, or of accuracy, requisite
for the estimation of the evidence proper to those particular departments
of knowledge.

§ 7. Logic, then, is the science of the operations of the understanding
which are subservient to the estimation of evidence: both the process
itself of advancing from known truths to unknown, and all other
intellectual operations in so far as auxiliary to this. It includes,
therefore, the operation of Naming; for language is an instrument of
thought, as well as a means of communicating our thoughts. It includes,
also, Definition, and Classification. For, the use of these operations
(putting all other minds than one’s own out of consideration) is to serve
not only for keeping our evidences and the conclusions from them permanent
and readily accessible in the memory, but for so marshaling the facts
which we may at any time be engaged in investigating, as to enable us to
perceive more clearly what evidence there is, and to judge with fewer
chances of error whether it be sufficient. These, therefore, are
operations specially instrumental to the estimation of evidence, and, as
such, are within the province of Logic. There are other more elementary
processes, concerned in all thinking, such as Conception, Memory, and the
like; but of these it is not necessary that Logic should take any peculiar
cognizance, since they have no special connection with the problem of
Evidence, further than that, like all other problems addressed to the
understanding, it presupposes them.

Our object, then, will be, to attempt a correct analysis of the
intellectual process called Reasoning or Inference, and of such other
mental operations as are intended to facilitate this: as well as, on the
foundation of this analysis, and _pari passu_ with it, to bring together
or frame a set of rules or canons for testing the sufficiency of any given
evidence to prove any given proposition.

With respect to the first part of this undertaking, I do not attempt to
decompose the mental operations in question into their ultimate elements.
It is enough if the analysis as far as it goes is correct, and if it goes
far enough for the practical purposes of logic considered as an art. The
separation of a complicated phenomenon into its component parts is not
like a connected and interdependent chain of proof. If one link of an
argument breaks, the whole drops to the ground; but one step toward an
analysis holds good and has an independent value, though we should never
be able to make a second. The results which have been obtained by
analytical chemistry are not the less valuable, though it should be
discovered that all which we now call simple substances are really
compounds. All other things are at any rate compounded of those elements:
whether the elements themselves admit of decomposition, is an important
inquiry, but does not affect the certainty of the science up to that
point.

I shall, accordingly, attempt to analyze the process of inference, and the
processes subordinate to inference, so far only as may be requisite for
ascertaining the difference between a correct and an incorrect performance
of those processes. The reason for thus limiting our design, is evident.
It has been said by objectors to logic, that we do not learn to use our
muscles by studying their anatomy. The fact is not quite fairly stated;
for if the action of any of our muscles were vitiated by local weakness,
or other physical defect, a knowledge of their anatomy might be very
necessary for effecting a cure. But we should be justly liable to the
criticism involved in this objection, were we, in a treatise on logic, to
carry the analysis of the reasoning process beyond the point at which any
inaccuracy which may have crept into it must become visible. In learning
bodily exercises (to carry on the same illustration) we do, and must,
analyze the bodily motions so far as is necessary for distinguishing those
which ought to be performed from those which ought not. To a similar
extent, and no further, it is necessary that the logician should analyze
the mental processes with which Logic is concerned. Logic has no interest
in carrying the analysis beyond the point at which it becomes apparent
whether the operations have in any individual case been rightly or wrongly
performed: in the same manner as the science of music teaches us to
discriminate between musical notes, and to know the combinations of which
they are susceptible, but not what number of vibrations in a second
correspond to each; which, though useful to be known, is useful for
totally different purposes. The extension of Logic as a Science is
determined by its necessities as an Art: whatever it does not need for its
practical ends, it leaves to the larger science which may be said to
correspond, not to any particular art, but to art in general; the science
which deals with the constitution of the human faculties; and to which, in
the part of our mental nature which concerns Logic, as well as in all
other parts, it belongs to decide what are ultimate facts, and what are
resolvable into other facts. And I believe it will be found that most of
the conclusions arrived at in this work have no necessary connection with
any particular views respecting the ulterior analysis. Logic is common
ground on which the partisans of Hartley and of Reid, of Locke and of
Kant, may meet and join hands. Particular and detached opinions of all
these thinkers will no doubt occasionally be controverted, since all of
them were logicians as well as metaphysicians; but the field on which
their principal battles have been fought, lies beyond the boundaries of
our science.

It can not, indeed, be pretended that logical principles can be altogether
irrelevant to those more abstruse discussions; nor is it possible but that
the view we are led to take of the problem which logic proposes, must have
a tendency favorable to the adoption of some one opinion, on these
controverted subjects, rather than another. For metaphysics, in
endeavoring to solve its own peculiar problem, must employ means, the
validity of which falls under the cognizance of logic. It proceeds, no
doubt, as far as possible, merely by a closer and more attentive
interrogation of our consciousness, or more properly speaking, of our
memory; and so far is not amenable to logic. But wherever this method is
insufficient to attain the end of its inquiries, it must proceed, like
other sciences, by means of evidence. Now, the moment this science begins
to draw inferences from evidence, logic becomes the sovereign judge
whether its inferences are well grounded, or what other inferences would
be so.

This, however, constitutes no nearer or other relation between logic and
metaphysics, than that which exists between logic and every other science.
And I can conscientiously affirm that no one proposition laid down in this
work has been adopted for the sake of establishing, or with any reference
to its fitness for being employed in establishing, preconceived opinions
in any department of knowledge or of inquiry on which the speculative
world is still undecided.(6)



                                 Book I.


OF NAMES AND PROPOSITIONS.


“La scolastique, qui produisit dans la logique, comme dans la morale, et
dans une partie de la métaphysique, une subtilité, une précision d’idées,
dont l’habitude inconnue aux anciens, a contribué plus qu’on ne croit au
progrès de la bonne philosophie.”—CONDORCET, _Vie de Turgot_.

“To the schoolmen the vulgar languages are principally indebted for what
precision and analytic subtlety they possess.”—SIR W. HAMILTON,
_Discussions in Philosophy_.



                                Chapter I.


Of The Necessity Of Commencing With An Analysis Of Language.


§ 1. It is so much the established practice of writers on logic to
commence their treatises by a few general observations (in most cases, it
is true, rather meagre) on Terms and their varieties, that it will,
perhaps, scarcely be required from me, in merely following the common
usage, to be as particular in assigning my reasons, as it is usually
expected that those should be who deviate from it.

The practice, indeed, is recommended by considerations far too obvious to
require a formal justification. Logic is a portion of the Art of Thinking:
Language is evidently, and by the admission of all philosophers, one of
the principal instruments or helps of thought; and any imperfection in the
instrument, or in the mode of employing it, is confessedly liable, still
more than in almost any other art, to confuse and impede the process, and
destroy all ground of confidence in the result. For a mind not previously
versed in the meaning and right use of the various kinds of words, to
attempt the study of methods of philosophizing, would be as if some one
should attempt to become an astronomical observer, having never learned to
adjust the focal distance of his optical instruments so as to see
distinctly.

Since Reasoning, or Inference, the principal subject of logic, is an
operation which usually takes place by means of words, and in complicated
cases can take place in no other way; those who have not a thorough
insight into the signification and purposes of words, will be under
chances, amounting almost to certainty, of reasoning or inferring
incorrectly. And logicians have generally felt that unless, in the very
first stage, they removed this source of error; unless they taught their
pupil to put away the glasses which distort the object, and to use those
which are adapted to his purpose in such a manner as to assist, not
perplex, his vision; he would not be in a condition to practice the
remaining part of their discipline with any prospect of advantage.
Therefore it is that an inquiry into language, so far as is needful to
guard against the errors to which it gives rise, has at all times been
deemed a necessary preliminary to the study of logic.

But there is another reason, of a still more fundamental nature, why the
import of words should be the earliest subject of the logician’s
consideration: because without it he can not examine into the import of
Propositions. Now this is a subject which stands on the very threshold of
the science of logic.

The object of logic, as defined in the Introductory Chapter, is to
ascertain how we come by that portion of our knowledge (much the greatest
portion) which is not intuitive: and by what criterion we can, in matters
not self-evident, distinguish between things proved and things not proved,
between what is worthy and what is unworthy of belief. Of the various
questions which present themselves to our inquiring faculties, some
receive an answer from direct consciousness, others, if resolved at all,
can only be resolved by means of evidence. Logic is concerned with these
last. But before inquiring into the mode of resolving questions, it is
necessary to inquire what are those which offer themselves; what questions
are conceivable; what inquiries are there, to which mankind have either
obtained, or been able to imagine it possible that they should obtain, an
answer. This point is best ascertained by a survey and analysis of
Propositions.

§ 2. The answer to every question which it is possible to frame, must be
contained in a Proposition, or Assertion. Whatever can be an object of
belief, or even of disbelief, must, when put into words, assume the form
of a proposition. All truth and all error lie in propositions. What, by a
convenient misapplication of an abstract term, we call a Truth, means
simply a True Proposition; and errors are false propositions. To know the
import of all possible propositions would be to know all questions which
can be raised, all matters which are susceptible of being either believed
or disbelieved. How many kinds of inquiries can be propounded; how many
kinds of judgments can be made; and how many kinds of propositions it is
possible to frame with a meaning, are but different forms of one and the
same question. Since, then, the objects of all Belief and of all Inquiry
express themselves in propositions, a sufficient scrutiny of Propositions
and of their varieties will apprise us what questions mankind have
actually asked of themselves, and what, in the nature of answers to those
questions, they have actually thought they had grounds to believe.

Now the first glance at a proposition shows that it is formed by putting
together two names. A proposition, according to the common simple
definition, which is sufficient for our purpose is, _discourse, in which
something is affirmed or denied of something_. Thus, in the proposition,
Gold is yellow, the quality yellow is affirmed of the substance _gold_. In
the proposition, Franklin was not born in England, the fact expressed by
the words _born in England_ is denied of the man Franklin.

Every proposition consists of three parts: the Subject, the Predicate, and
the Copula. The predicate is the name denoting that which is affirmed or
denied. The subject is the name denoting the person or thing which
something is affirmed or denied of. The copula is the sign denoting that
there is an affirmation or denial, and thereby enabling the hearer or
reader to distinguish a proposition from any other kind of discourse.
Thus, in the proposition, The earth is round, the Predicate is the word
_round_, which denotes the quality affirmed, or (as the phrase is)
predicated: _the earth_, words denoting the object which that quality is
affirmed of, compose the Subject; the word _is_, which serves as the
connecting mark between the subject and predicate, to show that one of
them is affirmed of the other, is called the Copula.

Dismissing, for the present, the copula, of which more will be said
hereafter, every proposition, then, consists of at least two names—brings
together two names, in a particular manner. This is already a first step
toward what we are in quest of. It appears from this, that for an act of
belief, _one_ object is not sufficient; the simplest act of belief
supposes, and has something to do with, _two_ objects—two names, to say
the least; and (since the names must be names of something) two _namable
things_. A large class of thinkers would cut the matter short by saying,
two _ideas_. They would say, that the subject and predicate are both of
them names of ideas; the idea of gold, for instance, and the idea of
yellow; and that what takes place (or part of what takes place) in the act
of belief consists in bringing (as it is often expressed) one of these
ideas under the other. But this we are not yet in a condition to say:
whether such be the correct mode of describing the phenomenon, is an after
consideration. The result with which for the present we must be contented,
is, that in every act of belief _two_ objects are in some manner taken
cognizance of; that there can be no belief claimed, or question
propounded, which does not embrace two distinct (either material or
intellectual) subjects of thought; each of them capable, or not, of being
conceived by itself, but incapable of being believed by itself.

I may say, for instance, “the sun.” The word has a meaning, and suggests
that meaning to the mind of any one who is listening to me. But suppose I
ask him, Whether it is true: whether he believes it? He can give no
answer. There is as yet nothing to believe, or to disbelieve. Now,
however, let me make, of all possible assertions respecting the sun, the
one which involves the least of reference to any object besides itself;
let me say, “the sun exists.” Here, at once, is something which a person
can say he believes. But here, instead of only one, we find two distinct
objects of conception: the sun is one object; existence is another. Let it
not be said that this second conception, existence, is involved in the
first; for the sun may be conceived as no longer existing. “The sun” does
not convey all the meaning that is conveyed by “the sun exists:” “my
father” does not include all the meaning of “my father exists,” for he may
be dead; “a round square” does not include the meaning of “a round square
exists,” for it does not and can not exist. When I say “the sun,” “my
father,” or a “round square,” I do not call upon the hearer for any belief
or disbelief, nor can either the one or the other be afforded me; but if I
say, “the sun exists,” “my father exists,” or “a round square exists,” I
call for belief; and should, in the first of the three instances, meet
with it; in the second, with belief or disbelief, as the case might be; in
the third, with disbelief.

§ 3. This first step in the analysis of the object of belief, which,
though so obvious, will be found to be not unimportant, is the only one
which we shall find it practicable to make without a preliminary survey of
language. If we attempt to proceed further in the same path, that is, to
analyze any further the import of Propositions; we find forced upon us, as
a subject of previous consideration, the import of Names. For every
proposition consists of two names; and every proposition affirms or denies
one of these names, of the other. Now what we do, what passes in our mind,
when we affirm or deny two names of one another, must depend on what they
are names of; since it is with reference to that, and not to the mere
names themselves, that we make the affirmation or denial. Here, therefore,
we find a new reason why the signification of names, and the relation
generally between names and the things signified by them, must occupy the
preliminary stage of the inquiry we are engaged in.

It may be objected that the meaning of names can guide us at most only to
the opinions, possibly the foolish and groundless opinions, which mankind
have formed concerning things, and that as the object of philosophy is
truth, not opinion, the philosopher should dismiss words and look into
things themselves, to ascertain what questions can be asked and answered
in regard to them. This advice (which no one has it in his power to
follow) is in reality an exhortation to discard the whole fruits of the
labors of his predecessors, and conduct himself as if he were the first
person who had ever turned an inquiring eye upon nature. What does any
one’s personal knowledge of Things amount to, after subtracting all which
he has acquired by means of the words of other people? Even after he has
learned as much as people usually do learn from others, will the notions
of things contained in his individual mind afford as sufficient a basis
for a _catalogue raisonné_ as the notions which are in the minds of all
mankind?

In any enumeration and classification of Things, which does not set out
from their names, no varieties of things will of course be comprehended
but those recognized by the particular inquirer; and it will still remain
to be established, by a subsequent examination of names, that the
enumeration has omitted nothing which ought to have been included. But if
we begin with names, and use them as our clue to the things, we bring at
once before us all the distinctions which have been recognized, not by a
single inquirer, but by all inquirers taken together. It doubtless may,
and I believe it will, be found, that mankind have multiplied the
varieties unnecessarily, and have imagined distinctions among things,
where there were only distinctions in the manner of naming them. But we
are not entitled to assume this in the commencement. We must begin by
recognizing the distinctions made by ordinary language. If some of these
appear, on a close examination, not to be fundamental, the enumeration of
the different kinds of realities may be abridged accordingly. But to
impose upon the facts in the first instance the yoke of a theory, while
the grounds of the theory are reserved for discussion in a subsequent
stage, is not a course which a logician can reasonably adopt.



                               Chapter II.


Of Names.


§ 1. “A name,” says Hobbes,(7) “is a word taken at pleasure to serve for a
mark which may raise in our mind a thought like to some thought we had
before, and which being pronounced to others, may be to them a sign of
what thought the speaker had(8) before in his mind.” This simple
definition of a name, as a word (or set of words) serving the double
purpose of a mark to recall to ourselves the likeness of a former thought,
and a sign to make it known to others, appears unexceptionable. Names,
indeed, do much more than this; but whatever else they do, grows out of,
and is the result of this: as will appear in its proper place.

Are names more properly said to be the names of things, or of our ideas of
things? The first is the expression in common use; the last is that of
some metaphysicians, who conceived that in adopting it they were
introducing a highly important distinction. The eminent thinker, just
quoted, seems to countenance the latter opinion. “But seeing,” he
continues, “names ordered in speech (as is defined) are signs of our
conceptions, it is manifest they are not signs of the things themselves;
for that the sound of this word _stone_ should be the sign of a stone, can
not be understood in any sense but this, that he that hears it collects
that he that pronounces it thinks of a stone.”

If it be merely meant that the conception alone, and not the thing itself,
is recalled by the name, or imparted to the hearer, this of course can not
be denied. Nevertheless, there seems good reason for adhering to the
common usage, and calling (as indeed Hobbes himself does in other places)
the word _sun_ the name of the sun, and not the name of our idea of the
sun. For names are not intended only to make the hearer conceive what we
conceive, but also to inform him what we believe. Now, when I use a name
for the purpose of expressing a belief, it is a belief concerning the
thing itself, not concerning my idea of it. When I say, “the sun is the
cause of day,” I do not mean that my idea of the sun causes or excites in
me the idea of day; or in other words, that thinking of the sun makes me
think of day. I mean, that a certain physical fact, which is called the
sun’s presence (and which, in the ultimate analysis, resolves itself into
sensations, not ideas) causes another physical fact, which is called day.
It seems proper to consider a word as the _name_ of that which we intend
to be understood by it when we use it; of that which any fact that we
assert of it is to be understood of; that, in short, concerning which,
when we employ the word, we intend to give information. Names, therefore,
shall always be spoken of in this work as the names of things themselves,
and not merely of our ideas of things.

But the question now arises, of what things? and to answer this it is
necessary to take into consideration the different kinds of names.

§ 2. It is usual, before examining the various classes into which names
are commonly divided, to begin by distinguishing from names of every
description, those words which are not names, but only parts of names.
Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the
inflected cases of nouns substantive, as _me_, _him_, _John’s_; and even
adjectives, as _large_, _heavy_. These words do not express things of
which any thing can be affirmed or denied. We can not say, Heavy fell, or
A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the
room. Unless, indeed, we are speaking of the mere words themselves, as
when we say, Truly is an English word, or, Heavy is an adjective. In that
case they are complete names—viz., names of those particular sounds, or of
those particular collections of written characters. This employment of a
word to denote the mere letters and syllables of which it is composed, was
termed by the schoolmen the _suppositio materialis_ of the word. In any
other sense we can not introduce one of these words into the subject of a
proposition, unless in combination with other words; as, A heavy _body_
fell, A truly _important fact_ was asserted, A _member_ of _parliament_
was in the room.

An adjective, however, is capable of standing by itself as the predicate
of a proposition; as when we say, Snow is white; and occasionally even as
the subject, for we may say, White is an agreeable color. The adjective is
often said to be so used by a grammatical ellipsis: Snow is white, instead
of Snow is a white object; White is an agreeable color, instead of, A
white color, or, The color white, is agreeable. The Greeks and Romans were
allowed, by the rules of their language, to employ this ellipsis
universally in the subject as well as in the predicate of a proposition.
In English this can not, generally speaking, be done. We may say, The
earth is round; but we can not say, Round is easily moved; we must say, A
round object. This distinction, however, is rather grammatical than
logical. Since there is no difference of meaning between _round_, and _a
round object_, it is only custom which prescribes that on any given
occasion one shall be used, and not the other. We shall, therefore,
without scruple, speak of adjectives as names, whether in their own right,
or as representative of the more circuitous forms of expression above
exemplified. The other classes of subsidiary words have no title whatever
to be considered as names. An adverb, or an accusative case, can not under
any circumstances (except when their mere letters and syllables are spoken
of) figure as one of the terms of a proposition.

Words which are not capable of being used as names, but only as parts of
names, were called by some of the schoolmen Syncategorematic terms: from
σὺν, with, and κατηγορέω, to predicate, because it was only _with_ some
other word that they could be predicated. A word which could be used
either as the subject or predicate of a proposition without being
accompanied by any other word, was termed by the same authorities a
Categorematic term. A combination of one or more Categorematic, and one or
more Syncategorematic words, as A heavy body, or A court of justice, they
sometimes called a _mixed_ term; but this seems a needless multiplication
of technical expressions. A mixed term is, in the only useful sense of the
word, Categorematic. It belongs to the class of what have been called
many-worded names.

For, as one word is frequently not a name, but only part of a name, so a
number of words often compose one single name, and no more. These words,
“The place which the wisdom or policy of antiquity had destined for the
residence of the Abyssinian princes,” form in the estimation of the
logician only one name; one Categorematic term. A mode of determining
whether any set of words makes only one name, or more than one, is by
predicating something of it, and observing whether, by this predication,
we make only one assertion or several. Thus, when we say, John Nokes, who
was the mayor of the town, died yesterday—by this predication we make but
one assertion; whence it appears that “John Nokes, who was the mayor of
the town,” is no more than one name. It is true that in this proposition,
besides the assertion that John Nokes died yesterday, there is included
another assertion, namely, that John Nokes was mayor of the town. But this
last assertion was already made: we did not make it by adding the
predicate, “died yesterday.” Suppose, however, that the words had been,
John Nokes _and_ the mayor of the town, they would have formed two names
instead of one. For when we say, John Nokes and the mayor of the town died
yesterday, we make two assertions: one, that John Nokes died yesterday;
the other, that the mayor of the town died yesterday.

It being needless to illustrate at any greater length the subject of
many-worded names, we proceed to the distinctions which have been
established among names, not according to the words they are composed of,
but according to their signification.

§ 3. All names are names of something, real or imaginary; but all things
have not names appropriated to them individually. For some individual
objects we require, and consequently have, separate distinguishing names;
there is a name for every person, and for every remarkable place. Other
objects, of which we have not occasion to speak so frequently, we do not
designate by a name of their own; but when the necessity arises for naming
them, we do so by putting together several words, each of which, by
itself, might be and is used for an indefinite number of other objects; as
when I say, _this stone_: “this” and “stone” being, each of them, names
that may be used of many other objects besides the particular one meant,
though the only object of which they can both be used at the given moment,
consistently with their signification, may be the one of which I wish to
speak.

Were this the sole purpose for which names, that are common to more things
than one, could be employed; if they only served, by mutually limiting
each other, to afford a designation for such individual objects as have no
names of their own: they could only be ranked among contrivances for
economizing the use of language. But it is evident that this is not their
sole function. It is by their means that we are enabled to assert
_general_ propositions; to affirm or deny any predicate of an indefinite
number of things at once. The distinction, therefore, between _general_
names, and _individual_ or _singular_ names, is fundamental; and may be
considered as the first grand division of names.

A general name is familiarly defined, a name which is capable of being
truly affirmed, in the same sense, of each of an indefinite number of
things. An individual or singular name is a name which is only capable of
being truly affirmed, in the same sense, of one thing.

Thus, _man_ is capable of being truly affirmed of John, George, Mary, and
other persons without assignable limit; and it is affirmed of all of them
in the same sense; for the word man expresses certain qualities, and when
we predicate it of those persons, we assert that they all possess those
qualities. But _John_ is only capable of being truly affirmed of one
single person, at least in the same sense. For, though there are many
persons who bear that name, it is not conferred upon them to indicate any
qualities, or any thing which belongs to them in common; and can not be
said to be affirmed of them in any _sense_ at all, consequently not in the
same sense. “The king who succeeded William the Conqueror,” is also an
individual name. For, that there can not be more than one person of whom
it can be truly affirmed, is implied in the meaning of the words. Even
“_the_ king,” when the occasion or the context defines the individual of
whom it is to be understood, may justly be regarded as an individual name.

It is not unusual, by way of explaining what is meant by a general name,
to say that it is the name of a _class_. But this, though a convenient
mode of expression for some purposes, is objectionable as a definition,
since it explains the clearer of two things by the more obscure. It would
be more logical to reverse the proposition, and turn it into a definition
of the word _class_: “A class is the indefinite multitude of individuals
denoted by a general name.”

It is necessary to distinguish _general_ from _collective_ names. A
general name is one which can be predicated of _each_ individual of a
multitude; a collective name can not be predicated of each separately, but
only of all taken together. “The 76th regiment of foot in the British
army,” which is a collective name, is not a general but an individual
name; for though it can be predicated of a multitude of individual
soldiers taken jointly, it can not be predicated of them severally. We may
say, Jones is a soldier, and Thompson is a soldier, and Smith is a
soldier, but we can not say, Jones is the 76th regiment, and Thompson is
the 76th regiment, and Smith is the 76th regiment. We can only say, Jones,
and Thompson, and Smith, and Brown, and so forth (enumerating all the
soldiers), are the 76th regiment.

“The 76th regiment” is a collective name, but not a general one: “a
regiment” is both a collective and a general name. General with respect to
all individual regiments, of each of which separately it can be affirmed:
collective with respect to the individual soldiers of whom any regiment is
composed.

§ 4. The second general division of names is into _concrete_ and
_abstract_. A concrete name is a name which stands for a thing; an
abstract name is a name which stands for an attribute of a thing. Thus
_John_, _the sea_, _this table_, are names of things. _White_, also, is a
name of a thing, or rather of things. Whiteness, again, is the name of a
quality or attribute of those things. Man is a name of many things;
humanity is a name of an attribute of those things. _Old_ is a name of
things: _old age_ is a name of one of their attributes.

I have used the words concrete and abstract in the sense annexed to them
by the schoolmen, who, notwithstanding the imperfections of their
philosophy, were unrivaled in the construction of technical language, and
whose definitions, in logic at least, though they never went more than a
little way into the subject, have seldom, I think, been altered but to be
spoiled. A practice, however, has grown up in more modern times, which, if
not introduced by Locke, has gained currency chiefly from his example, of
applying the expression “abstract name” to all names which are the result
of abstraction or generalization, and consequently to all general names,
instead of confining it to the names of attributes. The metaphysicians of
the Condillac school—whose admiration of Locke, passing over the
profoundest speculations of that truly original genius, usually fastens
with peculiar eagerness upon his weakest points—have gone on imitating him
in this abuse of language, until there is now some difficulty in restoring
the word to its original signification. A more wanton alteration in the
meaning of a word is rarely to be met with; for the expression _general
name_, the exact equivalent of which exists in all languages I am
acquainted with, was already available for the purpose to which _abstract_
has been misappropriated, while the misappropriation leaves that important
class of words, the names of attributes, without any compact distinctive
appellation. The old acceptation, however, has not gone so completely out
of use as to deprive those who still adhere to it of all chance of being
understood. By _abstract_, then, I shall always, in Logic proper, mean the
opposite of _concrete_; by an abstract name, the name of an attribute; by
a concrete name, the name of an object.

Do abstract names belong to the class of general, or to that of singular
names? Some of them are certainly general. I mean those which are names
not of one single and definite attribute, but of a class of attributes.
Such is the word _color_, which is a name common to whiteness, redness,
etc. Such is even the word whiteness, in respect of the different shades
of whiteness to which it is applied in common: the word magnitude, in
respect of the various degrees of magnitude and the various dimensions of
space; the word weight, in respect of the various degrees of weight. Such
also is the word _attribute_ itself, the common name of all particular
attributes. But when only one attribute, neither variable in degree nor in
kind, is designated by the name; as visibleness; tangibleness; equality;
squareness; milk-whiteness; then the name can hardly be considered
general; for though it denotes an attribute of many different objects, the
attribute itself is always conceived as one, not many.(9) To avoid
needless logomachies, the best course would probably be to consider these
names as neither general nor individual, and to place them in a class
apart.

It may be objected to our definition of an abstract name, that not only
the names which we have called abstract, but adjectives, which we have
placed in the concrete class, are names of attributes; that _white_, for
example, is as much the name of the color as _whiteness_ is. But (as
before remarked) a word ought to be considered as the name of that which
we intend to be understood by it when we put it to its principal use, that
is, when we employ it in predication. When we say snow is white, milk is
white, linen is white, we do not mean it to be understood that snow, or
linen, or milk, is a color. We mean that they are things having the color.
The reverse is the case with the word whiteness; what we affirm to _be_
whiteness is not snow, but the color of snow. Whiteness, therefore, is the
name of the color exclusively: white is a name of all things whatever
having the color; a name, not of the quality whiteness, but of every white
object. It is true, this name was given to all those various objects on
account of the quality; and we may therefore say, without impropriety,
that the quality forms part of its signification; but a name can only be
said to stand for, or to be a name of, the things of which it can be
predicated. We shall presently see that all names which can be said to
have any signification, all names by applying which to an individual we
give any information respecting that individual, may be said to _imply_ an
attribute of some sort; but they are not names of the attribute; it has
its own proper abstract name.

§ 5. This leads to the consideration of a third great division of names,
into _connotative_ and _non-connotative_, the latter sometimes, but
improperly, called _absolute_. This is one of the most important
distinctions which we shall have occasion to point out, and one of those
which go deepest into the nature of language.

A non-connotative term is one which signifies a subject only, or an
attribute only. A connotative term is one which denotes a subject, and
implies an attribute. By a subject is here meant any thing which possesses
attributes. Thus John, or London, or England, are names which signify a
subject only. Whiteness, length, virtue, signify an attribute only. None
of these names, therefore, are connotative. But _white_, _long_,
_virtuous_, are connotative. The word white, denotes all white things, as
snow, paper, the foam of the sea, etc., and implies, or in the language of
the schoolmen, _connotes_,(10) the attribute _whiteness_. The word white
is not predicated of the attribute, but of the subjects, snow, etc.; but
when we predicate it of them, we convey the meaning that the attribute
whiteness belongs to them. The same may be said of the other words above
cited. Virtuous, for example, is the name of a class, which includes
Socrates, Howard, the Man of Ross, and an undefinable number of other
individuals, past, present, and to come. These individuals, collectively
and severally, can alone be said with propriety to be denoted by the word:
of them alone can it properly be said to be a name. But it is a name
applied to all of them in consequence of an attribute which they are
supposed to possess in common, the attribute which has received the name
of virtue. It is applied to all beings that are considered to possess this
attribute; and to none which are not so considered.

All concrete general names are connotative. The word _man_, for example,
denotes Peter, Jane, John, and an indefinite number of other individuals,
of whom, taken as a class, it is the name. But it is applied to them,
because they possess, and to signify that they possess, certain
attributes. These seem to be, corporeity, animal life, rationality, and a
certain external form, which for distinction we call the human. Every
existing thing, which possessed all these attributes, would be called a
man; and any thing which possessed none of them, or only one, or two, or
even three of them without the fourth, would not be so called. For
example, if in the interior of Africa there were to be discovered a race
of animals possessing reason equal to that of human beings, but with the
form of an elephant, they would not be called men. Swift’s Houyhnhnms
would not be so called. Or if such newly-discovered beings possessed the
form of man without any vestige of reason, it is probable that some other
name than that of man would be found for them. How it happens that there
can be any doubt about the matter, will appear hereafter. The word _man_,
therefore, signifies all these attributes, and all subjects which possess
these attributes. But it can be predicated only of the subjects. What we
call men, are the subjects, the individual Stiles and Nokes; not the
qualities by which their humanity is constituted. The name, therefore, is
said to signify the subjects _directly_, the attributes _indirectly_; it
_denotes_ the subjects, and implies, or involves, or indicates, or as we
shall say henceforth _connotes_, the attributes. It is a connotative name.

Connotative names have hence been also called _denominative_, because the
subject which they denote is denominated by, or receives a name from the
attribute which they connote. Snow, and other objects, receive the name
white, because they possess the attribute which is called whiteness;
Peter, James, and others receive the name man because they possess the
attributes which are considered to constitute humanity. The attribute, or
attributes, may therefore be said to denominate those objects, or to give
them a common name.(11)

It has been seen that all concrete general names are connotative. Even
abstract names, though the names only of attributes, may in some instances
be justly considered as connotative; for attributes themselves may have
attributes ascribed to them; and a word which denotes attributes may
connote an attribute of those attributes. Of this description, for
example, is such a word as _fault_; equivalent to _bad_ or _hurtful
quality_. This word is a name common to many attributes, and connotes
hurtfulness, an attribute of those various attributes. When, for example,
we say that slowness, in a horse, is a fault, we do not mean that the slow
movement, the actual change of pace of the slow horse, is a bad thing, but
that the property or peculiarity of the horse, from which it derives that
name, the quality of being a slow mover, is an undesirable peculiarity.

In regard to those concrete names which are not general but individual, a
distinction must be made.

Proper names are not connotative: they denote the individuals who are
called by them; but they do not indicate or imply any attributes as
belonging to those individuals. When we name a child by the name Paul, or
a dog by the name Cæsar, these names are simply marks used to enable those
individuals to be made subjects of discourse. It may be said, indeed, that
we must have had some reason for giving them those names rather than any
others; and this is true; but the name, once given, is independent of the
reason. A man may have been named John, because that was the name of his
father; a town may have been named Dartmouth, because it is situated at
the mouth of the Dart. But it is no part of the signification of the word
John, that the father of the person so called bore the same name; nor even
of the word Dartmouth, to be situated at the mouth of the Dart. If sand
should choke up the mouth of the river, or an earthquake change its
course, and remove it to a distance from the town, the name of the town
would not necessarily be changed. That fact, therefore, can form no part
of the signification of the word; for otherwise, when the fact confessedly
ceased to be true, no one would any longer think of applying the name.
Proper names are attached to the objects themselves, and are not dependent
on the continuance of any attribute of the object.

But there is another kind of names, which, although they are individual
names—that is, predicable only of one object—are really connotative. For,
though we may give to an individual a name utterly unmeaning, which we
call a proper name—a word which answers the purpose of showing what thing
it is we are talking about, but not of telling any thing about it; yet a
name peculiar to an individual is not necessarily of this description. It
may be significant of some attribute, or some union of attributes, which,
being possessed by no object but one, determines the name exclusively to
that individual. “The sun” is a name of this description; “God,” when used
by a monotheist, is another. These, however, are scarcely examples of what
we are now attempting to illustrate, being, in strictness of language,
general, not individual names: for, however they may be _in fact_
predicable only of one object, there is nothing in the meaning of the
words themselves which implies this: and, accordingly, when we are
imagining and not affirming, we may speak of many suns; and the majority
of mankind have believed, and still believe, that there are many gods. But
it is easy to produce words which are real instances of connotative
individual names. It may be part of the meaning of the connotative name
itself, that there can exist but one individual possessing the attribute
which it connotes: as, for instance, “the _only_ son of John Stiles;” “the
_first_ emperor of Rome.” Or the attribute connoted may be a connection
with some determinate event, and the connection may be of such a kind as
only one individual could have; or may at least be such as only one
individual actually had; and this may be implied in the form of the
expression. “The father of Socrates” is an example of the one kind (since
Socrates could not have had two fathers); “the author of the Iliad,” “the
murderer of Henri Quatre,” of the second. For, though it is conceivable
that more persons than one might have participated in the authorship of
the Iliad, or in the murder of Henri Quatre, the employment of the article
_the_ implies that, in fact, this was not the case. What is here done by
the word _the_, is done in other cases by the context: thus, “Cæsar’s
army” is an individual name, if it appears from the context that the army
meant is that which Cæsar commanded in a particular battle. The still more
general expressions, “the Roman army,” or “the Christian army,” may be
individualized in a similar manner. Another case of frequent occurrence
has already been noticed; it is the following: The name, being a
many-worded one, may consist, in the first place, of a _general_ name,
capable therefore in itself of being affirmed of more things than one, but
which is, in the second place, so limited by other words joined with it,
that the entire expression can only be predicated of one object,
consistently with the meaning of the general term. This is exemplified in
such an instance as the following: “the present prime minister of
England.” Prime Minister of England is a general name; the attributes
which it connotes may be possessed by an indefinite number of persons: in
succession however, not simultaneously; since the meaning of the name
itself imports (among other things) that there can be only one such person
at a time. This being the case, and the application of the name being
afterward limited by the article and the word _present_, to such
individuals as possess the attributes at one indivisible point of time, it
becomes applicable only to one individual. And as this appears from the
meaning of the name, without any extrinsic proof, it is strictly an
individual name.

From the preceding observations it will easily be collected, that whenever
the names given to objects convey any information—that is, whenever they
have properly any meaning—the meaning resides not in what they _denote_,
but in what they _connote_. The only names of objects which connote
nothing are _proper_ names; and these have, strictly speaking, no
signification.(12)

If, like the robber in the Arabian Nights, we make a mark with chalk on a
house to enable us to know it again, the mark has a purpose, but it has
not properly any meaning. The chalk does not declare any thing about the
house; it does not mean, This is such a person’s house, or This is a house
which contains booty. The object of making the mark is merely distinction.
I say to myself, All these houses are so nearly alike that if I lose sight
of them I shall not again be able to distinguish that which I am now
looking at, from any of the others; I must therefore contrive to make the
appearance of this one house unlike that of the others, that I may
hereafter know when I see the mark—not indeed any attribute of the
house—but simply that it is the same house which I am now looking at.
Morgiana chalked all the other houses in a similar manner, and defeated
the scheme: how? simply by obliterating the difference of appearance
between that house and the others. The chalk was still there, but it no
longer served the purpose of a distinctive mark.

When we impose a proper name, we perform an operation in some degree
analogous to what the robber intended in chalking the house. We put a
mark, not indeed upon the object itself, but, so to speak, upon the idea
of the object. A proper name is but an unmeaning mark which we connect in
our minds with the idea of the object, in order that whenever the mark
meets our eyes or occurs to our thoughts, we may think of that individual
object. Not being attached to the thing itself, it does not, like the
chalk, enable us to distinguish the object when we see it; but it enables
us to distinguish it when it is spoken of, either in the records of our
own experience, or in the discourse of others; to know that what we find
asserted in any proposition of which it is the subject, is asserted of the
individual thing with which we were previously acquainted.

When we predicate of any thing its proper name; when we say, pointing to a
man, this is Brown or Smith, or pointing to a city, that it is York, we do
not, merely by so doing, convey to the reader any information about them,
except that those are their names. By enabling him to identify the
individuals, we may connect them with information previously possessed by
him; by saying, This is York, we may tell him that it contains the
Minster. But this is in virtue of what he has previously heard concerning
York; not by any thing implied in the name. It is otherwise when objects
are spoken of by connotative names. When we say, The town is built of
marble, we give the hearer what may be entirely new information, and this
merely by the signification of the many-worded connotative name, “built of
marble.” Such names are not signs of the mere objects, invented because we
have occasion to think and speak of those objects individually; but signs
which accompany an attribute; a kind of livery in which the attribute
clothes all objects which are recognized as possessing it. They are not
mere marks, but more, that is to say, significant marks; and the
connotation is what constitutes their significance.

As a proper name is said to be the name of the one individual which it is
predicated of, so (as well from the importance of adhering to analogy, as
for the other reasons formerly assigned) a connotative name ought to be
considered a name of all the various individuals which it is predicable
of, or in other words _denotes_, and not of what it connotes. But by
learning what things it is a name of, we do not learn the meaning of the
name: for to the same thing we may, with equal propriety, apply many
names, not equivalent in meaning. Thus, I call a certain man by the name
Sophroniscus: I call him by another name, The father of Socrates. Both
these are names of the same individual, but their meaning is altogether
different; they are applied to that individual for two different purposes:
the one, merely to distinguish him from other persons who are spoken of;
the other to indicate a fact relating to him, the fact that Socrates was
his son. I further apply to him these other expressions: a man, a Greek,
an Athenian, a sculptor, an old man, an honest man, a brave man. All these
are, or may be, names of Sophroniscus, not indeed of him alone, but of him
and each of an indefinite number of other human beings. Each of these
names is applied to Sophroniscus for a different reason, and by each
whoever understands its meaning is apprised of a distinct fact or number
of facts concerning him; but those who knew nothing about the names except
that they were applicable to Sophroniscus, would be altogether ignorant of
their meaning. It is even possible that I might know every single
individual of whom a given name could be with truth affirmed, and yet
could not be said to know the meaning of the name. A child knows who are
its brothers and sisters, long before it has any definite conception of
the nature of the facts which are involved in the signification of those
words.

In some cases it is not easy to decide precisely how much a particular
word does or does not connote; that is, we do not exactly know (the case
not having arisen) what degree of difference in the object would occasion
a difference in the name. Thus, it is clear that the word man, besides
animal life and rationality, connotes also a certain external form; but it
would be impossible to say precisely what form; that is, to decide how
great a deviation from the form ordinarily found in the beings whom we are
accustomed to call men, would suffice in a newly-discovered race to make
us refuse them the name of man. Rationality, also, being a quality which
admits of degrees, it has never been settled what is the lowest degree of
that quality which would entitle any creature to be considered a human
being. In all such cases, the meaning of the general name is so far
unsettled and vague; mankind have not come to any positive agreement about
the matter. When we come to treat of Classification, we shall have
occasion to show under what conditions this vagueness may exist without
practical inconvenience; and cases will appear in which the ends of
language are better promoted by it than by complete precision; in order
that, in natural history for instance, individuals or species of no very
marked character may be ranged with those more strongly characterized
individuals or species to which, in all their properties taken together,
they bear the nearest resemblance.

But this partial uncertainty in the connotation of names can only be free
from mischief when guarded by strict precautions. One of the chief
sources, indeed, of lax habits of thought, is the custom of using
connotative terms without a distinctly ascertained connotation, and with
no more precise notion of their meaning than can be loosely collected from
observing what objects they are used to denote. It is in this manner that
we all acquire, and inevitably so, our first knowledge of our vernacular
language. A child learns the meaning of the words _man_, or _white_, by
hearing them applied to a variety of individual objects, and finding out,
by a process of generalization and analysis which he could not himself
describe, what those different objects have in common. In the case of
these two words the process is so easy as to require no assistance from
culture; the objects called human beings, and the objects called white,
differing from all others by qualities of a peculiarly definite and
obvious character. But in many other cases, objects bear a general
resemblance to one another, which leads to their being familiarly classed
together under a common name, while, without more analytic habits than the
generality of mankind possess, it is not immediately apparent what are the
particular attributes, upon the possession of which in common by them all,
their general resemblance depends. When this is the case, people use the
name without any recognized connotation, that is, without any precise
meaning; they talk, and consequently think, vaguely, and remain contented
to attach only the same degree of significance to their own words, which a
child three years old attaches to the words brother and sister. The child
at least is seldom puzzled by the starting up of new individuals, on whom
he is ignorant whether or not to confer the title; because there is
usually an authority close at hand competent to solve all doubts. But a
similar resource does not exist in the generality of cases; and new
objects are continually presenting themselves to men, women, and children,
which they are called upon to class _proprio motu_. They, accordingly, do
this on no other principle than that of superficial similarity, giving to
each new object the name of that familiar object, the idea of which it
most readily recalls, or which, on a cursory inspection, it seems to them
most to resemble: as an unknown substance found in the ground will be
called, according to its texture, earth, sand, or a stone. In this manner,
names creep on from subject to subject, until all traces of a common
meaning sometimes disappear, and the word comes to denote a number of
things not only independently of any common attribute, but which have
actually no attribute in common; or none but what is shared by other
things to which the name is capriciously refused.(13) Even scientific
writers have aided in this perversion of general language from its
purpose; sometimes because, like the vulgar, they knew no better; and
sometimes in deference to that aversion to admit new words, which induces
mankind, on all subjects not considered technical, to attempt to make the
original stock of names serve with but little augmentation to express a
constantly increasing number of objects and distinctions, and,
consequently, to express them in a manner progressively more and more
imperfect.

To what a degree this loose mode of classing and denominating objects has
rendered the vocabulary of mental and moral philosophy unfit for the
purposes of accurate thinking, is best known to whoever has most meditated
on the present condition of those branches of knowledge. Since, however,
the introduction of a new technical language as the vehicle of
speculations on subjects belonging to the domain of daily discussion, is
extremely difficult to effect, and would not be free from inconvenience
even if effected, the problem for the philosopher, and one of the most
difficult which he has to resolve, is, in retaining the existing
phraseology, how best to alleviate its imperfections. This can only be
accomplished by giving to every general concrete name which there is
frequent occasion to predicate, a definite and fixed connotation; in order
that it may be known what attributes, when we call an object by that name,
we really mean to predicate of the object. And the question of most nicety
is, how to give this fixed connotation to a name, with the least possible
change in the objects which the name is habitually employed to denote;
with the least possible disarrangement, either by adding or subtraction,
of the group of objects which, in however imperfect a manner, it serves to
circumscribe and hold together; and with the least vitiation of the truth
of any propositions which are commonly received as true.

This desirable purpose, of giving a fixed connotation where it is wanting,
is the end aimed at whenever any one attempts to give a definition of a
general name already in use; every definition of a connotative name being
an attempt either merely to declare, or to declare and analyze, the
connotation of the name. And the fact, that no questions which have arisen
in the moral sciences have been subjects of keener controversy than the
definitions of almost all the leading expressions, is a proof how great an
extent the evil to which we have adverted has attained.

Names with indeterminate connotation are not to be confounded with names
which have more than one connotation, that is to say, ambiguous words. A
word may have several meanings, but all of them fixed and recognized ones;
as the word _post_, for example, or the word _box_, the various senses of
which it would be endless to enumerate. And the paucity of existing names,
in comparison with the demand for them, may often render it advisable and
even necessary to retain a name in this multiplicity of acceptations,
distinguishing these so clearly as to prevent their being confounded with
one another. Such a word may be considered as two or more names,
accidentally written and spoken alike.(14)

§ 6. The fourth principal division of names, is into _positive_ and
_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,
_not-tree_, _not-good_. To every positive concrete name, a corresponding
negative one might be framed. After giving a name to any one thing, or to
any plurality of things, we might create a second name which should be a
name of all things whatever, except that particular thing or things. These
negative names are employed whenever we have occasion to speak
collectively of all things other than some thing or class of things. When
the positive name is connotative, the corresponding negative name is
connotative likewise; but in a peculiar way, connoting not the presence
but the absence of an attribute. Thus, _not-white_ denotes all things
whatever except white things; and connotes the attribute of not possessing
whiteness. For the non-possession of any given attribute is also an
attribute, and may receive a name as such; and thus negative concrete
names may obtain negative abstract names to correspond to them.(15)

Names which are positive in form are often negative in reality, and others
are really positive though their form is negative. The word
_inconvenient_, for example, does not express the mere absence of
convenience; it expresses a positive attribute—that of being the cause of
discomfort or annoyance. So the word _unpleasant_, notwithstanding its
negative form, does not connote the mere absence of pleasantness, but a
less degree of what is signified by the word _painful_, which, it is
hardly necessary to say, is positive. _Idle_, on the other hand, is a word
which, though positive in form, expresses nothing but what would be
signified either by the phrase _not working_, or by the phrase _not
disposed to work_; and _sober_, either by _not drunk_ or by _not drunken_.

There is a class of names called _privative_. A privative name is
equivalent in its signification to a positive and a negative name taken
together; being the name of something which has once had a particular
attribute, or for some other reason might have been expected to have it,
but which has it not. Such is the word _blind_, which is not equivalent to
_not seeing_, or to _not capable of seeing_, for it would not, except by a
poetical or rhetorical figure, be applied to stocks and stones. A thing is
not usually said to be blind, unless the class to which it is most
familiarly referred, or to which it is referred on the particular
occasion, be chiefly composed of things which can see, as in the case of a
blind man, or a blind horse; or unless it is supposed for any reason that
it ought to see; as in saying of a man, that he rushed blindly into an
abyss, or of philosophers or the clergy that the greater part of them are
blind guides. The names called privative, therefore, connote two things;
the absence of certain attributes, and the presence of others, from which
the presence also of the former might naturally have been expected.

§ 7. The fifth leading division of names is into _relative_ and
_absolute_, or let us rather say, _relative_ and _non-relative_; for the
word absolute is put upon much too hard duty in metaphysics, not to be
willingly spared when its services can be dispensed with. It resembles the
word _civil_ in the language of jurisprudence, which stands for the
opposite of criminal, the opposite of ecclesiastical, the opposite of
military, the opposite of political—in short, the opposite of any positive
word which wants a negative.

Relative names are such as father, son; ruler, subject; like; equal;
unlike; unequal; longer, shorter; cause, effect. Their characteristic
property is, that they are always given in pairs. Every relative name
which is predicated of an object, supposes another object (or objects), of
which we may predicate either that same name or another relative name
which is said to be the _correlative_ of the former. Thus, when we call
any person a son, we suppose other persons who must be called parents.
When we call any event a cause, we suppose another event which is an
effect. When we say of any distance that it is longer, we suppose another
distance which is shorter. When we say of any object that it is like, we
mean that it is like some other object, which is also said to be like the
first. In this last case both objects receive the same name; the relative
term is its own correlative.

It is evident that these words, when concrete, are, like other concrete
general names, connotative; they denote a subject, and connote an
attribute; and each of them has, or might have, a corresponding abstract
name, to denote the attribute connoted by the concrete. Thus the concrete
_like_ has its abstract _likeness_; the concretes, father and son, have,
or might have, the abstracts, paternity, and filiety, or sonship. The
concrete name connotes an attribute, and the abstract name which answers
to it denotes that attribute. But of what nature is the attribute? Wherein
consists the peculiarity in the connotation of a relative name?

The attribute signified by a relative name, say some, is a relation; and
this they give, if not as a sufficient explanation, at least as the only
one attainable. If they are asked, What then is a relation? they do not
profess to be able to tell. It is generally regarded as something
peculiarly recondite and mysterious. I can not, however, perceive in what
respect it is more so than any other attribute; indeed, it appears to me
to be so in a somewhat less degree. I conceive rather, that it is by
examining into the signification of relative names, or, in other words,
into the nature of the attribute which they connote, that a clear insight
may best be obtained into the nature of all attributes: of all that is
meant by an attribute.

It is obvious, in fact, that if we take any two correlative names,
_father_ and _son_ for instance, though the objects _de_noted by the names
are different, they both, in a certain sense, connote the same thing. They
can not, indeed, be said to connote the same _attribute_: to be a father,
is not the same thing as to be a son. But when we call one man a father,
another a son, what we mean to affirm is a set of facts, which are exactly
the same in both cases. To predicate of A that he is the father of B, and
of B that he is the son of A, is to assert one and the same fact in
different words. The two propositions are exactly equivalent: neither of
them asserts more or asserts less than the other. The paternity of A and
the filiety of B are not two facts, but two modes of expressing the same
fact. That fact, when analysed, consists of a series of physical events or
phenomena, in which both A and B are parties concerned, and from which
they both derive names. What those names really connote, is this series of
events: that is the meaning, and the whole meaning, which either of them
is intended to convey. The series of events may be said to _constitute_
the relation; the schoolmen called it the foundation of the relation,
_fundamentum relationis_.

In this manner any fact, or series of facts, in which two different
objects are implicated, and which is therefore predicable of both of them,
may be either considered as constituting an attribute of the one, or an
attribute of the other. According as we consider it in the former, or in
the latter aspect, it is connoted by the one or the other of the two
correlative names. _Father_ connotes the fact, regarded as constituting an
attribute of A; _son_ connotes the same fact, as constituting an attribute
of B. It may evidently be regarded with equal propriety in either light.
And all that appears necessary to account for the existence of relative
names, is, that whenever there is a fact in which two individuals are
concerned, an attribute grounded on that fact may be ascribed to either of
these individuals.

A name, therefore, is said to be relative, when, over and above the object
which it denotes, it implies in its signification the existence of another
object, also deriving a denomination from the same fact which is the
ground of the first name. Or (to express the same meaning in other words)
a name is relative, when, being the name of one thing, its signification
can not be explained but by mentioning another. Or we may state it
thus—when the name can not be employed in discourse so as to have a
meaning, unless the name of some other thing than what it is itself the
name of, be either expressed or understood. These definitions are all, at
bottom, equivalent, being modes of variously expressing this one
distinctive circumstance—that every other attribute of an object might,
without any contradiction, be conceived still to exist if no object
besides that one had ever existed;(16) but those of its attributes which
are expressed by relative names, would on that supposition be swept away.

§ 8. Names have been further distinguished into _univocal_ and
_æquivocal_: these, however, are not two kinds of names, but two different
modes of employing names. A name is univocal, or applied univocally, with
respect to all things of which it can be predicated _in the same sense_;
it is æquivocal, or applied æquivocally, as respects those things of which
it is predicated in different senses. It is scarcely necessary to give
instances of a fact so familiar as the double meaning of a word. In
reality, as has been already observed, an æquivocal or ambiguous word is
not one name, but two names, accidentally coinciding in sound. _File_
meaning a steel instrument, and _file_ meaning a line of soldiers, have no
more title to be considered one word, because written alike, than _grease_
and _Greece_ have, because they are pronounced alike. They are one sound,
appropriated to form two different words.

An intermediate case is that of a name used _analogically_ or
metaphorically; that is, a name which is predicated of two things, not
univocally, or exactly in the same signification, but in significations
somewhat similar, and which being derived one from the other, one of them
may be considered the primary, and the other a secondary signification. As
when we speak of a brilliant light and a brilliant achievement. The word
is not applied in the same sense to the light and to the achievement; but
having been applied to the light in its original sense, that of brightness
to the eye, it is transferred to the achievement in a derivative
signification, supposed to be somewhat like the primitive one. The word,
however, is just as properly two names instead of one, in this case, as in
that of the most perfect ambiguity. And one of the commonest forms of
fallacious reasoning arising from ambiguity, is that of arguing from a
metaphorical expression as if it were literal; that is, as if a word, when
applied metaphorically, were the same name as when taken in its original
sense: which will be seen more particularly in its place.



                               Chapter III.


Of The Things Denoted By Names.


§ 1. Looking back now to the commencement of our inquiry, let us attempt
to measure how far it has advanced. Logic, we found, is the Theory of
Proof. But proof supposes something provable, which must be a Proposition
or Assertion; since nothing but a Proposition can be an object of belief,
or therefore of proof. A Proposition is, discourse which affirms or denies
something of some other thing. This is one step: there must, it seems, be
two things concerned in every act of belief. But what are these Things?
They can be no other than those signified by the two names, which being
joined together by a copula constitute the Proposition. If, therefore, we
knew what all names signify, we should know every thing which, in the
existing state of human knowledge, is capable either of being made a
subject of affirmation or denial, or of being itself affirmed or denied of
a subject. We have accordingly, in the preceding chapter, reviewed the
various kinds of Names, in order to ascertain what is signified by each of
them. And we have now carried this survey far enough to be able to take an
account of its results, and to exhibit an enumeration of all kinds of
Things which are capable of being made predicates, or of having any thing
predicated of them: after which to determine the import of Predication,
that is, of Propositions, can be no arduous task.

The necessity of an enumeration of Existences, as the basis of Logic, did
not escape the attention of the schoolmen, and of their master Aristotle,
the most comprehensive, if not also the most sagacious, of the ancient
philosophers. The Categories, or Predicaments—the former a Greek word, the
latter its literal translation in the Latin language—were believed to be
an enumeration of all things capable of being named; an enumeration by the
_summa genera_, _i.e._, the most extensive classes into which things could
be distributed; which, therefore, were so many highest Predicates, one or
other of which was supposed capable of being affirmed with truth of every
namable thing whatsoever. The following are the classes into which,
according to this school of philosophy, Things in general might be
reduced:

Οὐσία, Substantia.
Ποσὸν, Quantitas.
Ποιόν, Qualitas.
Πρός τι, Relatio.
Ποιεῖν, Actio.
Πάσχειν, Passio.
Ποῦ, Ubi.
Πότε, Quando.
Κεῖσθακ, Situs.
Ἔχειν, Habitus.

The imperfections of this classification are too obvious to require, and
its merits are not sufficient to reward, a minute examination. It is a
mere catalogue of the distinctions rudely marked out by the language of
familiar life, with little or no attempt to penetrate, by philosophic
analysis, to the _rationale_ even of those common distinctions. Such an
analysis, however superficially conducted, would have shown the
enumeration to be both redundant and defective. Some objects are omitted,
and others repeated several times under different heads. It is like a
division of animals into men, quadrupeds, horses, asses, and ponies. That,
for instance, could not be a very comprehensive view of the nature of
Relation which could exclude action, passivity, and local situation from
that category. The same observation applies to the categories Quando (or
position in time), and Ubi (or position in space); while the distinction
between the latter and Situs is merely verbal. The incongruity of erecting
into a _summum genus_ the class which forms the tenth category is
manifest. On the other hand, the enumeration takes no notice of any thing
besides substances and attributes. In what category are we to place
sensations, or any other feelings and states of mind; as hope, joy, fear;
sound, smell, taste; pain, pleasure; thought, judgment, conception, and
the like? Probably all these would have been placed by the Aristotelian
school in the categories of _actio_ and _passio_; and the relation of such
of them as are active, to their objects, and of such of them as are
passive, to their causes, would rightly be so placed; but the things
themselves, the feelings or states of mind, wrongly. Feelings, or states
of consciousness, are assuredly to be accounted among realities, but they
can not be reckoned either among substances or attributes.(17)

§ 2. Before recommencing, under better auspices, the attempt made with
such imperfect success by the early logicians, we must take notice of an
unfortunate ambiguity in all the concrete names which correspond to the
most general of all abstract terms, the word Existence. When we have
occasion for a name which shall be capable of denoting whatever exists, as
contradistinguished from non-entity or Nothing, there is hardly a word
applicable to the purpose which is not also, and even more familiarly,
taken in a sense in which it denotes only substances. But substances are
not all that exists; attributes, if such things are to be spoken of, must
be said to exist; feelings certainly exist. Yet when we speak of an
_object_, or of a _thing_, we are almost always supposed to mean a
substance. There seems a kind of contradiction in using such an expression
as that one _thing_ is merely an attribute of another thing. And the
announcement of a Classification of Things would, I believe, prepare most
readers for an enumeration like those in natural history, beginning with
the great divisions of animal, vegetable, and mineral, and subdividing
them into classes and orders. If, rejecting the word Thing, we endeavor to
find another of a more general import, or at least more exclusively
confined to that general import, a word denoting all that exists, and
connoting only simple existence; no word might be presumed fitter for such
a purpose than _being_: originally the present participle of a verb which
in one of its meanings is exactly equivalent to the verb _exists_; and
therefore suitable, even by its grammatical formation, to be the concrete
of the abstract _existence_. But this word, strange as the fact may
appear, is still more completely spoiled for the purpose which it seemed
expressly made for, than the word Thing. _Being_ is, by custom, exactly
synonymous with substance; except that it is free from a slight taint of a
second ambiguity; being implied impartially to matter and to mind, while
substance, though originally and in strictness applicable to both, is apt
to suggest in preference the idea of matter. Attributes are never called
Beings; nor are feelings. A Being is that which excites feelings, and
which possesses attributes. The soul is called a Being; God and angels are
called Beings; but if we were to say, extension, color, wisdom, virtue,
are beings, we should perhaps be suspected of thinking with some of the
ancients, that the cardinal virtues are animals; or, at the least, of
holding with the Platonic school the doctrine of self-existent Ideas, or
with the followers of Epicurus that of Sensible Forms, which detach
themselves in every direction from bodies, and by coming in contact with
our organs, cause our perceptions. We should be supposed, in short, to
believe that Attributes are Substances.

In consequence of this perversion of the word Being, philosophers looking
about for something to supply its place, laid their hands upon the word
Entity, a piece of barbarous Latin, invented by the schoolmen to be used
as an abstract name, in which class its grammatical form would seem to
place it: but being seized by logicians in distress to stop a leak in
their terminology, it has ever since been used as a concrete name. The
kindred word _essence_, born at the same time and of the same parents,
scarcely underwent a more complete transformation when, from being the
abstract of the verb _to be_, it came to denote something sufficiently
concrete to be inclosed in a glass bottle. The word Entity, since it
settled down into a concrete name, has retained its universality of
signification somewhat less impaired than any of the names before
mentioned. Yet the same gradual decay to which, after a certain age, all
the language of psychology seems liable, has been at work even here. If
you call virtue an _entity_, you are indeed somewhat less strongly
suspected of believing it to be a substance than if you called it a
_being_; but you are by no means free from the suspicion. Every word which
was originally intended to connote mere existence, seems, after a time, to
enlarge its connotation to _separate_ existence, or existence freed from
the condition of belonging to a substance; which condition being precisely
what constitutes an attribute, attributes are gradually shut out; and
along with them feelings, which in ninety-nine cases out of a hundred have
no other name than that of the attribute which is grounded on them.
Strange that when the greatest embarrassment felt by all who have any
considerable number of thoughts to express, is to find a sufficient
variety of precise words fitted to express them, there should be no
practice to which even scientific thinkers are more addicted than that of
taking valuable words to express ideas which are sufficiently expressed by
other words already appropriated to them.

When it is impossible to obtain good tools, the next best thing is to
understand thoroughly the defects of those we have. I have therefore
warned the reader of the ambiguity of the names which, for want of better,
I am necessitated to employ. It must now be the writer’s endeavor so to
employ them as in no case to leave the meaning doubtful or obscure. No one
of the above terms being altogether unambiguous, I shall not confine
myself to any one, but shall employ on each occasion the word which seems
least likely in the particular case to lead to misunderstanding; nor do I
pretend to use either these or any other words with a rigorous adherence
to one single sense. To do so would often leave us without a word to
express what is signified by a known word in some one or other of its
senses: unless authors had an unlimited license to coin new words,
together with (what it would be more difficult to assume) unlimited power
of making readers understand them. Nor would it be wise in a writer, on a
subject involving so much of abstraction, to deny himself the advantage
derived from even an improper use of a term, when, by means of it, some
familiar association is called up which brings the meaning home to the
mind, as it were by a flash.

The difficulty both to the writer and reader, of the attempt which must be
made to use vague words so as to convey a precise meaning, is not wholly a
matter of regret. It is not unfitting that logical treatises should afford
an example of that, to facilitate which is among the most important uses
of logic. Philosophical language will for a long time, and popular
language still longer, retain so much of vagueness and ambiguity, that
logic would be of little value if it did not, among its other advantages,
exercise the understanding in doing its work neatly and correctly with
these imperfect tools.

After this preamble it is time to proceed to our enumeration. We shall
commence with Feelings, the simplest class of namable things; the term
Feeling being of course understood in its most enlarged sense.



I. Feelings, Or States of Consciousness.


§ 3. A Feeling and a State of consciousness are, in the language of
philosophy, equivalent expressions: every thing is a feeling of which the
mind is conscious; every thing which it _feels_, or, in other words, which
forms a part of its own sentient existence. In popular language Feeling is
not always synonymous with State of Consciousness; being often taken more
peculiarly for those states which are conceived as belonging to the
sensitive, or to the emotional, phasis of our nature, and sometimes, with
a still narrower restriction, to the emotional alone, as distinguished
from what are conceived as belonging to the percipient or to the
intellectual phasis. But this is an admitted departure from correctness of
language; just as, by a popular perversion the exact converse of this, the
word Mind is withdrawn from its rightful generality of signification, and
restricted to the intellect. The still greater perversion by which Feeling
is sometimes confined not only to bodily sensations, but to the sensations
of a single sense, that of touch, needs not be more particularly adverted
to.

Feeling, in the proper sense of the term, is a genus, of which Sensation,
Emotion, and Thought, are subordinate species. Under the word Thought is
here to be included whatever we are internally conscious of when we are
said to think; from the consciousness we have when we think of a red color
without having it before our eyes, to the most recondite thoughts of a
philosopher or poet. Be it remembered, however, that by a thought is to be
understood what passes in the mind itself, and not any object external to
the mind, which the person is commonly said to be thinking of. He may be
thinking of the sun, or of God, but the sun and God are not thoughts; his
mental image, however, of the sun, and his idea of God, are thoughts;
states of his mind, not of the objects themselves; and so also is his
belief of the existence of the sun, or of God; or his disbelief, if the
case be so. Even imaginary objects (which are said to exist only in our
ideas) are to be distinguished from our ideas of them. I may think of a
hobgoblin, as I may think of the loaf which was eaten yesterday, or of the
flower which will bloom to-morrow. But the hobgoblin which never existed
is not the same thing with my idea of a hobgoblin, any more than the loaf
which once existed is the same thing with my idea of a loaf, or the flower
which does not yet exist, but which will exist, is the same with my idea
of a flower. They are all, not thoughts, but objects of thought; though at
the present time all the objects are alike non-existent.

In like manner, a Sensation is to be carefully distinguished from the
object which causes the sensation; our sensation of white from a white
object: nor is it less to be distinguished from the attribute whiteness,
which we ascribe to the object in consequence of its exciting the
sensation. Unfortunately for clearness and due discrimination in
considering these subjects, our sensations seldom receive separate names.
We have a name for the objects which produce in us a certain sensation:
the word _white_. We have a name for the quality in those objects, to
which we ascribe the sensation: the name _whiteness_. But when we speak of
the sensation itself (as we have not occasion to do this often except in
our scientific speculations), language, which adapts itself for the most
part only to the common uses of life, has provided us with no
single-worded or immediate designation; we must employ a circumlocution,
and say, The sensation of white, or The sensation of whiteness; we must
denominate the sensation either from the object, or from the attribute, by
which it is excited. Yet the sensation, though it never _does_, might very
well be _conceived_ to exist, without any thing whatever to excite it. We
can conceive it as arising spontaneously in the mind. But if it so arose,
we should have no name to denote it which would not be a misnomer. In the
case of our sensations of hearing we are better provided; we have the word
Sound, and a whole vocabulary of words to denote the various kinds of
sounds. For as we are often conscious of these sensations in the absence
of any perceptible object, we can more easily conceive having them in the
absence of any object whatever. We need only shut our eyes and listen to
music, to have a conception of a universe with nothing in it except
sounds, and ourselves hearing them: and what is easily conceived
separately, easily obtains a separate name. But in general our names of
sensations denote indiscriminately the sensation and the attribute. Thus,
_color_ stands for the sensations of white, red, etc., but also for the
quality in the colored object. We talk of the colors of things as among
their _properties_.

§ 4. In the case of sensations, another distinction has also to be kept in
view, which is often confounded, and never without mischievous
consequences. This is, the distinction between the sensation itself, and
the state of the bodily organs which precedes the sensation, and which
constitutes the physical agency by which it is produced. One of the
sources of confusion on this subject is the division commonly made of
feelings into Bodily and Mental. Philosophically speaking, there is no
foundation at all for this distinction: even sensations are states of the
sentient mind, not states of the body, as distinguished from it. What I am
conscious of when I see the color blue, is a feeling of blue color, which
is one thing; the picture on my retina, or the phenomenon of hitherto
mysterious nature which takes place in my optic nerve or in my brain, is
another thing, of which I am not at all conscious, and which scientific
investigation alone could have apprised me of. These are states of my
body; but the sensation of blue, which is the consequence of these states
of body, is not a state of body: that which perceives and is conscious is
called Mind. When sensations are called bodily feelings, it is only as
being the class of feelings which are immediately occasioned by bodily
states; whereas the other kinds of feelings, thoughts, for instance, or
emotions, are immediately excited not by any thing acting upon the bodily
organs, but by sensations, or by previous thoughts. This, however, is a
distinction not in our feelings, but in the agency which produces our
feelings: all of them when actually produced are states of mind.

Besides the affection of our bodily organs from without, and the sensation
thereby produced in our minds, many writers admit a third link in the
chain of phenomena, which they call a Perception, and which consists in
the recognition of an external object as the exciting cause of the
sensation. This perception, they say, is an _act_ of the mind, proceeding
from its own spontaneous activity; while in a sensation the mind is
passive, being merely acted upon by the outward object. And according to
some metaphysicians, it is by an act of the mind, similar to perception,
except in not being preceded by any sensation, that the existence of God,
the soul, and other hyperphysical objects, is recognized.

These acts of what is termed perception, whatever be the conclusion
ultimately come to respecting their nature, must, I conceive, take their
place among the varieties of feelings or states of mind. In so classing
them, I have not the smallest intention of declaring or insinuating any
theory as to the law of mind in which these mental processes may be
supposed to originate, or the conditions under which they may be
legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to
suppose must be meant in an analogous case(18)) to indicate that as they
are “_merely_ states of mind,” it is superfluous to inquire into their
distinguishing peculiarities. I abstain from the inquiry as irrelevant to
the science of logic. In these so-called perceptions, or direct
recognitions by the mind, of objects, whether physical or spiritual, which
are external to itself, I can see only cases of belief; but of belief
which claims to be intuitive, or independent of external evidence. When a
stone lies before me, I am conscious of certain sensations which I receive
from it; but if I say that these sensations come to me from an external
object which I _perceive_, the meaning of these words is, that receiving
the sensations, I intuitively _believe_ that an external cause of those
sensations exists. The laws of intuitive belief, and the conditions under
which it is legitimate, are a subject which, as we have already so often
remarked, belongs not to logic, but to the science of the ultimate laws of
the human mind.

To the same region of speculation belongs all that can be said respecting
the distinction which the German metaphysicians and their French and
English followers so elaborately draw between the _acts_ of the mind and
its merely passive _states_; between what it receives from, and what it
gives to, the crude materials of its experience. I am aware that with
reference to the view which those writers take of the primary elements of
thought and knowledge, this distinction is fundamental. But for the
present purpose, which is to examine, not the original groundwork of our
knowledge, but how we come by that portion of it which is not original;
the difference between active and passive states of mind is of secondary
importance. For us, they all are states of mind, they all are feelings; by
which, let it be said once more, I mean to imply nothing of passivity, but
simply that they are psychological facts, facts which take place in the
mind, and are to be carefully distinguished from the external or physical
facts with which they may be connected either as effects or as causes.

§ 5. Among active states of mind, there is, however, one species which
merits particular attention, because it forms a principal part of the
connotation of some important classes of names. I mean _volitions_, or
acts of the will. When we speak of sentient beings by relative names, a
large portion of the connotation of the name usually consists of the
actions of those beings; actions past, present, and possible or probable
future. Take, for instance, the words Sovereign and Subject. What meaning
do these words convey, but that of innumerable actions, done or to be done
by the sovereign and the subjects, to or in regard to one another
reciprocally? So with the words physician and patient, leader and
follower, tutor and pupil. In many cases the words also connote actions
which would be done under certain contingencies by persons other than
those denoted: as the words mortgagor and mortgagee, obligor and obligee,
and many other words expressive of legal relation, which connote what a
court of justice would do to enforce the legal obligation if not
fulfilled. There are also words which connote actions previously done by
persons other than those denoted either by the name itself or by its
correlative; as the word brother. From these instances, it may be seen how
large a portion of the connotation of names consists of actions. Now what
is an action? Not one thing, but a series of two things: the state of mind
called a volition, followed by an effect. The volition or intention to
produce the effect, is one thing; the effect produced in consequence of
the intention, is another thing; the two together constitute the action. I
form the purpose of instantly moving my arm; that is a state of my mind:
my arm (not being tied or paralytic) moves in obedience to my purpose;
that is a physical fact, consequent on a state of mind. The intention,
followed by the fact, or (if we prefer the expression) the fact when
preceded and caused by the intention, is called the action of moving my
arm.

§ 6. Of the first leading division of namable things, viz., Feelings or
States of Consciousness, we began by recognizing three subdivisions;
Sensations, Thoughts, and Emotions. The first two of these we have
illustrated at considerable length; the third, Emotions, not being
perplexed by similar ambiguities, does not require similar
exemplification. And, finally, we have found it necessary to add to these
three a fourth species, commonly known by the name Volitions. We shall now
proceed to the two remaining classes of namable things; all things which
are regarded as external to the mind being considered as belonging either
to the class of Substances or to that of Attributes.



II. Substances.


Logicians have endeavored to define Substance and Attribute; but their
definitions are not so much attempts to draw a distinction between the
things themselves, as instructions what difference it is customary to make
in the grammatical structure of the sentence, according as we are speaking
of substances or of attributes. Such definitions are rather lessons of
English, or of Greek, Latin, or German, than of mental philosophy. An
attribute, say the school logicians, must be the attribute _of_ something;
color, for example, must be the color _of_ something; goodness must be the
goodness _of_ something; and if this something should cease to exist, or
should cease to be connected with the attribute, the existence of the
attribute would be at an end. A substance, on the contrary, is
self-existent; in speaking about it, we need not put _of_ after its name.
A stone is not the stone of any thing; the moon is not the moon _of_ any
thing, but simply the moon. Unless, indeed, the name which we choose to
give to the substance be a relative name; if so, it must be followed
either by _of_, or by some other particle, implying, as that preposition
does, a reference to something else: but then the other characteristic
peculiarity of an attribute would fail; the _something_ might be
destroyed, and the substance might still subsist. Thus, a father must be
the father _of_ something, and so far resembles an attribute, in being
referred to something besides himself: if there were no child, there would
be no father: but this, when we look into the matter, only means that we
should not call him father. The man called father might still exist though
there were no child, as he existed before there was a child; and there
would be no contradiction in supposing him to exist, though the whole
universe except himself were destroyed. But destroy all white substances,
and where would be the attribute whiteness? Whiteness, without any white
thing, is a contradiction in terms.

This is the nearest approach to a solution of the difficulty, that will be
found in the common treatises on logic. It will scarcely be thought to be
a satisfactory one. If an attribute is distinguished from a substance by
being the attribute _of_ something, it seems highly necessary to
understand what is meant by _of_; a particle which needs explanation too
much itself, to be placed in front of the explanation of any thing else.
And as for the self-existence of substance, it is very true that a
substance may be conceived to exist without any other substance, but so
also may an attribute without any other attribute: and we can no more
imagine a substance without attributes than we can imagine attributes
without a substance.

Metaphysicians, however, have probed the question deeper, and given an
account of Substance considerably more satisfactory than this. Substances
are usually distinguished as Bodies or Minds. Of each of these,
philosophers have at length provided us with a definition which seems
unexceptionable.

§ 7. A body, according to the received doctrine of modern metaphysicians,
may be defined, the external cause to which we ascribe our sensations.
When I see and touch a piece of gold, I am conscious of a sensation of
yellow color, and sensations of hardness and weight; and by varying the
mode of handling, I may add to these sensations many others completely
distinct from them. The sensations are all of which I am directly
conscious; but I consider them as produced by something not only existing
independently of my will, but external to my bodily organs and to my mind.
This external something I call a body.

It may be asked, how come we to ascribe our sensations to any external
cause? And is there sufficient ground for so ascribing them? It is known,
that there are metaphysicians who have raised a controversy on the point;
maintaining that we are not warranted in referring our sensations to a
cause such as we understand by the word Body, or to any external cause
whatever. Though we have no concern here with this controversy, nor with
the metaphysical niceties on which it turns, one of the best ways of
showing what is meant by Substance is, to consider what position it is
necessary to take up, in order to maintain its existence against
opponents.

It is certain, then, that a part of our notion of a body consists of the
notion of a number of sensations of our own, or of other sentient beings,
habitually occurring simultaneously. My conception of the table at which I
am writing is compounded of its visible form and size, which are complex
sensations of sight; its tangible form and size, which are complex
sensations of our organs of touch and of our muscles; its weight, which is
also a sensation of touch and of the muscles; its color, which is a
sensation of sight; its hardness, which is a sensation of the muscles; its
composition, which is another word for all the varieties of sensation
which we receive under various circumstances from the wood of which it is
made, and so forth. All or most of these various sensations frequently
are, and, as we learn by experience, always might be, experienced
simultaneously, or in many different orders of succession at our own
choice: and hence the thought of any one of them makes us think of the
others, and the whole becomes mentally amalgamated into one mixed state of
consciousness, which, in the language of the school of Locke and Hartley,
is termed a Complex Idea.

Now, there are philosophers who have argued as follows: If we conceive an
orange to be divested of its natural color without acquiring any new one;
to lose its softness without becoming hard, its roundness without becoming
square or pentagonal, or of any other regular or irregular figure
whatever; to be deprived of size, of weight, of taste, of smell; to lose
all its mechanical and all its chemical properties, and acquire no new
ones; to become, in short, invisible, intangible, imperceptible not only
by all our senses, but by the senses of all other sentient beings, real or
possible; nothing, say these thinkers, would remain. For of what nature,
they ask, could be the residuum? and by what token could it manifest its
presence? To the unreflecting its existence seems to rest on the evidence
of the senses. But to the senses nothing is apparent except the
sensations. We know, indeed, that these sensations are bound together by
some law; they do not come together at random, but according to a
systematic order, which is part of the order established in the universe.
When we experience one of these sensations, we usually experience the
others also, or know that we have it in our power to experience them. But
a fixed law of connection, making the sensations occur together, does not,
say these philosophers, necessarily require what is called a substratum to
support them. The conception of a substratum is but one of many possible
forms in which that connection presents itself to our imagination; a mode
of, as it were, realizing the idea. If there be such a substratum, suppose
it at this instant miraculously annihilated, and let the sensations
continue to occur in the same order, and how would the substratum be
missed? By what signs should we be able to discover that its existence had
terminated? Should we not have as much reason to believe that it still
existed as we now have? And if we should not then be warranted in
believing it, how can we be so now? A body, therefore, according to these
metaphysicians, is not any thing intrinsically different from the
sensations which the body is said to produce in us; it is, in short, a set
of sensations, or rather, of possibilities of sensation, joined together
according to a fixed law.

The controversies to which these speculations have given rise, and the
doctrines which have been developed in the attempt to find a conclusive
answer to them, have been fruitful of important consequences to the
Science of Mind. The sensations (it was answered) which we are conscious
of, and which we receive, not at random, but joined together in a certain
uniform manner, imply not only a law or laws of connection, but a cause
external to our mind, which cause, by its own laws, determines the laws
according to which the sensations are connected and experienced. The
schoolmen used to call this external cause by the name we have already
employed, a _substratum_; and its attributes (as they expressed
themselves) _inhered_, literally _stuck_, in it. To this substratum the
name Matter is usually given in philosophical discussions. It was soon,
however, acknowledged by all who reflected on the subject, that the
existence of matter can not be proved by extrinsic evidence. The answer,
therefore, now usually made to Berkeley and his followers, is, that the
belief is intuitive; that mankind, in all ages, have felt themselves
compelled, by a necessity of their nature, to refer their sensations to an
external cause: that even those who deny it in theory, yield to the
necessity in practice, and both in speech, thought, and feeling, do,
equally with the vulgar, acknowledge their sensations to be the effects of
something external to them: this knowledge, therefore, it is affirmed, is
as evidently intuitive as our knowledge of our sensations themselves is
intuitive. And here the question merges in the fundamental problem of
metaphysics properly so called: to which science we leave it.

But although the extreme doctrine of the Idealist metaphysicians, that
objects are nothing but our sensations and the laws which connect them,
has not been generally adopted by subsequent thinkers; the point of most
real importance is one on which those metaphysicians are now very
generally considered to have made out their case: viz., that _all we know_
of objects is the sensations which they give us, and the order of the
occurrence of those sensations. Kant himself, on this point, is as
explicit as Berkeley or Locke. However firmly convinced that there exists
a universe of “Things in themselves,” totally distinct from the universe
of phenomena, or of things as they appear to our senses; and even when
bringing into use a technical expression (_Noumenon_) to denote what the
thing is in itself, as contrasted with the _representation_ of it in our
minds; he allows that this representation (the matter of which, he says,
consists of our sensations, though the form is given by the laws of the
mind itself) is all we know of the object: and that the real nature of the
Thing is, and by the constitution of our faculties ever must remain, at
least in the present state of existence, an impenetrable mystery to us.
“Of things absolutely or in themselves,” says Sir William Hamilton,(19)
“be they external, be they internal, we know nothing, or know them only as
incognizable; and become aware of their incomprehensible existence, only
as this is indirectly and accidentally revealed to us, through certain
qualities related to our faculties of knowledge, and which qualities,
again, we can not think as unconditional, irrelative, existent in and of
ourselves. All that we know is therefore phenomenal—phenomenal of the
unknown.”(20) The same doctrine is laid down in the clearest and strongest
terms by M. Cousin, whose observations on the subject are the more worthy
of attention, as, in consequence of the ultra-German and ontological
character of his philosophy in other respects, they may be regarded as the
admissions of an opponent.(21)

There is not the slightest reason for believing that what we call the
sensible qualities of the object are a type of any thing inherent in
itself, or bear any affinity to its own nature. A cause does not, as such,
resemble its effects; an east wind is not like the feeling of cold, nor
heat like the steam of boiling water. Why then should matter resemble our
sensations? Why should the inmost nature of fire or water resemble the
impressions made by those objects upon our senses?(22) Or on what
principle are we authorized to deduce from the effects, any thing
concerning the cause, except that it is a cause adequate to produce those
effects? It may, therefore, safely be laid down as a truth both obvious in
itself, and admitted by all whom it is at present necessary to take into
consideration, that, of the outward world, we know and can know absolutely
nothing, except the sensations which we experience from it.(23)

§ 8. Body having now been defined the external cause, and (according to
the more reasonable opinion) the unknown external cause, to which we refer
our sensations; it remains to frame a definition of Mind. Nor, after the
preceding observations, will this be difficult. For, as our conception of
a body is that of an unknown exciting cause of sensations, so our
conception of a mind is that of an unknown recipient or percipient, of
them; and not of them alone, but of all our other feelings. As body is
understood to be the mysterious something which excites the mind to feel,
so mind is the mysterious something which feels and thinks. It is
unnecessary to give in the case of mind, as we gave in the case of matter,
a particular statement of the skeptical system by which its existence as a
Thing in itself, distinct from the series of what are denominated its
states, is called in question. But it is necessary to remark, that on the
inmost nature (whatever be meant by inmost nature) of the thinking
principle, as well as on the inmost nature of matter, we are, and with our
faculties must always remain, entirely in the dark. All which we are aware
of, even in our own minds, is (in the words of James Mill) a certain
“thread of consciousness;” a series of feelings, that is, of sensations,
thoughts, emotions, and volitions, more or less numerous and complicated.
There is a something I call Myself, or, by another form of expression, my
mind, which I consider as distinct from these sensations, thoughts, etc.;
a something which I conceive to be not the thoughts, but the being that
has the thoughts, and which I can conceive as existing forever in a state
of quiescence, without any thoughts at all. But what this being is, though
it is myself, I have no knowledge, other than the series of its states of
consciousness. As bodies manifest themselves to me only through the
sensations of which I regard them as the causes, so the thinking
principle, or mind, in my own nature, makes itself known to me only by the
feelings of which it is conscious. I know nothing about myself, save my
capacities of feeling or being conscious (including, of course, thinking
and willing): and were I to learn any thing new concerning my own nature,
I can not with my present faculties conceive this new information to be
any thing else, than that I have some additional capacities, as yet
unknown to me, of feeling, thinking, or willing.

Thus, then, as body is the unsentient cause to which we are naturally
prompted to refer a certain portion of our feelings, so mind may be
described as the sentient _subject_ (in the scholastic sense of the term)
of all feelings; that which has or feels them. But of the nature of either
body or mind, further than the feelings which the former excites, and
which the latter experiences, we do not, according to the best existing
doctrine, know any thing; and if any thing, logic has nothing to do with
it, or with the manner in which the knowledge is acquired. With this
result we may conclude this portion of our subject, and pass to the third
and only remaining class or division of Namable Things.



III. Attributes: and, first, Qualities.


§ 9. From what has already been said of Substance, what is to be said of
Attribute is easily deducible. For if we know not, and can not know, any
thing of bodies but the sensations which they excite in us or in others,
those sensations must be all that we can, at bottom, mean by their
attributes; and the distinction which we verbally make between the
properties of things and the sensations we receive from them, must
originate in the convenience of discourse rather than in the nature of
what is signified by the terms.

Attributes are usually distributed under the three heads of Quality,
Quantity, and Relation. We shall come to the two latter presently: in the
first place we shall confine ourselves to the former.

Let us take, then, as our example, one of what are termed the sensible
qualities of objects, and let that example be whiteness. When we ascribe
whiteness to any substance, as, for instance, snow; when we say that snow
has the quality whiteness, what do we really assert? Simply, that when
snow is present to our organs, we have a particular sensation, which we
are accustomed to call the sensation of white. But how do I know that snow
is present? Obviously by the sensations which I derive from it, and not
otherwise. I infer that the object is present, because it gives me a
certain assemblage or series of sensations. And when I ascribe to it the
attribute whiteness, my meaning is only, that, of the sensations composing
this group or series, that which I call the sensation of white color is
one.

This is one view which may be taken of the subject. But there is also
another and a different view. It may be said, that it is true we _know_
nothing of sensible objects, except the sensations they excite in us; that
the fact of our receiving from snow the particular sensation which is
called a sensation of white, is the _ground_ on which we ascribe to that
substance the quality whiteness; the sole proof of its possessing that
quality. But because one thing may be the sole evidence of the existence
of another thing, it does not follow that the two are one and the same.
The attribute whiteness (it may be said) is not the fact of receiving the
sensation, but something in the object itself; a _power_ inherent in it;
something _in virtue_ of which the object produces the sensation. And when
we affirm that snow possesses the attribute whiteness, we do not merely
assert that the presence of snow produces in us that sensation, but that
it does so through, and by reason of, that power or quality.

For the purposes of logic it is not of material importance which of these
opinions we adopt. The full discussion of the subject belongs to the other
department of scientific inquiry, so often alluded to under the name of
metaphysics; but it may be said here, that for the doctrine of the
existence of a peculiar species of entities called qualities, I can see no
foundation except in a tendency of the human mind which is the cause of
many delusions. I mean, the disposition, wherever we meet with two names
which are not precisely synonymous, to suppose that they must be the names
of two different things; whereas in reality they may be names of the same
thing viewed in two different lights, or under different suppositions as
to surrounding circumstances. Because _quality_ and _sensation_ can not be
put indiscriminately one for the other, it is supposed that they can not
both signify the same thing, namely, the impression or feeling with which
we are affected through our senses by the presence of an object; though
there is at least no absurdity in supposing that this identical impression
or feeling may be called a sensation when considered merely in itself, and
a quality when looked at in relation to any one of the numerous objects,
the presence of which to our organs excites in our minds that among
various other sensations or feelings. And if this be admissible as a
supposition, it rests with those who contend for an entity _per se_ called
a quality, to show that their opinion is preferable, or is any thing in
fact but a lingering remnant of the old doctrine of occult causes; the
very absurdity which Molière so happily ridiculed when he made one of his
pedantic physicians account for the fact that opium produces sleep by the
maxim, Because it has a soporific virtue.

It is evident that when the physician stated that opium has a soporific
virtue, he did not account for, but merely asserted over again, the fact
that it produces sleep. In like manner, when we say that snow is white
because it has the quality of whiteness, we are only re-asserting in more
technical language the fact that it excites in us the sensation of white.
If it be said that the sensation must have some cause, I answer, its cause
is the presence of the assemblage of phenomena which is termed the object.
When we have asserted that as often as the object is present, and our
organs in their normal state, the sensation takes place, we have stated
all that we know about the matter. There is no need, after assigning a
certain and intelligible cause, to suppose an occult cause besides, for
the purpose of enabling the real cause to produce its effect. If I am
asked, why does the presence of the object cause this sensation in me, I
can not tell: I can only say that such is my nature, and the nature of the
object; that the fact forms a part of the constitution of things. And to
this we must at last come, even after interpolating the imaginary entity.
Whatever number of links the chain of causes and effects may consist of,
how any one link produces the one which is next to it, remains equally
inexplicable to us. It is as easy to comprehend that the object should
produce the sensation directly and at once, as that it should produce the
same sensation by the aid of something else called the _power_ of
producing it.

But, as the difficulties which may be felt in adopting this view of the
subject can not be removed without discussions transcending the bounds of
our science, I content myself with a passing indication, and shall, for
the purposes of logic, adopt a language compatible with either view of the
nature of qualities. I shall say—what at least admits of no dispute—that
the quality of whiteness ascribed to the object snow, is _grounded_ on its
exciting in us the sensation of white; and adopting the language already
used by the school logicians in the case of the kind of attributes called
Relations, I shall term the sensation of white the _foundation_ of the
quality whiteness. For logical purposes the sensation is the only
essential part of what is meant by the word; the only part which we ever
can be concerned in proving. When that is proved, the quality is proved;
if an object excites a sensation, it has, of course, the power of exciting
it.



IV. Relations.


§ 10. The _qualities_ of a body, we have said, are the attributes grounded
on the sensations which the presence of that particular body to our organs
excites in our minds. But when we ascribe to any object the kind of
attribute called a Relation, the foundation of the attribute must be
something in which other objects are concerned besides itself and the
percipient.

As there may with propriety be said to be a relation between any two
things to which two correlative names are or may be given, we may expect
to discover what constitutes a relation in general, if we enumerate the
principal cases in which mankind have imposed correlative names, and
observe what these cases have in common.

What, then, is the character which is possessed in common by states of
circumstances so heterogeneous and discordant as these: one thing _like_
another; one thing _unlike_ another; one thing _near_ another; one thing
_far from_ another; one thing _before_, _after_, _along with_ another; one
thing _greater_, _equal_, _less_, than another; one thing the _cause_ of
another, the _effect_ of another; one person the _master_, _servant_,
_child_, _parent_, _debtor_, _creditor_, _sovereign_, _subject_,
_attorney_, _client_, of another, and so on?

Omitting, for the present, the case of Resemblance, (a relation which
requires to be considered separately,) there seems to be one thing common
to all these cases, and only one; that in each of them there exists or
occurs, or has existed or occurred, or may be expected to exist or occur,
some fact or phenomenon, into which the two things which are said to be
related to each other, both enter as parties concerned. This fact, or
phenomenon, is what the Aristotelian logicians called the _fundamentum
relationis_. Thus in the relation of greater and less between two
magnitudes, the _fundamentum relationis_ is the fact that one of the two
magnitudes could, under certain conditions, be included in, without
entirely filling, the space occupied by the other magnitude. In the
relation of master and servant, the _fundamentum relationis_ is the fact
that the one has undertaken, or is compelled, to perform certain services
for the benefit and at the bidding of the other. Examples might be
indefinitely multiplied; but it is already obvious that whenever two
things are said to be related, there is some fact, or series of facts,
into which they both enter; and that whenever any two things are involved
in some one fact, or series of facts, we may ascribe to those two things a
mutual relation grounded on the fact. Even if they have nothing in common
but what is common to all things, that they are members of the universe,
we call that a relation, and denominate them fellow-creatures,
fellow-beings, or fellow-denizens of the universe. But in proportion as
the fact into which the two objects enter as parts is of a more special
and peculiar, or of a more complicated nature, so also is the relation
grounded upon it. And there are as many conceivable relations as there are
conceivable kinds of fact in which two things can be jointly concerned.

In the same manner, therefore, as a quality is an attribute grounded on
the fact that a certain sensation or sensations are produced in us by the
object, so an attribute grounded on some fact into which the object enters
jointly with another object, is a relation between it and that other
object. But the fact in the latter case consists of the very same kind of
elements as the fact in the former; namely, states of consciousness. In
the case, for example, of any legal relation, as debtor and creditor,
principal and agent, guardian and ward, the _fundamentum relationis_
consists entirely of thoughts, feelings, and volitions (actual or
contingent), either of the persons themselves or of other persons
concerned in the same series of transactions; as, for instance, the
intentions which would be formed by a judge, in case a complaint were made
to his tribunal of the infringement of any of the legal obligations
imposed by the relation; and the acts which the judge would perform in
consequence; acts being (as we have already seen) another word for
intentions followed by an effect, and that effect being but another word
for sensations, or some other feelings, occasioned either to the agent
himself or to somebody else. There is no part of what the names expressive
of the relation imply, that is not resolvable into states of
consciousness; outward objects being, no doubt, supposed throughout as the
causes by which some of those states of consciousness are excited, and
minds as the subjects by which all of them are experienced, but neither
the external objects nor the minds making their existence known otherwise
than by the states of consciousness.

Cases of relation are not always so complicated as those to which we last
alluded. The simplest of all cases of relation are those expressed by the
words antecedent and consequent, and by the word simultaneous. If we say,
for instance, that dawn preceded sunrise, the fact in which the two
things, dawn and sunrise, were jointly concerned, consisted only of the
two things themselves; no third thing entered into the fact or phenomenon
at all. Unless, indeed, we choose to call the succession of the two
objects a third thing; but their succession is not something added to the
things themselves; it is something involved in them. Dawn and sunrise
announce themselves to our consciousness by two successive sensations. Our
consciousness of the succession of these sensations is not a third
sensation or feeling added to them; we have not first the two feelings,
and then a feeling of their succession. To have two feelings at all,
implies having them either successively, or else simultaneously.
Sensations, or other feelings, being given, succession and
simultaneousness are the two conditions, to the alternative of which they
are subjected by the nature of our faculties; and no one has been able, or
needs expect, to analyze the matter any further.

§ 11. In a somewhat similar position are two other sorts of relations,
Likeness and Unlikeness. I have two sensations; we will suppose them to be
simple ones; two sensations of white, or one sensation of white and
another of black. I call the first two sensations _like_; the last two
_unlike_. What is the fact or phenomenon constituting the _fundamentum_ of
this relation? The two sensations first, and then what we call a feeling
of resemblance, or of want of resemblance. Let us confine ourselves to the
former case. Resemblance is evidently a feeling; a state of the
consciousness of the observer. Whether the feeling of the resemblance of
the two colors be a third state of consciousness, which I have _after_
having the two sensations of color, or whether (like the feeling of their
succession) it is involved in the sensations themselves, may be a matter
of discussion. But in either case, these feelings of resemblance, and of
its opposite dissimilarity, are parts of our nature; and parts so far from
being capable of analysis, that they are presupposed in every attempt to
analyze any of our other feelings. Likeness and unlikeness, therefore, as
well as antecedence, sequence, and simultaneousness, must stand apart
among relations, as things _sui generis_. They are attributes grounded on
facts, that is, on states of consciousness, but on states which are
peculiar, unresolvable, and inexplicable.

But, though likeness or unlikeness can not be resolved into any thing
else, complex cases of likeness or unlikeness can be resolved into simpler
ones. When we say of two things which consist of parts, that they are like
one another, the likeness of the wholes does admit of analysis; it is
compounded of likenesses between the various parts respectively, and of
likeness in their arrangement. Of how vast a variety of resemblances of
parts must that resemblance be composed, which induces us to say that a
portrait, or a landscape, is like its original. If one person mimics
another with any success, of how many simple likenesses must the general
or complex likeness be compounded: likeness in a succession of bodily
postures; likeness in voice, or in the accents and intonations of the
voice; likeness in the choice of words, and in the thoughts or sentiments
expressed, whether by word, countenance, or gesture.

All likeness and unlikeness of which we have any cognizance, resolve
themselves into likeness and unlikeness between states of our own, or some
other, mind. When we say that one body is like another, (since we know
nothing of bodies but the sensations which they excite,) we mean really
that there is a resemblance between the sensations excited by the two
bodies, or between some portions at least of those sensations. If we say
that two attributes are like one another (since we know nothing of
attributes except the sensations or states of feeling on which they are
grounded), we mean really that those sensations, or states of feeling,
resemble each other. We may also say that two relations are alike. The
fact of resemblance between relations is sometimes called _analogy_,
forming one of the numerous meanings of that word. The relation in which
Priam stood to Hector, namely, that of father and son, resembles the
relation in which Philip stood to Alexander; resembles it so closely that
they are called the same relation. The relation in which Cromwell stood to
England resembles the relation in which Napoleon stood to France, though
not so closely as to be called the same relation. The meaning in both
these instances must be, that a resemblance existed between the facts
which constituted the _fundamentum relationis_.

This resemblance may exist in all conceivable gradations, from perfect
undistinguishableness to something extremely slight. When we say, that a
thought suggested to the mind of a person of genius is like a seed cast
into the ground, because the former produces a multitude of other
thoughts, and the latter a multitude of other seeds, this is saying that
between the relation of an inventive mind to a thought contained in it,
and the relation of a fertile soil to a seed contained in it, there exists
a resemblance: the real resemblance being in the two _fundamenta
relationis_, in each of which there occurs a germ, producing by its
development a multitude of other things similar to itself. And as,
whenever two objects are jointly concerned in a phenomenon, this
constitutes a relation between those objects, so, if we suppose a second
pair of objects concerned in a second phenomenon, the slightest
resemblance between the two phenomena is sufficient to admit of its being
said that the two relations resemble; provided, of course, the points of
resemblance are found in those portions of the two phenomena respectively
which are connoted by the relative names.

While speaking of resemblance, it is necessary to take notice of an
ambiguity of language, against which scarcely any one is sufficiently on
his guard. Resemblance, when it exists in the highest degree of all,
amounting to undistinguishableness, is often called identity, and the two
similar things are said to be the same. I say often, not always; for we do
not say that two visible objects, two persons, for instance, are the same,
because they are so much alike that one might be mistaken for the other:
but we constantly use this mode of expression when speaking of feelings;
as when I say that the sight of any object gives me the _same_ sensation
or emotion to-day that it did yesterday, or the _same_ which it gives to
some other person. This is evidently an incorrect application of the word
_same_; for the feeling which I had yesterday is gone, never to return;
what I have to-day is another feeling, exactly like the former, perhaps,
but distinct from it; and it is evident that two different persons can not
be experiencing the same feeling, in the sense in which we say that they
are both sitting at the same table. By a similar ambiguity we say, that
two persons are ill of the _same_ disease; that two persons hold the
_same_ office; not in the sense in which we say that they are engaged in
the same adventure, or sailing in the same ship, but in the sense that
they fill offices exactly similar, though, perhaps, in distant places.
Great confusion of ideas is often produced, and many fallacies engendered,
in otherwise enlightened understandings, by not being sufficiently alive
to the fact (in itself not always to be avoided), that they use the same
name to express ideas so different as those of identity and
undistinguishable resemblance. Among modern writers, Archbishop Whately
stands almost alone in having drawn attention to this distinction, and to
the ambiguity connected with it.

Several relations, generally called by other names, are really cases of
resemblance. As, for example, equality; which is but another word for the
exact resemblance commonly called identity, considered as subsisting
between things in respect of their _quantity_. And this example forms a
suitable transition to the third and last of the three heads under which,
as already remarked, Attributes are commonly arranged.



V. Quantity.


§ 12. Let us imagine two things, between which there is no difference
(that is, no dissimilarity), except in quantity alone; for instance, a
gallon of water, and more than a gallon of water. A gallon of water, like
any other external object, makes its presence known to us by a set of
sensations which it excites. Ten gallons of water are also an external
object, making its presence known to us in a similar manner; and as we do
not mistake ten gallons of water for a gallon of water, it is plain that
the set of sensations is more or less different in the two cases. In like
manner, a gallon of water, and a gallon of wine, are two external objects,
making their presence known by two sets of sensations, which sensations
are different from each other. In the first case, however, we say that the
difference is in quantity; in the last there is a difference in quality,
while the quantity of the water and of the wine is the same. What is the
real distinction between the two cases? It is not within the province of
Logic to analyze it; nor to decide whether it is susceptible of analysis
or not. For us the following considerations are sufficient: It is evident
that the sensations I receive from the gallon of water, and those I
receive from the gallon of wine, are not the same, that is, not precisely
alike; neither are they altogether unlike: they are partly similar, partly
dissimilar; and that in which they resemble is precisely that in which
alone the gallon of water and the ten gallons do not resemble. That in
which the gallon of water and the gallon of wine are like each other, and
in which the gallon and the ten gallons of water are unlike each other, is
called their quantity. This likeness and unlikeness I do not pretend to
explain, no more than any other kind of likeness or unlikeness. But my
object is to show, that when we say of two things that they differ in
quantity, just as when we say that they differ in quality, the assertion
is always grounded on a difference in the sensations which they excite.
Nobody, I presume, will say, that to see, or to lift, or to drink, ten
gallons of water, does not include in itself a different set of sensations
from those of seeing, lifting, or drinking one gallon; or that to see or
handle a foot-rule, and to see or handle a yard-measure made exactly like
it, are the same sensations. I do not undertake to say what the difference
in the sensations is. Every body knows, and nobody can tell; no more than
any one could tell what white is to a person who had never had the
sensation. But the difference, so far as cognizable by our faculties, lies
in the sensations. Whatever difference we say there is in the things
themselves, is, in this as in all other cases, grounded, and grounded
exclusively, on a difference in the sensations excited by them.



VI. Attributes Concluded.


§ 13. Thus, then, all the attributes of bodies which are classed under
Quality or Quantity, are grounded on the sensations which we receive from
those bodies, and may be defined, the powers which the bodies have of
exciting those sensations. And the same general explanation has been found
to apply to most of the attributes usually classed under the head of
Relation. They, too, are grounded on some fact or phenomenon into which
the related objects enter as parts; that fact or phenomenon having no
meaning and no existence to us, except the series of sensations or other
states of consciousness by which it makes itself known; and the relation
being simply the power or capacity which the object possesses of taking
part along with the correlated object in the production of that series of
sensations or states of consciousness. We have been obliged, indeed, to
recognize a somewhat different character in certain peculiar relations,
those of succession and simultaneity, of likeness and unlikeness. These,
not being grounded on any fact or phenomenon distinct from the related
objects themselves, do not admit of the same kind of analysis. But these
relations, though not, like other relations, grounded on states of
consciousness, are themselves states of consciousness: resemblance is
nothing but our feeling of resemblance; succession is nothing but our
feeling of succession. Or, if this be disputed (and we can not, without
transgressing the bounds of our science, discuss it here), at least our
knowledge of these relations, and even our possibility of knowledge, is
confined to those which subsist between sensations, or other states of
consciousness; for, though we ascribe resemblance, or succession, or
simultaneity, to objects and to attributes, it is always in virtue of
resemblance or succession or simultaneity in the sensations or states of
consciousness which those objects excite, and on which those attributes
are grounded.

§ 14. In the preceding investigation we have, for the sake of simplicity,
considered bodies only, and omitted minds. But what we have said, is
applicable, _mutatis mutandis_, to the latter. The attributes of minds, as
well as those of bodies, are grounded on states of feeling or
consciousness. But in the case of a mind, we have to consider its own
states, as well as those which it produces in other minds. Every attribute
of a mind consists either in being itself affected in a certain way, or
affecting other minds in a certain way. Considered in itself, we can
predicate nothing of it but the series of its own feelings. When we say of
any mind, that it is devout, or superstitious, or meditative, or cheerful,
we mean that the ideas, emotions, or volitions implied in those words,
form a frequently recurring part of the series of feelings, or states of
consciousness, which fill up the sentient existence of that mind.

In addition, however, to those attributes of a mind which are grounded on
its own states of feeling, attributes may also be ascribed to it, in the
same manner as to a body, grounded on the feelings which it excites in
other minds. A mind does not, indeed, like a body, excite sensations, but
it may excite thoughts or emotions. The most important example of
attributes ascribed on this ground, is the employment of terms expressive
of approbation or blame. When, for example, we say of any character, or
(in other words) of any mind, that it is admirable, we mean that the
contemplation of it excites the sentiment of admiration; and indeed
somewhat more, for the word implies that we not only feel admiration, but
approve that sentiment in ourselves. In some cases, under the semblance of
a single attribute, two are really predicated: one of them, a state of the
mind itself; the other, a state with which other minds are affected by
thinking of it. As when we say of any one that he is generous. The word
generosity expresses a certain state of mind, but being a term of praise,
it also expresses that this state of mind excites in us another mental
state, called approbation. The assertion made, therefore, is twofold, and
of the following purport: Certain feelings form habitually a part of this
person’s sentient existence; and the idea of those feelings of his,
excites the sentiment of approbation in ourselves or others.

As we thus ascribe attributes to minds on the ground of ideas and
emotions, so may we to bodies on similar grounds, and not solely on the
ground of sensations: as in speaking of the beauty of a statue; since this
attribute is grounded on the peculiar feeling of pleasure which the statue
produces in our minds; which is not a sensation, but an emotion.



VII. General Results.


§ 15. Our survey of the varieties of Things which have been, or which are
capable of being, named—which have been, or are capable of being, either
predicated of other Things, or themselves made the subject of
predications—is now concluded.

Our enumeration commenced with Feelings. These we scrupulously
distinguished from the objects which excite them, and from the organs by
which they are, or may be supposed to be, conveyed. Feelings are of four
sorts: Sensations, Thoughts, Emotions, and Volitions. What are called
Perceptions are merely a particular case of Belief, and Belief is a kind
of thought. Actions are merely volitions followed by an effect.

After Feelings we proceeded to Substances. These are either Bodies or
Minds. Without entering into the grounds of the metaphysical doubts which
have been raised concerning the existence of Matter and Mind as objective
realities, we stated as sufficient for us the conclusion in which the best
thinkers are now for the most part agreed, that all we can know of Matter
is the sensations which it gives us, and the order of occurrence of those
sensations; and that while the substance Body is the unknown cause of our
sensations, the substance Mind is the unknown recipient.

The only remaining class of Namable Things is Attributes; and these are of
three kinds, Quality, Relation, and Quantity. Qualities, like substances,
are known to us no otherwise than by the sensations or other states of
consciousness which they excite: and while, in compliance with common
usage, we have continued to speak of them as a distinct class of Things,
we showed that in predicating them no one means to predicate any thing but
those sensations or states of consciousness, on which they may be said to
be grounded, and by which alone they can be defined or described.
Relations, except the simple cases of likeness and unlikeness, succession
and simultaneity, are similarly grounded on some fact or phenomenon, that
is, on some series of sensations or states of consciousness, more or less
complicated. The third species of Attribute, Quantity, is also manifestly
grounded on something in our sensations or states of feeling, since there
is an indubitable difference in the sensations excited by a larger and a
smaller bulk, or by a greater or a less degree of intensity, in any object
of sense or of consciousness. All attributes, therefore, are to us nothing
but either our sensations and other states of feeling, or something
inextricably involved therein; and to this even the peculiar and simple
relations just adverted to are not exceptions. Those peculiar relations,
however, are so important, and, even if they might in strictness be
classed among states of consciousness, are so fundamentally distinct from
any other of those states, that it would be a vain subtlety to bring them
under that common description, and it is necessary that they should be
classed apart.(24)

As the result, therefore, of our analysis, we obtain the following as an
enumeration and classification of all Namable Things:

1st. Feelings, or States of Consciousness.

2d. The Minds which experience those feelings.

3d. The Bodies, or external objects which excite certain of those
feelings, together with the powers or properties whereby they excite them;
these latter (at least) being included rather in compliance with common
opinion, and because their existence is taken for granted in the common
language from which I can not prudently deviate, than because the
recognition of such powers or properties as real existences appears to be
warranted by a sound philosophy.

4th, and last. The Successions and Co-existences, the Likenesses and
Unlikenesses, between feelings or states of consciousness. Those
relations, when considered as subsisting between other things, exist in
reality only between the states of consciousness which those things, if
bodies, excite, if minds, either excite or experience.

This, until a better can be suggested, may serve as a substitute for the
Categories of Aristotle considered as a classification of Existences. The
practical application of it will appear when we commence the inquiry into
the Import of Propositions; in other words, when we inquire what it is
which the mind actually believes, when it gives what is called its assent
to a proposition.

These four classes comprising, if the classification be correct, all
Namable Things, these or some of them must of course compose the
signification of all names: and of these, or some of them, is made up
whatever we call a fact.

For distinction’s sake, every fact which is solely composed of feelings or
states of consciousness considered as such, is often called a
Psychological or Subjective fact; while every fact which is composed,
either wholly or in part, of something different from these, that is, of
substances and attributes, is called an Objective fact. We may say, then,
that every objective fact is grounded on a corresponding subjective one;
and has no meaning to us (apart from the subjective fact which corresponds
to it), except as a name for the unknown and inscrutable process by which
that subjective or psychological fact is brought to pass.



                               Chapter IV.


Of Propositions.


§ 1. In treating of Propositions, as already in treating of Names, some
considerations of a comparatively elementary nature respecting their form
and varieties must be premised, before entering upon that analysis of the
import conveyed by them, which is the real subject and purpose of this
preliminary book.

A proposition, we have before said, is a portion of discourse in which a
predicate is affirmed or denied of a subject. A predicate and a subject
are all that is necessarily required to make up a proposition: but as we
can not conclude from merely seeing two names put together, that they are
a predicate and a subject, that is, that one of them is intended to be
affirmed or denied of the other, it is necessary that there should be some
mode or form of indicating that such is the intention; some sign to
distinguish a predication from any other kind of discourse. This is
sometimes done by a slight alteration of one of the words, called an
_inflection_; as when we say, Fire burns; the change of the second word
from _burn_ to _burns_ showing that we mean to affirm the predicate burn
of the subject fire. But this function is more commonly fulfilled by the
word _is_, when an affirmation is intended, _is not_, when a negation; or
by some other part of the verb _to be_. The word which thus serves the
purpose of a sign of predication is called, as we formerly observed, the
_copula_. It is important that there should be no indistinctness in our
conception of the nature and office of the copula; for confused notions
respecting it are among the causes which have spread mysticism over the
field of logic, and perverted its speculations into logomachies.

It is apt to be supposed that the copula is something more than a mere
sign of predication; that it also signifies existence. In the proposition,
Socrates is just, it may seem to be implied not only that the quality
_just_ can be affirmed of Socrates, but moreover that Socrates _is_, that
is to say, exists. This, however, only shows that there is an ambiguity in
the word _is_; a word which not only performs the function of the copula
in affirmations, but has also a meaning of its own, in virtue of which it
may itself be made the predicate of a proposition. That the employment of
it as a copula does not necessarily include the affirmation of existence,
appears from such a proposition as this, A centaur is a fiction of the
poets; where it can not possibly be implied that a centaur exists, since
the proposition itself expressly asserts that the thing has no real
existence.

Many volumes might be filled with the frivolous speculations concerning
the nature of Being (το ὄν, οὐσία, Ens, Entitas, Essentia, and the like),
which have arisen from overlooking this double meaning of the word _to
be_; from supposing that when it signifies _to exist_, and when it
signifies to _be_ some specified thing, as to _be_ a man, to _be_
Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a
nonentity, it must still, at bottom, answer to the same idea; and that a
meaning must be found for it which shall suit all these cases. The fog
which rose from this narrow spot diffused itself at an early period over
the whole surface of metaphysics. Yet it becomes us not to triumph over
the great intellects of Plato and Aristotle because we are now able to
preserve ourselves from many errors into which they, perhaps inevitably,
fell. The fire-teazer of a modern steam-engine produces by his exertions
far greater effects than Milo of Crotona could, but he is not therefore a
stronger man. The Greeks seldom knew any language but their own. This
rendered it far more difficult for them than it is for us, to acquire a
readiness in detecting ambiguities. One of the advantages of having
accurately studied a plurality of languages, especially of those languages
which eminent thinkers have used as the vehicle of their thoughts, is the
practical lesson we learn respecting the ambiguities of words, by finding
that the same word in one language corresponds, on different occasions, to
different words in another. When not thus exercised, even the strongest
understandings find it difficult to believe that things which have a
common name, have not in some respect or other a common nature; and often
expend much labor very unprofitably (as was frequently done by the two
philosophers just mentioned) in vain attempts to discover in what this
common nature consists. But, the habit once formed, intellects much
inferior are capable of detecting even ambiguities which are common to
many languages: and it is surprising that the one now under consideration,
though it exists in the modern languages as well as in the ancient, should
have been overlooked by almost all authors. The quantity of futile
speculation which had been caused by a misapprehension of the nature of
the copula, was hinted at by Hobbes; but Mr. James Mill(25) was, I
believe, the first who distinctly characterized the ambiguity, and pointed
out how many errors in the received systems of philosophy it has had to
answer for. It has, indeed, misled the moderns scarcely less than the
ancients, though their mistakes, because our understandings are not yet so
completely emancipated from their influence, do not appear equally
irrational.

We shall now briefly review the principal distinctions which exist among
propositions, and the technical terms most commonly in use to express
those distinctions.

§ 2. A proposition being a portion of discourse in which something is
affirmed or denied of something, the first division of propositions is
into affirmative and negative. An affirmative proposition is that in which
the predicate is _affirmed_ of the subject; as, Cæsar is dead. A negative
proposition is that in which the predicate is _denied_ of the subject; as,
Cæsar is not dead. The copula, in this last species of proposition,
consists of the words _is not_, which are the sign of negation; _is_ being
the sign of affirmation.

Some logicians, among whom may be mentioned Hobbes, state this distinction
differently; they recognize only one form of copula, _is_, and attach the
negative sign to the predicate. “Cæsar is dead,” and “Cæsar is not dead,”
according to these writers, are propositions agreeing not in the subject
and predicate, but in the subject only. They do not consider “dead,” but
“not dead,” to be the predicate of the second proposition, and they
accordingly define a negative proposition to be one in which the predicate
is a negative name. The point, though not of much practical moment,
deserves notice as an example (not unfrequent in logic) where by means of
an apparent simplification, but which is merely verbal, matters are made
more complex than before. The notion of these writers was, that they could
get rid of the distinction between affirming and denying, by treating
every case of denying as the affirming of a negative name. But what is
meant by a negative name? A name expressive of the _absence_ of an
attribute. So that when we affirm a negative name, what we are really
predicating is absence and not presence; we are asserting not that any
thing is, but that something is not; to express which operation no word
seems so proper as the word denying. The fundamental distinction is
between a fact and the non-existence of that fact; between seeing
something and not seeing it, between Cæsar’s being dead and his not being
dead; and if this were a merely verbal distinction, the generalization
which brings both within the same form of assertion would be a real
simplification: the distinction, however, being real, and in the facts, it
is the generalization confounding the distinction that is merely verbal;
and tends to obscure the subject, by treating the difference between two
kinds of truths as if it were only a difference between two kinds of
words. To put things together, and to put them or keep them asunder, will
remain different operations, whatever tricks we may play with language.

A remark of a similar nature may be applied to most of those distinctions
among propositions which are said to have reference to their _modality_;
as, difference of tense or time; the sun _did_ rise, the sun _is_ rising,
the sun _will_ rise. These differences, like that between affirmation and
negation, might be glossed over by considering the incident of time as a
mere modification of the predicate: thus, The sun is _an object having
risen_, The sun is _an object now rising_, The sun is _an object to rise
hereafter_. But the simplification would be merely verbal. Past, present,
and future, do not constitute so many different kinds of rising; they are
designations belonging to the event asserted, to the _sun’s_ rising
to-day. They affect, not the predicate, but the applicability of the
predicate to the particular subject. That which we affirm to be past,
present, or future, is not what the subject signifies, nor what the
predicate signifies, but specifically and expressly what the predication
signifies; what is expressed only by the proposition as such, and not by
either or both of the terms. Therefore the circumstance of time is
properly considered as attaching to the copula, which is the sign of
predication, and not to the predicate. If the same can not be said of such
modifications as these, Cæsar _may_ be dead; Cæsar is _perhaps_ dead; it
is _possible_ that Cæsar is dead; it is only because these fall altogether
under another head, being properly assertions not of any thing relating to
the fact itself, but of the state of our own mind in regard to it; namely,
our absence of disbelief of it. Thus “Cæsar may be dead” means “I am not
sure that Cæsar is alive.”

§ 3. The next division of propositions is into Simple and Complex; more
aptly (by Professor Bain(26)) termed Compound. A simple proposition is
that in which one predicate is affirmed or denied of one subject. A
compound proposition is that in which there is more than one predicate, or
more than one subject, or both.

At first sight this division has the air of an absurdity; a solemn
distinction of things into one and more than one; as if we were to divide
horses into single horses and teams of horses. And it is true that what is
called a complex (or compound) proposition is often not a proposition at
all, but several propositions, held together by a conjunction. Such, for
example, is this: Cæsar is dead, and Brutus is alive: or even this, Cæsar
is dead, _but_ Brutus is alive. There are here two distinct assertions;
and we might as well call a street a complex house, as these two
propositions a complex proposition. It is true that the syncategorematic
words _and_ and _but_ have a meaning; but that meaning is so far from
making the two propositions one, that it adds a third proposition to them.
All particles are abbreviations, and generally abbreviations of
propositions; a kind of short-hand, whereby something which, to be
expressed fully, would have required a proposition or a series of
propositions, is suggested to the mind at once. Thus the words, Cæsar is
dead and Brutus is alive, are equivalent to these: Cæsar is dead; Brutus
is alive; it is desired that the two preceding propositions should be
thought of together. If the words were, Cæsar is dead, _but_ Brutus is
alive, the sense would be equivalent to the same three propositions
together with a fourth; “between the two preceding propositions there
exists a contrast:” viz., either between the two facts themselves, or
between the feelings with which it is desired that they should be
regarded.

In the instances cited the two propositions are kept visibly distinct,
each subject having its separate predicate, and each predicate its
separate subject. For brevity, however, and to avoid repetition, the
propositions are often blended together: as in this, “Peter and James
preached at Jerusalem and in Galilee,” which contains four propositions:
Peter preached at Jerusalem, Peter preached in Galilee, James preached at
Jerusalem, James preached in Galilee.

We have seen that when the two or more propositions comprised in what is
called a complex proposition are stated absolutely, and not under any
condition or proviso, it is not a proposition at all, but a plurality of
propositions; since what it expresses is not a single assertion, but
several assertions, which, if true when joined, are true also when
separated. But there is a kind of proposition which, though it contains a
plurality of subjects and of predicates, and may be said in one sense of
the word to consist of several propositions, contains but one assertion;
and its truth does not at all imply that of the simple propositions which
compose it. An example of this is, when the simple propositions are
connected by the particle _or_; as, either A is B or C is D; or by the
particle _if_; as, A is B if C is D. In the former case, the proposition
is called _disjunctive_, in the latter, _conditional_: the name
_hypothetical_ was originally common to both.

As has been well remarked by Archbishop Whately and others, the
disjunctive form is resolvable into the conditional; every disjunctive
proposition being equivalent to two or more conditional ones. “Either A is
B or C is D,” means, “if A is not B, C is D; and if C is not D, A is B.”
All hypothetical propositions, therefore, though disjunctive in form, are
conditional in meaning; and the words hypothetical and conditional may be,
as indeed they generally are, used synonymously. Propositions in which the
assertion is not dependent on a condition, are said, in the language of
logicians, to be _categorical_.

A hypothetical proposition is not, like the pretended complex propositions
which we previously considered, a mere aggregation of simple propositions.
The simple propositions which form part of the words in which it is
couched, form no part of the assertion which it conveys. When we say, If
the Koran comes from God, Mohammed is the prophet of God, we do not intend
to affirm either that the Koran does come from God, or that Mohammed is
really his prophet. Neither of these simple propositions may be true, and
yet the truth of the hypothetical proposition may be indisputable. What is
asserted is not the truth of either of the propositions, but the
inferribility of the one from the other. What, then, is the subject, and
what the predicate of the hypothetical proposition? “The Koran” is not the
subject of it, nor is “Mohammed:” for nothing is affirmed or denied either
of the Koran or of Mohammed. The real subject of the predication is the
entire proposition, “Mohammed is the prophet of God;” and the affirmation
is, that this is a legitimate inference from the proposition, “The Koran
comes from God.” The subject and predicate, therefore, of a hypothetical
proposition are names of propositions. The subject is some one
proposition. The predicate is a general relative name applicable to
propositions; of this form—“an inference from so and so.” A fresh instance
is here afforded of the remark, that particles are abbreviations; since
“_If_ A is B, C is D,” is found to be an abbreviation of the following:
“The proposition C is D, is a legitimate inference from the proposition A
is B.”

The distinction, therefore, between hypothetical and categorical
propositions is not so great as it at first appears. In the conditional,
as well as in the categorical form, one predicate is affirmed of one
subject, and no more: but a conditional proposition is a proposition
concerning a proposition; the subject of the assertion is itself an
assertion. Nor is this a property peculiar to hypothetical propositions.
There are other classes of assertions concerning propositions. Like other
things, a proposition has attributes which may be predicated of it. The
attribute predicated of it in a hypothetical proposition, is that of being
an inference from a certain other proposition. But this is only one of
many attributes that might be predicated. We may say, That the whole is
greater than its part, is an axiom in mathematics: That the Holy Ghost
proceeds from the Father alone, is a tenet of the Greek Church: The
doctrine of the divine right of kings was renounced by Parliament at the
Revolution: The infallibility of the Pope has no countenance from
Scripture. In all these cases the subject of the predication is an entire
proposition. That which these different predicates are affirmed of, is
_the proposition_, “the whole is greater than its part;” _the
proposition_, “the Holy Ghost proceeds from the Father alone;” _the
proposition_, “kings have a divine right;” _the proposition_, “the Pope is
infallible.”

Seeing, then, that there is much less difference between hypothetical
propositions and any others, than one might be led to imagine from their
form, we should be at a loss to account for the conspicuous position which
they have been selected to fill in treatises on logic, if we did not
remember that what they predicate of a proposition, namely, its being an
inference from something else, is precisely that one of its attributes
with which most of all a logician is concerned.

§ 4. The next of the common divisions of Propositions is into Universal,
Particular, Indefinite, and Singular: a distinction founded on the degree
of generality in which the name, which is the subject of the proposition,
is to be understood. The following are examples:

_All men_ are mortal—Universal.
_Some men_ are mortal—Particular.
_Man_ is mortal—Indefinite.
_Julius Cæsar_ is mortal—Singular.

The proposition is Singular, when the subject is an individual name. The
individual name needs not be a proper name. “The Founder of Christianity
was crucified,” is as much a singular proposition as “Christ was
crucified.”

When the name which is the subject of the proposition is a general name,
we may intend to affirm or deny the predicate, either of all the things
that the subject denotes, or only of some. When the predicate is affirmed
or denied of all and each of the things denoted by the subject, the
proposition is universal; when of some undefined portion of them only, it
is particular. Thus, All men are mortal; Every man is mortal; are
universal propositions. No man is immortal, is also a universal
proposition, since the predicate, immortal, is denied of each and every
individual denoted by the term man; the negative proposition being exactly
equivalent to the following, Every man is not-immortal. But “some men are
wise,” “some men are not wise,” are particular propositions; the predicate
_wise_ being in the one case affirmed and in the other denied not of each
and every individual denoted by the term man, but only of each and every
one of some portion of those individuals, without specifying what portion;
for if this were specified, the proposition would be changed either into a
singular proposition, or into a universal proposition with a different
subject; as, for instance, “all _properly instructed_ men are wise.” There
are other forms of particular propositions; as, “_Most_ men are
imperfectly educated:” it being immaterial how large a portion of the
subject the predicate is asserted of, as long as it is left uncertain how
that portion is to be distinguished from the rest.(27)

When the form of the expression does not clearly show whether the general
name which is the subject of the proposition is meant to stand for all the
individuals denoted by it, or only for some of them, the proposition is,
by some logicians, called Indefinite; but this, as Archbishop Whately
observes, is a solecism, of the same nature as that committed by some
grammarians when in their list of genders they enumerate the _doubtful_
gender. The speaker must mean to assert the proposition either as a
universal or as a particular proposition, though he has failed to declare
which: and it often happens that though the words do not show which of the
two he intends, the context, or the custom of speech, supplies the
deficiency. Thus, when it is affirmed that “Man is mortal,” nobody doubts
that the assertion is intended of all human beings; and the word
indicative of universality is commonly omitted, only because the meaning
is evident without it. In the proposition, “Wine is good,” it is
understood with equal readiness, though for somewhat different reasons,
that the assertion is not intended to be universal, but particular.(28) As
is observed by Professor Bain,(29) the chief examples of Indefinite
propositions occur “with names of material, which are the subjects
sometimes of universal, and at other times of particular predication.
‘Food is chemically constituted by carbon, oxygen, etc.,’ is a proposition
of universal quantity; the meaning is all food—all kinds of food. ‘Food is
necessary to animal life’ is a case of particular quantity; the meaning is
some sort of food, not necessarily all sorts. ‘Metal is requisite in order
to strength’ does not mean all kinds of metal. ‘Gold will make a way,’
means a portion of gold.”

When a general name stands for each and every individual which it is a
name of, or in other words, which it denotes, it is said by logicians to
be _distributed_, or taken distributively. Thus, in the proposition, All
men are mortal, the subject, Man, is distributed, because mortality is
affirmed of each and every man. The predicate, Mortal, is not distributed,
because the only mortals who are spoken of in the proposition are those
who happen to be men; while the word may, for aught that appears, and in
fact does, comprehend within it an indefinite number of objects besides
men. In the proposition, Some men are mortal, both the predicate and the
subject are undistributed. In the following, No men have wings, both the
predicate and the subject are distributed. Not only is the attribute of
having wings denied of the entire class Man, but that class is severed and
cast out from the whole of the class Winged, and not merely from some part
of that class.

This phraseology, which is of great service in stating and demonstrating
the rules of the syllogism, enables us to express very concisely the
definitions of a universal and a particular proposition. A universal
proposition is that of which the subject is distributed; a particular
proposition is that of which the subject is undistributed.

There are many more distinctions among propositions than those we have
here stated, some of them of considerable importance. But, for explaining
and illustrating these, more suitable opportunities will occur in the
sequel.



                                Chapter V.


Of The Import Of Propositions.


§ 1. An inquiry into the nature of propositions must have one of two
objects: to analyze the state of mind called Belief, or to analyze what is
believed. All language recognizes a difference between a doctrine or
opinion, and the fact of entertaining the opinion; between assent, and
what is assented to.

Logic, according to the conception here formed of it, has no concern with
the nature of the act of judging or believing; the consideration of that
act, as a phenomenon of the mind, belongs to another science.
Philosophers, however, from Descartes downward, and especially from the
era of Leibnitz and Locke, have by no means observed this distinction; and
would have treated with great disrespect any attempt to analyze the import
of Propositions, unless founded on an analysis of the act of Judgment. A
proposition, they would have said, is but the expression in words of a
Judgment. The thing expressed, not the mere verbal expression, is the
important matter. When the mind assents to a proposition, it judges. Let
us find out what the mind does when it judges, and we shall know what
propositions mean, and not otherwise.

Conformably to these views, almost all the writers on Logic in the last
two centuries, whether English, German, or French, have made their theory
of Propositions, from one end to the other, a theory of Judgments. They
considered a Proposition, or a Judgment, for they used the two words
indiscriminately, to consist in affirming or denying one _idea_ of
another. To judge, was to put two ideas together, or to bring one idea
under another, or to compare two ideas, or to perceive the agreement or
disagreement between two ideas: and the whole doctrine of Propositions,
together with the theory of Reasoning (always necessarily founded on the
theory of Propositions), was stated as if Ideas, or Conceptions, or
whatever other term the writer preferred as a name for mental
representations generally, constituted essentially the subject-matter and
substance of those operations.

It is, of course, true, that in any case of judgment, as for instance when
we judge that gold is yellow, a process takes place in our minds, of which
some one or other of these theories is a partially correct account. We
must have the idea of gold and the idea of yellow, and these two ideas
must be brought together in our mind. But in the first place, it is
evident that this is only a part of what takes place; for we may put two
ideas together without any act of belief; as when we merely imagine
something, such as a golden mountain; or when we actually disbelieve: for
in order even to disbelieve that Mohammed was an apostle of God, we must
put the idea of Mohammed and that of an apostle of God together. To
determine what it is that happens in the case of assent or dissent besides
putting two ideas together, is one of the most intricate of metaphysical
problems. But whatever the solution may be, we may venture to assert that
it can have nothing whatever to do with the import of propositions; for
this reason, that propositions (except sometimes when the mind itself is
the subject treated of) are not assertions respecting our ideas of things,
but assertions respecting the things themselves. In order to believe that
gold is yellow, I must, indeed, have the idea of gold, and the idea of
yellow, and something having reference to those ideas must take place in
my mind; but my belief has not reference to the ideas, it has reference to
the things. What I believe, is a fact relating to the outward thing, gold,
and to the impression made by that outward thing upon the human organs;
not a fact relating to my conception of gold, which would be a fact in my
mental history, not a fact of external nature. It is true, that in order
to believe this fact in external nature, another fact must take place in
my mind, a process must be performed upon my ideas; but so it must in
every thing else that I do. I can not dig the ground unless I have the
idea of the ground, and of a spade, and of all the other things I am
operating upon, and unless I put those ideas together.(30) But it would be
a very ridiculous description of digging the ground to say that it is
putting one idea into another. Digging is an operation which is performed
upon the things themselves, though it can not be performed unless I have
in my mind the ideas of them. And in like manner, believing is an act
which has for its subject the facts themselves, though a previous mental
conception of the facts is an indispensable condition. When I say that
fire causes heat, do I mean that my idea of fire causes my idea of heat?
No: I mean that the natural phenomenon, fire, causes the natural
phenomenon, heat. When I mean to assert any thing respecting the ideas, I
give them their proper name, I call them ideas: as when I say, that a
child’s idea of a battle is unlike the reality, or that the ideas
entertained of the Deity have a great effect on the characters of mankind.

The notion that what is of primary importance to the logician in a
proposition, is the relation between the two _ideas_ corresponding to the
subject and predicate (instead of the relation between the two _phenomena_
which they respectively express), seems to me one of the most fatal errors
ever introduced into the philosophy of Logic; and the principal cause why
the theory of the science has made such inconsiderable progress during the
last two centuries. The treatises on Logic, and on the branches of Mental
Philosophy connected with Logic, which have been produced since the
intrusion of this cardinal error, though sometimes written by men of
extraordinary abilities and attainments, almost always tacitly imply a
theory that the investigation of truth consists in contemplating and
handling our ideas, or conceptions of things, instead of the things
themselves: a doctrine tantamount to the assertion, that the only mode of
acquiring knowledge of nature is to study it at second hand, as
represented in our own minds. Meanwhile, inquiries into every kind of
natural phenomena were incessantly establishing great and fruitful truths
on most important subjects, by processes upon which these views of the
nature of Judgment and Reasoning threw no light, and in which they
afforded no assistance whatever. No wonder that those who knew by
practical experience how truths are arrived at, should deem a science
futile, which consisted chiefly of such speculations. What has been done
for the advancement of Logic since these doctrines came into vogue, has
been done not by professed logicians, but by discoverers in the other
sciences; in whose methods of investigation many principles of logic, not
previously thought of, have successively come forth into light, but who
have generally committed the error of supposing that nothing whatever was
known of the art of philosophizing by the old logicians, because their
modern interpreters have written to so little purpose respecting it.

We have to inquire, then, on the present occasion, not into Judgment, but
judgments; not into the act of believing, but into the thing believed.
What is the immediate object of belief in a Proposition? What is the
matter of fact signified by it? What is it to which, when I assert the
proposition, I give my assent, and call upon others to give theirs? What
is that which is expressed by the form of discourse called a Proposition,
and the conformity of which to fact constitutes the truth of the
proposition?

§ 2. One of the clearest and most consecutive thinkers whom this country
or the world has produced, I mean Hobbes, has given the following answer
to this question. In every proposition (says he) what is signified is, the
belief of the speaker that the predicate is a name of the same thing of
which the subject is a name; and if it really is so, the proposition is
true. Thus the proposition, All men are living beings (he would say) is
true, because _living being_ is a name of every thing of which _man_ is a
name. All men are six feet high, is not true, because _six feet high_ is
not a name of every thing (though it is of some things) of which _man_ is
a name.

What is stated in this theory as the definition of a true proposition,
must be allowed to be a property which all true propositions possess. The
subject and predicate being both of them names of things, if they were
names of quite different things the one name could not, consistently with
its signification, be predicated of the other. If it be true that some men
are copper-colored, it must be true—and the proposition does really
assert—that among the individuals denoted by the name man, there are some
who are also among those denoted by the name copper-colored. If it be true
that all oxen ruminate, it must be true that all the individuals denoted
by the name ox are also among those denoted by the name ruminating; and
whoever asserts that all oxen ruminate, undoubtedly does assert that this
relation subsists between the two names.

The assertion, therefore, which, according to Hobbes, is the only one made
in any proposition, really is made in every proposition: and his analysis
has consequently one of the requisites for being the true one. We may go a
step further; it is the only analysis that is rigorously true of all
propositions without exception. What he gives as the meaning of
propositions, is part of the meaning of all propositions, and the whole
meaning of some. This, however, only shows what an extremely minute
fragment of meaning it is quite possible to include within the logical
formula of a proposition. It does not show that no proposition means more.
To warrant us in putting together two words with a copula between them, it
is really enough that the thing or things denoted by one of the names
should be capable, without violation of usage, of being called by the
other name also. If, then, this be all the meaning necessarily implied in
the form of discourse called a Proposition, why do I object to it as the
scientific definition of what a proposition means? Because, though the
mere collocation which makes the proposition a proposition, conveys no
more than this scanty amount of meaning, that same collocation combined
with other circumstances, that _form_ combined with other _matter_, does
convey more, and the proposition in those other circumstances does assert
more, than merely that relation between the two names.

The only propositions of which Hobbes’s principle is a sufficient account,
are that limited and unimportant class in which both the predicate and the
subject are proper names. For, as has already been remarked, proper names
have strictly no meaning; they are mere marks for individual objects: and
when a proper name is predicated of another proper name, all the
signification conveyed is, that both the names are marks for the same
object. But this is precisely what Hobbes produces as a theory of
predication in general. His doctrine is a full explanation of such
predications as these: Hyde was Clarendon, or, Tully is Cicero. It
exhausts the meaning of those propositions. But it is a sadly inadequate
theory of any others. That it should ever have been thought of as such,
can be accounted for only by the fact, that Hobbes, in common with the
other Nominalists, bestowed little or no attention upon the _connotation_
of words; and sought for their meaning exclusively in what they _denote_:
as if all names had been (what none but proper names really are) marks put
upon individuals; and as if there were no difference between a proper and
a general name, except that the first denotes only one individual, and the
last a greater number.

It has been seen, however, that the meaning of all names, except proper
names and that portion of the class of abstract names which are not
connotative, resides in the connotation. When, therefore, we are analyzing
the meaning of any proposition in which the predicate and the subject, or
either of them, are connotative names, it is to the connotation of those
terms that we must exclusively look, and not to what they _denote_, or in
the language of Hobbes (language so far correct) are names of.

In asserting that the truth of a proposition depends on the conformity of
import between its terms, as, for instance, that the proposition, Socrates
is wise, is a true proposition, because Socrates and wise are names
applicable to, or, as he expresses it, names of, the same person; it is
very remarkable that so powerful a thinker should not have asked himself
the question, But how came they to be names of the same person? Surely not
because such was the intention of those who invented the words. When
mankind fixed the meaning of the word wise, they were not thinking of
Socrates, nor, when his parents gave him the name of Socrates, were they
thinking of wisdom. The names _happen_ to fit the same person because of a
certain _fact_, which fact was not known, nor in being, when the names
were invented. If we want to know what the fact is, we shall find the clue
to it in the _connotation_ of the names.

A bird or a stone, a man, or a wise man, means simply, an object having
such and such attributes. The real meaning of the word man, is those
attributes, and not Smith, Brown, and the remainder of the individuals.
The word _mortal_, in like manner connotes a certain attribute or
attributes; and when we say, All men are mortal, the meaning of the
proposition is, that all beings which possess the one set of attributes,
possess also the other. If, in our experience, the attributes connoted by
_man_ are always accompanied by the attribute connoted by _mortal_, it
will follow as a consequence, that the class _man_ will be wholly included
in the class _mortal_, and that _mortal_ will be a name of all things of
which _man_ is a name: but why? Those objects are brought under the name,
by possessing the attributes connoted by it: but their possession of the
attributes is the real condition on which the truth of the proposition
depends; not their being called by the name. Connotative names do not
precede, but follow, the attributes which they connote. If one attribute
happens to be always found in conjunction with another attribute, the
concrete names which answer to those attributes will of course be
predicable of the same subjects, and may be said, in Hobbes’s language (in
the propriety of which on this occasion I fully concur), to be two names
for the same things. But the possibility of a concurrent application of
the two names, is a mere consequence of the conjunction between the two
attributes, and was, in most cases, never thought of when the names were
introduced and their signification fixed. That the diamond is combustible,
was a proposition certainly not dreamed of when the words Diamond and
Combustible first received their meaning; and could not have been
discovered by the most ingenious and refined analysis of the signification
of those words. It was found out by a very different process, namely, by
exerting the senses, and learning from them, that the attribute of
combustibility existed in the diamonds upon which the experiment was
tried; the number or character of the experiments being such, that what
was true of those individuals might be concluded to be true of all
substances “called by the name,” that is, of all substances possessing the
attributes which the name connotes. The assertion, therefore, when
analyzed, is, that wherever we find certain attributes, there will be
found a certain other attribute: which is not a question of the
signification of names, but of laws of nature; the order existing among
phenomena.

§ 3. Although Hobbes’s theory of Predication has not, in the terms in
which he stated it, met with a very favorable reception from subsequent
thinkers, a theory virtually identical with it, and not by any means so
perspicuously expressed, may almost be said to have taken the rank of an
established opinion. The most generally received notion of Predication
decidedly is that it consists in referring something to a class, _i.e._,
either placing an individual under a class, or placing one class under
another class. Thus, the proposition, Man is mortal, asserts, according to
this view of it, that the class man is included in the class mortal.
“Plato is a philosopher,” asserts that the individual Plato is one of
those who compose the class philosopher. If the proposition is negative,
then instead of placing something in a class, it is said to exclude
something from a class. Thus, if the following be the proposition, The
elephant is not carnivorous; what is asserted (according to this theory)
is, that the elephant is excluded from the class carnivorous, or is not
numbered among the things comprising that class. There is no real
difference, except in language, between this theory of Predication and the
theory of Hobbes. For a class _is_ absolutely nothing but an indefinite
number of individuals denoted by a general name. The name given to them in
common, is what makes them a class. To refer any thing to a class,
therefore, is to look upon it as one of the things which are to be called
by that common name. To exclude it from a class, is to say that the common
name is not applicable to it.

How widely these views of predication have prevailed, is evident from
this, that they are the basis of the celebrated _dictum de omni et nullo_.
When the syllogism is resolved, by all who treat of it, into an inference
that what is true of a class is true of all things whatever that belong to
the class; and when this is laid down by almost all professed logicians as
the ultimate principle to which all reasoning owes its validity; it is
clear that in the general estimation of logicians, the propositions of
which reasonings are composed can be the expression of nothing but the
process of dividing things into classes, and referring every thing to its
proper class.

This theory appears to me a signal example of a logical error very often
committed in logic, that of ὕστερον προτέρον, or explaining a thing by
something which presupposes it. When I say that snow is white, I may and
ought to be thinking of snow as a class, because I am asserting a
proposition as true of all snow: but I am certainly not thinking of white
objects as a class; I am thinking of no white object whatever except snow,
but only of that, and of the sensation of white which it gives me. When,
indeed, I have judged, or assented to the propositions, that snow is
white, and that several other things are also white, I gradually begin to
think of white objects as a class, including snow and those other things.
But this is a conception which followed, not preceded, those judgments,
and therefore can not be given as an explanation of them. Instead of
explaining the effect by the cause, this doctrine explains the cause by
the effect, and is, I conceive, founded on a latent misconception of the
nature of classification.

There is a sort of language very generally prevalent in these discussions,
which seems to suppose that classification is an arrangement and grouping
of definite and known individuals: that when names were imposed, mankind
took into consideration all the individual objects in the universe,
distributed them into parcels or lists, and gave to the objects of each
list a common name, repeating this operation _toties quoties_ until they
had invented all the general names of which language consists; which
having been once done, if a question subsequently arises whether a certain
general name can be truly predicated of a certain particular object, we
have only (as it were) to read the roll of the objects upon which that
name was conferred, and see whether the object about which the question
arises is to be found among them. The framers of language (it would seem
to be supposed) have predetermined all the objects that are to compose
each class, and we have only to refer to the record of an antecedent
decision.

So absurd a doctrine will be owned by nobody when thus nakedly stated; but
if the commonly received explanations of classification and naming do not
imply this theory, it requires to be shown how they admit of being
reconciled with any other.

General names are not marks put upon definite objects; classes are not
made by drawing a line round a given number of assignable individuals. The
objects which compose any given class are perpetually fluctuating. We may
frame a class without knowing the individuals, or even any of the
individuals, of which it may be composed; we may do so while believing
that no such individuals exist. If by the _meaning_ of a general name are
to be understood the things which it is the name of, no general name,
except by accident, has a fixed meaning at all, or ever long retains the
same meaning. The only mode in which any general name has a definite
meaning, is by being a name of an indefinite variety of things; namely, of
all things, known or unknown, past, present, or future, which possess
certain definite attributes. When, by studying not the meaning of words,
but the phenomena of nature, we discover that these attributes are
possessed by some object not previously known to possess them (as when
chemists found that the diamond was combustible), we include this new
object in the class; but it did not already belong to the class. We place
the individual in the class because the proposition is true; the
proposition is not true because the object is placed in the class.(31)

It will appear hereafter, in treating of reasoning, how much the theory of
that intellectual process has been vitiated by the influence of these
erroneous notions, and by the habit which they exemplify of assimilating
all the operations of the human understanding which have truth for their
object, to processes of mere classification and naming. Unfortunately, the
minds which have been entangled in this net are precisely those which have
escaped the other cardinal error commented upon in the beginning of the
present chapter. Since the revolution which dislodged Aristotle from the
schools, logicians may almost be divided into those who have looked upon
reasoning as essentially an affair of Ideas, and those who have looked
upon it as essentially an affair of Names.

Although, however, Hobbes’s theory of Predication, according to the
well-known remark of Leibnitz, and the avowal of Hobbes himself,(32)
renders truth and falsity completely arbitrary, with no standard but the
will of men, it must not be concluded that either Hobbes, or any of the
other thinkers who have in the main agreed with him, did in fact consider
the distinction between truth and error as less real, or attached less
importance to it, than other people. To suppose that they did so would
argue total unacquaintance with their other speculations. But this shows
how little hold their doctrine possessed over their own minds. No person,
at bottom, ever imagined that there was nothing more in truth than
propriety of expression; than using language in conformity to a previous
convention. When the inquiry was brought down from generals to a
particular case, it has always been acknowledged that there is a
distinction between verbal and real questions; that some false
propositions are uttered from ignorance of the meaning of words, but that
in others the source of the error is a misapprehension of things; that a
person who has not the use of language at all may form propositions
mentally, and that they may be untrue—that is, he may believe as matters
of fact what are not really so. This last admission can not be made in
stronger terms than it is by Hobbes himself,(33) though he will not allow
such erroneous belief to be called falsity, but only error. And he has
himself laid down, in other places, doctrines in which the true theory of
predication is by implication contained. He distinctly says that general
names are given to things on account of their attributes, and that
abstract names are the names of those attributes. “Abstract is that which
in any subject denotes the cause of the concrete name.... And these causes
of names are the same with the causes of our conceptions, namely, some
power of action, or affection, of the thing conceived, which some call the
manner by which any thing works upon our senses, but by most men they are
called _accidents_.”(34) It is strange that having gone so far, he should
not have gone one step further, and seen that what he calls the cause of
the concrete name, is in reality the meaning of it; and that when we
predicate of any subject a name which is given _because_ of an attribute
(or, as he calls it, an accident), our object is not to affirm the name,
but, by means of the name, to affirm the attribute.

§ 4. Let the predicate be, as we have said, a connotative term; and to
take the simplest case first, let the subject be a proper name: “The
summit of Chimborazo is white.” The word white connotes an attribute which
is possessed by the individual object designated by the words “summit of
Chimborazo;” which attribute consists in the physical fact, of its
exciting in human beings the sensation which we call a sensation of white.
It will be admitted that, by asserting the proposition, we wish to
communicate information of that physical fact, and are not thinking of the
names, except as the necessary means of making that communication. The
meaning of the proposition, therefore, is, that the individual thing
denoted by the subject, has the attributes connoted by the predicate.

If we now suppose the subject also to be a connotative name, the meaning
expressed by the proposition has advanced a step further in complication.
Let us first suppose the proposition to be universal, as well as
affirmative: “All men are mortal.” In this case, as in the last, what the
proposition asserts (or expresses a belief of) is, of course, that the
objects denoted by the subject (man) possess the attributes connoted by
the predicate (mortal). But the characteristic of this case is, that the
objects are no longer _individually_ designated. They are pointed out only
by some of their attributes: they are the objects called men, that is,
possessing the attributes connoted by the name man; and the only thing
known of them may be those attributes: indeed, as the proposition is
general, and the objects denoted by the subject are therefore indefinite
in number, most of them are not known individually at all. The assertion,
therefore, is not, as before, that the attributes which the predicate
connotes are possessed by any given individual, or by any number of
individuals previously known as John, Thomas, etc., but that those
attributes are possessed by each and every individual possessing certain
other attributes; that whatever has the attributes connoted by the
subject, has also those connoted by the predicate; that the latter set of
attributes _constantly accompany_ the former set. Whatever has the
attributes of man has the attribute of mortality; mortality constantly
accompanies the attributes of man.(35)

If it be remembered that every attribute is _grounded_ on some fact or
phenomenon, either of outward sense or of inward consciousness, and that
to _possess_ an attribute is another phrase for being the cause of, or
forming part of, the fact or phenomenon upon which the attribute is
grounded; we may add one more step to complete the analysis. The
proposition which asserts that one attribute always accompanies another
attribute, really asserts thereby no other thing than this, that one
phenomenon always accompanies another phenomenon; insomuch that where we
find the latter, we have assurance of the existence of the former. Thus,
in the proposition, All men are mortal, the word man connotes the
attributes which we ascribe to a certain kind of living creatures, on the
ground of certain phenomena which they exhibit, and which are partly
physical phenomena, namely the impressions made on our senses by their
bodily form and structure, and partly mental phenomena, namely the
sentient and intellectual life which they have of their own. All this is
understood when we utter the word man, by any one to whom the meaning of
the word is known. Now, when we say, Man is mortal, we mean that wherever
these various physical and mental phenomena are all found, there we have
assurance that the other physical and mental phenomenon, called death,
will not fail to take place. The proposition does not affirm _when_; for
the connotation of the word _mortal_ goes no further than to the
occurrence of the phenomenon at some time or other, leaving the particular
time undecided.

§ 5. We have already proceeded far enough, not only to demonstrate the
error of Hobbes, but to ascertain the real import of by far the most
numerous class of propositions. The object of belief in a proposition,
when it asserts any thing more than the meaning of words, is generally, as
in the cases which we have examined, either the co-existence or the
sequence of two phenomena. At the very commencement of our inquiry, we
found that every act of belief implied two Things: we have now ascertained
what, in the most frequent case, these two things are, namely, two
Phenomena; in other words, two states of consciousness; and what it is
which the proposition affirms (or denies) to subsist between them, namely,
either succession or co-existence. And this case includes innumerable
instances which no one, previous to reflection, would think of referring
to it. Take the following example: A generous person is worthy of honor.
Who would expect to recognize here a case of co-existence between
phenomena? But so it is. The attribute which causes a person to be termed
generous, is ascribed to him on the ground of states of his mind, and
particulars of his conduct: both are phenomena: the former are facts of
internal consciousness; the latter, so far as distinct from the former,
are physical facts, or perceptions of the senses. Worthy of honor admits
of a similar analysis. Honor, as here used, means a state of approving and
admiring emotion, followed on occasion by corresponding outward acts.
“Worthy of honor” connotes all this, together with our approval of the act
of showing honor. All these are phenomena; states of internal
consciousness, accompanied or followed by physical facts. When we say, A
generous person is worthy of honor, we affirm co-existence between the two
complicated phenomena connoted by the two terms respectively. We affirm,
that wherever and whenever the inward feelings and outward facts implied
in the word generosity have place, then and there the existence and
manifestation of an inward feeling, honor, would be followed in our minds
by another inward feeling, approval.

After the analysis, in a former chapter, of the import of names, many
examples are not needed to illustrate the import of propositions. When
there is any obscurity, or difficulty, it does not lie in the meaning of
the proposition, but in the meaning of the names which compose it; in the
extremely complicated connotation of many words; the immense multitude and
prolonged series of facts which often constitute the phenomenon connoted
by a name. But where it is seen what the phenomenon is, there is seldom
any difficulty in seeing that the assertion conveyed by the proposition
is, the co-existence of one such phenomenon with another; or the
succession of one such phenomenon to another: so that where the one is
found, we may calculate on finding the other, though perhaps not
conversely.

This, however, though the most common, is not the only meaning which
propositions are ever intended to convey. In the first place, sequences
and co-existences are not only asserted respecting Phenomena; we make
propositions also respecting those hidden causes of phenomena, which are
named substances and attributes. A substance, however, being to us nothing
but either that which causes, or that which is conscious of, phenomena;
and the same being true, _mutatis mutandis_, of attributes; no assertion
can be made, at least with a meaning, concerning these unknown and
unknowable entities, except in virtue of the Phenomena by which alone they
manifest themselves to our faculties. When we say Socrates was
contemporary with the Peloponnesian war, the foundation of this assertion,
as of all assertions concerning substances, is an assertion concerning the
phenomena which they exhibit—namely, that the series of facts by which
Socrates manifested himself to mankind, and the series of mental states
which constituted his sentient existence, went on simultaneously with the
series of facts known by the name of the Peloponnesian war. Still, the
proposition as commonly understood does not assert that alone; it asserts
that the Thing in itself, the _noumenon_ Socrates, was existing, and doing
or experiencing those various facts during the same time. Co-existence and
sequence, therefore, may be affirmed or denied not only between phenomena,
but between noumena, or between a noumenon and phenomena. And both of
noumena and of phenomena we may affirm simple existence. But what is a
noumenon? An unknown cause. In affirming, therefore, the existence of a
noumenon, we affirm causation. Here, therefore, are two additional kinds
of fact, capable of being asserted in a proposition. Besides the
propositions which assert Sequence or Co-existence, there are some which
assert simple Existence;(36) and others assert Causation, which, subject
to the explanations which will follow in the Third Book, must be
considered provisionally as a distinct and peculiar kind of assertion.

§ 6. To these four kinds of matter-of-fact or assertion, must be added a
fifth, Resemblance. This was a species of attribute which we found it
impossible to analyze; for which no _fundamentum_, distinct from the
objects themselves, could be assigned. Besides propositions which assert a
sequence or co-existence between two phenomena, there are therefore also
propositions which assert resemblance between them; as, This color is like
that color; The heat of to-day is _equal_ to the heat of yesterday. It is
true that such an assertion might with some plausibility be brought within
the description of an affirmation of sequence, by considering it as an
assertion that the simultaneous contemplation of the two colors is
_followed_ by a specific feeling termed the feeling of resemblance. But
there would be nothing gained by incumbering ourselves, especially in this
place, with a generalization which may be looked upon as strained. Logic
does not undertake to analyze mental facts into their ultimate elements.
Resemblance between two phenomena is more intelligible in itself than any
explanation could make it, and under any classification must remain
specifically distinct from the ordinary cases of sequence and
co-existence.

It is sometimes said, that all propositions whatever, of which the
predicate is a general name, do, in point of fact, affirm or deny
resemblance. All such propositions affirm that a thing belongs to a class;
but things being classed together according to their resemblance, every
thing is of course classed with the things which it is supposed to
resemble most; and thence, it may be said, when we affirm that Gold is a
metal, or that Socrates is a man, the affirmation intended is, that gold
resembles other metals, and Socrates other men, more nearly than they
resemble the objects contained in any other of the classes co-ordinate
with these.

There is some slight degree of foundation for this remark, but no more
than a slight degree. The arrangement of things into classes, such as the
class _metal_, or the class _man_, is grounded indeed on a resemblance
among the things which are placed in the same class, but not on a mere
general resemblance: the resemblance it is grounded on consists in the
possession by all those things, of certain common peculiarities; and those
peculiarities it is which the terms connote, and which the propositions
consequently assert; not the resemblance. For though when I say, Gold is a
metal, I say by implication that if there be any other metals it must
resemble them, yet if there were no other metals I might still assert the
proposition with the same meaning as at present, namely, that gold has the
various properties implied in the word metal; just as it might be said,
Christians are men, even if there were no men who were not Christians.
Propositions, therefore, in which objects are referred to a class because
they possess the attributes constituting the class, are so far from
asserting nothing but resemblance, that they do not, properly speaking,
assert resemblance at all.

But we remarked some time ago (and the reasons of the remark will be more
fully entered into in a subsequent Book(37)) that there is sometimes a
convenience in extending the boundaries of a class so as to include things
which possess in a very inferior degree, if in any, some of the
characteristic properties of the class—provided they resemble that class
more than any other, insomuch that the general propositions which are true
of the class, will be nearer to being true of those things than any other
equally general propositions. For instance, there are substances called
metals which have very few of the properties by which metals are commonly
recognized; and almost every great family of plants or animals has a few
anomalous genera or species on its borders, which are admitted into it by
a sort of courtesy, and concerning which it has been matter of discussion
to what family they properly belonged. Now when the class-name is
predicated of any object of this description, we do, by so predicating it,
affirm resemblance and nothing more. And in order to be scrupulously
correct it ought to be said, that in every case in which we predicate a
general name, we affirm, not absolutely that the object possesses the
properties designated by the name, but that it _either_ possesses those
properties, or if it does not, at any rate resembles the things which do
so, more than it resembles any other things. In most cases, however, it is
unnecessary to suppose any such alternative, the latter of the two grounds
being very seldom that on which the assertion is made: and when it is,
there is generally some slight difference in the form of the expression,
as, This species (or genus) is _considered_, or _may be ranked_, as
belonging to such and such a family: we should hardly say positively that
it does belong to it, unless it possessed unequivocally the properties of
which the class-name is scientifically significant.

There is still another exceptional case, in which, though the predicate is
the name of a class, yet in predicating it we affirm nothing but
resemblance, the class being founded not on resemblance in any given
particular, but on general unanalyzable resemblance. The classes in
question are those into which our simple sensations, or other simple
feelings, are divided. Sensations of white, for instance, are classed
together, not because we can take them to pieces, and say they are alike
in this, and not alike in that, but because we feel them to be alike
altogether, though in different degrees. When, therefore, I say, The color
I saw yesterday was a white color, or, The sensation I feel is one of
tightness, in both cases the attribute I affirm of the color or of the
other sensation is mere resemblance—simple _likeness_ to sensations which
I have had before, and which have had those names bestowed upon them. The
names of feelings, like other concrete general names, are connotative; but
they connote a mere resemblance. When predicated of any individual
feeling, the information they convey is that of its likeness to the other
feelings which we have been accustomed to call by the same name. Thus much
may suffice in illustration of the kind of propositions in which the
matter-of-fact asserted (or denied) is simple Resemblance.

Existence, Co-existence, Sequence, Causation, Resemblance: one or other of
these is asserted (or denied) in every proposition which is not merely
verbal. This five-fold division is an exhaustive classification of
matters-of-fact; of all things that can be believed, or tendered for
belief; of all questions that can be propounded, and all answers that can
be returned to them.

Professor Bain(38) distinguishes two kinds of Propositions of
Co-existence. “In the one kind, account is taken of Place; they may be
described as propositions of Order in Place.” In the other kind, the
co-existence which is predicated is termed by Mr. Bain Co-inherence of
Attributes. “This is a distinct variety of Propositions of Co-existence.
Instead of an arrangement in place with numerical intervals, we have the
concurrence of two or more attributes or powers in the same part or
locality. A mass of gold contains, in every atom, the concurring
attributes that mark the substance—weight, hardness, color, lustre,
incorrosibility, etc. An animal, besides having parts situated in place,
has co-inhering functions in the same parts, exerted by the very same
masses and molecules of its substance.... The Mind, which affords no
Propositions of Order in Place, has co-inhering functions. We affirm mind
to contain Feeling, Will, and Thought, not in local separation, but in
commingling exercise. The concurring properties of minerals, of plants,
and of the bodily and the mental structure of animals, are united in
affirmations of co-inherence.”

The distinction is real and important. But, as has been seen, an
Attribute, when it is any thing but a simple unanalyzable Resemblance
between the subject and some other things, consists in causing impressions
of some sort on consciousness. Consequently, the co-inherence of two
attributes is but the co-existence of the two states of consciousness
implied in their meaning: with the difference, however, that this
co-existence is sometimes potential only, the attribute being considered
as in existence, though the fact on which it is grounded may not be
actually, but only potentially present. Snow, for instance, is, with great
convenience, said to be white even in a state of total darkness, because,
though we are not now conscious of the color, we shall be conscious of it
as soon as morning breaks. Co-inherence of attributes is therefore still a
case, though a complex one, of co-existence of states of consciousness; a
totally different thing, however, from Order in Place. Being a part of
simultaneity, it belongs not to Place but to Time.

We may therefore (and we shall sometimes find it a convenience) instead of
Co-existence and Sequence, say, for greater particularity, Order in Place
and Order in Time: Order in Place being a specific mode of co-existence,
not necessary to be more particularly analyzed here; while the mere fact
of co-existence, whether between actual sensations, or between the
potentialities of causing them, known by the name of attributes, may be
classed, together with Sequence, under the head of Order in Time.

§ 7. In the foregoing inquiry into the import of propositions, we have
thought it necessary to analyze directly those alone, in which the terms
of the proposition (or the predicate at least) are concrete terms. But, in
doing so, we have indirectly analyzed those in which the terms are
abstract. The distinction between an abstract term and its corresponding
concrete, does not turn upon any difference in what they are appointed to
signify; for the real signification of a concrete general name is, as we
have so often said, its connotation; and what the concrete term connotes,
forms the entire meaning of the abstract name. Since there is nothing in
the import of an abstract name which is not in the import of the
corresponding concrete, it is natural to suppose that neither can there be
any thing in the import of a proposition of which the terms are abstract,
but what there is in some proposition which can be framed of concrete
terms.

And this presumption a closer examination will confirm. An abstract name
is the name of an attribute, or combination of attributes. The
corresponding concrete is a name given to things, because of, and in order
to express, their possessing that attribute, or that combination of
attributes. When, therefore, we predicate of any thing a concrete name,
the attribute is what we in reality predicate of it. But it has now been
shown that in all propositions of which the predicate is a concrete name,
what is really predicated is one of five things: Existence, Co-existence,
Causation, Sequence, or Resemblance. An attribute, therefore, is
necessarily either an existence, a co-existence, a causation, a sequence,
or a resemblance. When a proposition consists of a subject and predicate
which are abstract terms, it consists of terms which must necessarily
signify one or other of these things. When we predicate of any thing an
abstract name, we affirm of the thing that it is one or other of these
five things; that it is a case of Existence, or of Co-existence, or of
Causation, or of Sequence, or of Resemblance.

It is impossible to imagine any proposition expressed in abstract terms,
which can not be transformed into a precisely equivalent proposition in
which the terms are concrete; namely, either the concrete names which
connote the attributes themselves, or the names of the _fundamenta_ of
those attributes; the facts or phenomena on which they are grounded. To
illustrate the latter case, let us take this proposition, of which the
subject only is an abstract name, “Thoughtlessness is dangerous.”
Thoughtlessness is an attribute, grounded on the facts which we call
thoughtless actions; and the proposition is equivalent to this,
Thoughtless actions are dangerous. In the next example the predicate as
well as the subject are abstract names: “Whiteness is a color;” or “The
color of snow is a whiteness.” These attributes being grounded on
sensations, the equivalent propositions in the concrete would be, The
sensation of white is one of the sensations called those of color—The
sensation of sight, caused by looking at snow, is one of the sensations
called sensations of white. In these propositions, as we have before seen,
the matter-of-fact asserted is a Resemblance. In the following examples,
the concrete terms are those which directly correspond to the abstract
names; connoting the attribute which these denote. “Prudence is a virtue:”
this may be rendered, “All prudent persons, _in so far as_ prudent, are
virtuous:” “Courage is deserving of honor;” thus, “All courageous persons
are deserving of honor _in so far_ as they are courageous:” which is
equivalent to this—“All courageous persons deserve an addition to the
honor, or a diminution of the disgrace, which would attach to them on
other grounds.”

In order to throw still further light upon the import of propositions of
which the terms are abstract, we will subject one of the examples given
above to a minuter analysis. The proposition we shall select is the
following: “Prudence is a virtue.” Let us substitute for the word virtue
an equivalent but more definite expression, such as “a mental quality
beneficial to society,” or “a mental quality pleasing to God,” or whatever
else we adopt as the definition of virtue. What the proposition asserts is
a sequence, accompanied with causation; namely, that benefit to society,
or that the approval of God, is consequent on, and caused by, prudence.
Here is a sequence; but between what? We understand the consequent of the
sequence, but we have yet to analyze the antecedent. Prudence is an
attribute; and, in connection with it, two things besides itself are to be
considered; prudent persons, who are the _subjects_ of the attribute, and
prudential conduct, which may be called the _foundation_ of it. Now is
either of these the antecedent? and, first, is it meant, that the approval
of God, or benefit to society, is attendant upon all prudent _persons_?
No; except _in so far_ as they are prudent; for prudent persons who are
scoundrels can seldom, on the whole, be beneficial to society, nor can
they be acceptable to a good being. Is it upon prudential _conduct_, then,
that divine approbation and benefit to mankind are supposed to be
invariably consequent? Neither is this the assertion meant, when it is
said that prudence is a virtue; except with the same reservation as
before, and for the same reason, namely, that prudential conduct, although
in _so far as_ it is prudential it is beneficial to society, may yet, by
reason of some other of its qualities, be productive of an injury
outweighing the benefit, and deserve a displeasure exceeding the
approbation which would be due to the prudence. Neither the substance,
therefore (viz., the person), nor the phenomenon (the conduct), is an
antecedent on which the other term of the sequence is universally
consequent. But the proposition, “Prudence is a virtue,” is a universal
proposition. What is it, then, upon which the proposition affirms the
effects in question to be universally consequent? Upon that in the person,
and in the conduct, which causes them to be called prudent, and which is
equally in them when the action, though prudent, is wicked; namely, a
correct foresight of consequences, a just estimation of their importance
to the object in view, and repression of any unreflecting impulse at
variance with the deliberate purpose. These, which are states of the
person’s mind, are the real antecedent in the sequence, the real cause in
the causation, asserted by the proposition. But these are also the real
ground, or foundation, of the attribute Prudence; since wherever these
states of mind exist we may predicate prudence, even before we know
whether any conduct has followed. And in this manner every assertion
respecting an attribute, may be transformed into an assertion exactly
equivalent respecting the fact or phenomenon which is the ground of the
attribute. And no case can be assigned, where that which is predicated of
the fact or phenomenon, does not belong to one or other of the five
species formerly enumerated: it is either simple Existence, or it is some
Sequence, Co-existence, Causation, or Resemblance.

And as these five are the only things which can be affirmed, so are they
the only things which can be denied. “No horses are web-footed” denies
that the attributes of a horse ever co-exist with web-feet. It is scarcely
necessary to apply the same analysis to Particular affirmations and
negations. “Some birds are web-footed,” affirms that, with the attributes
connoted by _bird_, the phenomenon web-feet is sometimes co-existent:
“Some birds are not web-footed,” asserts that there are other instances in
which this co-existence does not have place. Any further explanation of a
thing which, if the previous exposition has been assented to, is so
obvious, may here be spared.



                               Chapter VI.


Of Propositions Merely Verbal.


§ 1. As a preparation for the inquiry which is the proper object of Logic,
namely, in what manner propositions are to be proved, we have found it
necessary to inquire what they contain which requires, or is susceptible
of, proof; or (which is the same thing) what they assert. In the course of
this preliminary investigation into the import of Propositions, we
examined the opinion of the Conceptualists, that a proposition is the
expression of a relation between two ideas; and the doctrine of the
extreme Nominalists, that it is the expression of an agreement or
disagreement between the meanings of two names. We decided that, as
general theories, both of these are erroneous; and that, though
propositions may be made both respecting names and respecting ideas,
neither the one nor the other are the subject-matter of Propositions
considered generally. We then examined the different kinds of
Propositions, and found that, with the exception of those which are merely
verbal, they assert five different kinds of matters of fact, namely,
Existence, Order in Place, Order in Time, Causation, and Resemblance; that
in every proposition one of these five is either affirmed, or denied, of
some fact or phenomenon, or of some object the unknown source of a fact or
phenomenon.

In distinguishing, however, the different kinds of matters of fact
asserted in propositions, we reserved one class of propositions, which do
not relate to any matter of fact, in the proper sense of the term at all,
but to the meaning of names. Since names and their signification are
entirely arbitrary, such propositions are not, strictly speaking,
susceptible of truth or falsity, but only of conformity or disconformity
to usage or convention; and all the proof they are capable of, is proof of
usage; proof that the words have been employed by others in the
acceptation in which the speaker or writer desires to use them. These
propositions occupy, however, a conspicuous place in philosophy; and their
nature and characteristics are of as much importance in logic, as those of
any of the other classes of propositions previously adverted to.

If all propositions respecting the signification of words were as simple
and unimportant as those which served us for examples when examining
Hobbes’s theory of predication, viz., those of which the subject and
predicate are proper names, and which assert only that those names have,
or that they have not, been conventionally assigned to the same
individual, there would be little to attract to such propositions the
attention of philosophers. But the class of merely verbal propositions
embraces not only much more than these, but much more than any
propositions which at first sight present themselves as verbal;
comprehending a kind of assertions which have been regarded not only as
relating to things, but as having actually a more intimate relation with
them than any other propositions whatever. The student in philosophy will
perceive that I allude to the distinction on which so much stress was laid
by the schoolmen, and which has been retained either under the same or
under other names by most metaphysicians to the present day, viz., between
what were called _essential_, and what were called _accidental_,
propositions, and between essential and accidental properties or
attributes.

§ 2. Almost all metaphysicians prior to Locke, as well as many since his
time, have made a great mystery of Essential Predication, and of
predicates which are said to be of the _essence_ of the subject. The
essence of a thing, they said, was that without which the thing could
neither be, nor be conceived to be. Thus, rationality was of the essence
of man, because without rationality, man could not be conceived to exist.
The different attributes which made up the essence of the thing were
called its essential properties; and a proposition in which any of these
were predicated of it was called an Essential Proposition, and was
considered to go deeper into the nature of the thing, and to convey more
important information respecting it, than any other proposition could do.
All properties, not of the essence of the thing, were called its
accidents; were supposed to have nothing at all, or nothing comparatively,
to do with its inmost nature; and the propositions in which any of these
were predicated of it were called Accidental Propositions. A connection
may be traced between this distinction, which originated with the
schoolmen, and the well-known dogmas of _substantiæ secundæ_ or general
substances, and _substantial forms_, doctrines which under varieties of
language pervaded alike the Aristotelian and the Platonic schools, and of
which more of the spirit has come down to modern times than might be
conjectured from the disuse of the phraseology. The false views of the
nature of classification and generalization which prevailed among the
schoolmen, and of which these dogmas were the technical expression, afford
the only explanation which can be given of their having misunderstood the
real nature of those Essences which held so conspicuous a place in their
philosophy. They said, truly, that _man_ can not be conceived without
rationality. But though _man_ can not, a being may be conceived exactly
like a man in all points except that one quality, and those others which
are the conditions or consequences of it. All, therefore, which is really
true in the assertion that man can not be conceived without rationality,
is only, that if he had not rationality, he would not be reputed a man.
There is no impossibility in conceiving the _thing_, nor, for aught we
know, in its existing: the impossibility is in the conventions of
language, which will not allow the thing, even if it exist, to be called
by the name which is reserved for rational beings. Rationality, in short,
is involved in the meaning of the word man: is one of the attributes
connoted by the name. The essence of man, simply means the whole of the
attributes connoted by the word; and any one of those attributes taken
singly, is an essential property of man.

But these reflections, so easy to us, would have been difficult to persons
who thought, as most of the later Aristotelians did, that objects were
made what they were called, that gold (for instance) was made gold, not by
the possession of certain properties to which mankind have chosen to
attach that name, but by participation in the nature of a general
substance, called gold in general, which substance, together with all the
properties that belonged to it, _inhered_ in every individual piece of
gold.(39) As they did not consider these universal substances to be
attached to all general names, but only to some, they thought that an
object borrowed only a part of its properties from a universal substance,
and that the rest belonged to it individually: the former they called its
essence, and the latter its accidents. The scholastic doctrine of essences
long survived the theory on which it rested, that of the existence of real
entities corresponding to general terms; and it was reserved for Locke, at
the end of the seventeenth century, to convince philosophers that the
supposed essences of classes were merely the signification of their names;
nor, among the signal services which his writings rendered to philosophy,
was there one more needful or more valuable.

Now, as the most familiar of the general names by which an object is
designated usually connotes not one only, but several attributes of the
object, each of which attributes separately forms also the bond of union
of some class, and the meaning of some general name; we may predicate of a
name which connotes a variety of attributes, another name which connotes
only one of these attributes, or some smaller number of them than all. In
such cases, the universal affirmative proposition will be true; since
whatever possesses the whole of any set of attributes, must possess any
part of that same set. A proposition of this sort, however, conveys no
information to any one who previously understood the whole meaning of the
terms. The propositions, Every man is a corporeal being, Every man is a
living creature, Every man is rational, convey no knowledge to any one who
was already aware of the entire meaning of the word _man_, for the meaning
of the word includes all this: and that every _man_ has the attributes
connoted by all these predicates, is already asserted when he is called a
man. Now, of this nature are all the propositions which have been called
essential. They are, in fact, identical propositions.

It is true that a proposition which predicates any attribute, even though
it be one implied in the name, is in most cases understood to involve a
tacit assertion that there _exists_ a thing corresponding to the name, and
possessing the attributes connoted by it; and this implied assertion may
convey information, even to those who understood the meaning of the name.
But all information of this sort, conveyed by all the essential
propositions of which man can be made the subject, is included in the
assertion, Men exist. And this assumption of real existence is, after all,
the result of an imperfection of language. It arises from the ambiguity of
the copula, which, in addition to its proper office of a mark to show that
an assertion is made, is also, as formerly remarked, a concrete word
connoting existence. The actual existence of the subject of the
proposition is therefore only apparently, not really, implied in the
predication, if an essential one: we may say, A ghost is a disembodied
spirit, without believing in ghosts. But an accidental, or non-essential,
affirmation, does imply the real existence of the subject, because in the
case of a non-existent subject there is nothing for the proposition to
assert. Such a proposition as, The ghost of a murdered person haunts the
couch of the murderer, can only have a meaning if understood as implying a
belief in ghosts; for since the signification of the word ghost implies
nothing of the kind, the speaker either means nothing, or means to assert
a thing which he wishes to be believed to have really taken place.

It will be hereafter seen that when any important consequences seem to
follow, as in mathematics, from an essential proposition, or, in other
words, from a proposition involved in the meaning of a name, what they
really flow from is the tacit assumption of the real existence of the
objects so named. Apart from this assumption of real existence, the class
of propositions in which the predicate is of the essence of the subject
(that is, in which the predicate connotes the whole or part of what the
subject connotes, but nothing besides) answer no purpose but that of
unfolding the whole or some part of the meaning of the name, to those who
did not previously know it. Accordingly, the most useful, and in
strictness the only useful kind of essential propositions, are
Definitions: which, to be complete, should unfold the whole of what is
involved in the meaning of the word defined; that is (when it is a
connotative word), the whole of what it connotes. In defining a name,
however, it is not usual to specify its entire connotation, but so much
only as is sufficient to mark out the objects usually denoted by it from
all other known objects. And sometimes a merely accidental property, not
involved in the meaning of the name, answers this purpose equally well.
The various kinds of definition which these distinctions give rise to, and
the purposes to which they are respectively subservient, will be minutely
considered in the proper place.

§ 3. According to the above view of essential propositions, no proposition
can be reckoned such which relates to an individual by name, that is, in
which the subject is a proper name. Individuals have no essences. When the
schoolmen talked of the essence of an individual, they did not mean the
properties implied in its name, for the names of individuals imply no
properties. They regarded as of the essence of an individual, whatever was
of the essence of the species in which they were accustomed to place that
individual; _i.e._, of the class to which it was most familiarly referred,
and to which, therefore, they conceived that it by nature belonged. Thus,
because the proposition Man is a rational being, was an essential
proposition, they affirmed the same thing of the proposition, Julius Cæsar
is a rational being. This followed very naturally if genera and species
were to be considered as entities, distinct from, but _inhering_ in, the
individuals composing them. If _man_ was a substance inhering in each
individual man, the _essence_ of man (whatever that might mean) was
naturally supposed to accompany it; to inhere in John Thompson, and to
form the _common essence_ of Thompson and Julius Cæsar. It might then be
fairly said, that rationality, being of the essence of Man, was of the
essence also of Thompson. But if Man altogether be only the individual men
and a name bestowed upon them in consequence of certain common properties,
what becomes of John Thompson’s essence?

A fundamental error is seldom expelled from philosophy by a single
victory. It retreats slowly, defends every inch of ground, and often,
after it has been driven from the open country, retains a footing in some
remote fastness. The essences of individuals were an unmeaning figment
arising from a misapprehension of the essences of classes, yet even Locke,
when he extirpated the parent error, could not shake himself free from
that which was its fruit. He distinguished two sorts of essences, Real and
Nominal. His nominal essences were the essences of classes, explained
nearly as we have now explained them. Nor is any thing wanting to render
the third book of Locke’s Essay a nearly unexceptional treatise on the
connotation of names, except to free its language from the assumption of
what are called Abstract Ideas, which unfortunately is involved in the
phraseology, though not necessarily connected with the thoughts contained
in that immortal Third Book.(40) But besides nominal essences, he admitted
real essences, or essences of individual objects, which he supposed to be
the causes of the sensible properties of those objects. We know not (said
he) what these are (and this acknowledgment rendered the fiction
comparatively innocuous); but if we did, we could, from them alone,
demonstrate the sensible properties of the object, as the properties of
the triangle are demonstrated from the definition of the triangle. I shall
have occasion to revert to this theory in treating of Demonstration, and
of the conditions under which one property of a thing admits of being
demonstrated from another property. It is enough here to remark that,
according to this definition, the real essence of an object has, in the
progress of physics, come to be conceived as nearly equivalent, in the
case of bodies, to their corpuscular structure: what it is now supposed to
mean in the case of any other entities, I would not take upon myself to
define.

§ 4. An essential proposition, then, is one which is purely verbal; which
asserts of a thing under a particular name, only what is asserted of it in
the fact of calling it by that name; and which, therefore, either gives no
information, or gives it respecting the name, not the thing.
Non-essential, or accidental propositions, on the contrary, may be called
Real Propositions, in opposition to Verbal. They predicate of a thing some
fact not involved in the signification of the name by which the
proposition speaks of it; some attribute not connoted by that name. Such
are all propositions concerning things individually designated, and all
general or particular propositions in which the predicate connotes any
attribute not connoted by the subject. All these, if true, add to our
knowledge: they convey information, not already involved in the names
employed. When I am told that all, or even that some objects, which have
certain qualities, or which stand in certain relations, have also certain
other qualities, or stand in certain other relations, I learn from this
proposition a new fact; a fact not included in my knowledge of the meaning
of the words, nor even of the existence of Things answering to the
signification of those words. It is this class of propositions only which
are in themselves instructive, or from which any instructive propositions
can be inferred.(41)

Nothing has probably contributed more to the opinion so long prevalent of
the futility of the school logic, than the circumstance that almost all
the examples used in the common school books to illustrate the doctrine of
predication and that of the syllogism, consist of essential propositions.
They were usually taken either from the branches or from the main trunk of
the Predicamental Tree, which included nothing but what was of the
_essence_ of the species: _Omne corpus est substantia_, _Omne animal est
corpus_, _Omnis homo est corpus_, _Omnis homo est animal_, _Omnis homo est
rationalis_, and so forth. It is far from wonderful that the syllogistic
art should have been thought to be of no use in assisting correct
reasoning, when almost the only propositions which, in the hands of its
professed teachers, it was employed to prove, were such as every one
assented to without proof the moment he comprehended the meaning of the
words; and stood exactly on a level, in point of evidence, with the
premises from which they were drawn. I have, therefore, throughout this
work, avoided the employment of essential propositions as examples, except
where the nature of the principle to be illustrated specifically required
them.

§ 5. With respect to propositions which do convey information—which assert
something of a Thing, under a name that does not already presuppose what
is about to be asserted; there are two different aspects in which these,
or rather such of them as are general propositions, may be considered: we
may either look at them as portions of speculative truth, or as memoranda
for practical use. According as we consider propositions in one or the
other of these lights, their import may be conveniently expressed in one
or in the other of two formulas.

According to the formula which we have hitherto employed, and which is
best adapted to express the import of the proposition as a portion of our
theoretical knowledge, All men are mortal, means that the attributes of
man are always accompanied by the attribute mortality: No men are gods,
means that the attributes of man are never accompanied by the attributes,
or at least never by all the attributes, signified by the word god. But
when the proposition is considered as a memorandum for practical use, we
shall find a different mode of expressing the same meaning better adapted
to indicate the office which the proposition performs. The practical use
of a proposition is, to apprise or remind us what we have to expect, in
any individual case which comes within the assertion contained in the
proposition. In reference to this purpose, the proposition, All men are
mortal, means that the attributes of man are _evidence of_, are a _mark_
of, mortality; an indication by which the presence of that attribute is
made manifest. No men are gods, means that the attributes of man are a
mark or evidence that some or all of the attributes understood to belong
to a god are not there; that where the former are, we need not expect to
find the latter.

These two forms of expression are at bottom equivalent; but the one points
the attention more directly to what a proposition means, the latter to the
manner in which it is to be used.

Now it is to be observed that Reasoning (the subject to which we are next
to proceed) is a process into which propositions enter not as ultimate
results, but as means to the establishment of other propositions. We may
expect, therefore, that the mode of exhibiting the import of a general
proposition which shows it in its application to practical use, will best
express the function which propositions perform in Reasoning. And
accordingly, in the theory of Reasoning, the mode of viewing the subject
which considers a Proposition as asserting that one fact or phenomenon is
a _mark_ or _evidence_ of another fact or phenomenon, will be found almost
indispensable. For the purposes of that Theory, the best mode of defining
the import of a proposition is not the mode which shows most clearly what
it is in itself, but that which most distinctly suggests the manner in
which it may be made available for advancing from it to other
propositions.



                               Chapter VII.


Of The Nature Of Classification, And The Five Predicables.


§ 1. In examining into the nature of general propositions, we have
adverted much less than is usual with logicians to the ideas of a Class,
and Classification; ideas which, since the Realist doctrine of General
Substances went out of vogue, have formed the basis of almost every
attempt at a philosophical theory of general terms and general
propositions. We have considered general names as having a meaning, quite
independently of their being the names of classes. That circumstance is in
truth accidental, it being wholly immaterial to the signification of the
name whether there are many objects, or only one, to which it happens to
be applicable, or whether there be any at all. God is as much a general
term to the Christian or Jew as to the Polytheist; and dragon, hippogriff,
chimera, mermaid, ghost, are as much so as if real objects existed,
corresponding to those names. Every name the signification of which is
constituted by attributes, is potentially a name of an indefinite number
of objects; but it needs not be actually the name of any; and if of any,
it may be the name of only one. As soon as we employ a name to connote
attributes, the things, be they more or fewer, which happen to possess
those attributes, are constituted _ipso facto_ a class. But in predicating
the name we predicate only the attributes; and the fact of belonging to a
class does not, in many cases, come into view at all.

Although, however, Predication does not presuppose Classification, and
though the theory of Names and of Propositions is not cleared up, but only
encumbered, by intruding the idea of classification into it, there is
nevertheless a close connection between Classification and the employment
of General Names. By every general name which we introduce, we create a
class, if there be any things, real or imaginary, to compose it; that is,
any Things corresponding to the signification of the name. Classes,
therefore, mostly owe their existence to general language. But general
language, also, though that is not the most common case, sometimes owes
its existence to classes. A general, which is as much as to say a
significant, name, is indeed mostly introduced because we have a
signification to express by it; because we need a word by means of which
to predicate the attributes which it connotes. But it is also true that a
name is sometimes introduced because we have found it convenient to create
a class; because we have thought it useful for the regulation of our
mental operations, that a certain group of objects should be thought of
together. A naturalist, for purposes connected with his particular
science, sees reason to distribute the animal or vegetable creation into
certain groups rather than into any others, and he requires a name to
bind, as it were, each of his groups together. It must not, however, be
supposed that such names, when introduced, differ in any respect, as to
their mode of signification, from other connotative names. The classes
which they denote are, as much as any other classes, constituted by
certain common attributes, and their names are significant of those
attributes, and of nothing else. The names of Cuvier’s classes and orders,
_Plantigrades_, _Digitigrades_, etc., are as much the expression of
attributes as if those names had preceded, instead of grown out of, his
classification of animals. The only peculiarity of the case is, that the
convenience of classification was here the primary motive for introducing
the names; while in other cases the name is introduced as a means of
predication, and the formation of a class denoted by it is only an
indirect consequence.

The principles which ought to regulate Classification, as a logical
process subservient to the investigation of truth, can not be discussed to
any purpose until a much later stage of our inquiry. But, of
Classification as resulting from, and implied in, the fact of employing
general language, we can not forbear to treat here, without leaving the
theory of general names, and of their employment in predication, mutilated
and formless.

§ 2. This portion of the theory of general language is the subject of what
is termed the doctrine of the Predicables; a set of distinctions handed
down from Aristotle, and his follower Porphyry, many of which have taken a
firm root in scientific, and some of them even in popular, phraseology.
The predicables are a fivefold division of General Names, not grounded as
usual on a difference in their meaning, that is, in the attribute which
they connote, but on a difference in the kind of class which they denote.
We may predicate of a thing five different varieties of class-name:

A _genus_ of the thing: (γὲνος).
A _species_: (εἶσος).
A _differentia_: (διαφορὰ).
A _proprium_: (ἰδιών).
An _accidens_: (συμβεβηκός).

It is to be remarked of these distinctions, that they express, not what
the predicate is in its own meaning, but what relation it bears to the
subject of which it happens on the particular occasion to be predicated.
There are not some names which are exclusively genera, and others which
are exclusively species, or differentiæ; but the same name is referred to
one or another predicable, according to the subject of which it is
predicated on the particular occasion. _Animal_, for instance, is a genus
with respect to man, or John; a species with respect to Substance, or
Being. _Rectangular_ is one of the Differentiæ of a geometrical square; it
is merely one of the Accidentia of the table at which I am writing. The
words genus, species, etc., are therefore relative terms; they are names
applied to certain predicates, to express the relation between them and
some given subject: a relation grounded, as we shall see, not on what the
predicate connotes, but on the class which it denotes, and on the place
which, in some given classification, that class occupies relatively to the
particular subject.

§ 3. Of these five names, two, Genus and Species, are not only used by
naturalists in a technical acceptation not precisely agreeing with their
philosophical meaning, but have also acquired a popular acceptation, much
more general than either. In this popular sense any two classes, one of
which includes the whole of the other and more, may be called a Genus and
a Species. Such, for instance, are Animal and Man; Man and Mathematician.
Animal is a Genus; Man and Brute are its two species; or we may divide it
into a greater number of species, as man, horse, dog, etc. _Biped_, or
_two-footed animal_, may also be considered a genus, of which man and bird
are two species. _Taste_ is a genus, of which sweet taste, sour taste,
salt taste, etc., are species. _Virtue_ is a genus; justice, prudence,
courage, fortitude, generosity, etc., are its species.

The same class which is a genus with reference to the sub-classes or
species included in it, may be itself a species with reference to a more
comprehensive, or, as it is often called, a superior genus. Man is a
species with reference to animal, but a genus with reference to the
species Mathematician. Animal is a genus, divided into two species, man
and brute; but animal is also a species, which, with another species,
vegetable, makes up the genus, organized being. Biped is a genus with
reference to man and bird, but a species with respect to the superior
genus, animal. Taste is a genus divided into species, but also a species
of the genus sensation. Virtue, a genus with reference to justice,
temperance, etc., is one of the species of the genus, mental quality.

In this popular sense the words Genus and Species have passed into common
discourse. And it should be observed that in ordinary parlance, not the
name of the class, but the class itself, is said to be the genus or
species; not, of course, the class in the sense of each individual of the
class, but the individuals collectively, considered as an aggregate whole;
the name by which the class is designated being then called not the genus
or species, but the generic or specific name. And this is an admissible
form of expression; nor is it of any importance which of the two modes of
speaking we adopt, provided the rest of our language is consistent with
it; but, if we call the class itself the genus, we must not talk of
predicating the genus. We predicate of man the _name_ mortal; and by
predicating the name, we may be said, in an intelligible sense, to
predicate what the name expresses, the _attribute_ mortality; but in no
allowable sense of the word predication do we predicate of man the _class_
mortal. We predicate of him the fact of belonging to the class.

By the Aristotelian logicians, the terms genus and species were used in a
more restricted sense. They did not admit every class which could be
divided into other classes to be a genus, or every class which could be
included in a larger class to be a species. Animal was by them considered
a genus; man and brute co-ordinate species under that genus: _biped_,
however, would not have been admitted to be a genus with reference to man,
but a _proprium_ or _accidens_ only. It was requisite, according to their
theory, that genus and species should be of the _essence_ of the subject.
Animal was of the essence of man; biped was not. And in every
classification they considered some one class as the lowest or _infima_
species. Man, for instance, was a lowest species. Any further divisions
into which the class might be capable of being broken down, as man into
white, black, and red man, or into priest and layman, they did not admit
to be species.

It has been seen, however, in the preceding chapter, that the distinction
between the essence of a class, and the attributes or properties which are
not of its essence—a distinction which has given occasion to so much
abstruse speculation, and to which so mysterious a character was formerly,
and by many writers is still, attached—amounts to nothing more than the
difference between those attributes of the class which are, and those
which are not, involved in the signification of the class-name. As applied
to individuals, the word Essence, we found, has no meaning, except in
connection with the exploded tenets of the Realists; and what the
schoolmen chose to call the essence of an individual, was simply the
essence of the class to which that individual was most familiarly
referred.

Is there no difference, then, save this merely verbal one, between the
classes which the schoolmen admitted to be genera or species, and those to
which they refused the title? Is it an error to regard some of the
differences which exist among objects as differences _in kind_ (_genere_
or _specie_), and others only as differences in the accidents? Were the
schoolmen right or wrong in giving to some of the classes into which
things may be divided, the name of _kinds_, and considering others as
secondary divisions, grounded on differences of a comparatively
superficial nature? Examination will show that the Aristotelians did mean
something by this distinction, and something important; but which, being
but indistinctly conceived, was inadequately expressed by the phraseology
of essences, and the various other modes of speech to which they had
recourse.

§ 4. It is a fundamental principle in logic, that the power of framing
classes is unlimited, as long as there is any (even the smallest)
difference to found a distinction upon. Take any attribute whatever, and
if some things have it, and others have not, we may ground on the
attribute a division of all things into two classes; and we actually do
so, the moment we create a name which connotes the attribute. The number
of possible classes, therefore, is boundless; and there are as many actual
classes (either of real or of imaginary things) as there are general
names, positive and negative together.

But if we contemplate any one of the classes so formed, such as the class
animal or plant, or the class sulphur or phosphorus, or the class white or
red, and consider in what particulars the individuals included in the
class differ from those which do not come within it, we find a very
remarkable diversity in this respect between some classes and others.
There are some classes, the things contained in which differ from other
things only in certain particulars which may be numbered, while others
differ in more than can be numbered, more even than we need ever expect to
know. Some classes have little or nothing in common to characterize them
by, except precisely what is connoted by the name: white things, for
example, are not distinguished by any common properties except whiteness;
or if they are, it is only by such as are in some way dependent on, or
connected with, whiteness. But a hundred generations have not exhausted
the common properties of animals or of plants, of sulphur or of
phosphorus; nor do we suppose them to be exhaustible, but proceed to new
observations and experiments, in the full confidence of discovering new
properties which were by no means implied in those we previously knew.
While, if any one were to propose for investigation the common properties
of all things which are of the same color, the same shape, or the same
specific gravity, the absurdity would be palpable. We have no ground to
believe that any such common properties exist, except such as may be shown
to be involved in the supposition itself, or to be derivable from it by
some law of causation. It appears, therefore, that the properties, on
which we ground our classes, sometimes exhaust all that the class has in
common, or contain it all by some mode of implication; but in other
instances we make a selection of a few properties from among not only a
greater number, but a number inexhaustible by us, and to which as we know
no bounds, they may, so far as we are concerned, be regarded as infinite.

There is no impropriety in saying that, of these two classifications, the
one answers to a much more radical distinction in the things themselves,
than the other does. And if any one even chooses to say that the one
classification is made by nature, the other by us for our convenience, he
will be right; provided he means no more than this: Where a certain
apparent difference between things (though perhaps in itself of little
moment) answers to we know not what number of other differences, pervading
not only their known properties, but properties yet undiscovered, it is
not optional but imperative to recognize this difference as the foundation
of a specific distinction; while, on the contrary, differences that are
merely finite and determinate, like those designated by the words white,
black, or red, may be disregarded if the purpose for which the
classification is made does not require attention to those particular
properties. The differences, however, are made by nature, in both cases;
while the recognition of those differences as grounds of classification
and of naming, is, equally in both cases, the act of man: only in the one
case, the ends of language and of classification would be subverted if no
notice were taken of the difference, while in the other case, the
necessity of taking notice of it depends on the importance or unimportance
of the particular qualities in which the difference happens to consist.

Now, these classes, distinguished by unknown multitudes of properties, and
not solely by a few determinate ones—which are parted off from one another
by an unfathomable chasm, instead of a mere ordinary ditch with a visible
bottom—are the only classes which, by the Aristotelian logicians, were
considered as genera or species. Differences which extended only to a
certain property or properties, and there terminated, they considered as
differences only in the _accidents_ of things; but where any class
differed from other things by an infinite series of differences, known and
unknown, they considered the distinction as one of _kind_, and spoke of it
as being an _essential_ difference, which is also one of the current
meanings of that vague expression at the present day.

Conceiving the schoolmen to have been justified in drawing a broad line of
separation between these two kinds of classes and of class-distinctions, I
shall not only retain the division itself, but continue to express it in
their language. According to that language, the proximate (or lowest) Kind
to which any individual is referrible, is called its species. Conformably
to this, Isaac Newton would be said to be of the species man. There are
indeed numerous sub-classes included in the class man, to which Newton
also belongs; for example, Christian, and Englishman, and Mathematician.
But these, though distinct classes, are not, in our sense of the term,
distinct Kinds of men. A Christian, for example, differs from other human
beings; but he differs only in the attribute which the word expresses,
namely, belief in Christianity, and whatever else that implies, either as
involved in the fact itself, or connected with it through some law of
cause and effect. We should never think of inquiring what properties,
unconnected with Christianity, either as cause or effect, are common to
all Christians and peculiar to them; while in regard to all Men,
physiologists are perpetually carrying on such an inquiry; nor is the
answer ever likely to be completed. Man, therefore, we may call a species;
Christian, or Mathematician, we can not.

Note here, that it is by no means intended to imply that there may not be
different Kinds, or logical species, of man. The various races and
temperaments, the two sexes, and even the various ages, may be differences
of kind, within our meaning of the term. I do not say that they are so.
For in the progress of physiology it may almost be said to be made out,
that the differences which really exist between different races, sexes,
etc., follow as consequences, under laws of nature, from a small number of
primary differences which can be precisely determined, and which, as the
phrase is, _account for_ all the rest. If this be so, these are not
distinctions in kind; no more than Christian, Jew, Mussulman, and Pagan, a
difference which also carries many consequences along with it. And in this
way classes are often mistaken for real Kinds, which are afterward proved
not to be so. But if it turned out that the differences were not capable
of being thus accounted for, then Caucasian, Mongolian, Negro, etc., would
be really different Kinds of human beings, and entitled to be ranked as
species by the logician; though not by the naturalist. For (as already
noticed) the word species is used in a different signification in logic
and in natural history. By the naturalist, organized beings are not
usually said to be of different species, if it is supposed that they have
descended from the same stock. That, however, is a sense artificially
given to the word, for the technical purposes of a particular science. To
the logician, if a negro and a white man differ in the same manner
(however less in degree) as a horse and a camel do, that is, if their
differences are inexhaustible, and not referrible to any common cause,
they are different species, whether they are descended from common
ancestors or not. But if their differences can all be traced to climate
and habits, or to some one or a few special differences in structure, they
are not, in the logician’s view, specifically distinct.

When the _infima species_, or proximate Kind, to which an individual
belongs, has been ascertained, the properties common to that Kind include
necessarily the whole of the common properties of every other real Kind to
which the individual can be referrible. Let the individual, for example,
be Socrates, and the proximate Kind, man. Animal, or living creature, is
also a real kind, and includes Socrates; but, since it likewise includes
man, or in other words, since all men are animals, the properties common
to animals form a portion of the common properties of the sub-class, man.
And if there be any class which includes Socrates without including man,
that class is not a real Kind. Let the class, for example, be
_flat-nosed_; that being a class which includes Socrates, without
including all men. To determine whether it is a real Kind, we must ask
ourselves this question: Have all flat-nosed animals, in addition to
whatever is implied in their flat noses, any common properties, other than
those which are common to all animals whatever? If they had; if a flat
nose were a mark or index to an indefinite number of other peculiarities,
not deducible from the former by an ascertainable law, then out of the
class man we might cut another class, flat-nosed man, which, according to
our definition, would be a Kind. But if we could do this, man would not
be, as it was assumed to be, the proximate Kind. Therefore, the properties
of the proximate Kind do comprehend those (whether known or unknown) of
all other Kinds to which the individual belongs; which was the point we
undertook to prove. And hence, every other Kind which is predicable of the
individual, will be to the proximate Kind in the relation of a genus,
according to even the popular acceptation of the terms genus and species;
that is, it will be a larger class, including it and more.

We are now able to fix the logical meaning of these terms. Every class
which is a real Kind, that is, which is distinguished from all other
classes by an indeterminate multitude of properties not derivable from one
another, is either a genus or a species. A Kind which is not divisible
into other Kinds, can not be a genus, because it has no species under it;
but it is itself a species, both with reference to the individuals below
and to the genera above (Species Prædicabilis and Species Subjicibilis).
But every Kind which admits of division into real Kinds (as animal into
mammal, bird, fish, etc., or bird into various species of birds) is a
genus to all below it, a species to all genera in which it is itself
included. And here we may close this part of the discussion, and pass to
the three remaining predicables, Differentia, Proprium, and Accidens.

§ 5. To begin with Differentia. This word is correlative with the words
genus and species, and as all admit, it signifies the attribute which
distinguishes a given species from every other species of the same genus.
This is so far clear: but we may still ask, which of the distinguishing
attributes it signifies. For we have seen that every Kind (and a species
must be a Kind) is distinguished from other Kinds, not by any one
attribute, but by an indefinite number. Man, for instance, is a species of
the genus animal: Rational (or rationality, for it is of no consequence
here whether we use the concrete or the abstract form) is generally
assigned by logicians as the Differentia; and doubtless this attribute
serves the purpose of distinction: but it has also been remarked of man,
that he is a cooking animal; the only animal that dresses its food. This,
therefore, is another of the attributes by which the species man is
distinguished from other species of the same genus: would this attribute
serve equally well for a differentia? The Aristotelians say No; having
laid it down that the differentia must, like the genus and species, be of
the _essence_ of the subject.

And here we lose even that vestige of a meaning grounded in the nature of
the things themselves, which may be supposed to be attached to the word
essence when it is said that genus and species must be of the essence of
the thing. There can be no doubt that when the schoolmen talked of the
essences of things as opposed to their accidents, they had confusedly in
view the distinction between differences of kind, and the differences
which are not of kind; they meant to intimate that genera and species must
be Kinds. Their notion of the essence of a thing was a vague notion of a
something which makes it what it is, _i.e._, which makes it the Kind of
thing that it is—which causes it to have all that variety of properties
which distinguish its Kind. But when the matter came to be looked at more
closely, nobody could discover what caused the thing to have all those
properties, nor even that there was any thing which caused it to have
them. Logicians, however, not liking to admit this, and being unable to
detect what made the thing to be what it was, satisfied themselves with
what made it to be what it was called. Of the innumerable properties,
known and unknown, that are common to the class man, a portion only, and
of course a very small portion, are connoted by its name; these few,
however, will naturally have been thus distinguished from the rest either
for their greater obviousness, or for greater supposed importance. These
properties, then, which were connoted by the name, logicians seized upon,
and called them the essence of the species; and not stopping there, they
affirmed them, in the case of the _infima species_, to be the essence of
the individual too; for it was their maxim, that the species contained the
“whole essence” of the thing. Metaphysics, that fertile field of delusion
propagated by language, does not afford a more signal instance of such
delusion. On this account it was that rationality, being connoted by the
name man, was allowed to be a differentia of the class; but the
peculiarity of cooking their food, not being connoted, was relegated to
the class of accidental properties.

The distinction, therefore, between Differentia, Proprium, and Accidens,
is not grounded in the nature of things, but in the connotation of names;
and we must seek it there, if we wish to find what it is.

From the fact that the genus includes the species, in other words
_de_notes more than the species, or is predicable of a greater number of
individuals, it follows that the species must connote more than the genus.
It must connote all the attributes which the genus connotes, or there
would be nothing to prevent it from denoting individuals not included in
the genus. And it must connote something besides, otherwise it would
include the whole genus. Animal denotes all the individuals denoted by
man, and many more. Man, therefore, must connote all that animal connotes,
otherwise there might be men who are not animals; and it must connote
something more than animal connotes, otherwise all animals would be men.
This surplus of connotation—this which the species connotes over and above
the connotation of the genus—is the Differentia, or specific difference;
or, to state the same proposition in other words, the Differentia is that
which must be added to the connotation of the genus, to complete the
connotation of the species.

The word man, for instance, exclusively of what it connotes in common with
animal, also connotes rationality, and at least some approximation to that
external form which we all know, but which as we have no name for it
considered in itself, we are content to call the human. The Differentia,
or specific difference, therefore, of man, as referred to the genus
animal, is that outward form and the possession of reason. The
Aristotelians said, the possession of reason, without the outward form.
But if they adhered to this, they would have been obliged to call the
Houyhnhnms men. The question never arose, and they were never called upon
to decide how such a case would have affected their notion of
essentiality. However this may be, they were satisfied with taking such a
portion of the differentia as sufficed to distinguish the species from all
other _existing_ things, though by so doing they might not exhaust the
connotation of the name.

§ 6. And here, to prevent the notion of differentia from being restricted
within too narrow limits, it is necessary to remark, that a species, even
as referred to the same genus, will not always have the same differentia,
but a different one, according to the principle and purpose which preside
over the particular classification. For example, a naturalist surveys the
various kinds of animals, and looks out for the classification of them
most in accordance with the order in which, for zoological purposes, he
considers it desirable that we should think of them. With this view he
finds it advisable that one of his fundamental divisions should be into
warm-blooded and cold-blooded animals; or into animals which breathe with
lungs and those which breathe with gills; or into carnivorous, and
frugivorous or graminivorous; or into those which walk on the flat part
and those which walk on the extremity of the foot, a distinction on which
two of Cuvier’s families are founded. In doing this, the naturalist
creates as many new classes; which are by no means those to which the
individual animal is familiarly and spontaneously referred; nor should we
ever think of assigning to them so prominent a position in our arrangement
of the animal kingdom, unless for a preconceived purpose of scientific
convenience. And to the liberty of doing this there is no limit. In the
examples we have given, most of the classes are real Kinds, since each of
the peculiarities is an index to a multitude of properties belonging to
the class which it characterizes: but even if the case were otherwise—if
the other properties of those classes could all be derived, by any process
known to us, from the one peculiarity on which the class is founded—even
then, if these derivative properties were of primary importance for the
purposes of the naturalist, he would be warranted in founding his primary
divisions on them.

If, however, practical convenience is a sufficient warrant for making the
main demarcations in our arrangement of objects run in lines not
coinciding with any distinction of Kind, and so creating genera and
species in the popular sense which are not genera or species in the
rigorous sense at all; _à fortiori_ must we be warranted, when our genera
and species _are_ real genera and species, in marking the distinction
between them by those of their properties which considerations of
practical convenience most strongly recommend. If we cut a species out of
a given genus—the species man, for instance, out of the genus animal—with
an intention on our part that the peculiarity by which we are to be guided
in the application of the name man should be rationality, then rationality
is the differentia of the species man. Suppose, however, that being
naturalists, we, for the purposes of our particular study, cut out of the
genus animal the same species man, but with an intention that the
distinction between man and all other species of animal should be, not
rationality, but the possession of “four incisors in each jaw, tusks
solitary, and erect posture.” It is evident that the word man, when used
by us as naturalists, no longer connotes rationality, but connotes the
three other properties specified; for that which we have expressly in view
when we impose a name, assuredly forms part of the meaning of that name.
We may, therefore, lay it down as a maxim, that wherever there is a Genus,
and a Species marked out from that genus by an assignable differentia, the
name of the species must be connotative, and must connote the differentia;
but the connotation may be special—not involved in the signification of
the term as ordinarily used, but given to it when employed as a term of
art or science. The word Man in common use, connotes rationality and a
certain form, but does not connote the number or character of the teeth;
in the Linnæan system it connotes the number of incisor and canine teeth,
but does not connote rationality nor any particular form. The word _man_
has, therefore, two different meanings; though not commonly considered as
ambiguous, because it happens in both cases to _de_note the same
individual objects. But a case is conceivable in which the ambiguity would
become evident: we have only to imagine that some new kind of animal were
discovered, having Linnæus’s three characteristics of humanity, but not
rational, or not of the human form. In ordinary parlance, these animals
would not be called men; but in natural history they must still be called
so by those, if any there should be, who adhere to the Linnæan
classification; and the question would arise, whether the word should
continue to be used in two senses, or the classification be given up, and
the technical sense of the term be abandoned along with it.

Words not otherwise connotative may, in the mode just adverted to, acquire
a special or technical connotation. Thus the word whiteness, as we have so
often remarked, connotes nothing; it merely denotes the attribute
corresponding to a certain sensation: but if we are making a
classification of colors, and desire to justify, or even merely to point
out, the particular place assigned to whiteness in our arrangement, we may
define it “the color produced by the mixture of all the simple rays;” and
this fact, though by no means implied in the meaning of the word whiteness
as ordinarily used, but only known by subsequent scientific investigation,
is part of its meaning in the particular essay or treatise, and becomes
the differentia of the species.(42)

The differentia, therefore, of a species may be defined to be, that part
of the connotation of the specific name, whether ordinary or special and
technical, which distinguishes the species in question from all other
species of the genus to which on the particular occasion we are referring
it.

§ 7. Having disposed of Genus, Species, and Differentia, we shall not find
much difficulty in attaining a clear conception of the distinction between
the other two predicables, as well as between them and the first three.

In the Aristotelian phraseology, Genus and Differentia are of the
_essence_ of the subject; by which, as we have seen, is really meant that
the properties signified by the genus and those signified by the
differentia, form part of the connotation of the name denoting the
species. Proprium and Accidens, on the other hand, form no part of the
essence, but are predicated of the species only _accidentally_. Both are
Accidents, in the wider sense in which the accidents of a thing are
opposed to its essence; though, in the doctrine of the Predicables,
Accidens is used for one sort of accident only, Proprium being another
sort. Proprium, continue the schoolmen, is predicated _accidentally_,
indeed, but _necessarily_; or, as they further explain it, signifies an
attribute which is not indeed part of the essence, but which flows from,
or is a consequence of, the essence, and is, therefore, inseparably
attached to the species; _e.g._, the various properties of a triangle,
which, though no part of its definition, must necessarily be possessed by
whatever comes under that definition. Accidens, on the contrary, has no
connection whatever with the essence, but may come and go, and the species
still remain what it was before. If a species could exist without its
Propria, it must be capable of existing without that on which its Propria
are necessarily consequent, and therefore without its essence, without
that which constitutes it a species. But an Accidens, whether separable or
inseparable from the species in actual experience, may be supposed
separated, without the necessity of supposing any other alteration; or at
least, without supposing any of the essential properties of the species to
be altered, since with them an Accidens has no connection.

A Proprium, therefore, of the species, may be defined, any attribute which
belongs to all the individuals included in the species, and which, though
not connoted by the specific name (either ordinarily if the classification
we are considering be for ordinary purposes, or specially if it be for a
special purpose), yet follows from some attribute which the name either
ordinarily or specially connotes.

One attribute may follow from another in two ways; and there are
consequently two kinds of Proprium. It may follow as a conclusion follows
premises, or it may follow as an effect follows a cause. Thus, the
attribute of having the opposite sides equal, which is not one of those
connoted by the word Parallelogram, nevertheless follows from those
connoted by it, namely, from having the opposite sides straight lines and
parallel, and the number of sides four. The attribute, therefore, of
having the opposite sides equal, is a Proprium of the class parallelogram;
and a Proprium of the first kind, which follows from the connoted
attributes by way of _demonstration_. The attribute of being capable of
understanding language, is a Proprium of the species man, since without
being connoted by the word, it follows from an attribute which the word
does connote, viz., from the attribute of rationality. But this is a
Proprium of the second kind, which follows by way of _causation_. How it
is that one property of a thing follows, or can be inferred, from another;
under what conditions this is possible, and what is the exact meaning of
the phrase; are among the questions which will occupy us in the two
succeeding Books. At present it needs only be said, that whether a
Proprium follows by demonstration or by causation, it follows
_necessarily_; that is to say, its not following would be inconsistent
with some law which we regard as a part of the constitution either of our
thinking faculty or of the universe.

§ 8. Under the remaining predicable, Accidens, are included all attributes
of a thing which are neither involved in the signification of the name
(whether ordinarily or as a term of art), nor have, so far as we know, any
necessary connection with attributes which are so involved. They are
commonly divided into Separable and Inseparable Accidents. Inseparable
accidents are those which—although we know of no connection between them
and the attributes constitutive of the species, and although, therefore,
so far as we are aware, they might be absent without making the name
inapplicable and the species a different species—are yet never in fact
known to be absent. A concise mode of expressing the same meaning is, that
inseparable accidents are properties which are universal to the species,
but not necessary to it. Thus, blackness is an attribute of a crow, and,
as far as we know, a universal one. But if we were to discover a race of
white birds, in other respects resembling crows, we should not say, These
are not crows; we should say, These are white crows. Crow, therefore, does
not connote blackness; nor, from any of the attributes which it does
connote, whether as a word in popular use or as a term of art, could
blackness be inferred. Not only, therefore, can we conceive a white crow,
but we know of no reason why such an animal should not exist. Since,
however, none but black crows are known to exist, blackness, in the
present state of our knowledge, ranks as an accident, but an inseparable
accident, of the species crow.

Separable Accidents are those which are found, in point of fact, to be
sometimes absent from the species; which are not only not necessary, but
not even universal. They are such as do not belong to every individual of
the species, but only to some individuals; or if to all, not at all times.
Thus the color of a European is one of the separable accidents of the
species man, because it is not an attribute of all human creatures. Being
born, is also (speaking in the logical sense) a separable accident of the
species man, because, though an attribute of all human beings, it is so
only at one particular time. _A fortiori_ those attributes which are not
constant even in the same individual, as, to be in one or in another
place, to be hot or cold, sitting or walking, must be ranked as separable
accidents.



                              Chapter VIII.


Of Definition.


§ 1. One necessary part of the theory of Names and of Propositions remains
to be treated of in this place: the theory of Definitions. As being the
most important of the class of propositions which we have characterized as
purely verbal, they have already received some notice in the chapter
preceding the last. But their fuller treatment was at that time postponed,
because definition is so closely connected with classification, that,
until the nature of the latter process is in some measure understood, the
former can not be discussed to much purpose.

The simplest and most correct notion of a Definition is, a proposition
declaratory of the meaning of a word; namely, either the meaning which it
bears in common acceptation, or that which the speaker or writer, for the
particular purposes of his discourse, intends to annex to it.

The definition of a word being the proposition which enunciates its
meaning, words which have no meaning are unsusceptible of definition.
Proper names, therefore, can not be defined. A proper name being a mere
mark put upon an individual, and of which it is the characteristic
property to be destitute of meaning, its meaning can not of course be
declared; though we may indicate by language, as we might indicate still
more conveniently by pointing with the finger, upon what individual that
particular mark has been, or is intended to be, put. It is no definition
of “John Thomson” to say he is “the son of General Thomson;” for the name
John Thomson does not express this. Neither is it any definition of “John
Thomson” to say he is “the man now crossing the street.” These
propositions may serve to make known who is the particular man to whom the
name belongs, but that may be done still more unambiguously by pointing to
him, which, however, has not been esteemed one of the modes of definition.

In the case of connotative names, the meaning, as has been so often
observed, is the connotation; and the definition of a connotative name, is
the proposition which declares its connotation. This might be done either
directly or indirectly. The direct mode would be by a proposition in this
form: “Man” (or whatsoever the word may be) “is a name connoting such and
such attributes,” or “is a name which, when predicated of any thing,
signifies the possession of such and such attributes by that thing.” Or
thus: Man is every thing which possesses such and such attributes: Man is
every thing which possesses corporeity, organization, life, rationality,
and certain peculiarities of external form.

This form of definition is the most precise and least equivocal of any;
but it is not brief enough, and is besides too technical for common
discourse. The more usual mode of declaring the connotation of a name, is
to predicate of it another name or names of known signification, which
connote the same aggregation of attributes. This may be done either by
predicating of the name intended to be defined, another connotative name
exactly synonymous, as, “Man is a human being,” which is not commonly
accounted a definition at all; or by predicating two or more connotative
names, which make up among them the whole connotation of the name to be
defined. In this last case, again, we may either compose our definition of
as many connotative names as there are attributes, each attribute being
connoted by one, as, Man is a corporeal, organized, animated, rational
being, shaped so and so; or we employ names which connote several of the
attributes at once, as, Man is a rational _animal_, shaped so and so.

The definition of a name, according to this view of it, is the sum total
of all the _essential_ propositions which can be framed with that name for
their subject. All propositions the truth of which is implied in the name,
all those which we are made aware of by merely hearing the name, are
included in the definition, if complete, and may be evolved from it
without the aid of any other premises; whether the definition expresses
them in two or three words, or in a larger number. It is, therefore, not
without reason that Condillac and other writers have affirmed a definition
to be an _analysis_. To resolve any complex whole into the elements of
which it is compounded, is the meaning of analysis: and this we do when we
replace one word which connotes a set of attributes collectively, by two
or more which connote the same attributes singly, or in smaller groups.

§ 2. From this, however, the question naturally arises, in what manner are
we to define a name which connotes only a single attribute: for instance,
“white,” which connotes nothing but whiteness; “rational,” which connotes
nothing but the possession of reason. It might seem that the meaning of
such names could only be declared in two ways; by a synonymous term, if
any such can be found; or in the direct way already alluded to: “White is
a name connoting the attribute whiteness.” Let us see, however, whether
the analysis of the meaning of the name, that is, the breaking down of
that meaning into several parts, admits of being carried farther. Without
at present deciding this question as to the word _white_, it is obvious
that in the case of _rational_ some further explanation may be given of
its meaning than is contained in the proposition, “Rational is that which
possesses the attribute of reason;” since the attribute reason itself
admits of being defined. And here we must turn our attention to the
definitions of attributes, or rather of the names of attributes, that is,
of abstract names.

In regard to such names of attributes as are connotative, and express
attributes of those attributes, there is no difficulty: like other
connotative names, they are defined by declaring their connotation. Thus
the word _fault_ may be defined, “a quality productive of evil or
inconvenience.” Sometimes, again, the attribute to be defined is not one
attribute, but a union of several: we have only, therefore, to put
together the names of all the attributes taken separately, and we obtain
the definition of the name which belongs to them all taken together; a
definition which will correspond exactly to that of the corresponding
concrete name. For, as we define a concrete name by enumerating the
attributes which it connotes, and as the attributes connoted by a concrete
name form the entire signification of the corresponding abstract name, the
same enumeration will serve for the definition of both. Thus, if the
definition of a _human being_ be this, “a being, corporeal, animated,
rational, shaped so and so,” the definition of _humanity_ will be
corporeity and animal life, combined with rationality, and with such and
such a shape.

When, on the other hand, the abstract name does not express a complication
of attributes, but a single attribute, we must remember that every
attribute is grounded on some fact or phenomenon, from which, and which
alone, it derives its meaning. To that fact or phenomenon, called in a
former chapter the foundation of the attribute, we must, therefore, have
recourse for its definition. Now, the foundation of the attribute may be a
phenomenon of any degree of complexity, consisting of many different
parts, either co-existent or in succession. To obtain a definition of the
attribute, we must analyze the phenomenon into these parts. Eloquence, for
example, is the name of one attribute only; but this attribute is grounded
on external effects of a complicated nature, flowing from acts of the
person to whom we ascribe the attribute; and by resolving this phenomenon
of causation into its two parts, the cause and the effect, we obtain a
definition of eloquence, viz. the power of influencing the feelings by
speech or writing.

A name, therefore, whether concrete or abstract, admits of definition,
provided we are able to analyze, that is, to distinguish into parts, the
attribute or set of attributes which constitute the meaning both of the
concrete name and of the corresponding abstract: if a set of attributes,
by enumerating them; if a single attribute, by dissecting the fact or
phenomenon (whether of perception or of internal consciousness) which is
the foundation of the attribute. But, further, even when the fact is one
of our simple feelings or states of consciousness, and therefore
unsusceptible of analysis, the names both of the object and of the
attribute still admit of definition; or rather, would do so if all our
simple feelings had names. Whiteness may be defined, the property or power
of exciting the sensation of white. A white object may be defined, an
object which excites the sensation of white. The only names which are
unsusceptible of definition, because their meaning is unsusceptible of
analysis, are the names of the simple feelings themselves. These are in
the same condition as proper names. They are not indeed, like proper
names, unmeaning; for the words _sensation of white_ signify, that the
sensation which I so denominate resembles other sensations which I
remember to have had before, and to have called by that name. But as we
have no words by which to recall those former sensations, except the very
word which we seek to define, or some other which, being exactly
synonymous with it, requires definition as much, words can not unfold the
signification of this class of names; and we are obliged to make a direct
appeal to the personal experience of the individual whom we address.

§ 3. Having stated what seems to be the true idea of a Definition, I
proceed to examine some opinions of philosophers, and some popular
conceptions on the subject, which conflict more or less with that idea.

The only adequate definition of a name is, as already remarked, one which
declares the facts, and the whole of the facts, which the name involves in
its signification. But with most persons the object of a definition does
not embrace so much; they look for nothing more, in a definition, than a
guide to the correct use of the term—a protection against applying it in a
manner inconsistent with custom and convention. Any thing, therefore, is
to them a sufficient definition of a term, which will serve as a correct
index to what the term _de_notes; though not embracing the whole, and
sometimes, perhaps, not even any part, of what it connotes. This gives
rise to two sorts of imperfect, or unscientific definition; Essential but
incomplete Definitions, and Accidental Definitions, or Descriptions. In
the former, a connotative name is defined by a part only of its
connotation; in the latter, by something which forms no part of the
connotation at all.

An example of the first kind of imperfect definitions is the following:
Man is a rational animal. It is impossible to consider this as a complete
definition of the word Man, since (as before remarked) if we adhered to it
we should be obliged to call the Houyhnhnms men; but as there happen to be
no Houyhnhnms, this imperfect definition is sufficient to mark out and
distinguish from all other things, the objects at present denoted by
“man;” all the beings actually known to exist, of whom the name is
predicable. Though the word is defined by some only among the attributes
which it connotes, not by all, it happens that all known objects which
possess the enumerated attributes, possess also those which are omitted;
so that the field of predication which the word covers, and the employment
of it which is conformable to usage, are as well indicated by the
inadequate definition as by an adequate one. Such definitions, however,
are always liable to be overthrown by the discovery of new objects in
nature.

Definitions of this kind are what logicians have had in view, when they
laid down the rule, that the definition of a species should be _per genus
et differentiam_. Differentia being seldom taken to mean the whole of the
peculiarities constitutive of the species, but some one of those
peculiarities only, a complete definition would be _per genus et
differentias_, rather than _differentiam_. It would include, with the name
of the superior genus, not merely _some_ attribute which distinguishes the
species intended to be defined from all other species of the same genus,
but _all_ the attributes implied in the name of the species, which the
name of the superior genus has not already implied. The assertion,
however, that a definition must of necessity consist of a genus and
differentiæ, is not tenable. It was early remarked by logicians, that the
_summum genus_ in any classification, having no genus superior to itself,
could not be defined in this manner. Yet we have seen that all names,
except those of our elementary feelings, are susceptible of definition in
the strictest sense; by setting forth in words the constituent parts of
the fact or phenomenon, of which the connotation of every word is
ultimately composed.

§ 4. Although the first kind of imperfect definition (which defines a
connotative term by a part only of what it connotes, but a part sufficient
to mark out correctly the boundaries of its denotation), has been
considered by the ancients, and by logicians in general, as a complete
definition; it has always been deemed necessary that the attributes
employed should really form part of the connotation; for the rule was that
the definition must be drawn from the _essence_ of the class; and this
would not have been the case if it had been in any degree made up of
attributes not connoted by the name. The second kind of imperfect
definition, therefore, in which the name of a class is defined by any of
its accidents—that is, by attributes which are not included in its
connotation—has been rejected from the rank of genuine Definition by all
logicians, and has been termed Description.

This kind of imperfect definition, however, takes its rise from the same
cause as the other, namely, the willingness to accept as a definition any
thing which, whether it expounds the meaning of the name or not, enables
us to discriminate the things denoted by the name from all other things,
and consequently to employ the term in predication without deviating from
established usage. This purpose is duly answered by stating any (no matter
what) of the attributes which are common to the whole of the class, and
peculiar to it; or any combination of attributes which happens to be
peculiar to it, though separately each of those attributes may be common
to it with some other things. It is only necessary that the definition (or
description) thus formed, should be _convertible_ with the name which it
professes to define; that is, should be exactly co-extensive with it,
being predicable of every thing of which it is predicable, and of nothing
of which it is not predicable; though the attributes specified may have no
connection with those which mankind had in view when they formed or
recognized the class, and gave it a name. The following are correct
definitions of Man, according to this test: Man is a mammiferous animal,
having (by nature) two hands (for the human species answers to this
description, and no other animal does): Man is an animal who cooks his
food: Man is a featherless biped.

What would otherwise be a mere description, may be raised to the rank of a
real definition by the peculiar purpose which the speaker or writer has in
view. As was seen in the preceding chapter, it may, for the ends of a
particular art or science, or for the more convenient statement of an
author’s particular doctrines, be advisable to give to some general name,
without altering its denotation, a special connotation, different from its
ordinary one. When this is done, a definition of the name by means of the
attributes which make up the special connotation, though in general a mere
accidental definition or description, becomes on the particular occasion
and for the particular purpose a complete and genuine definition. This
actually occurs with respect to one of the preceding examples, “Man is a
mammiferous animal having two hands,” which is the scientific definition
of man, considered as one of the species in Cuvier’s distribution of the
animal kingdom.

In cases of this sort, though the definition is still a declaration of the
meaning which in the particular instance the name is appointed to convey,
it can not be said that to state the meaning of the word is the purpose of
the definition. The purpose is not to expound a name, but a
classification. The special meaning which Cuvier assigned to the word Man
(quite foreign to its ordinary meaning, though involving no change in the
denotation of the word), was incidental to a plan of arranging animals
into classes on a certain principle, that is, according to a certain set
of distinctions. And since the definition of Man according to the ordinary
connotation of the word, though it would have answered every other purpose
of a definition, would not have pointed out the place which the species
ought to occupy in that particular classification; he gave the word a
special connotation, that he might be able to define it by the kind of
attributes on which, for reasons of scientific convenience, he had
resolved to found his division of animated nature.

Scientific definitions, whether they are definitions of scientific terms,
or of common terms used in a scientific sense, are almost always of the
kind last spoken of: their main purpose is to serve as the landmarks of
scientific classification. And since the classifications in any science
are continually modified as scientific knowledge advances, the definitions
in the sciences are also constantly varying. A striking instance is
afforded by the words Acid and Alkali, especially the former. As
experimental discovery advanced, the substances classed with acids have
been constantly multiplying, and by a natural consequence the attributes
connoted by the word have receded and become fewer. At first it connoted
the attributes, of combining with an alkali to form a neutral substance
(called a salt); being compounded of a base and oxygen; causticity to the
taste and touch; fluidity, etc. The true analysis of muriatic acid, into
chlorine and hydrogen, caused the second property, composition from a base
and oxygen, to be excluded from the connotation. The same discovery fixed
the attention of chemists upon hydrogen as an important element in acids;
and more recent discoveries having led to the recognition of its presence
in sulphuric, nitric, and many other acids, where its existence was not
previously suspected, there is now a tendency to include the presence of
this element in the connotation of the word. But carbonic acid, silica,
sulphurous acid, have no hydrogen in their composition; that property can
not, therefore, be connoted by the term, unless those substances are no
longer to be considered acids. Causticity and fluidity have long since
been excluded from the characteristics of the class, by the inclusion of
silica and many other substances in it; and the formation of neutral
bodies by combination with alkalis, together with such electro-chemical
peculiarities as this is supposed to imply, are now the only _differentiæ_
which form the fixed connotation of the word Acid, as a term of chemical
science.

What is true of the definition of any term of science, is of course true
of the definition of a science itself; and accordingly (as observed in the
Introductory Chapter of this work), the definition of a science must
necessarily be progressive and provisional. Any extension of knowledge or
alteration in the current opinions respecting the subject-matter, may lead
to a change more or less extensive in the particulars included in the
science; and its composition being thus altered, it may easily happen that
a different set of characteristics will be found better adapted as
differentiæ for defining its name.

In the same manner in which a special or technical definition has for its
object to expound the artificial classification out of which it grows; the
Aristotelian logicians seem to have imagined that it was also the business
of ordinary definition to expound the ordinary, and what they deemed the
natural, classification of things, namely, the division of them into
Kinds; and to show the place which each Kind occupies, as superior,
collateral, or subordinate, among other Kinds. This notion would account
for the rule that all definition must necessarily be _per genus et
differentiam_, and would also explain why a single differentia was deemed
sufficient. But to expound, or express in words, a distinction of Kind,
has already been shown to be an impossibility: the very meaning of a Kind
is, that the properties which distinguish it do not grow out of one
another, and can not therefore be set forth in words, even by implication,
otherwise than by enumerating them all: and all are not known, nor are
ever likely to be so. It is idle, therefore, to look to this as one of the
purposes of a definition: while, if it be only required that the
definition of a Kind should indicate what kinds include it or are included
by it, any definitions which expound the connotation of the names will do
this: for the name of each class must necessarily connote enough of its
properties to fix the boundaries of the class. If the definition,
therefore, be a full statement of the connotation, it is all that a
definition can be required to be.(43)

§ 5. Of the two incomplete and popular modes of definition, and in what
they differ from the complete or philosophical mode, enough has now been
said. We shall next examine an ancient doctrine, once generally prevalent
and still by no means exploded, which I regard as the source of a great
part of the obscurity hanging over some of the most important processes of
the understanding in the pursuit of truth. According to this, the
definitions of which we have now treated are only one of two sorts into
which definitions may be divided, viz., definitions of names, and
definitions of things. The former are intended to explain the meaning of a
term; the latter, the nature of a thing; the last being incomparably the
most important.

This opinion was held by the ancient philosophers, and by their followers,
with the exception of the Nominalists; but as the spirit of modern
metaphysics, until a recent period, has been on the whole a Nominalist
spirit, the notion of definitions of things has been to a certain extent
in abeyance, still continuing, however, to breed confusion in logic, by
its consequences indeed rather than by itself. Yet the doctrine in its own
proper form now and then breaks out, and has appeared (among other places)
where it was scarcely to be expected, in a justly admired word, Archbishop
Whately’s _Logic_.(44) In a review of that work published by me in the
_Westminster __ Review_ for January, 1828, and containing some opinions
which I no longer entertain, I find the following observations on the
question now before us; observations with which my present view of that
question is still sufficiently in accordance.

“The distinction between nominal and real definitions, between definitions
of words and what are called definitions of things, though conformable to
the ideas of most of the Aristotelian logicians, can not, as it appears to
us, be maintained. We apprehend that no definition is ever intended to
‘explain and unfold the nature of a thing.’ It is some confirmation of our
opinion, that none of those writers who have thought that there were
definitions of things, have ever succeeded in discovering any criterion by
which the definition of a thing can be distinguished from any other
proposition relating to the thing. The definition, they say, unfolds the
nature of the thing: but no definition can unfold its whole nature; and
every proposition in which any quality whatever is predicated of the
thing, unfolds some part of its nature. The true state of the case we take
to be this. All definitions are of names, and of names only; but, in some
definitions, it is clearly apparent, that nothing is intended except to
explain the meaning of the word; while in others, besides explaining the
meaning of the word, it is intended to be implied that there exists a
thing, corresponding to the word. Whether this be or be not implied in any
given case, can not be collected from the mere form of the expression. ‘A
centaur is an animal with the upper parts of a man and the lower parts of
a horse,’ and ‘A triangle is a rectilineal figure with three sides,’ are,
in form, expressions precisely similar; although in the former it is not
implied that any _thing_, conformable to the term, really exists, while in
the latter it is; as may be seen by substituting in both definitions, the
word _means_ for _is_. In the first expression, ‘A centaur means an
animal,’ etc., the sense would remain unchanged: in the second, ‘A
triangle means,’ etc., the meaning would be altered, since it would be
obviously impossible to deduce any of the truths of geometry from a
proposition expressive only of the manner in which we intend to employ a
particular sign.

“There are, therefore, expressions, commonly passing for definitions,
which include in themselves more than the mere explanation of the meaning
of a term. But it is not correct to call an expression of this sort a
peculiar kind of definition. Its difference from the other kind consists
in this, that it is not a definition, but a definition and something more.
The definition above given of a triangle, obviously comprises not one, but
two propositions, perfectly distinguishable. The one is, ‘There may exist
a figure, bounded by three straight lines;’ the other, ‘And this figure
may be termed a triangle.’ The former of these propositions is not a
definition at all: the latter is a mere nominal definition, or explanation
of the use and application of a term. The first is susceptible of truth or
falsehood, and may therefore be made the foundation of a train of
reasoning. The latter can neither be true nor false; the only character it
is susceptible of is that of conformity or disconformity to the ordinary
usage of language.”

There is a real distinction, then, between definitions of names, and what
are erroneously called definitions of things; but it is, that the latter,
along with the meaning of a name, covertly asserts a matter of fact. This
covert assertion is not a definition, but a postulate. The definition is a
mere identical proposition, which gives information only about the use of
language, and from which no conclusions affecting matters of fact can
possibly be drawn. The accompanying postulate, on the other hand, affirms
a fact, which may lead to consequences of every degree of importance. It
affirms the actual or possible existence of Things possessing the
combination of attributes set forth in the definition; and this, if true,
may be foundation sufficient on which to build a whole fabric of
scientific truth.

We have already made, and shall often have to repeat, the remark, that the
philosophers who overthrew Realism by no means got rid of the consequences
of Realism, but retained long afterward, in their own philosophy, numerous
propositions which could only have a rational meaning as part of a
Realistic system. It had been handed down from Aristotle, and probably
from earlier times, as an obvious truth, that the science of Geometry is
deduced from definitions. This, so long as a definition was considered to
be a proposition “unfolding the nature of the thing,” did well enough. But
Hobbes followed, and rejected utterly the notion that a definition
declares the nature of the thing, or does any thing but state the meaning
of a name; yet he continued to affirm as broadly as any of his
predecessors, that the ἀρχαὶ, _principia_, or original premises of
mathematics, and even of all science, are definitions; producing the
singular paradox, that systems of scientific truth, nay, all truths
whatever at which we arrive by reasoning, are deduced from the arbitrary
conventions of mankind concerning the signification of words.

To save the credit of the doctrine that definitions are the premises of
scientific knowledge, the proviso is sometimes added, that they are so
only under a certain condition, namely, that they be framed conformably to
the phenomena of nature; that is, that they ascribe such meanings to terms
as shall suit objects actually existing. But this is only an instance of
the attempt so often made, to escape from the necessity of abandoning old
language after the ideas which it expresses have been exchanged for
contrary ones. From the meaning of a name (we are told) it is possible to
infer physical facts, provided the name has corresponding to it an
existing thing. But if this proviso be necessary, from which of the two is
the inference really drawn? From the existence of a thing having the
properties, or from the existence of a name meaning them?

Take, for instance, any of the definitions laid down as premises in
Euclid’s Elements; the definition, let us say, of a circle. This, being
analyzed, consists of two propositions; the one an assumption with respect
to a matter of fact, the other a genuine definition. “A figure may exist,
having all the points in the line which bounds it equally distant from a
single point within it:” “Any figure possessing this property is called a
circle.” Let us look at one of the demonstrations which are said to depend
on this definition, and observe to which of the two propositions contained
in it the demonstration really appeals. “About the centre A, describe the
circle B C D.”

Here is an assumption that a figure, such as the definition expresses,
_may_ be described; which is no other than the postulate, or covert
assumption, involved in the so-called definition. But whether that figure
be called a circle or not is quite immaterial. The purpose would be as
well answered, in all respects except brevity, were we to say, “Through
the point B, draw a line returning into itself, of which every point shall
be at an equal distance from the point A.” By this the definition of a
circle would be got rid of, and rendered needless; but not the postulate
implied in it; without that the demonstration could not stand. The circle
being now described, let us proceed to the consequence. “Since B C D is a
circle, the radius B A is equal to the radius C A.” B A is equal to C A,
not because B C D is a circle, but because B C D is a figure with the
radii equal. Our warrant for assuming that such a figure about the centre
A, with the radius B A, may be made to exist, is the postulate. Whether
the admissibility of these postulates rests on intuition, or on proof, may
be a matter of dispute; but in either case they are the premises on which
the theorems depend; and while these are retained it would make no
difference in the certainty of geometrical truths, though every definition
in Euclid, and every technical term therein defined, were laid aside.

It is, perhaps, superfluous to dwell at so much length on what is so
nearly self-evident; but when a distinction, obvious as it may appear, has
been confounded, and by powerful intellects, it is better to say too much
than too little for the purpose of rendering such mistakes impossible in
future. I will, therefore detain the reader while I point out one of the
absurd consequences flowing from the supposition that definitions, as
such, are the premises in any of our reasonings, except such as relate to
words only. If this supposition were true, we might argue correctly from
true premises, and arrive at a false conclusion. We should only have to
assume as a premise the definition of a nonentity; or rather of a name
which has no entity corresponding to it. Let this, for instance, be our
definition:


    A dragon is a serpent breathing flame.


This proposition, considered only as a definition, is indisputably
correct. A dragon _is_ a serpent breathing flame: the word _means_ that.
The tacit assumption, indeed (if there were any such understood
assertion), of the existence of an object with properties corresponding to
the definition, would, in the present instance, be false. Out of this
definition we may carve the premises of the following syllogism:


    A dragon is a thing which breathes flame:
    A dragon is a serpent:


From which the conclusion is,


    Therefore some serpent or serpents breathe flame:


an unexceptionable syllogism in the first mode of the third figure, in
which both premises are true and yet the conclusion false; which every
logician knows to be an absurdity. The conclusion being false and the
syllogism correct, the premises can not be true. But the premises,
considered as parts of a definition, are true. Therefore, the premises
considered as parts of a definition can not be the real ones. The real
premises must be—


    A dragon is a _really existing_ thing which breathes flame:
    A dragon is a _really existing_ serpent:


which implied premises being false, the falsity of the conclusion presents
no absurdity.

If we would determine what conclusion follows from the same ostensible
premises when the tacit assumption of real existence is left out, let us,
according to the recommendation in a previous page, substitute _means_ for
_is_. We then have—


    Dragon is _a word meaning_ a thing which breathes flame:
    Dragon is _a word meaning_ a serpent:


From which the conclusion is,


    Some _word or words which mean_ a serpent, also mean a thing which
    breathes flame:


where the conclusion (as well as the premises) is true, and is the only
kind of conclusion which can ever follow from a definition, namely, a
proposition relating to the meaning of words.

There is still another shape into which we may transform this syllogism.
We may suppose the middle term to be the designation neither of a thing
nor of a name, but of an idea. We then have—


    The _idea of_ a dragon is _an idea of_ a thing which breathes
                flame:
    The _idea of_ a dragon is _an idea of_ a serpent:
    Therefore, there is _an idea of_ a serpent, which is _an idea of_
                a thing breathing flame.


Here the conclusion is true, and also the premises; but the premises are
not definitions. They are propositions affirming that an idea existing in
the mind, includes certain ideal elements. The truth of the conclusion
follows from the existence of the psychological phenomenon called the idea
of a dragon; and therefore still from the tacit assumption of a matter of
fact.(45)

When, as in this last syllogism, the conclusion is a proposition
respecting an idea, the assumption on which it depends may be merely that
of the existence of an idea. But when the conclusion is a proposition
concerning a Thing, the postulate involved in the definition which stands
as the apparent premise, is the existence of a thing conformable to the
definition, and not merely of an idea conformable to it. This assumption
of real existence we always convey the impression that we intend to make,
when we profess to define any name which is already known to be a name of
really existing objects. On this account it is, that the assumption was
not necessarily implied in the definition of a dragon, while there was no
doubt of its being included in the definition of a circle.

§ 6. One of the circumstances which have contributed to keep up the
notion, that demonstrative truths follow from definitions rather than from
the postulates implied in those definitions, is, that the postulates, even
in those sciences which are considered to surpass all others in
demonstrative certainty, are not always exactly true. It is not true that
a circle exists, or can be described, which has all its radii _exactly_
equal. Such accuracy is ideal only; it is not found in nature, still less
can it be realized by art. People had a difficulty, therefore, in
conceiving that the most certain of all conclusions could rest on premises
which, instead of being certainly true, are certainly not true to the full
extent asserted. This apparent paradox will be examined when we come to
treat of Demonstration; where we shall be able to show that as much of the
postulate is true, as is required to support as much as is true of the
conclusion. Philosophers, however, to whom this view had not occurred, or
whom it did not satisfy, have thought it indispensable that there should
be found in definitions something _more_ certain, or at least more
accurately true, than the implied postulate of the real existence of a
corresponding object. And this something they flattered themselves they
had found, when they laid it down that a definition is a statement and
analysis not of the mere meaning of a word, nor yet of the nature of a
thing, but of an idea. Thus, the proposition, “A circle is a plane figure
bounded by a line all the points of which are at an equal distance from a
given point within it,” was considered by them, not as an assertion that
any real circle has that property (which would not be exactly true), but
that we _conceive_ a circle as having it; that our abstract idea of a
circle is an idea of a figure with its radii exactly equal.

Conformably to this it is said, that the subject-matter of mathematics,
and of every other demonstrative science, is not things as they really
exist, but abstractions of the mind. A geometrical line is a line without
breadth; but no such line exists in nature; it is a notion merely
suggested to the mind by its experience of nature. The definition (it is
said) is a definition of this mental line, not of any actual line: and it
is only of the mental line, not of any line existing in nature, that the
theorems of geometry are accurately true.

Allowing this doctrine respecting the nature of demonstrative truth to be
correct (which, in a subsequent place, I shall endeavor to prove that it
is not); even on that supposition, the conclusions which seem to follow
from a definition, do not follow from the definition as such, but from an
implied postulate. Even if it be true that there is no object in nature
answering to the definition of a line, and that the geometrical properties
of lines are not true of any lines in nature, but only of the idea of a
line; the definition, at all events, postulates the real existence of such
an idea: it assumes that the mind can frame, or rather has framed, the
notion of length without breadth, and without any other sensible property
whatever. To me, indeed, it appears that the mind can not form any such
notion; it can not conceive length without breadth; it can only, in
contemplating objects, attend to their length, exclusively of their other
sensible qualities, and so determine what properties may be predicated of
them in virtue of their length alone. If this be true, the postulate
involved in the geometrical definition of a line, is the real existence,
not of length without breadth, but merely of length, that is, of long
objects. This is quite enough to support all the truths of geometry, since
every property of a geometrical line is really a property of all physical
objects in so far as possessing length. But even what I hold to be the
false doctrine on the subject, leaves the conclusion that our reasonings
are grounded on the matters of fact postulated in definitions, and not on
the definitions themselves, entirely unaffected; and accordingly this
conclusion is one which I have in common with Dr. Whewell, in his
_Philosophy of the Inductive Sciences_: though, on the nature of
demonstrative truth, Dr. Whewell’s opinions are greatly at variance with
mine. And here, as in many other instances, I gladly acknowledge that his
writings are eminently serviceable in clearing from confusion the initial
steps in the analysis of the mental processes, even where his views
respecting the ultimate analysis are such as (though with unfeigned
respect) I can not but regard as fundamentally erroneous.

§ 7. Although, according to the opinion here presented, Definitions are
properly of names only, and not of things, it does not follow from this
that definitions are arbitrary. How to define a name, may not only be an
inquiry of considerable difficulty and intricacy, but may involve
considerations going deep into the nature of the things which are denoted
by the name. Such, for instance, are the inquiries which form the subjects
of the most important of Plato’s Dialogues; as, “What is rhetoric?” the
topic of the Gorgias, or, “What is justice?” that of the Republic. Such,
also, is the question scornfully asked by Pilate, “What is truth?” and the
fundamental question with speculative moralists in all ages, “What is
virtue?”

It would be a mistake to represent these difficult and noble inquiries as
having nothing in view beyond ascertaining the conventional meaning of a
name. They are inquiries not so much to determine what is, as what should
be, the meaning of a name; which, like other practical questions of
terminology, requires for its solution that we should enter, and sometimes
enter very deeply, into the properties not merely of names but of the
things named.

Although the meaning of every concrete general name resides in the
attributes which it connotes, the objects were named before the
attributes; as appears from the fact that in all languages, abstract names
are mostly compounds or other derivatives of the concrete names which
correspond to them. Connotative names, therefore, were, after proper
names, the first which were used: and in the simpler cases, no doubt, a
distinct connotation was present to the minds of those who first used the
name, and was distinctly intended by them to be conveyed by it. The first
person who used the word white, as applied to snow or to any other object,
knew, no doubt, very well what quality he intended to predicate, and had a
perfectly distinct conception in his mind of the attribute signified by
the name.

But where the resemblances and differences on which our classifications
are founded are not of this palpable and easily determinable kind;
especially where they consist not in any one quality but in a number of
qualities, the effects of which, being blended together, are not very
easily discriminated, and referred each to its true source; it often
happens that names are applied to namable objects, with no distinct
connotation present to the minds of those who apply them. They are only
influenced by a general resemblance between the new object and all or some
of the old familiar objects which they have been accustomed to call by
that name. This, as we have seen, is the law which even the mind of the
philosopher must follow, in giving names to the simple elementary feelings
of our nature: but, where the things to be named are complex wholes, a
philosopher is not content with noticing a general resemblance; he
examines what the resemblance consists in: and he only gives the same name
to things which resemble one another in the same definite particulars. The
philosopher, therefore, habitually employs his general names with a
definite connotation. But language was not made, and can only in some
small degree be mended, by philosophers. In the minds of the real arbiters
of language, general names, especially where the classes they denote can
not be brought before the tribunal of the outward senses to be identified
and discriminated, connote little more than a vague gross resemblance to
the things which they were earliest, or have been most, accustomed to call
by those names. When, for instance, ordinary persons predicate the words
_just_ or _unjust_ of any action, _noble_ or _mean_ of any sentiment,
expression, or demeanor, _statesman_ or _charlatan_ of any personage
figuring in politics, do they mean to affirm of those various subjects any
determinate attributes, of whatever kind? No: they merely recognize, as
they think, some likeness, more or less vague and loose, between these and
some other things which they have been accustomed to denominate or to hear
denominated by those appellations.

Language, as Sir James Mackintosh used to say of governments, “is not
made, but grows.” A name is not imposed at once and by previous purpose
upon a _class_ of objects, but is first applied to one thing, and then
extended by a series of transitions to another and another. By this
process (as has been remarked by several writers, and illustrated with
great force and clearness by Dugald Stewart in his Philosophical Essays) a
name not unfrequently passes by successive links of resemblance from one
object to another, until it becomes applied to things having nothing in
common with the first things to which the name was given; which, however,
do not, for that reason, drop the name; so that it at last denotes a
confused huddle of objects, having nothing whatever in common; and
connotes nothing, not even a vague and general resemblance. When a name
has fallen into this state, in which by predicating it of any object we
assert literally nothing about the object, it has become unfit for the
purposes either of thought or of the communication of thought; and can
only be made serviceable by stripping it of some part of its multifarious
denotation, and confining it to objects possessed of some attributes in
common, which it may be made to connote. Such are the inconveniences of a
language which “is not made, but grows.” Like the governments which are in
a similar case, it may be compared to a road which is not made but has
made itself: it requires continual mending in order to be passable.

From this it is already evident, why the question respecting the
definition of an abstract name is often one of so much difficulty. The
question, What is justice? is, in other words, What is the attribute which
mankind mean to predicate when they call an action just? To which the
first answer is, that having come to no precise agreement on the point,
they do not mean to predicate distinctly any attribute at all.
Nevertheless, all believe that there is some common attribute belonging to
all the actions which they are in the habit of calling just. The question
then must be, whether there is any such common attribute? and, in the
first place, whether mankind agree sufficiently with one another as to the
particular actions which they do or do not call just, to render the
inquiry, what quality those actions have in common, a possible one: if so,
whether the actions really have any quality in common; and if they have,
what it is. Of these three, the first alone is an inquiry into usage and
convention; the other two are inquiries into matters of fact. And if the
second question (whether the actions form a class at all) has been
answered negatively, there remains a fourth, often more arduous than all
the rest, namely, how best to form a class artificially, which the name
may denote.

And here it is fitting to remark, that the study of the spontaneous growth
of languages is of the utmost importance to those who would logically
remodel them. The classifications rudely made by established language,
when retouched, as they almost all require to be, by the hands of the
logician, are often themselves excellently suited to his purposes. As
compared with the classifications of a philosopher, they are like the
customary law of a country, which has grown up as it were spontaneously,
compared with laws methodized and digested into a code: the former are a
far less perfect instrument than the latter; but being the result of a
long, though unscientific, course of experience, they contain a mass of
materials which may be made very usefully available in the formation of
the systematic body of written law. In like manner, the established
grouping of objects under a common name, even when founded only on a gross
and general resemblance, is evidence, in the first place, that the
resemblance is obvious, and therefore considerable; and, in the next
place, that it is a resemblance which has struck great numbers of persons
during a series of years and ages. Even when a name, by successive
extensions, has come to be applied to things among which there does not
exist this gross resemblance common to them all, still at every step in
its progress we shall find such a resemblance. And these transitions of
the meaning of words are often an index to real connections between the
things denoted by them, which might otherwise escape the notice of
thinkers; of those at least who, from using a different language, or from
any difference in their habitual associations, have fixed their attention
in preference on some other aspect of the things. The history of
philosophy abounds in examples of such oversights, committed for want of
perceiving the hidden link that connected together the seemingly disparate
meanings of some ambiguous word.(46)

Whenever the inquiry into the definition of the name of any real object
consists of any thing else than a mere comparison of authorities, we
tacitly assume that a meaning must be found for the name, compatible with
its continuing to denote, if possible all, but at any rate the greater or
the more important part, of the things of which it is commonly predicated.
The inquiry, therefore, into the definition, is an inquiry into the
resemblances and differences among those things: whether there be any
resemblance running through them all; if not, through what portion of them
such a general resemblance can be traced: and finally, what are the common
attributes, the possession of which gives to them all, or to that portion
of them, the character of resemblance which has led to their being classed
together. When these common attributes have been ascertained and
specified, the name which belongs in common to the resembling objects
acquires a distinct instead of a vague connotation; and by possessing this
distinct connotation, becomes susceptible of definition.

In giving a distinct connotation to the general name, the philosopher will
endeavor to fix upon such attributes as, while they are common to all the
things usually denoted by the name, are also of greatest importance in
themselves; either directly, or from the number, the conspicuousness, or
the interesting character, of the consequences to which they lead. He will
select, as far as possible, such _differentiæ_ as lead to the greatest
number of interesting _propria_. For these, rather than the more obscure
and recondite qualities on which they often depend, give that general
character and aspect to a set of objects, which determine the groups into
which they naturally fall. But to penetrate to the more hidden agreement
on which these obvious and superficial agreements depend, is often one of
the most difficult of scientific problems. As it is among the most
difficult, so it seldom fails to be among the most important. And since
upon the result of this inquiry respecting the causes of the properties of
a class of things, there incidentally depends the question what shall be
the meaning of a word; some of the most profound and most valuable
investigations which philosophy presents to us, have been introduced by,
and have offered themselves under the guise of, inquiries into the
definition of a name.



                                 Book II.


OF REASONING.


    Διωρισμένων δε τούτων λέγωμεν ἤδη, διά τίνων, καὶ πότε, καὶ πῶς
    γίνεται πᾶς συλλογισμός ὕστερον δὲ λεκτέον περὶ ἀποδείξεως.
    Πρότερον γὰρ περὶ συλλογισμοῦ λεκτέον, ἥ περὶ ἀποδείξεως, διὰ τὸ
    καθόλου μᾶλλον εἰναὶ τὸν συλλογισμόν. Ἡ μέν γὰρ ἀπόδειξις,
    συλλογισμός τις; ὁ συλλογισμός δὲ ού πᾶς, ἀπόδειξις.—ARIST.,
    _Analyt. Prior._, l. i., cap. 4.



                                Chapter I.


Of Inference, Or Reasoning, In General.


§ 1. In the preceding Book, we have been occupied not with the nature of
Proof, but with the nature of Assertion: the import conveyed by a
Proposition, whether that Proposition be true or false; not the means by
which to discriminate true from false Propositions. The proper subject,
however, of Logic is Proof. Before we could understand what Proof is, it
was necessary to understand what that is to which proof is applicable;
what that is which can be a subject of belief or disbelief, of affirmation
or denial; what, in short, the different kinds of Propositions assert.

This preliminary inquiry we have prosecuted to a definite result.
Assertion, in the first place, relates either to the meaning of words, or
to some property of the things which words signify. Assertions respecting
the meaning of words, among which definitions are the most important, hold
a place, and an indispensable one, in philosophy; but as the meaning of
words is essentially arbitrary, this class of assertions are not
susceptible of truth or falsity, nor therefore of proof or disproof.
Assertions respecting Things, or what may be called Real Propositions, in
contradistinction to verbal ones, are of various sorts. We have analyzed
the import of each sort, and have ascertained the nature of the things
they relate to, and the nature of what they severally assert respecting
those things. We found that whatever be the form of the proposition, and
whatever its nominal subject or predicate, the real subject of every
proposition is some one or more facts or phenomena of consciousness, or
some one or more of the hidden causes or powers to which we ascribe those
facts; and that what is predicated or asserted, either in the affirmative
or negative, of those phenomena or those powers, is always either
Existence, Order in Place, Order in Time, Causation, or Resemblance. This,
then, is the theory of the Import of Propositions, reduced to its ultimate
elements: but there is another and a less abstruse expression for it,
which, though stopping short in an earlier stage of the analysis, is
sufficiently scientific for many of the purposes for which such a general
expression is required. This expression recognizes the commonly received
distinction between Subject and Attribute, and gives the following as the
analysis of the meaning of propositions:—Every Proposition asserts, that
some given subject does or does not possess some attribute; or that some
attribute is or is not (either in all or in some portion of the subjects
in which it is met with) conjoined with some other attribute.

We shall now for the present take our leave of this portion of our
inquiry, and proceed to the peculiar problem of the Science of Logic,
namely, how the assertions, of which we have analyzed the import, are
proved or disproved; such of them, at least, as, not being amenable to
direct consciousness or intuition, are appropriate subjects of proof.

We say of a fact or statement, that it is proved, when we believe its
truth by reason of some other fact or statement from which it is said to
_follow_. Most of the propositions, whether affirmative or negative,
universal, particular, or singular, which we believe, are not believed on
their own evidence, but on the ground of something previously assented to,
from which they are said to be _inferred_. To infer a proposition from a
previous proposition or propositions; to give credence to it, or claim
credence for it, as a conclusion from something else; is to _reason_, in
the most extensive sense of the term. There is a narrower sense, in which
the name reasoning is confined to the form of inference which is termed
ratiocination, and of which the syllogism is the general type. The reasons
for not conforming to this restricted use of the term were stated in an
earlier stage of our inquiry, and additional motives will be suggested by
the considerations on which we are now about to enter.

§ 2. In proceeding to take into consideration the cases in which
inferences can legitimately be drawn, we shall first mention some cases in
which the inference is apparent, not real; and which require notice
chiefly that they may not be confounded with cases of inference properly
so called. This occurs when the proposition ostensibly inferred from
another, appears on analysis to be merely a repetition of the same, or
part of the same, assertion, which was contained in the first. All the
cases mentioned in books of Logic as examples of equipollency or
equivalence of propositions, are of this nature. Thus, if we were to
argue, No man is incapable of reason, for every man is rational; or, All
men are mortal, for no man is exempt from death; it would be plain that we
were not proving the proposition, but only appealing to another mode of
wording it, which may or may not be more readily comprehensible by the
hearer, or better adapted to suggest the real proof, but which contains in
itself no shadow of proof.

Another case is where, from a universal proposition, we affect to infer
another which differs from it only in being particular: as All A is B,
therefore Some A is B: No A is B, therefore Some A is not B. This, too, is
not to conclude one proposition from another, but to repeat a second time
something which had been asserted at first; with the difference, that we
do not here repeat the whole of the previous assertion, but only an
indefinite part of it.

A third case is where, the antecedent having affirmed a predicate of a
given subject, the consequent affirms of the same subject something
already connoted by the former predicate: as, Socrates is a man, therefore
Socrates is a living creature; where all that is connoted by living
creature was affirmed of Socrates when he was asserted to be a man. If the
propositions are negative, we must invert their order, thus: Socrates is
not a living creature, therefore he is not a man; for if we deny the less,
the greater, which includes it, is already denied by implication. These,
therefore, are not really cases of inference; and yet the trivial examples
by which, in manuals of Logic, the rules of the syllogism are illustrated,
are often of this ill-chosen kind; formal demonstrations of conclusions to
which whoever understands the terms used in the statement of the data, has
already, and consciously, assented.(47)

The most complex case of this sort of apparent inference is what is called
the Conversion of propositions; which consists in turning the predicate
into a subject, and the subject into a predicate, and framing out of the
same terms thus reversed, another proposition, which must be true if the
former is true. Thus, from the particular affirmative proposition, Some A
is B, we may infer that Some B is A. From the universal negative, No A is
B, we may conclude that No B is A. From the universal affirmative
proposition, All A is B, it can not be inferred that all B is A; though
all water is liquid, it is not implied that all liquid is water; but it is
implied that some liquid is so; and hence the proposition, All A is B, is
legitimately convertible into Some B is A. This process, which converts a
universal proposition into a particular, is termed conversion _per
accidens_. From the proposition, Some A is not B, we can not even infer
that some B is not A; though some men are not Englishmen, it does not
follow that some Englishmen are not men. The only mode usually recognized
of converting a particular negative proposition, is in the form, Some A is
not B, therefore something which is not B is A; and this is termed
conversion by contraposition. In this case, however, the predicate and
subject are not merely reversed, but one of them is changed. Instead of
[A] and [B], the terms of the new proposition are [a thing which is not
B], and [A]. The original proposition, Some A _is not_ B, is first changed
into a proposition equipollent with it, Some A _is_ “a thing which is not
B;” and the proposition, being now no longer a particular negative, but a
particular affirmative, admits of conversion in the first mode, or as it
is called, _simple_ conversion.(48)

In all these cases there is not really any inference; there is in the
conclusion no new truth, nothing but what was already asserted in the
premises, and obvious to whoever apprehends them. The fact asserted in the
conclusion is either the very same fact, or part of the fact, asserted in
the original proposition. This follows from our previous analysis of the
Import of Propositions. When we say, for example, that some lawful
sovereigns are tyrants, what is the meaning of the assertion? That the
attributes connoted by the term “lawful sovereign,” and the attributes
connoted by the term “tyrant,” sometimes co-exist in the same individual.
Now this is also precisely what we mean, when we say that some tyrants are
lawful sovereigns; which, therefore, is not a second proposition inferred
from the first, any more than the English translation of Euclid’s Elements
is a collection of theorems different from and consequences of, those
contained in the Greek original. Again, if we assert that no great general
is a rash man, we mean that the attributes connoted by “great general,”
and those connoted by “rash,” never co-exist in the same subject; which is
also the exact meaning which would be expressed by saying, that no rash
man is a great general. When we say that all quadrupeds are warm-blooded,
we assert, not only that the attributes connoted by “quadruped” and those
connoted by “warm-blooded” sometimes co-exist, but that the former never
exist without the latter: now the proposition, Some warm-blooded creatures
are quadrupeds, expresses the first half of this meaning, dropping the
latter half; and therefore has been already affirmed in the antecedent
proposition, All quadrupeds are warm-blooded. But that _all_ warm-blooded
creatures are quadrupeds, or, in other words, that the attributes connoted
by “warm-blooded” never exist without those connoted by “quadruped,” has
not been asserted, and can not be inferred. In order to re-assert, in an
inverted form, the whole of what was affirmed in the proposition, All
quadrupeds are warm-blooded, we must convert it by contraposition, thus,
Nothing which is not warm-blooded is a quadruped. This proposition, and
the one from which it is derived, are exactly equivalent, and either of
them may be substituted for the other; for, to say that when the
attributes of a quadruped are present, those of a warm-blooded creature
are present, is to say that when the latter are absent the former are
absent.

In a manual for young students, it would be proper to dwell at greater
length on the conversion and equipollency of propositions. For though that
can not be called reasoning or inference which is a mere re-assertion in
different words of what had been asserted before, there is no more
important intellectual habit, nor any the cultivation of which falls more
strictly within the province of the art of logic, than that of discerning
rapidly and surely the identity of an assertion when disguised under
diversity of language. That important chapter in logical treatises which
relates to the Opposition of Propositions, and the excellent technical
language which logic provides for distinguishing the different kinds or
modes of opposition, are of use chiefly for this purpose. Such
considerations as these, that contrary propositions may both be false, but
can not both be true; that subcontrary propositions may both be true, but
can not both be false; that of two contradictory propositions one must be
true and the other false; that of two subalternate propositions the truth
of the universal proves the truth of the particular, and the falsity of
the particular proves the falsity of the universal, but not _vicè
versa_;(49) are apt to appear, at first sight, very technical and
mysterious, but when explained, seem almost too obvious to require so
formal a statement, since the same amount of explanation which is
necessary to make the principles intelligible, would enable the truths
which they convey to be apprehended in any particular case which can
occur. In this respect, however, these axioms of logic are on a level with
those of mathematics. That things which are equal to the same thing are
equal to one another, is as obvious in any particular case as it is in the
general statement: and if no such general maxim had ever been laid down,
the demonstrations in Euclid would never have halted for any difficulty in
stepping across the gap which this axiom at present serves to bridge over.
Yet no one has ever censured writers on geometry, for placing a list of
these elementary generalizations at the head of their treatises, as a
first exercise to the learner of the faculty which will be required in him
at every step, that of apprehending a _general_ truth. And the student of
logic, in the discussion even of such truths as we have cited above,
acquires habits of circumspect interpretation of words, and of exactly
measuring the length and breadth of his assertions, which are among the
most indispensable conditions of any considerable mental attainment, and
which it is one of the primary objects of logical discipline to cultivate.

§ 3. Having noticed, in order to exclude from the province of Reasoning or
Inference properly so called, the cases in which the progression from one
truth to another is only apparent, the logical consequent being a mere
repetition of the logical antecedent; we now pass to those which are cases
of inference in the proper acceptation of the term, those in which we set
out from known truths, to arrive at others really distinct from them.

Reasoning, in the extended sense in which I use the term, and in which it
is synonymous with Inference, is popularly said to be of two kinds:
reasoning from particulars to generals, and reasoning from generals to
particulars; the former being called Induction, the latter Ratiocination
or Syllogism. It will presently be shown that there is a third species of
reasoning, which falls under neither of these descriptions, and which,
nevertheless, is not only valid, but is the foundation of both the others.

It is necessary to observe, that the expressions, reasoning from
particulars to generals, and reasoning from generals to particulars, are
recommended by brevity rather than by precision, and do not adequately
mark, without the aid of a commentary, the distinction between Induction
(in the sense now adverted to) and Ratiocination. The meaning intended by
these expressions is, that Induction is inferring a proposition from
propositions _less general_ than itself, and Ratiocination is inferring a
proposition from propositions _equally_ or _more_ general. When, from the
observation of a number of individual instances, we ascend to a general
proposition, or when, by combining a number of general propositions, we
conclude from them another proposition still more general, the process,
which is substantially the same in both instances, is called Induction.
When from a general proposition, not alone (for from a single proposition
nothing can be concluded which is not involved in the terms), but by
combining it with other propositions, we infer a proposition of the same
degree of generality with itself, or a less general proposition, or a
proposition merely individual, the process is Ratiocination. When, in
short, the conclusion is more general than the largest of the premises,
the argument is commonly called Induction; when less general, or equally
general, it is Ratiocination.

As all experience begins with individual cases, and proceeds from them to
generals, it might seem most conformable to the natural order of thought
that Induction should be treated of before we touch upon Ratiocination. It
will, however, be advantageous, in a science which aims at tracing our
acquired knowledge to its sources, that the inquirer should commence with
the latter rather than with the earlier stages of the process of
constructing our knowledge; and should trace derivative truths backward to
the truths from which they are deduced, and on which they depend for their
evidence, before attempting to point out the original spring from which
both ultimately take their rise. The advantages of this order of
proceeding in the present instance will manifest themselves as we advance,
in a manner superseding the necessity of any further justification or
explanation.

Of Induction, therefore, we shall say no more at present, than that it at
least is, without doubt, a process of real inference. The conclusion in an
induction embraces more than is contained in the premises. The principle
or law collected from particular instances, the general proposition in
which we embody the result of our experience, covers a much larger extent
of ground than the individual experiments which form its basis. A
principle ascertained by experience, is more than a mere summing up of
what has been specifically observed in the individual cases which have
been examined; it is a generalization grounded on those cases, and
expressive of our belief, that what we there found true is true in an
indefinite number of cases which we have not examined, and are never
likely to examine. The nature and grounds of this inference, and the
conditions necessary to make it legitimate, will be the subject of
discussion in the Third Book: but that such inference really takes place
is not susceptible of question. In every induction we proceed from truths
which we knew, to truths which we did not know; from facts certified by
observation, to facts which we have not observed, and even to facts not
capable of being now observed; future facts, for example; but which we do
not hesitate to believe on the sole evidence of the induction itself.

Induction, then, is a real process of Reasoning or Inference. Whether, and
in what sense, as much can be said of the Syllogism, remains to be
determined by the examination into which we are about to enter.



                               Chapter II.


Of Ratiocination, Or Syllogism.


§ 1. The analysis of the Syllogism has been so accurately and fully
performed in the common manuals of Logic, that in the present work, which
is not designed as a manual, it is sufficient to recapitulate, _memoriæ
causâ_, the leading results of that analysis, as a foundation for the
remarks to be afterward made on the functions of the Syllogism, and the
place which it holds in science.

To a legitimate syllogism it is essential that there should be three, and
no more than three, propositions, namely, the conclusion, or proposition
to be proved, and two other propositions which together prove it, and
which are called the premises. It is essential that there should be three,
and no more than three, terms, namely, the subject and predicate of the
conclusion, and another called the middle term, which must be found in
both premises, since it is by means of it that the other two terms are to
be connected together. The predicate of the conclusion is called the major
term of the syllogism; the subject of the conclusion is called the minor
term. As there can be but three terms, the major and minor terms must each
be found in one, and only one, of the premises, together with the middle
term which is in them both. The premise which contains the middle term and
the major term is called the major premise; that which contains the middle
term and the minor term is called the minor premise.

Syllogisms are divided by some logicians into three _figures_, by others
into four, according to the position of the middle term, which may either
be the subject in both premises, the predicate in both, or the subject in
one and the predicate in the other. The most common case is that in which
the middle term is the subject of the major premise and the predicate of
the minor. This is reckoned as the first figure. When the middle term is
the predicate in both premises, the syllogism belongs to the second
figure; when it is the subject in both, to the third. In the fourth figure
the middle term is the subject of the minor premise and the predicate of
the major. Those writers who reckon no more than three figures, include
this case in the first.

Each figure is divided into _moods_, according to what are called the
_quantity_ and _quality_ of the propositions, that is, according as they
are universal or particular, affirmative or negative. The following are
examples of all the legitimate moods, that is, all those in which the
conclusion correctly follows from the premises. A is the minor term, C the
major, B the middle term.

FIRST FIGURE.

All B is C   No B is C    All B is C    No B is C
All A is B   All A is B   Some A is B   Some A is B
therefore    therefore    therefore     therefore
All A is C   No A is C    Some A is C   Some A is not C

SECOND FIGURE.

No C is B    All C is B   No C is B         All C is B
All A is B   No A is B    Some A is B       Some A is not B
therefore    therefore    therefore         therefore
No A is C    No A is C    Some A is not C   Some A is not C

THIRD FIGURE.

All B is    No B is C   Some B is   All B is    Some B is   No B is C
C                       C           C           not C
All B is    All B is    All B is    Some B is   All B is    Some B is
A           A           A           A           A           A
therefore   therefore   therefore   therefore   therefore   therefore
Some A is   Some A is   Some A is   Some A is   Some A is   Some A is
C           not C       C           C           not C       not C

FOURTH FIGURE.

All C is B    All C is B   Some C is B   No C is B    No C is B
All B is A    No B is A    All B is A    All B is A   Some B is A
therefore     therefore    therefore     therefore    therefore
Some A is C   Some A is    Some A is C   Some A is    Some A is
              not C                      not C        not C

In these exemplars, or blank forms for making syllogisms, no place is
assigned to _singular_ propositions; not, of course, because such
propositions are not used in ratiocination, but because, their predicate
being affirmed or denied of the whole of the subject, they are ranked, for
the purposes of the syllogism, with universal propositions. Thus, these
two syllogisms—

All men are mortal,     All men are mortal,
All kings are men,      Socrates is a man,
therefore               therefore
All kings are mortal,   Socrates is mortal,

are arguments precisely similar, and are both ranked in the first mood of
the first figure.(50)

The reasons why syllogisms in any of the above forms are legitimate, that
is, why, if the premises are true, the conclusion must inevitably be so,
and why this is not the case in any other possible mood (that is, in any
other combination of universal and particular, affirmative and negative
propositions), any person taking interest in these inquiries may be
presumed to have either learned from the common-school books of the
syllogistic logic, or to be capable of discovering for himself. The reader
may, however, be referred, for every needful explanation, to Archbishop
Whately’s _Elements of Logic_, where he will find stated with
philosophical precision, and explained with remarkable perspicuity, the
whole of the common doctrine of the syllogism.

All valid ratiocination; all reasoning by which, from general propositions
previously admitted, other propositions equally or less general are
inferred; may be exhibited in some of the above forms. The whole of
Euclid, for example, might be thrown without difficulty into a series of
syllogisms, regular in mood and figure.

Though a syllogism framed according to any of these formulæ is a valid
argument, all correct ratiocination admits of being stated in syllogisms
of the first figure alone. The rules for throwing an argument in any of
the other figures into the first figure, are called rules for the
_reduction_ of syllogisms. It is done by the _conversion_ of one or other,
or both, of the premises. Thus an argument in the first mood of the second
figure, as—

No C is B
All A is B
therefore
No A is C,

may be reduced as follows. The proposition, No C is B, being a universal
negative, admits of simple conversion, and may be changed into No B is C,
which, as we showed, is the very same assertion in other words—the same
fact differently expressed. This transformation having been effected, the
argument assumes the following form:

No B is C
All A is B
therefore
No A is C,

which is a good syllogism in the second mood of the first figure. Again,
an argument in the first mood of the third figure must resemble the
following:

All B is C
All B is A
therefore
Some A is C,

where the minor premise, All B is A, conformably to what was laid down in
the last chapter respecting universal affirmatives, does not admit of
simple conversion, but may be converted _per accidens_, thus, Some A is B;
which, though it does not express the whole of what is asserted in the
proposition All B is A, expresses, as was formerly shown, part of it, and
must therefore be true if the whole is true. We have, then, as the result
of the reduction, the following syllogism in the third mood of the first
figure:

All B is C
Some A is B,

from which it obviously follows, that

Some A is C.

In the same manner, or in a manner on which after these examples it is not
necessary to enlarge, every mood of the second, third, and fourth figures
may be reduced to some one of the four moods of the first. In other words,
every conclusion which can be proved in any of the last three figures, may
be proved in the first figure from the same premises, with a slight
alteration in the mere manner of expressing them. Every valid
ratiocination, therefore, may be stated in the first figure, that is, in
one of the following forms:

Every B is C   No B is C
All A is B,    All A is B,
Some A is B,   Some A is B,
therefore      therefore
All A is C.    No A is C.
Some A is C.   Some A is not C.

Or, if more significant symbols are preferred:

To prove an affirmative, the argument must admit of being stated in this
form:

All animals are mortal;
All men/Some men/Socrates are animals;
therefore
All men/Some men/Socrates are mortal.

To prove a negative, the argument must be capable of being expressed in
this form:

No one who is capable of self-control is necessarily vicious;

No one who is capable of self-control is necessarily vicious;
All negroes/Some negroes/Mr. A’s negro are capable of self-control;
therefore
No negroes are/Some negroes are not/Mr. A’s negro is not necessarily
vicious.

Though all ratiocination admits of being thrown into one or the other of
these forms, and sometimes gains considerably by the transformation, both
in clearness and in the obviousness of its consequence; there are, no
doubt, cases in which the argument falls more naturally into one of the
other three figures, and in which its conclusiveness is more apparent at
the first glance in those figures, than when reduced to the first. Thus,
if the proposition were that pagans may be virtuous, and the evidence to
prove it were the example of Aristides; a syllogism in the third figure,

Aristides was virtuous,
Aristides was a pagan,
therefore
Some pagan was virtuous,

would be a more natural mode of stating the argument, and would carry
conviction more instantly home, than the same ratiocination strained into
the first figure, thus—

Aristides was virtuous,
Some pagan was Aristides,
therefore
Some pagan was virtuous.

A German philosopher, Lambert, whose _Neues Organon_ (published in the
year 1764) contains among other things one of the most elaborate and
complete expositions which had ever been made of the syllogistic doctrine,
has expressly examined what sort of arguments fall most naturally and
suitably into each of the four figures; and his investigation is
characterized by great ingenuity and clearness of thought.(51) The
argument, however, is one and the same, in whichever figure it is
expressed; since, as we have already seen, the premises of a syllogism in
the second, third, or fourth figure, and those of the syllogism in the
first figure to which it may be reduced, are the same premises in every
thing except language, or, at least, as much of them as contributes to the
proof of the conclusion is the same. We are therefore at liberty, in
conformity with the general opinion of logicians, to consider the two
elementary forms of the first figure as the universal types of all correct
ratiocination; the one, when the conclusion to be proved is affirmative,
the other, when it is negative; even though certain arguments may have a
tendency to clothe themselves in the forms of the second, third, and
fourth figures; which, however, can not possibly happen with the only
class of arguments which are of first-rate scientific importance, those in
which the conclusion is a universal affirmative, such conclusions being
susceptible of proof in the first figure alone.(52)

§ 2. On examining, then, these two general formulæ, we find that in both
of them, one premise, the major, is a universal proposition; and according
as this is affirmative or negative, the conclusion is so too. All
ratiocination, therefore, starts from a _general_ proposition, principle,
or assumption: a proposition in which a predicate is affirmed or denied of
an entire class; that is, in which some attribute, or the negation of some
attribute, is asserted of an indefinite number of objects distinguished by
a common characteristic, and designated, in consequence, by a common name.

The other premise is always affirmative, and asserts that something (which
may be either an individual, a class, or part of a class) belongs to, or
is included in, the class respecting which something was affirmed or
denied in the major premise. It follows that the attribute affirmed or
denied of the entire class may (if that affirmation or denial was correct)
be affirmed or denied of the object or objects alleged to be included in
the class: and this is precisely the assertion made in the conclusion.

Whether or not the foregoing is an adequate account of the constituent
parts of the syllogism, will be presently considered; but as far as it
goes it is a true account. It has accordingly been generalized, and
erected into a logical maxim, on which all ratiocination is said to be
founded, insomuch that to reason, and to apply the maxim, are supposed to
be one and the same thing. The maxim is, That whatever can be affirmed (or
denied) of a class, may be affirmed (or denied) of every thing included in
the class. This axiom, supposed to be the basis of the syllogistic theory,
is termed by logicians the _dictum de omni et nullo_.

This maxim, however, when considered as a principle of reasoning, appears
suited to a system of metaphysics once indeed generally received, but
which for the last two centuries has been considered as finally abandoned,
though there have not been wanting in our own day attempts at its revival.
So long as what are termed Universals were regarded as a peculiar kind of
substances, having an objective existence distinct from the individual
objects classed under them, the _dictum de omni_ conveyed an important
meaning; because it expressed the intercommunity of nature, which it was
necessary on that theory that we should suppose to exist between those
general substances and the particular substances which were subordinated
to them. That every thing predicable of the universal was predicable of
the various individuals contained under it, was then no identical
proposition, but a statement of what was conceived as a fundamental law of
the universe. The assertion that the entire nature and properties of the
_substantia secunda_ formed part of the nature and properties of each of
the individual substances called by the same name; that the properties of
Man, for example, were properties of all men; was a proposition of real
significance when man did not _mean_ all men, but something inherent in
men, and vastly superior to them in dignity. Now, however, when it is
known that a class, a universal, a genus or species, is not an entity _per
se_, but neither more nor less than the individual substances themselves
which are placed in the class, and that there is nothing real in the
matter except those objects, a common name given to them, and common
attributes indicated by the name; what, I should be glad to know, do we
learn by being told, that whatever can be affirmed of a class, may be
affirmed of every object contained in the class? The class _is_ nothing
but the objects contained in it: and the _dictum de omni_ merely amounts
to the identical proposition, that whatever is true of certain objects, is
true of each of those objects. If all ratiocination were no more than the
application of this maxim to particular cases, the syllogism would indeed
be, what it has so often been declared to be, solemn trifling. The _dictum
de omni_ is on a par with another truth, which in its time was also
reckoned of great importance, “Whatever is, is.” To give any real meaning
to the _dictum de omni_, we must consider it not as an axiom, but as a
definition; we must look upon it as intended to explain, in a circuitous
and paraphrastic manner, the meaning of the word _class_.

An error which seemed finally refuted and dislodged from thought, often
needs only put on a new suit of phrases, to be welcomed back to its old
quarters, and allowed to repose unquestioned for another cycle of ages.
Modern philosophers have not been sparing in their contempt for the
scholastic dogma that genera and species are a peculiar kind of
substances, which general substances being the only permanent things,
while the individual substances comprehended under them are in a perpetual
flux, knowledge, which necessarily imports stability, can only have
relation to those general substances or universals, and not to the facts
or particulars included under them. Yet, though nominally rejected, this
very doctrine, whether disguised under the Abstract Ideas of Locke (whose
speculations, however, it has less vitiated than those of perhaps any
other writer who has been infected with it), under the ultra-nominalism of
Hobbes and Condillac, or the ontology of the later German schools, has
never ceased to poison philosophy. Once accustomed to consider scientific
investigation as essentially consisting in the study of universals, men
did not drop this habit of thought when they ceased to regard universals
as possessing an independent existence: and even those who went the length
of considering them as mere names, could not free themselves from the
notion that the investigation of truth consisted entirely or partly in
some kind of conjuration or juggle with those names. When a philosopher
adopted fully the Nominalist view of the signification of general
language, retaining along with it the _dictum de omni_ as the foundation
of all reasoning, two such premises fairly put together were likely, if he
was a consistent thinker, to land him in rather startling conclusions.
Accordingly it has been seriously held, by writers of deserved celebrity,
that the process of arriving at new truths by reasoning consists in the
mere substitution of one set of arbitrary signs for another; a doctrine
which they suppose to derive irresistible confirmation from the example of
algebra. If there were any process in sorcery or necromancy more
preternatural than this, I should be much surprised. The culminating point
of this philosophy is the noted aphorism of Condillac, that a science is
nothing, or scarcely any thing, but _une langue bien faite_; in other
words, that the one sufficient rule for discovering the nature and
properties of objects is to name them properly: as if the reverse were not
the truth, that it is impossible to name them properly except in
proportion as we are already acquainted with their nature and properties.
Can it be necessary to say, that none, not even the most trivial knowledge
with respect to Things, ever was or could be originally got at by any
conceivable manipulation of mere names, as such; and that what can be
learned from names, is only what somebody who used the names knew before?
Philosophical analysis confirms the indication of common sense, that the
function of names is but that of enabling us to _remember_ and to
_communicate_ our thoughts. That they also strengthen, even to an
incalculable extent, the power of thought itself, is most true: but they
do this by no intrinsic and peculiar virtue; they do it by the power
inherent in an artificial memory, an instrument of which few have
adequately considered the immense potency. As an artificial memory,
language truly is, what it has so often been called, an instrument of
thought; but it is one thing to be the instrument, and another to be the
exclusive subject upon which the instrument is exercised. We think,
indeed, to a considerable extent, by means of names, but what we think of,
are the things called by those names; and there can not be a greater error
than to imagine that thought can be carried on with nothing in our mind
but names, or that we can make the names think for us.

§ 3. Those who considered the _dictum de omni_ as the foundation of the
syllogism, looked upon arguments in a manner corresponding to the
erroneous view which Hobbes took of propositions. Because there are some
propositions which are merely verbal, Hobbes, in order apparently that his
definition might be rigorously universal, defined a proposition as if no
propositions declared any thing except the meaning of words. If Hobbes was
right; if no further account than this could be given of the import of
propositions; no theory could be given but the commonly received one, of
the combination of propositions in a syllogism. If the minor premise
asserted nothing more than that something belongs to a class, and if the
major premise asserted nothing of that class except that it is included in
another class, the conclusion would only be that what was included in the
lower class is included in the higher, and the result, therefore, nothing
except that the classification is consistent with itself. But we have seen
that it is no sufficient account of the meaning of a proposition, to say
that it refers something to, or excludes something from, a class. Every
proposition which conveys real information asserts a matter of fact,
dependent on the laws of nature, and not on classification. It asserts
that a given object does or does not possess a given attribute; or it
asserts that two attributes, or sets of attributes, do or do not
(constantly or occasionally) co-exist. Since such is the purport of all
propositions which convey any real knowledge, and since ratiocination is a
mode of acquiring real knowledge, any theory of ratiocination which does
not recognize this import of propositions, can not, we may be sure, be the
true one.

Applying this view of propositions to the two premises of a syllogism, we
obtain the following results. The major premise, which, as already
remarked, is always universal, asserts, that all things which have a
certain attribute (or attributes) have or have not along with it, a
certain other attribute (or attributes). The minor premise asserts that
the thing or set of things which are the subject of that premise, have the
first-mentioned attribute; and the conclusion is, that they have (or that
they have not), the second. Thus in our former example,

All men are mortal,
Socrates is a man,
therefore
Socrates is mortal,

the subject and predicate of the major premise are connotative terms,
denoting objects and connoting attributes. The assertion in the major
premise is, that along with one of the two sets of attributes, we always
find the other: that the attributes connoted by “man” never exist unless
conjoined with the attribute called mortality. The assertion in the minor
premise is that the individual named Socrates possesses the former
attributes; and it is concluded that he possesses also the attribute
mortality. Or, if both the premises are general propositions, as

All men are mortal,
All kings are men,
therefore
All kings are mortal,

the minor premise asserts that the attributes denoted by kingship only
exist in conjunction with those signified by the word man. The major
asserts as before, that the last-mentioned attributes are never found
without the attribute of mortality. The conclusion is, that wherever the
attributes of kingship are found, that of mortality is found also.

If the major premise were negative, as, No men are omnipotent, it would
assert, not that the attributes connoted by “man” never exist without, but
that they never exist with, those connoted by “omnipotent:” from which,
together with the minor premise, it is concluded, that the same
incompatibility exists between the attribute omnipotence and those
constituting a king. In a similar manner we might analyze any other
example of the syllogism.

If we generalize this process, and look out for the principle or law
involved in every such inference, and presupposed in every syllogism, the
propositions of which are any thing more than merely verbal; we find, not
the unmeaning _dictum de omni et nullo_, but a fundamental principle, or
rather two principles, strikingly resembling the axioms of mathematics.
The first, which is the principle of affirmative syllogisms, is, that
things which co-exist with the same thing, co-exist with one another: or
(still more precisely) a thing which co-exists with another thing, which
other co-exists with a third thing, also co-exists with that third thing.
The second is the principle of negative syllogisms, and is to this effect:
that a thing which co-exists with another thing, with which other a third
thing does not co-exist, is not co-existent with that third thing. These
axioms manifestly relate to facts, and not to conventions; and one or
other of them is the ground of the legitimacy of every argument in which
facts and not conventions are the matter treated of.(53)

§ 4. It remains to translate this exposition of the syllogism from the one
into the other of the two languages in which we formerly remarked(54) that
all propositions, and of course therefore all combinations of
propositions, might be expressed. We observed that a proposition might be
considered in two different lights; as a portion of our knowledge of
nature, or as a memorandum for our guidance. Under the former, or
speculative aspect, an affirmative general proposition is an assertion of
a speculative truth, viz., that whatever has a certain attribute has a
certain other attribute. Under the other aspect, it is to be regarded not
as a part of our knowledge, but as an aid for our practical exigencies, by
enabling us, when we see or learn that an object possesses one of the two
attributes, to infer that it possesses the other; thus employing the first
attribute as a mark or evidence of the second. Thus regarded, every
syllogism comes within the following general formula:

Attribute A is a mark of attribute B,
The given object has the mark A,
therefore
The given object has the attribute B.

Referred to this type, the arguments which we have lately cited as
specimens of the syllogism, will express themselves in the following
manner:

The attributes of man are a mark of the attribute mortality,
Socrates has the attributes of man,
therefore
Socrates has the attribute mortality.

And again,

The attributes of man are a mark of the attribute mortality,
The attributes of a king are a mark of the attributes of man,
therefore
The attributes of a king are a mark of the attribute mortality.

And, lastly,

The attributes of man are a mark of the absence of the attribute
omnipotence,
The attributes of a king are a mark of the attributes of man,
therefore
The attributes of a king are a mark of the absence of the attribute
signified by the word omnipotent (or, are evidence of the absence of that
attribute).

To correspond with this alteration in the form of the syllogisms, the
axioms on which the syllogistic process is founded must undergo a
corresponding transformation. In this altered phraseology, both those
axioms may be brought under one general expression; namely, that whatever
has any mark, has that which it is a mark of. Or, when the minor premise
as well as the major is universal, we may state it thus: Whatever is a
mark of any mark, is a mark of that which this last is a mark of. To trace
the identity of these axioms with those previously laid down, may be left
to the intelligent reader. We shall find, as we proceed, the great
convenience of the phraseology into which we have last thrown them, and
which is better adapted than any I am acquainted with, to express with
precision and force what is aimed at, and actually accomplished, in every
case of the ascertainment of a truth by ratiocination.(55)



                               Chapter III.


Of The Functions And Logical Value Of The Syllogism.


§ 1. We have shown what is the real nature of the truths with which the
Syllogism is conversant, in contradistinction to the more superficial
manner in which their import is conceived in the common theory; and what
are the fundamental axioms on which its probative force or conclusiveness
depends. We have now to inquire, whether the syllogistic process, that of
reasoning from generals to particulars, is, or is not, a process of
inference; a progress from the known to the unknown: a means of coming to
a knowledge of something which we did not know before.

Logicians have been remarkably unanimous in their mode of answering this
question. It is universally allowed that a syllogism is vicious if there
be any thing more in the conclusion than was assumed in the premises. But
this is, in fact, to say, that nothing ever was, or can be, proved by
syllogism, which was not known, or assumed to be known, before. Is
ratiocination, then, not a process of inference? And is the syllogism, to
which the word reasoning has so often been represented to be exclusively
appropriate, not really entitled to be called reasoning at all? This seems
an inevitable consequence of the doctrine, admitted by all writers on the
subject, that a syllogism can prove no more than is involved in the
premises. Yet the acknowledgment so explicitly made, has not prevented one
set of writers from continuing to represent the syllogism as the correct
analysis of what the mind actually performs in discovering and proving the
larger half of the truths, whether of science or of daily life, which we
believe; while those who have avoided this inconsistency, and followed out
the general theorem respecting the logical value of the syllogism to its
legitimate corollary, have been led to impute uselessness and frivolity to
the syllogistic theory itself, on the ground of the _petitio principii_
which they allege to be inherent in every syllogism. As I believe both
these opinions to be fundamentally erroneous, I must request the attention
of the reader to certain considerations, without which any just
appreciation of the true character of the syllogism, and the functions it
performs in philosophy, appears to me impossible; but which seem to have
been either overlooked, or insufficiently adverted to, both by the
defenders of the syllogistic theory and by its assailants.

§ 2. It must be granted that in every syllogism, considered as an argument
to prove the conclusion, there is a _petitio principii_. When we say,

All men are mortal,
Socrates is a man,
therefore
Socrates is mortal;

it is unanswerably urged by the adversaries of the syllogistic theory,
that the proposition, Socrates is mortal, is presupposed in the more
general assumption, All men are mortal: that we can not be assured of the
mortality of all men, unless we are already certain of the mortality of
every individual man: that if it be still doubtful whether Socrates, or
any other individual we choose to name, be mortal or not, the same degree
of uncertainty must hang over the assertion, All men are mortal: that the
general principle, instead of being given as evidence of the particular
case, can not itself be taken for true without exception, until every
shadow of doubt which could affect any case comprised with it, is
dispelled by evidence _aliundè_; and then what remains for the syllogism
to prove? That, in short, no reasoning from generals to particulars can,
as such, prove any thing: since from a general principle we can not infer
any particulars, but those which the principle itself assumes as known.

This doctrine appears to me irrefragable; and if logicians, though unable
to dispute it, have usually exhibited a strong disposition to explain it
away, this was not because they could discover any flaw in the argument
itself, but because the contrary opinion seemed to rest on arguments
equally indisputable. In the syllogism last referred to, for example, or
in any of those which we previously constructed, is it not evident that
the conclusion may, to the person to whom the syllogism is presented, be
actually and _bona fide_ a new truth? Is it not matter of daily experience
that truths previously unthought of, facts which have not been, and can
not be, directly observed, are arrived at by way of general reasoning? We
believe that the Duke of Wellington is mortal. We do not know this by
direct observation, so long as he is not yet dead. If we were asked how,
this being the case, we know the duke to be mortal, we should probably
answer, Because all men are so. Here, therefore, we arrive at the
knowledge of a truth not (as yet) susceptible of observation, by a
reasoning which admits of being exhibited in the following syllogism:

All men are mortal,
The Duke of Wellington is a man,
therefore
The Duke of Wellington is mortal.

And since a large portion of our knowledge is thus acquired, logicians
have persisted in representing the syllogism as a process of inference or
proof; though none of them has cleared up the difficulty which arises from
the inconsistency between that assertion, and the principle, that if there
be any thing in the conclusion which was not already asserted in the
premises, the argument is vicious. For it is impossible to attach any
serious scientific value to such a mere salvo, as the distinction drawn
between being involved _by implication_ in the premises, and being
directly asserted in them. When Archbishop Whately says(56) that the
object of reasoning is “merely to expand and unfold the assertions wrapped
up, as it were, and implied in those with which we set out, and to bring a
person to perceive and acknowledge the full force of that which he has
admitted,” he does not, I think, meet the real difficulty requiring to be
explained, namely, how it happens that a science, like geometry, _can_ be
all “wrapped up” in a few definitions and axioms. Nor does this defense of
the syllogism differ much from what its assailants urge against it as an
accusation, when they charge it with being of no use except to those who
seek to press the consequences of an admission into which a person has
been entrapped without having considered and understood its full force.
When you admitted the major premise, you asserted the conclusion; but,
says Archbishop Whately, you asserted it by implication merely: this,
however, can here only mean that you asserted it unconsciously; that you
did not know you were asserting it; but, if so, the difficulty revives in
this shape—Ought you not to have known? Were you warranted in asserting
the general proposition without having satisfied yourself of the truth of
every thing which it fairly includes? And if not, is not the syllogistic
art _prima facie_ what its assailants affirm it to be, a contrivance for
catching you in a trap, and holding you fast in it?(57)

§ 3. From this difficulty there appears to be but one issue. The
proposition that the Duke of Wellington is mortal, is evidently an
inference; it is got at as a conclusion from something else; but do we, in
reality, conclude it from the proposition, All men are mortal? I answer,
no.

The error committed is, I conceive, that of overlooking the distinction
between two parts of the process of philosophizing, the inferring part,
and the registering part; and ascribing to the latter the functions of the
former. The mistake is that of referring a person to his own notes for the
origin of his knowledge. If a person is asked a question, and is at the
moment unable to answer it, he may refresh his memory by turning to a
memorandum which he carries about with him. But if he were asked, how the
fact came to his knowledge, he would scarcely answer, because it was set
down in his note-book: unless the book was written, like the Koran, with a
quill from the wing of the angel Gabriel.

Assuming that the proposition, The Duke of Wellington is mortal, is
immediately an inference from the proposition, All men are mortal; whence
do we derive our knowledge of that general truth? Of course from
observation. Now, all which man can observe are individual cases. From
these all general truths must be drawn, and into these they may be again
resolved; for a general truth is but an aggregate of particular truths; a
comprehensive expression, by which an indefinite number of individual
facts are affirmed or denied at once. But a general proposition is not
merely a compendious form for recording and preserving in the memory a
number of particular facts, all of which have been observed.
Generalization is not a process of mere naming, it is also a process of
inference. From instances which we have observed, we feel warranted in
concluding, that what we found true in those instances, holds in all
similar ones, past, present, and future, however numerous they may be. We
then, by that valuable contrivance of language which enables us to speak
of many as if they were one, record all that we have observed, together
with all that we infer from our observations, in one concise expression;
and have thus only one proposition, instead of an endless number, to
remember or to communicate. The results of many observations and
inferences, and instructions for making innumerable inferences in
unforeseen cases, are compressed into one short sentence.

When, therefore, we conclude from the death of John and Thomas, and every
other person we ever heard of in whose case the experiment had been fairly
tried, that the Duke of Wellington is mortal like the rest; we may,
indeed, pass through the generalization, All men are mortal, as an
intermediate stage; but it is not in the latter half of the process, the
descent from all men to the Duke of Wellington, that the _inference_
resides. The inference is finished when we have asserted that all men are
mortal. What remains to be performed afterward is merely deciphering our
own notes.

Archbishop Whately has contended that syllogizing, or reasoning from
generals to particulars, is not, agreeably to the vulgar idea, a peculiar
_mode_ of reasoning, but the philosophical analysis of _the_ mode in which
all men reason, and must do so if they reason at all. With the deference
due to so high an authority, I can not help thinking that the vulgar
notion is, in this case, the more correct. If, from our experience of
John, Thomas, etc., who once were living, but are now dead, we are
entitled to conclude that all human beings are mortal, we might surely
without any logical inconsequence have concluded at once from those
instances, that the Duke of Wellington is mortal. The mortality of John,
Thomas, and others is, after all, the whole evidence we have for the
mortality of the Duke of Wellington. Not one iota is added to the proof by
interpolating a general proposition. Since the individual cases are all
the evidence we can possess, evidence which no logical form into which we
choose to throw it can make greater than it is; and since that evidence is
either sufficient in itself, or, if insufficient for the one purpose, can
not be sufficient for the other; I am unable to see why we should be
forbidden to take the shortest cut from these sufficient premises to the
conclusion, and constrained to travel the “high priori road,” by the
arbitrary fiat of logicians. I can not perceive why it should be
impossible to journey from one place to another unless we “march up a
hill, and then march down again.” It may be the safest road, and there may
be a resting-place at the top of the hill, affording a commanding view of
the surrounding country; but for the mere purpose of arriving at our
journey’s end, our taking that road is perfectly optional; it is a
question of time, trouble, and danger.

Not only _may_ we reason from particulars to particulars without passing
through generals, but we perpetually do so reason. All our earliest
inferences are of this nature. From the first dawn of intelligence we draw
inferences, but years elapse before we learn the use of general language.
The child, who, having burned his fingers, avoids to thrust them again
into the fire, has reasoned or inferred, though he has never thought of
the general maxim, Fire burns. He knows from memory that he has been
burned, and on this evidence believes, when he sees a candle, that if he
puts his finger into the flame of it, he will be burned again. He believes
this in every case which happens to arise; but without looking, in each
instance, beyond the present case. He is not generalizing; he is inferring
a particular from particulars. In the same way, also, brutes reason. There
is no ground for attributing to any of the lower animals the use of signs,
of such a nature as to render general propositions possible. But those
animals profit by experience, and avoid what they have found to cause them
pain, in the same manner, though not always with the same skill, as a
human creature. Not only the burned child, but the burned dog, dreads the
fire.

I believe that, in point of fact, when drawing inferences from our
personal experience, and not from maxims handed down to us by books or
tradition, we much oftener conclude from particulars to particulars
directly, than through the intermediate agency of any general proposition.
We are constantly reasoning from ourselves to other people, or from one
person to another, without giving ourselves the trouble to erect our
observations into general maxims of human or external nature. When we
conclude that some person will, on some given occasion, feel or act so and
so, we sometimes judge from an enlarged consideration of the manner in
which human beings in general, or persons of some particular character,
are accustomed to feel and act; but much oftener from merely recollecting
the feelings and conduct of the same person in some previous instance, or
from considering how we should feel or act ourselves. It is not only the
village matron, who, when called to a consultation upon the case of a
neighbor’s child, pronounces on the evil and its remedy simply on the
recollection and authority of what she accounts the similar case of her
Lucy. We all, where we have no definite maxims to steer by, guide
ourselves in the same way: and if we have an extensive experience, and
retain its impressions strongly, we may acquire in this manner a very
considerable power of accurate judgment, which we may be utterly incapable
of justifying or of communicating to others. Among the higher order of
practical intellects there have been many of whom it was remarked how
admirably they suited their means to their ends, without being able to
give any sufficient reasons for what they did; and applied, or seemed to
apply, recondite principles which they were wholly unable to state. This
is a natural consequence of having a mind stored with appropriate
particulars, and having been long accustomed to reason at once from these
to fresh particulars, without practicing the habit of stating to one’s
self or to others the corresponding general propositions. An old warrior,
on a rapid glance at the outlines of the ground, is able at once to give
the necessary orders for a skillful arrangement of his troops; though if
he has received little theoretical instruction, and has seldom been called
upon to answer to other people for his conduct, he may never have had in
his mind a single general theorem respecting the relation between ground
and array. But his experience of encampments, in circumstances more or
less similar, has left a number of vivid, unexpressed, ungeneralized
analogies in his mind, the most appropriate of which, instantly suggesting
itself, determines him to a judicious arrangement.

The skill of an uneducated person in the use of weapons, or of tools, is
of a precisely similar nature. The savage who executes unerringly the
exact throw which brings down his game, or his enemy, in the manner most
suited to his purpose, under the operation of all the conditions
necessarily involved, the weight and form of the weapon, the direction and
distance of the object, the action of the wind, etc., owes this power to a
long series of previous experiments, the results of which he certainly
never framed into any verbal theorems or rules. The same thing may
generally be said of any other extraordinary manual dexterity. Not long
ago a Scotch manufacturer procured from England, at a high rate of wages,
a working dyer, famous for producing very fine colors, with the view of
teaching to his other workmen the same skill. The workman came; but his
mode of proportioning the ingredients, in which lay the secret of the
effects he produced, was by taking them up in handfuls, while the common
method was to weigh them. The manufacturer sought to make him turn his
handling system into an equivalent weighing system, that the general
principle of his peculiar mode of proceeding might be ascertained. This,
however, the man found himself quite unable to do, and therefore could
impart his skill to nobody. He had, from the individual cases of his own
experience, established a connection in his mind between fine effects of
color, and tactual perceptions in handling his dyeing materials; and from
these perceptions he could, in any particular case, infer the means to be
employed, and the effects which would be produced, but could not put
others in possession of the grounds on which he proceeded, from having
never generalized them in his own mind, or expressed them in language.

Almost every one knows Lord Mansfield’s advice to a man of practical good
sense, who, being appointed governor of a colony, had to preside in its
courts of justice, without previous judicial practice or legal education.
The advice was to give his decision boldly, for it would probably be
right; but never to venture on assigning reasons, for they would almost
infallibly be wrong. In cases like this, which are of no uncommon
occurrence, it would be absurd to suppose that the bad reason was the
source of the good decision. Lord Mansfield knew that if any reason were
assigned it would be necessarily an afterthought, the judge being _in
fact_ guided by impressions from past experience, without the circuitous
process of framing general principles from them, and that if he attempted
to frame any such he would assuredly fail. Lord Mansfield, however, would
not have doubted that a man of equal experience who had also a mind stored
with general propositions derived by legitimate induction from that
experience, would have been greatly preferable as a judge, to one, however
sagacious, who could not be trusted with the explanation and justification
of his own judgments. The cases of men of talent performing wonderful
things they know not how, are examples of the rudest and most spontaneous
form of the operations of superior minds. It is a defect in them, and
often a source of errors, not to have generalized as they went on; but
generalization, though a help, the most important indeed of all helps, is
not an essential.

Even the scientifically instructed, who possess, in the form of general
propositions, a systematic record of the results of the experience of
mankind, need not always revert to those general propositions in order to
apply that experience to a new case. It is justly remarked by Dugald
Stewart, that though the reasonings in mathematics depend entirely on the
axioms, it is by no means necessary to our seeing the conclusiveness of
the proof, that the axioms should be expressly adverted to. When it is
inferred that AB is equal to CD because each of them is equal to EF, the
most uncultivated understanding, as soon as the propositions were
understood, would assent to the inference, without having ever heard of
the general truth that “things which are equal to the same thing are equal
to one another.” This remark of Stewart, consistently followed out, goes
to the root, as I conceive, of the philosophy of ratiocination; and it is
to be regretted that he himself stopped short at a much more limited
application of it. He saw that the general propositions on which a
reasoning is said to depend, may, in certain cases, be altogether omitted,
without impairing its probative force. But he imagined this to be a
peculiarity belonging to axioms; and argued from it, that axioms are not
the foundations or first principles of geometry, from which all the other
truths of the science are synthetically deduced (as the laws of motion and
of the composition of forces in dynamics, the equal mobility of fluids in
hydrostatics, the laws of reflection and refraction in optics, are the
first principles of those sciences); but are merely necessary assumptions,
self-evident indeed, and the denial of which would annihilate all
demonstration, but from which, as premises, nothing can be demonstrated.
In the present, as in many other instances, this thoughtful and elegant
writer has perceived an important truth, but only by halves. Finding, in
the case of geometrical axioms, that general names have not any talismanic
virtue for conjuring new truths out of the well where they lie hid, and
not seeing that this is equally true in every other case of
generalization, he contended that axioms are in their nature barren of
consequences, and that the really fruitful truths, the real first
principles of geometry, are the definitions; that the definition, for
example, of the circle is to the properties of the circle, what the laws
of equilibrium and of the pressure of the atmosphere are to the rise of
the mercury in the Torricellian tube. Yet all that he had asserted
respecting the function to which the axioms are confined in the
demonstrations of geometry, holds equally true of the definitions. Every
demonstration in Euclid might be carried on without them. This is apparent
from the ordinary process of proving a proposition of geometry by means of
a diagram. What assumption, in fact, do we set out from, to demonstrate by
a diagram any of the properties of the circle? Not that in all circles the
radii are equal, but only that they are so in the circle ABC. As our
warrant for assuming this, we appeal, it is true, to the definition of a
circle in general; but it is only necessary that the assumption be granted
in the case of the particular circle supposed. From this, which is not a
general but a singular proposition, combined with other propositions of a
similar kind, some of which _when generalized_ are called definitions, and
other axioms, we prove that a certain conclusion is true, not of all
circles, but of the particular circle ABC; or at least would be so, if the
facts precisely accorded with our assumptions. The enunciation, as it is
called, that is, the general theorem which stands at the head of the
demonstration, is not the proposition actually demonstrated. One instance
only is demonstrated: but the process by which this is done, is a process
which, when we consider its nature, we perceive might be exactly copied in
an indefinite number of other instances; in every instance which conforms
to certain conditions. The contrivance of general language furnishing us
with terms which connote these conditions, we are able to assert this
indefinite multitude of truths in a single expression, and this expression
is the general theorem. By dropping the use of diagrams, and substituting,
in the demonstrations, general phrases for the letters of the alphabet, we
might prove the general theorem directly, that is, we might demonstrate
all the cases at once; and to do this we must, of course, employ as our
premises, the axioms and definitions in their general form. But this only
means, that if we can prove an individual conclusion by assuming an
individual fact, then in whatever case we are warranted in making an
exactly similar assumption, we may draw an exactly similar conclusion. The
definition is a sort of notice to ourselves and others, what assumptions
we think ourselves entitled to make. And so in all cases, the general
propositions, whether called definitions, axioms, or laws of nature, which
we lay down at the beginning of our reasonings, are merely abridged
statements, in a kind of short-hand, of the particular facts, which, as
occasion arises, we either think we may proceed on as proved, or intend to
assume. In any one demonstration it is enough if we assume for a
particular case suitably selected, what by the statement of the definition
or principle we announce that we intend to assume in all cases which may
arise. The definition of the circle, therefore, is to one of Euclid’s
demonstrations, exactly what, according to Stewart, the axioms are; that
is, the demonstration does not depend on it, but yet if we deny it the
demonstration fails. The proof does not rest on the general assumption,
but on a similar assumption confined to the particular case: that case,
however, being chosen as a specimen or paradigm of the whole class of
cases included in the theorem, there can be no ground for making the
assumption in that case which does not exist in every other; and to deny
the assumption as a general truth, is to deny the right of making it in
the particular instance.

There are, undoubtedly, the most ample reasons for stating both the
principles and the theorems in their general form, and these will be
explained presently, so far as explanation is requisite. But, that
unpracticed learners, even in making use of one theorem to demonstrate
another, reason rather from particular to particular than from the general
proposition, is manifest from the difficulty they find in applying a
theorem to a case in which the configuration of the diagram is extremely
unlike that of the diagram by which the original theorem was demonstrated.
A difficulty which, except in cases of unusual mental power, long practice
can alone remove, and removes chiefly by rendering us familiar with all
the configurations consistent with the general conditions of the theorem.

§ 4. From the considerations now adduced, the following conclusions seem
to be established. All inference is from particulars to particulars:
General propositions are merely registers of such inferences already made,
and short formulæ for making more: The major premise of a syllogism,
consequently, is a formula of this description: and the conclusion is not
an inference drawn _from_ the formula, but an inference drawn _according_
to the formula: the real logical antecedent, or premise, being the
particular facts from which the general proposition was collected by
induction. Those facts, and the individual instances which supplied them,
may have been forgotten: but a record remains, not indeed descriptive of
the facts themselves, but showing how those cases may be distinguished,
respecting which, the facts, when known, were considered to warrant a
given inference. According to the indications of this record we draw our
conclusion: which is, to all intents and purposes, a conclusion from the
forgotten facts. For this it is essential that we should read the record
correctly: and the rules of the syllogism are a set of precautions to
insure our doing so.

This view of the functions of the syllogism is confirmed by the
consideration of precisely those cases which might be expected to be least
favorable to it, namely, those in which ratiocination is independent of
any previous induction. We have already observed that the syllogism, in
the ordinary course of our reasoning, is only the latter half of the
process of traveling from premises to a conclusion. There are, however,
some peculiar cases in which it is the whole process. Particulars alone
are capable of being subjected to observation; and all knowledge which is
derived from observation, begins, therefore, of necessity, in particulars;
but our knowledge may, in cases of certain descriptions, be conceived as
coming to us from other sources than observation. It may present itself as
coming from testimony, which, on the occasion and for the purpose in hand,
is accepted as of an authoritative character: and the information thus
communicated, may be conceived to comprise not only particular facts but
general propositions, as when a scientific doctrine is accepted without
examination on the authority of writers, or a theological doctrine on that
of Scripture. Or the generalization may not be, in the ordinary sense, an
assertion at all, but a command; a law, not in the philosophical, but in
the moral and political sense of the term: an expression of the desire of
a superior, that we, or any number of other persons, shall conform our
conduct to certain general instructions. So far as this asserts a fact,
namely, a volition of the legislator, that fact is an individual fact, and
the proposition, therefore, is not a general proposition. But the
description therein contained of the conduct which it is the will of the
legislator that his subjects should observe, is general. The proposition
asserts, not that all men _are_ any thing, but that all men _shall_ do
something.

In both these cases the generalities are the original data, and the
particulars are elicited from them by a process which correctly resolves
itself into a series of syllogisms. The real nature, however, of the
supposed deductive process, is evident enough. The only point to be
determined is, whether the authority which declared the general
proposition, intended to include this case in it; and whether the
legislator intended his command to apply to the present case among others,
or not. This is ascertained by examining whether the case possesses the
marks by which, as those authorities have signified, the cases which they
meant to certify or to influence may be known. The object of the inquiry
is to make out the witness’s or the legislator’s intention, through the
indication given by their words. This is a question, as the Germans
express it, of hermeneutics. The operation is not a process of inference,
but a process of interpretation.

In this last phrase we have obtained an expression which appears to me to
characterize, more aptly than any other, the functions of the syllogism in
all cases. When the premises are given by authority, the function of
Reasoning is to ascertain the testimony of a witness, or the will of a
legislator, by interpreting the signs in which the one has intimated his
assertion and the other his command. In like manner, when the premises are
derived from observation, the function of Reasoning is to ascertain what
we (or our predecessors) formerly thought might be inferred from the
observed facts, and to do this by interpreting a memorandum of ours, or of
theirs. The memorandum reminds us, that from evidence, more or less
carefully weighed, it formerly appeared that a certain attribute might be
inferred wherever we perceive a certain mark. The proposition, All men are
mortal (for instance) shows that we have had experience from which we
thought it followed that the attributes connoted by the term man, are a
mark of mortality. But when we conclude that the Duke of Wellington is
mortal, we do not infer this from the memorandum, but from the former
experience. All that we infer from the memorandum is our own previous
belief, (or that of those who transmitted to us the proposition),
concerning the inferences which that former experience would warrant.

This view of the nature of the syllogism renders consistent and
intelligible what otherwise remains obscure and confused in the theory of
Archbishop Whately and other enlightened defenders of the syllogistic
doctrine, respecting the limits to which its functions are confined. They
affirm in as explicit terms as can be used, that the sole office of
general reasoning is to prevent inconsistency in our opinions; to prevent
us from assenting to any thing, the truth of which would contradict
something to which we had previously on good grounds given our assent. And
they tell us, that the sole ground which a syllogism affords for assenting
to the conclusion, is that the supposition of its being false, combined
with the supposition that the premises are true, would lead to a
contradiction in terms. Now this would be but a lame account of the real
grounds which we have for believing the facts which we learn from
reasoning, in contradistinction to observation. The true reason why we
believe that the Duke of Wellington will die, is that his fathers, and our
fathers, and all other persons who were contemporary with them, have died.
Those facts are the real premises of the reasoning. But we are not led to
infer the conclusion from those premises, by the necessity of avoiding any
verbal inconsistency. There is no contradiction in supposing that all
those persons have died, and that the Duke of Wellington may,
notwithstanding, live forever. But there would be a contradiction if we
first, on the ground of those same premises, made a general assertion
including and covering the case of the Duke of Wellington, and then
refused to stand to it in the individual case. There is an inconsistency
to be avoided between the memorandum we make of the inferences which may
be justly drawn in future cases, and the inferences we actually draw in
those cases when they arise. With this view we interpret our own formula,
precisely as a judge interprets a law: in order that we may avoid drawing
any inferences not conformable to our former intention, as a judge avoids
giving any decision not conformable to the legislator’s intention. The
rules for this interpretation are the rules of the syllogism: and its sole
purpose is to maintain consistency between the conclusions we draw in
every particular case, and the previous general directions for drawing
them; whether those general directions were framed by ourselves as the
result of induction, or were received by us from an authority competent to
give them.

§ 5. In the above observations it has, I think, been shown, that, though
there is always a process of reasoning or inference where a syllogism is
used, the syllogism is not a correct analysis of that process of reasoning
or inference; which is, on the contrary (when not a mere inference from
testimony), an inference from particulars to particulars; authorized by a
previous inference from particulars to generals, and substantially the
same with it; of the nature, therefore, of Induction. But while these
conclusions appear to me undeniable, I must yet enter a protest, as strong
as that of Archbishop Whately himself, against the doctrine that the
syllogistic art is useless for the purposes of reasoning. The reasoning
lies in the act of generalization, not in interpreting the record of that
act; but the syllogistic form is an indispensable collateral security for
the correctness of the generalization itself.

It has already been seen, that if we have a collection of particulars
sufficient for grounding an induction, we need not frame a general
proposition; we may reason at once from those particulars to other
particulars. But it is to be remarked withal, that whenever, from a set of
particular cases, we can legitimately draw any inference, we may
legitimately make our inference a general one. If, from observation and
experiment, we can conclude to one new case, so may we to an indefinite
number. If that which has held true in our past experience will therefore
hold in time to come, it will hold not merely in some individual case, but
in all cases of some given description. Every induction, therefore, which
suffices to prove one fact, proves an indefinite multitude of facts: the
experience which justifies a single prediction must be such as will
suffice to bear out a general theorem. This theorem it is extremely
important to ascertain and declare, in its broadest form of generality;
and thus to place before our minds, in its full extent, the whole of what
our evidence must prove if it proves any thing.

This throwing of the whole body of possible inferences from a given set of
particulars, into one general expression, operates as a security for their
being just inferences, in more ways than one. First, the general principle
presents a larger object to the imagination than any of the singular
propositions which it contains. A process of thought which leads to a
comprehensive generality, is felt as of greater importance than one which
terminates in an insulated fact; and the mind is, even unconsciously, led
to bestow greater attention upon the process, and to weigh more carefully
the sufficiency of the experience appealed to, for supporting the
inference grounded upon it. There is another, and a more important,
advantage. In reasoning from a course of individual observations to some
new and unobserved case, which we are but imperfectly acquainted with (or
we should not be inquiring into it), and in which, since we are inquiring
into it, we probably feel a peculiar interest; there is very little to
prevent us from giving way to negligence, or to any bias which may affect
our wishes or our imagination, and, under that influence, accepting
insufficient evidence as sufficient. But if, instead of concluding
straight to the particular case, we place before ourselves an entire class
of facts—the whole contents of a general proposition, every tittle of
which is legitimately inferable from our premises, if that one particular
conclusion is so; there is then a considerable likelihood that if the
premises are insufficient, and the general inference therefore,
groundless, it will comprise within it some fact or facts the reverse of
which we already know to be true; and we shall thus discover the error in
our generalization by a _reductio ad impossibile_.

Thus if, during the reign of Marcus Aurelius, a subject of the Roman
empire, under the bias naturally given to the imagination and expectations
by the lives and characters of the Antonines, had been disposed to expect
that Commodus would be a just ruler; supposing him to stop there, he might
only have been undeceived by sad experience. But if he reflected that this
expectation could not be justifiable unless from the same evidence he was
warranted in concluding some general proposition, as, for instance, that
all Roman emperors are just rulers; he would immediately have thought of
Nero, Domitian, and other instances, which, showing the falsity of the
general conclusion, and therefore the insufficiency of the premises, would
have warned him that those premises could not prove in the instance of
Commodus, what they were inadequate to prove in any collection of cases in
which his was included.

The advantage, in judging whether any controverted inference is
legitimate, of referring to a parallel case, is universally acknowledged.
But by ascending to the general proposition, we bring under our view not
one parallel case only, but all possible parallel cases at once; all cases
to which the same set of evidentiary considerations are applicable.

When, therefore, we argue from a number of known cases to another case
supposed to be analogous, it is always possible, and generally
advantageous, to divert our argument into the circuitous channel of an
induction from those known cases to a general proposition, and a
subsequent application of that general proposition to the unknown case.
This second part of the operation, which, as before observed, is
essentially a process of interpretation, will be resolvable into a
syllogism or a series of syllogisms, the majors of which will be general
propositions embracing whole classes of cases; every one of which
propositions must be true in all its extent, if the argument is
maintainable. If, therefore, any fact fairly coming within the range of
one of these general propositions, and consequently asserted by it, is
known or suspected to be other than the proposition asserts it to be, this
mode of stating the argument causes us to know or to suspect that the
original observations, which are the real grounds of our conclusion, are
not sufficient to support it. And in proportion to the greater chance of
our detecting the inconclusiveness of our evidence, will be the increased
reliance we are entitled to place in it if no such evidence of defect
shall appear.

The value, therefore, of the syllogistic form, and of the rules for using
it correctly, does not consist in their being the form and the rules
according to which our reasonings are necessarily, or even usually, made;
but in their furnishing us with a mode in which those reasonings may
always be represented, and which is admirably calculated, if they are
inconclusive, to bring their inconclusiveness to light. An induction from
particulars to generals, followed by a syllogistic process from those
generals to other particulars, is a form in which we may always state our
reasonings if we please. It is not a form in which we _must_ reason, but
it is a form in which we _may_ reason, and into which it is indispensable
to throw our reasoning, when there is any doubt of its validity: though
when the case is familiar and little complicated, and there is no
suspicion of error, we may, and do, reason at once from the known
particular cases to unknown ones.(58)

These are the uses of syllogism, as a mode of verifying any given
argument. Its ulterior uses, as respects the general course of our
intellectual operations, hardly require illustration, being in fact the
acknowledged uses of general language. They amount substantially to this,
that the inductions may be made once for all: a single careful
interrogation of experience may suffice, and the result may be registered
in the form of a general proposition, which is committed to memory or to
writing, and from which afterward we have only to syllogize. The
particulars of our experiments may then be dismissed from the memory, in
which it would be impossible to retain so great a multitude of details;
while the knowledge which those details afforded for future use, and which
would otherwise be lost as soon as the observations were forgotten, or as
their record became too bulky for reference, is retained in a commodious
and immediately available shape by means of general language.

Against this advantage is to be set the countervailing inconvenience, that
inferences originally made on insufficient evidence become consecrated,
and, as it were, hardened into general maxims; and the mind cleaves to
them from habit, after it has outgrown any liability to be misled by
similar fallacious appearances if they were now for the first time
presented; but having forgotten the particulars, it does not think of
revising its own former decision. An inevitable drawback, which, however
considerable in itself, forms evidently but a small set-off against the
immense benefits of general language.

The use of the syllogism is in truth no other than the use of general
propositions in reasoning. We _can_ reason without them; in simple and
obvious cases we habitually do so; minds of great sagacity can do it in
cases not simple and obvious, provided their experience supplies them with
instances essentially similar to every combination of circumstances likely
to arise. But other minds, and the same minds where they have not the same
pre-eminent advantages of personal experience, are quite helpless without
the aid of general propositions, wherever the case presents the smallest
complication; and if we made no general propositions, few persons would
get much beyond those simple inferences which are drawn by the more
intelligent of the brutes. Though not necessary to reasoning, general
propositions are necessary to any considerable progress in reasoning. It
is, therefore, natural and indispensable to separate the process of
investigation into two parts; and obtain general formulæ for determining
what inferences may be drawn, before the occasion arises for drawing the
inferences. The work of drawing them is then that of applying the formulæ;
and the rules of syllogism are a system of securities for the correctness
of the application.

§ 6. To complete the series of considerations connected with the
philosophical character of the syllogism, it is requisite to consider,
since the syllogism is not the universal type of the reasoning process,
what is the real type. This resolves itself into the question, what is the
nature of the minor premise, and in what manner it contributes to
establish the conclusion: for as to the major, we now fully understand,
that the place which it nominally occupies in our reasonings, properly
belongs to the individual facts or observations of which it expresses the
general result; the major itself being no real part of the argument, but
an intermediate halting-place for the mind, interposed by an artifice of
language between the real premises and the conclusion, by way of a
security, which it is in a most material degree, for the correctness of
the process. The minor, however, being an indispensable part of the
syllogistic expression of an argument, without doubt either is, or
corresponds to, an equally indispensable part of the argument itself, and
we have only to inquire what part.

It is perhaps worth while to notice here a speculation of a philosopher to
whom mental science is much indebted, but who, though a very penetrating,
was a very hasty thinker, and whose want of due circumspection rendered
him fully as remarkable for what he did not see, as for what he saw. I
allude to Dr. Thomas Brown, whose theory of ratiocination is peculiar. He
saw the _petitio principii_ which is inherent in every syllogism, if we
consider the major to be itself the evidence by which the conclusion is
proved, instead of being, what in fact it is, an assertion of the
existence of evidence sufficient to prove any conclusion of a given
description. Seeing this, Dr. Brown not only failed to see the immense
advantage, in point of security for correctness, which is gained by
interposing this step between the real evidence and the conclusion; but he
thought it incumbent on him to strike out the major altogether from the
reasoning process, without substituting any thing else, and maintained
that our reasonings consist only of the minor premise and the conclusion,
Socrates is a man, therefore Socrates is mortal: thus actually
suppressing, as an unnecessary step in the argument, the appeal to former
experience. The absurdity of this was disguised from him by the opinion he
adopted, that reasoning is merely analyzing our own general notions, or
abstract ideas; and that the proposition, Socrates is mortal, is evolved
from the proposition, Socrates is a man, simply by recognizing the notion
of mortality as already contained in the notion we form of a man.

After the explanations so fully entered into on the subject of
propositions, much further discussion can not be necessary to make the
radical error of this view of ratiocination apparent. If the word man
connoted mortality; if the meaning of “mortal” were involved in the
meaning of “man;” we might, undoubtedly, evolve the conclusion from the
minor alone, because the minor would have already asserted it. But if, as
is in fact the case, the word man does not connote mortality, how does it
appear that in the mind of every person who admits Socrates to be a man,
the idea of man must include the idea of mortality? Dr. Brown could not
help seeing this difficulty, and in order to avoid it, was led, contrary
to his intention, to re-establish, under another name, that step in the
argument which corresponds to the major, by affirming the necessity of
_previously perceiving_ the relation between the idea of man and the idea
of mortal. If the reasoner has not previously perceived this relation, he
will not, says Dr. Brown, infer because Socrates is a man, that Socrates
is mortal. But even this admission, though amounting to a surrender of the
doctrine that an argument consists of the minor and the conclusion alone,
will not save the remainder of Dr. Brown’s theory. The failure of assent
to the argument does not take place merely because the reasoner, for want
of due analysis, does not perceive that his idea of man includes the idea
of mortality; it takes place, much more commonly, because in his mind that
relation between the two ideas has never existed. And in truth it never
does exist, except as the result of experience. Consenting, for the sake
of the argument, to discuss the question on a supposition of which we have
recognized the radical incorrectness, namely, that the meaning of a
proposition relates to the ideas of the things spoken of, and not to the
things themselves; I must yet observe, that the idea of man, as a
universal idea, the common property of all rational creatures, can not
involve any thing but what is strictly implied in the name. If any one
includes in his own private idea of man, as no doubt is always the case,
some other attributes, such for instance as mortality, he does so only as
the consequence of experience, after having satisfied himself that all men
possess that attribute: so that whatever the idea contains, in any
person’s mind, beyond what is included in the conventional signification
of the word, has been added to it as the result of assent to a
proposition; while Dr. Brown’s theory requires us to suppose, on the
contrary, that assent to the proposition is produced by evolving, through
an analytic process, this very element out of the idea. This theory,
therefore, may be considered as sufficiently refuted; and the minor
premise must be regarded as totally insufficient to prove the conclusion,
except with the assistance of the major, or of that which the major
represents, namely, the various singular propositions expressive of the
series of observations, of which the generalization called the major
premise is the result.

In the argument, then, which proves that Socrates is mortal, one
indispensable part of the premises will be as follows: “My father, and my
father’s father, A, B, C, and an indefinite number of other persons, were
mortal;” which is only an expression in different words of the observed
fact that they have died. This is the major premise divested of the
_petitio principii_, and cut down to as much as is really known by direct
evidence.

In order to connect this proposition with the conclusion Socrates is
mortal, the additional link necessary is such a proposition as the
following: “Socrates resembles my father, and my father’s father, and the
other individuals specified.” This proposition we assert when we say that
Socrates is a man. By saying so we likewise assert in what respect he
resembles them, namely, in the attributes connoted by the word man. And we
conclude that he further resembles them in the attribute mortality.

§ 7. We have thus obtained what we were seeking, a universal type of the
reasoning process. We find it resolvable in all cases into the following
elements: Certain individuals have a given attribute; an individual or
individuals resemble the former in certain other attributes; therefore
they resemble them also in the given attribute. This type of ratiocination
does not claim, like the syllogism, to be conclusive from the mere form of
the expression; nor can it possibly be so. That one proposition does or
does not assert the very fact which was already asserted in another, may
appear from the form of the expression, that is, from a comparison of the
language; but when the two propositions assert facts which are _bona fide_
different, whether the one fact proves the other or not can never appear
from the language, but must depend on other considerations. Whether, from
the attributes in which Socrates resembles those men who have heretofore
died, it is allowable to infer that he resembles them also in being
mortal, is a question of Induction; and is to be decided by the principles
or canons which we shall hereafter recognize as tests of the correct
performance of that great mental operation.

Meanwhile, however, it is certain, as before remarked, that if this
inference can be drawn as to Socrates, it can be drawn as to all others
who resemble the observed individuals in the same attributes in which he
resembles them; that is (to express the thing concisely) of all mankind.
If, therefore, the argument be admissible in the case of Socrates, we are
at liberty, once for all, to treat the possession of the attributes of man
as a mark, or satisfactory evidence, of the attribute of mortality. This
we do by laying down the universal proposition, All men are mortal, and
interpreting this, as occasion arises, in its application to Socrates and
others. By this means we establish a very convenient division of the
entire logical operation into two steps; first, that of ascertaining what
attributes are marks of mortality; and, secondly, whether any given
individuals possess those marks. And it will generally be advisable, in
our speculations on the reasoning process, to consider this double
operation as in fact taking place, and all reasoning as carried on in the
form into which it must necessarily be thrown to enable us to apply to it
any test of its correct performance.

Although, therefore, all processes of thought in which the ultimate
premises are particulars, whether we conclude from particulars to a
general formula, or from particulars to other particulars according to
that formula, are equally Induction; we shall yet, conformably to usage,
consider the name Induction as more peculiarly belonging to the process of
establishing the general proposition, and the remaining operation, which
is substantially that of interpreting the general proposition, we shall
call by its usual name, Deduction. And we shall consider every process by
which any thing is inferred respecting an unobserved case, as consisting
of an Induction followed by a Deduction; because, although the process
needs not necessarily be carried on in this form, it is always susceptible
of the form, and must be thrown into it when assurance of scientific
accuracy is needed and desired.

§ 8. The theory of the syllogism laid down in the preceding pages, has
obtained, among other important adhesions, three of peculiar value: those
of Sir John Herschel,(59) Dr. Whewell,(60) and Mr. Bailey;(61) Sir John
Herschel considering the doctrine, though not strictly “a discovery,”
having been anticipated by Berkeley,(62) to be “one of the greatest steps
which have yet been made in the philosophy of Logic.” “When we consider”
(to quote the further words of the same authority) “the inveteracy of the
habits and prejudices which it has cast to the winds,” there is no cause
for misgiving in the fact that other thinkers, no less entitled to
consideration, have formed a very different estimate of it. Their
principal objection can not be better or more succinctly stated than by
borrowing a sentence from Archbishop Whately.(63) “In every case where an
inference is drawn from Induction (unless that name is to be given to a
mere random guess without any grounds at all) we must form a judgment that
the instance or instances adduced are _sufficient_ to authorize the
conclusion; that it is _allowable_ to take these instances as a sample
warranting an inference respecting the whole class;” and the expression of
this judgment in words (it has been said by several of my critics) _is_
the major premise.

I quite admit that the major is an affirmation of the sufficiency of the
evidence on which the conclusion rests. That it is so, is the very essence
of my own theory. And whoever admits that the major premise is _only_
this, adopts the theory in its essentials.

But I can not concede that this recognition of the sufficiency of the
evidence—that is, of the correctness of the induction—is a part of the
induction itself; unless we ought to say that it is a part of every thing
we do, to satisfy ourselves that it has been done rightly. We conclude
from known instances to unknown by the impulse of the generalizing
propensity; and (until after a considerable amount of practice and mental
discipline) the question of the sufficiency of the evidence is only raised
by a retrospective act, turning back upon our own footsteps, and examining
whether we were warranted in doing what we have provisionally done. To
speak of this reflex operation as part of the original one, requiring to
be expressed in words in order that the verbal formula may correctly
represent the psychological process, appears to me false psychology.(64)
We review our syllogistic as well as our inductive processes, and
recognize that they have been correctly performed; but logicians do not
add a third premise to the syllogism, to express this act of recognition.
A careful copyist verifies his transcript by collating it with the
original; and if no error appears, he recognizes that the transcript has
been correctly made. But we do not call the examination of the copy a part
of the act of copying.

The conclusion in an induction is inferred from the evidence itself, and
not from a recognition of the sufficiency of the evidence; as I infer that
my friend is walking toward me because I see him, and not because I
recognize that my eyes are open, and that eyesight is a means of
knowledge. In all operations which require care, it is good to assure
ourselves that the process has been performed accurately; but the testing
of the process is not the process itself; and, besides, may have been
omitted altogether, and yet the process be correct. It is precisely
because that operation is omitted in ordinary unscientific reasoning, that
there is any thing gained in certainty by throwing reasoning into the
syllogistic form. To make sure, as far as possible, that it shall not be
omitted, we make the testing operation a part of the reasoning process
itself. We insist that the inference from particulars to particulars shall
pass through a general proposition. But this is a security for good
reasoning, not a condition of all reasoning; and in some cases not even a
security. Our most familiar inferences are all made before we learn the
use of general propositions; and a person of untutored sagacity will
skillfully apply his acquired experience to adjacent cases, though he
would bungle grievously in fixing the limits of the appropriate general
theorem. But though he may conclude rightly, he never, properly speaking,
knows whether he has done so or not; he has not tested his reasoning. Now,
this is precisely what forms of reasoning do for us. We do not need them
to enable us to reason, but to enable us to know whether we reason
correctly.

In still further answer to the objection, it may be added that—even when
the test has been applied, and the sufficiency of the evidence
recognized—if it is sufficient to support the general proposition, it is
sufficient also to support an inference from particulars to particulars
without passing through the general proposition. The inquirer who has
logically satisfied himself that the conditions of legitimate induction
were realized in the cases A, B, C, would be as much justified in
concluding directly to the Duke of Wellington as in concluding to all men.
The general conclusion is never legitimate, unless the particular one
would be so too; and in no sense, intelligible to me, can the particular
conclusion be said to be drawn from the general one. Whenever there is
ground for drawing any conclusion at all from particular instances, there
is ground for a general conclusion; but that this general conclusion
should be actually drawn, however useful, can not be an indispensable
condition of the validity of the inference in the particular case. A man
gives away sixpence by the same power by which he disposes of his whole
fortune; but it is not necessary to the legality of the smaller act, that
he should make a formal assertion of his right to the greater one.

Some additional remarks, in reply to minor objections, are appended.(65)

§ 9. The preceding considerations enable us to understand the true nature
of what is termed, by recent writers, Formal Logic, and the relation
between it and Logic in the widest sense. Logic, as I conceive it, is the
entire theory of the ascertainment of reasoned or inferred truth. Formal
Logic, therefore, which Sir William Hamilton from his own point of view,
and Archbishop Whately from his, have represented as the whole of Logic
properly so called, is really a very subordinate part of it, not being
directly concerned with the process of Reasoning or Inference in the sense
in which that process is a part of the Investigation of Truth. What, then,
is Formal Logic? The name seems to be properly applied to all that portion
of doctrine which relates to the equivalence of different modes of
expression; the rules for determining when assertions in a given form
imply or suppose the truth or falsity of other assertions. This includes
the theory of the Import of Propositions, and of their Conversion,
Æquipollence, and Opposition; of those falsely called Inductions (to be
hereafter spoken of)(66), in which the apparent generalization is a mere
abridged statement of cases known individually; and finally, of the
syllogism: while the theory of Naming, and of (what is inseparably
connected with it) Definition, though belonging still more to the other
and larger kind of logic than to this, is a necessary preliminary to this.
The end aimed at by Formal Logic, and attained by the observance of its
precepts, is not truth, but consistency. It has been seen that this is the
only direct purpose of the rules of the syllogism; the intention and
effect of which is simply to keep our inferences or conclusions in
complete consistency with our general formulæ or directions for drawing
them. The Logic of Consistency is a necessary auxiliary to the logic of
truth, not only because what is inconsistent with itself or with other
truths can not be true, but also because truth can only be successfully
pursued by drawing inferences from experience, which, if warrantable at
all, admit of being generalized, and, to test their warrantableness,
require to be exhibited in a generalized form; after which the correctness
of their application to particular cases is a question which specially
concerns the Logic of Consistency. This Logic, not requiring any
preliminary knowledge of the processes or conclusions of the various
sciences, may be studied with benefit in a much earlier stage of education
than the Logic of Truth: and the practice which has empirically obtained
of teaching it apart, through elementary treatises which do not attempt to
include any thing else, though the reasons assigned for the practice are
in general very far from philosophical, admits of philosophical
justification.



                               Chapter IV.


Of Trains Of Reasoning, And Deductive Sciences.


§ 1. In our analysis of the syllogism, it appeared that the minor premise
always affirms a resemblance between a new case and some cases previously
known; while the major premise asserts something which, having been found
true of those known cases, we consider ourselves warranted in holding true
of any other case resembling the former in certain given particulars.

If all ratiocinations resembled, as to the minor premise, the examples
which were exclusively employed in the preceding chapter; if the
resemblance, which that premise asserts, were obvious to the senses, as in
the proposition “Socrates is a man,” or were at once ascertainable by
direct observation; there would be no necessity for trains of reasoning,
and Deductive or Ratiocinative Sciences would not exist. Trains of
reasoning exist only for the sake of extending an induction founded, as
all inductions must be, on observed cases, to other cases in which we not
only can not directly observe the fact which is to be proved, but can not
directly observe even the mark which is to prove it.

§ 2. Suppose the syllogism to be, All cows ruminate, the animal which is
before me is a cow, therefore it ruminates. The minor, if true at all, is
obviously so: the only premise the establishment of which requires any
anterior process of inquiry, is the major; and provided the induction of
which that premise is the expression was correctly performed, the
conclusion respecting the animal now present will be instantly drawn;
because, as soon as she is compared with the formula, she will be
identified as being included in it. But suppose the syllogism to be the
following: All arsenic is poisonous, the substance which is before me is
arsenic, therefore it is poisonous. The truth of the minor may not here be
obvious at first sight; it may not be intuitively evident, but may itself
be known only by inference. It may be the conclusion of another argument,
which, thrown into the syllogistic form, would stand thus: Whatever when
lighted produces a dark spot on a piece of white porcelain held in the
flame, which spot is soluble in hypochloride of calcium, is arsenic; the
substance before me conforms to this condition; therefore it is arsenic.
To establish, therefore, the ultimate conclusion, The substance before me
is poisonous, requires a process, which, in order to be syllogistically
expressed, stands in need of two syllogisms; and we have a Train of
Reasoning.

When, however, we thus add syllogism to syllogism, we are really adding
induction to induction. Two separate inductions must have taken place to
render this chain of inference possible; inductions founded, probably, on
different sets of individual instances, but which converge in their
results, so that the instance which is the subject of inquiry comes within
the range of them both. The record of these inductions is contained in the
majors of the two syllogisms. First, we, or others for us, have examined
various objects which yielded under the given circumstances a dark spot
with the given property, and found that they possessed the properties
connoted by the word arsenic; they were metallic, volatile, their vapor
had a smell of garlic, and so forth. Next, we, or others for us, have
examined various specimens which possessed this metallic and volatile
character, whose vapor had this smell, etc., and have invariably found
that they were poisonous. The first observation we judge that we may
extend to all substances whatever which yield that particular kind of dark
spot; the second, to all metallic and volatile substances resembling those
we examined; and consequently, not to those only which are seen to be
such, but to those which are concluded to be such by the prior induction.
The substance before us is only seen to come within one of these
inductions; but by means of this one, it is brought within the other. We
are still, as before, concluding from particulars to particulars; but we
are now concluding from particulars observed, to other particulars which
are not, as in the simple case, _seen_ to resemble them in material
points, but _inferred_ to do so, because resembling them in something
else, which we have been led by quite a different set of instances to
consider as a mark of the former resemblance.

This first example of a train of reasoning is still extremely simple, the
series consisting of only two syllogisms. The following is somewhat more
complicated: No government, which earnestly seeks the good of its
subjects, is likely to be overthrown; some particular government earnestly
seeks the good of its subjects, therefore it is not likely to be
overthrown. The major premise in this argument we shall suppose not to be
derived from considerations _a priori_, but to be a generalization from
history, which, whether correct or erroneous, must have been founded on
observation of governments concerning whose desire of the good of their
subjects there was no doubt. It has been found, or thought to be found,
that these were not easily overthrown, and it has been deemed that those
instances warranted an extension of the same predicate to any and every
government which resembles them in the attribute of desiring earnestly the
good of its subjects. But _does_ the government in question thus resemble
them? This may be debated _pro_ and _con_ by many arguments, and must, in
any case, be proved by another induction; for we can not directly observe
the sentiments and desires of the persons who carry on the government. To
prove the minor, therefore, we require an argument in this form: Every
government which acts in a certain manner, desires the good of its
subjects; the supposed government acts in that particular manner,
therefore it desires the good of its subjects. But is it true that the
government acts in the manner supposed? This minor also may require proof;
still another induction, as thus: What is asserted by intelligent and
disinterested witnesses, may be believed to be true; that the government
acts in this manner, is asserted by such witnesses, therefore it may be
believed to be true. The argument hence consists of three steps. Having
the evidence of our senses that the case of the government under
consideration resembles a number of former cases, in the circumstance of
having something asserted respecting it by intelligent and disinterested
witnesses, we infer, first, that, as in those former instances, so in this
instance, the assertion is true. Secondly, what was asserted of the
government being that it acts in a particular manner, and other
governments or persons having been observed to act in the same manner, the
government in question is brought into known resemblance with those other
governments or persons; and since they were known to desire the good of
the people, it is thereupon, by a second induction, inferred that the
particular government spoken of, desires the good of the people. This
brings that government into known resemblance with the other governments
which were thought likely to escape revolution, and thence, by a third
induction, it is concluded that this particular government is also likely
to escape. This is still reasoning from particulars to particulars, but we
now reason to the new instance from three distinct sets of former
instances: to one only of those sets of instances do we directly perceive
the new one to be similar; but from that similarity we inductively infer
that it has the attribute by which it is assimilated to the next set, and
brought within the corresponding induction; after which by a repetition of
the same operation we infer it to be similar to the third set, and hence a
third induction conducts us to the ultimate conclusion.

§ 3. Notwithstanding the superior complication of these examples, compared
with those by which in the preceding chapter we illustrated the general
theory of reasoning, every doctrine which we then laid down holds equally
true in these more intricate cases. The successive general propositions
are not steps in the reasoning, are not intermediate links in the chain of
inference, between the particulars observed and those to which we apply
the observation. If we had sufficiently capacious memories, and a
sufficient power of maintaining order among a huge mass of details, the
reasoning could go on without any general propositions; they are mere
formulæ for inferring particulars from particulars. The principle of
general reasoning is (as before explained), that if, from observation of
certain known particulars, what was seen to be true of them can be
inferred to be true of any others, it may be inferred of all others which
are of a certain description. And in order that we may never fail to draw
this conclusion in a new case when it can be drawn correctly, and may
avoid drawing it when it can not, we determine once for all what are the
distinguishing marks by which such cases may be recognized. The subsequent
process is merely that of identifying an object, and ascertaining it to
have those marks; whether we identify it by the very marks themselves, or
by others which we have ascertained (through another and a similar
process) to be marks of those marks. The real inference is always from
particulars to particulars, from the observed instances to an unobserved
one: but in drawing this inference, we conform to a formula which we have
adopted for our guidance in such operations, and which is a record of the
criteria by which we thought we had ascertained that we might distinguish
when the inference could, and when it could not, be drawn. The real
premises are the individual observations, even though they may have been
forgotten, or, being the observations of others and not of ourselves, may,
to us, never have been known: but we have before us proof that we or
others once thought them sufficient for an induction, and we have marks to
show whether any new case is one of those to which, if then known, the
induction would have been deemed to extend. These marks we either
recognize at once, or by the aid of other marks, which by another previous
induction we collected to be marks of the first. Even these marks of marks
may only be recognized through a third set of marks; and we may have a
train of reasoning, of any length, to bring a new case within the scope of
an induction grounded on particulars its similarity to which is only
ascertained in this indirect manner.

Thus, in the preceding example, the ultimate inductive inference was, that
a certain government was not likely to be overthrown; this inference was
drawn according to a formula in which desire of the public good was set
down as a mark of not being likely to be overthrown; a mark of this mark
was, acting in a particular manner; and a mark of acting in that manner
was, being asserted to do so by intelligent and disinterested witnesses:
this mark, the government under discussion was recognized by the senses as
possessing. Hence that government fell within the last induction, and by
it was brought within all the others. The perceived resemblance of the
case to one set of observed particular cases, brought it into known
resemblance with another set, and that with a third.

In the more complex branches of knowledge, the deductions seldom consist,
as in the examples hitherto exhibited, of a single chain, _a_ a mark of
_b, b_ of _c, c_ of _d_, therefore _a_ a mark of _d_. They consist (to
carry on the same metaphor) of several chains united at the extremity, as
thus: _a_ a mark of _d, b_ of _e, c_ of _f, d e f_ of _n_, therefore _a b
c_ a mark of _n_. Suppose, for example, the following combination of
circumstances: 1st, rays of light impinging on a reflecting surface; 2d,
that surface parabolic; 3d, those rays parallel to each other and to the
axis of the surface. It is to be proved that the concourse of these three
circumstances is a mark that the reflected rays will pass through the
focus of the parabolic surface. Now, each of the three circumstances is
singly a mark of something material to the case. Rays of light impinging
on a reflecting surface are a mark that those rays will be reflected at an
angle equal to the angle of incidence. The parabolic form of the surface,
is a mark that, from any point of it, a line drawn to the focus and a line
parallel to the axis will make equal angles with the surface. And finally,
the parallelism of the rays to the axis is a mark that their angle of
incidence coincides with one of these equal angles. The three marks taken
together are therefore a mark of all these three things united. But the
three united are evidently a mark that the angle of reflection must
coincide with the other of the two equal angles, that formed by a line
drawn to the focus; and this again, by the fundamental axiom concerning
straight lines, is a mark that the reflected rays pass through the focus.
Most chains of physical deduction are of this more complicated type; and
even in mathematics such are abundant, as in all propositions where the
hypothesis includes numerous conditions: “_If_ a circle be taken, and _if_
within that circle a point be taken, not the centre, and _if_ straight
lines be drawn from that point to the circumference, then,” etc.

§ 4. The considerations now stated remove a serious difficulty from the
view we have taken of reasoning; which view might otherwise have seemed
not easily reconcilable with the fact that there are Deductive or
Ratiocinative Sciences. It might seem to follow, if all reasoning be
induction, that the difficulties of philosophical investigation must lie
in the inductions exclusively, and that when these were easy, and
susceptible of no doubt or hesitation, there could be no science, or, at
least, no difficulties in science. The existence, for example, of an
extensive Science of Mathematics, requiring the highest scientific genius
in those who contributed to its creation, and calling for a most continued
and vigorous exertion of intellect in order to appropriate it when
created, may seem hard to be accounted for on the foregoing theory. But
the considerations more recently adduced remove the mystery, by showing,
that even when the inductions themselves are obvious, there may be much
difficulty in finding whether the particular case which is the subject of
inquiry comes within them; and ample room for scientific ingenuity in so
combining various inductions, as, by means of one within which the case
evidently falls, to bring it within others in which it can not be directly
seen to be included.

When the more obvious of the inductions which can be made in any science
from direct observations, have been made, and general formulas have been
framed, determining the limits within which these inductions are
applicable; as often as a new case can be at once seen to come within one
of the formulas, the induction is applied to the new case, and the
business is ended. But new cases are continually arising, which do not
obviously come within any formula whereby the question we want solved in
respect of them could be answered. Let us take an instance from geometry:
and as it is taken only for illustration, let the reader concede to us for
the present, what we shall endeavor to prove in the next chapter, that the
first principles of geometry are results of induction. Our example shall
be the fifth proposition of the first book of Euclid. The inquiry is, Are
the angles at the base of an isosceles triangle equal or unequal? The
first thing to be considered is, what inductions we have, from which we
can infer equality or inequality. For inferring equality we have the
following formulæ: Things which being applied to each other coincide, are
equals. Things which are equal to the same thing are equals. A whole and
the sum of its parts are equals. The sums of equal things are equals. The
differences of equal things are equals. There are no other original
formulæ to prove equality. For inferring inequality we have the following:
A whole and its parts are unequals. The sums of equal things and unequal
things are unequals. The differences of equal things and unequal things
are unequals. In all, eight formulæ. The angles at the base of an
isosceles triangle do not obviously come within any of these. The formulæ
specify certain marks of equality and of inequality, but the angles can
not be perceived intuitively to have any of those marks. On examination it
appears that they have; and we ultimately succeed in bringing them within
the formula, “The differences of equal things are equal.” Whence comes the
difficulty of recognizing these angles as the differences of equal things?
Because each of them is the difference not of one pair only, but of
innumerable pairs of angles; and out of these we had to imagine and select
two, which could either be intuitively perceived to be equals, or
possessed some of the marks of equality set down in the various formulæ.
By an exercise of ingenuity, which, on the part of the first inventor,
deserves to be regarded as considerable, two pairs of angles were hit
upon, which united these requisites. First, it could be perceived
intuitively that their differences were the angles at the base; and,
secondly, they possessed one of the marks of equality, namely, coincidence
when applied to one another. This coincidence, however, was not perceived
intuitively, but inferred, in conformity to another formula.

For greater clearness, I subjoin an analysis of the demonstration. Euclid,
it will be remembered, demonstrates his fifth proposition by means of the
fourth. This it is not allowable for us to do, because we are undertaking
to trace deductive truths not to prior deductions, but to their original
inductive foundation. We must, therefore, use the premises of the fourth
proposition instead of its conclusion, and prove the fifth directly from
first principles. To do so requires six formulas. (We presuppose an
equilateral triangle, whose vertices are A, D, E, with point B on the side
AD, and point C on the side AE, such that BC is parallel to DE. We must
begin, as in Euclid, by prolonging the equal sides AB, AC, to equal
distances, and joining the extremities BE, DC.)

FIRST FORMULA.—_The sums of equals are equal._

AD and AE are sums of equals by the supposition. Having that mark of
equality, they are concluded by this formula to be equal.

SECOND FORMULA.—_Equal straight lines or angles, being applied to one
another, coincide._

AC, AB, are within this formula by supposition; AD, AE, have been brought
within it by the preceding step. The angle at A considered as an angle of
the triangle ABE, and the same angle considered as an angle of the
triangle ACD, are of course within the formula. All these pairs,
therefore, possess the property which, according to the second formula, is
a mark that when applied to one another they will coincide. Conceive them,
then, applied to one another, by turning over the triangle ABE, and laying
it on the triangle ACD in such a manner that AB of the one shall lie upon
AC of the other. Then, by the equality of the angles, AE will lie on AD.
But AB and AC, AE and AD are equals; therefore they will coincide
altogether, and of course at their extremities, D, E, and B, C.

THIRD FORMULA.—_Straight lines, having their extremities coincident,
coincide._

BE and CD have been brought within this formula by the preceding
induction; they will, therefore, coincide.

FOURTH FORMULA.—_Angles, having their sides coincident, coincide._

The third induction having shown that BE and CD coincide, and the second
that AB, AC, coincide, the angles ABE and ACD are thereby brought within
the fourth formula, and accordingly coincide.

FIFTH FORMULA.—_Things which coincide are equal._

The angles ABE and ACD are brought within this formula by the induction
immediately preceding. This train of reasoning being also applicable,
_mutatis mutandis_, to the angles EBC, DCB, these also are brought within
the fifth formula. And, finally,

SIXTH FORMULA.—_The differences of equals are equal._

The angle ABC being the difference of ABE, CBE, and the angle ACB being
the difference of ACD, DCB; which have been proved to be equals; ABC and
ACB are brought within the last formula by the whole of the previous
process.

The difficulty here encountered is chiefly that of figuring to ourselves
the two angles at the base of the triangle ABC as remainders made by
cutting one pair of angles out of another, while each pair shall be
corresponding angles of triangles which have two sides and the intervening
angle equal. It is by this happy contrivance that so many different
inductions are brought to bear upon the same particular case. And this not
being at all an obvious thought, it may be seen from an example so near
the threshold of mathematics, how much scope there may well be for
scientific dexterity in the higher branches of that and other sciences, in
order so to combine a few simple inductions, as to bring within each of
them innumerable cases which are not obviously included in it; and how
long, and numerous, and complicated may be the processes necessary for
bringing the inductions together, even when each induction may itself be
very easy and simple. All the inductions involved in all geometry are
comprised in those simple ones, the formulæ of which are the Axioms, and a
few of the so-called Definitions. The remainder of the science is made up
of the processes employed for bringing unforeseen cases within these
inductions; or (in syllogistic language) for proving the minors necessary
to complete the syllogisms; the majors being the definitions and axioms.
In those definitions and axioms are laid down the whole of the marks, by
an artful combination of which it has been found possible to discover and
prove all that is proved in geometry. The marks being so few, and the
inductions which furnish them being so obvious and familiar; the
connecting of several of them together, which constitutes Deductions, or
Trains of Reasoning, forms the whole difficulty of the science, and, with
a trifling exception, its whole bulk; and hence Geometry is a Deductive
Science.

§ 5. It will be seen hereafter(67) that there are weighty scientific
reasons for giving to every science as much of the character of a
Deductive Science as possible; for endeavoring to construct the science
from the fewest and the simplest possible inductions, and to make these,
by any combinations however complicated, suffice for proving even such
truths, relating to complex cases, as could be proved, if we chose, by
inductions from specific experience. Every branch of natural philosophy
was originally experimental; each generalization rested on a special
induction, and was derived from its own distinct set of observations and
experiments. From being sciences of pure experiment, as the phrase is, or,
to speak more correctly, sciences in which the reasonings mostly consist
of no more than one step, and are expressed by single syllogisms, all
these sciences have become to some extent, and some of them in nearly the
whole of their extent, sciences of pure reasoning; whereby multitudes of
truths, already known by induction from as many different sets of
experiments, have come to be exhibited as deductions or corollaries from
inductive propositions of a simpler and more universal character. Thus
mechanics, hydrostatics, optics, acoustics, thermology, have successively
been rendered mathematical; and astronomy was brought by Newton within the
laws of general mechanics. Why it is that the substitution of this
circuitous mode of proceeding for a process apparently much easier and
more natural, is held, and justly, to be the greatest triumph of the
investigation of nature, we are not, in this stage of our inquiry,
prepared to examine. But it is necessary to remark, that although, by this
progressive transformation, all sciences tend to become more and more
Deductive, they are not, therefore, the less Inductive; every step in the
Deduction is still an Induction. The opposition is not between the terms
Deductive and Inductive, but between Deductive and Experimental. A science
is experimental, in proportion as every new case, which presents any
peculiar features, stands in need of a new set of observations and
experiments—a fresh induction. It is deductive, in proportion as it can
draw conclusions, respecting cases of a new kind, by processes which bring
those cases under old inductions; by ascertaining that cases which can not
be observed to have the requisite marks, have, however, marks of those
marks.

We can now, therefore, perceive what is the generic distinction between
sciences which can be made Deductive, and those which must as yet remain
Experimental. The difference consists in our having been able, or not yet
able, to discover marks of marks. If by our various inductions we have
been able to proceed no further than to such propositions as these, _a_ a
mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of _d_, or c
and _d_ marks of one another, without any thing to connect _a_ or _b_ with
_c_ or _d_; we have a science of detached and mutually independent
generalizations, such as these, that acids redden vegetable blues, and
that alkalies color them green; from neither of which propositions could
we, directly or indirectly, infer the other: and a science, so far as it
is composed of such propositions, is purely experimental. Chemistry, in
the present state of our knowledge, has not yet thrown off this character.
There are other sciences, however, of which the propositions are of this
kind: _a_ a mark of _b, b_ a mark of _c, c_ of _d, d_ of _e_, etc. In
these sciences we can mount the ladder from _a_ to _e_ by a process of
ratiocination; we can conclude that _a_ is a mark of _e_, and that every
object which has the mark _a_ has the property _e_, although, perhaps, we
never were able to observe _a_ and _e_ together, and although even _d_,
our only direct mark of _e_, may not be perceptible in those objects, but
only inferable. Or, varying the first metaphor, we may be said to get from
_a_ to _e_ underground: the marks _b_, _c_, _d_, which indicate the route,
must all be possessed somewhere by the objects concerning which we are
inquiring; but they are below the surface: _a_ is the only mark that is
visible, and by it we are able to trace in succession all the rest.

§ 6. We can now understand how an experimental may transform itself into a
deductive science by the mere progress of experiment. In an experimental
science, the inductions, as we have said, lie detached, as, _a_ a mark of
_b, c_ a mark of _d_, _e_ a mark of _f_, and so on: now, a new set of
instances, and a consequent new induction, may at any time bridge over the
interval between two of these unconnected arches; _b_, for example, may be
ascertained to be a mark of _c_, which enables us thenceforth to prove
deductively that _a_ is a mark of _c_. Or, as sometimes happens, some
comprehensive induction may raise an arch high in the air, which bridges
over hosts of them at once; _b_, _d_, _f_, and all the rest, turning out
to be marks of some one thing, or of things between which a connection has
already been traced. As when Newton discovered that the motions, whether
regular or apparently anomalous, of all the bodies of the solar system
(each of which motions had been inferred by a separate logical operation,
from separate marks), were all marks of moving round a common centre, with
a centripetal force varying directly as the mass, and inversely as the
square of the distance from that centre. This is the greatest example
which has yet occurred of the transformation, at one stroke, of a science
which was still to a great degree merely experimental, into a deductive
science.

Transformations of the same nature, but on a smaller scale, continually
take place in the less advanced branches of physical knowledge, without
enabling them to throw off the character of experimental sciences. Thus
with regard to the two unconnected propositions before cited, namely,
Acids redden vegetable blues, Alkalies make them green; it is remarked by
Liebig, that all blue coloring matters which are reddened by acids (as
well as, reciprocally, all red coloring matters which are rendered blue by
alkalies) contain nitrogen: and it is quite possible that this
circumstance may one day furnish a bond of connection between the two
propositions in question, by showing that the antagonistic action of acids
and alkalies in producing or destroying the color blue, is the result of
some one, more general, law. Although this connecting of detached
generalizations is so much gain, it tends but little to give a deductive
character to any science as a whole; because the new courses of
observation and experiment, which thus enable us to connect together a few
general truths, usually make known to us a still greater number of
unconnected new ones. Hence chemistry, though similar extensions and
simplifications of its generalizations are continually taking place, is
still in the main an experimental science; and is likely so to continue
unless some comprehensive induction should be hereafter arrived at, which,
like Newton’s, shall connect a vast number of the smaller known inductions
together, and change the whole method of the science at once. Chemistry
has already one great generalization, which, though relating to one of the
subordinate aspects of chemical phenomena, possesses within its limited
sphere this comprehensive character; the principle of Dalton, called the
atomic theory, or the doctrine of chemical equivalents: which by enabling
us to a certain extent to foresee the proportions in which two substances
will combine, before the experiment has been tried, constitutes
undoubtedly a source of new chemical truths obtainable by deduction, as
well as a connecting principle for all truths of the same description
previously obtained by experiment.

§ 7. The discoveries which change the method of a science from
experimental to deductive, mostly consist in establishing, either by
deduction or by direct experiment, that the varieties of a particular
phenomenon uniformly accompany the varieties of some other phenomenon
better known. Thus the science of sound, which previously stood in the
lowest rank of merely experimental science, became deductive when it was
proved by experiment that every variety of sound was consequent on, and
therefore a mark of, a distinct and definable variety of oscillatory
motion among the particles of the transmitting medium. When this was
ascertained, it followed that every relation of succession or co-existence
which obtained between phenomena of the more known class, obtained also
between the phenomena which correspond to them in the other class. Every
sound, being a mark of a particular oscillatory motion, became a mark of
every thing which, by the laws of dynamics, was known to be inferable from
that motion; and every thing which by those same laws was a mark of any
oscillatory motion among the particles of an elastic medium, became a mark
of the corresponding sound. And thus many truths, not before suspected,
concerning sound, become deducible from the known laws of the propagation
of motion through an elastic medium; while facts already empirically known
respecting sound, become an indication of corresponding properties of
vibrating bodies, previously undiscovered.

But the grand agent for transforming experimental into deductive sciences,
is the science of number. The properties of number, alone among all known
phenomena, are, in the most rigorous sense, properties of all things
whatever. All things are not colored, or ponderable, or even extended; but
all things are numerable. And if we consider this science in its whole
extent, from common arithmetic up to the calculus of variations, the
truths already ascertained seem all but infinite, and admit of indefinite
extension.

These truths, though affirmable of all things whatever, of course apply to
them only in respect of their quantity. But if it comes to be discovered
that variations of quality in any class of phenomena, correspond regularly
to variations of quantity either in those same or in some other phenomena;
every formula of mathematics applicable to quantities which vary in that
particular manner, becomes a mark of a corresponding general truth,
respecting the variations in quality which accompany them: and the science
of quantity being (as far as any science can be) altogether deductive, the
theory of that particular kind of qualities becomes, to this extent,
deductive likewise.

The most striking instance in point which history affords (though not an
example of an experimental science rendered deductive, but of an
unparalleled extension given to the deductive process in a science which
was deductive already), is the revolution in geometry which originated
with Descartes, and was completed by Clairaut. These great mathematicians
pointed out the importance of the fact, that to every variety of position
in points, direction in lines, or form in curves or surfaces (all of which
are Qualities), there corresponds a peculiar relation of quantity between
either two or three rectilineal co-ordinates; insomuch that if the law
were known according to which those co-ordinates vary relatively to one
another, every other geometrical property of the line or surface in
question, whether relating to quantity or quality, would be capable of
being inferred. Hence it followed that every geometrical question could be
solved, if the corresponding algebraical one could; and geometry received
an accession (actual or potential) of new truths, corresponding to every
property of numbers which the progress of the calculus had brought, or
might in future bring, to light. In the same general manner, mechanics,
astronomy, and in a less degree, every branch of natural philosophy
commonly so called, have been made algebraical. The varieties of physical
phenomena with which those sciences are conversant, have been found to
answer to determinable varieties in the quantity of some circumstance or
other; or at least to varieties of form or position, for which
corresponding equations of quantity had already been, or were susceptible
of being, discovered by geometers.

In these various transformations, the propositions of the science of
number do but fulfill the function proper to all propositions forming a
train of reasoning, viz., that of enabling us to arrive in an indirect
method, by marks of marks, at such of the properties of objects as we can
not directly ascertain (or not so conveniently) by experiment. We travel
from a given visible or tangible fact, through the truths of numbers, to
the facts sought. The given fact is a mark that a certain relation
subsists between the quantities of some of the elements concerned; while
the fact sought presupposes a certain relation between the quantities of
some other elements: now, if these last quantities are dependent in some
known manner upon the former, or _vicè versa_, we can argue from the
numerical relation between the one set of quantities, to determine that
which subsists between the other set; the theorems of the calculus
affording the intermediate links. And thus one of the two physical facts
becomes a mark of the other, by being a mark of a mark of a mark of it.



                                Chapter V.


Of Demonstration, And Necessary Truths.


§ 1. If, as laid down in the two preceding chapters, the foundation of all
sciences, even deductive or demonstrative sciences, is Induction; if every
step in the ratiocinations even of geometry is an act of induction; and if
a train of reasoning is but bringing many inductions to bear upon the same
subject of inquiry, and drawing a case within one induction by means of
another; wherein lies the peculiar certainty always ascribed to the
sciences which are entirely, or almost entirely, deductive? Why are they
called the Exact Sciences? Why are mathematical certainty, and the
evidence of demonstration, common phrases to express the very highest
degree of assurance attainable by reason? Why are mathematics by almost
all philosophers, and (by some) even those branches of natural philosophy
which, through the medium of mathematics, have been converted into
deductive sciences, considered to be independent of the evidence of
experience and observation, and characterized as systems of Necessary
Truth?

The answer I conceive to be, that this character of necessity, ascribed to
the truths of mathematics, and (even with some reservations to be
hereafter made) the peculiar certainty attributed to them, is an illusion;
in order to sustain which, it is necessary to suppose that those truths
relate to, and express the properties of, purely imaginary objects. It is
acknowledged that the conclusions of geometry are deduced, partly at
least, from the so-called Definitions, and that those definitions are
assumed to be correct representations, as far as they go, of the objects
with which geometry is conversant. Now we have pointed out that, from a
definition as such, no proposition, unless it be one concerning the
meaning of a word, can ever follow; and that what apparently follows from
a definition, follows in reality from an implied assumption that there
exists a real thing conformable thereto. This assumption, in the case of
the definitions of geometry, is not strictly true: there exist no real
things exactly conformable to the definitions. There exist no points
without magnitude; no lines without breadth, nor perfectly straight; no
circles with all their radii exactly equal, nor squares with all their
angles perfectly right. It will perhaps be said that the assumption does
not extend to the actual, but only to the possible, existence of such
things. I answer that, according to any test we have of possibility, they
are not even possible. Their existence, so far as we can form any
judgment, would seem to be inconsistent with the physical constitution of
our planet at least, if not of the universe. To get rid of this
difficulty, and at the same time to save the credit of the supposed system
of necessary truth, it is customary to say that the points, lines,
circles, and squares which are the subject of geometry, exist in our
conceptions merely, and are part of our minds; which minds, by working on
their own materials, construct an _a priori_ science, the evidence of
which is purely mental, and has nothing whatever to do with outward
experience. By howsoever high authorities this doctrine may have been
sanctioned, it appears to me psychologically incorrect. The points, lines,
circles, and squares which any one has in his mind, are (I apprehend)
simply copies of the points, lines, circles, and squares which he has
known in his experience. Our idea of a point, I apprehend to be simply our
idea of the _minimum visibile_, the smallest portion of surface which we
can see. A line, as defined by geometers, is wholly inconceivable. We can
reason about a line as if it had no breadth; because we have a power,
which is the foundation of all the control we can exercise over the
operations of our minds; the power, when a perception is present to our
senses, or a conception to our intellects, of _attending_ to a part only
of that perception or conception, instead of the whole. But we can not
_conceive_ a line without breadth; we can form no mental picture of such a
line: all the lines which we have in our minds are lines possessing
breadth. If any one doubts this, we may refer him to his own experience. I
much question if any one who fancies that he can conceive what is called a
mathematical line, thinks so from the evidence of his consciousness: I
suspect it is rather because he supposes that unless such a conception
were possible, mathematics could not exist as a science: a supposition
which there will be no difficulty in showing to be entirely groundless.

Since, then, neither in nature, nor in the human mind, do there exist any
objects exactly corresponding to the definitions of geometry, while yet
that science can not be supposed to be conversant about nonentities;
nothing remains but to consider geometry as conversant with such lines,
angles, and figures, as really exist; and the definitions, as they are
called, must be regarded as some of our first and most obvious
generalizations concerning those natural objects. The correctness of those
generalizations, as generalizations, is without a flaw: the equality of
all the radii of a circle is true of all circles, so far as it is true of
any one: but it is not exactly true of any circle; it is only nearly true;
so nearly that no error of any importance in practice will be incurred by
feigning it to be exactly true. When we have occasion to extend these
inductions, or their consequences, to cases in which the error would be
appreciable—to lines of perceptible breadth or thickness, parallels which
deviate sensibly from equidistance, and the like—we correct our
conclusions, by combining with them a fresh set of propositions relating
to the aberration; just as we also take in propositions relating to the
physical or chemical properties of the material, if those properties
happen to introduce any modification into the result; which they easily
may, even with respect to figure and magnitude, as in the case, for
instance, of expansion by heat. So long, however, as there exists no
practical necessity for attending to any of the properties of the object
except its geometrical properties, or to any of the natural irregularities
in those, it is convenient to neglect the consideration of the other
properties and of the irregularities, and to reason as if these did not
exist: accordingly, we formally announce in the definitions, that we
intend to proceed on this plan. But it is an error to suppose, because we
resolve to confine our attention to a certain number of the properties of
an object, that we therefore conceive, or have an idea of, the object,
denuded of its other properties. We are thinking, all the time, of
precisely such objects as we have seen and touched, and with all the
properties which naturally belong to them; but, for scientific
convenience, we feign them to be divested of all properties, except those
which are material to our purpose, and in regard to which we design to
consider them.

The peculiar accuracy, supposed to be characteristic of the first
principles of geometry, thus appears to be fictitious. The assertions on
which the reasonings of the science are founded, do not, any more than in
other sciences, exactly correspond with the fact; but we suppose that they
do so, for the sake of tracing the consequences which follow from the
supposition. The opinion of Dugald Stewart respecting the foundations of
geometry, is, I conceive, substantially correct; that it is built on
hypotheses; that it owes to this alone the peculiar certainty supposed to
distinguish it; and that in any science whatever, by reasoning from a set
of hypotheses, we may obtain a body of conclusions as certain as those of
geometry, that is, as strictly in accordance with the hypotheses, and as
irresistibly compelling assent, _on condition_ that those hypotheses are
true.(68)

When, therefore, it is affirmed that the conclusions of geometry are
necessary truths, the necessity consists in reality only in this, that
they correctly follow from the suppositions from which they are deduced.
Those suppositions are so far from being necessary, that they are not even
true; they purposely depart, more or less widely, from the truth. The only
sense in which necessity can be ascribed to the conclusions of any
scientific investigation, is that of legitimately following from some
assumption, which, by the conditions of the inquiry, is not to be
questioned. In this relation, of course, the derivative truths of every
deductive science must stand to the inductions, or assumptions, on which
the science is founded, and which, whether true or untrue, certain or
doubtful in themselves, are always supposed certain for the purposes of
the particular science. And therefore the conclusions of all deductive
sciences were said by the ancients to be necessary propositions. We have
observed already that to be predicated necessarily was characteristic of
the predicable Proprium, and that a proprium was any property of a thing
which could be deduced from its essence, that is, from the properties
included in its definition.

§ 2. The important doctrine of Dugald Stewart, which I have endeavored to
enforce, has been contested by Dr. Whewell, both in the dissertation
appended to his excellent _Mechanical Euclid_, and in his elaborate work
on the _Philosophy of the Inductive Sciences_; in which last he also
replies to an article in the Edinburgh Review (ascribed to a writer of
great scientific eminence), in which Stewart’s opinion was defended
against his former strictures. The supposed refutation of Stewart consists
in proving against him (as has also been done in this work) that the
premises of geometry are not definitions, but assumptions of the real
existence of things corresponding to those definitions. This, however, is
doing little for Dr. Whewell’s purpose; for it is these very assumptions
which are asserted to be hypotheses, and which he, if he denies that
geometry is founded on hypotheses, must show to be absolute truths. All he
does, however, is to observe, that they, at any rate, are not _arbitrary_
hypotheses; that we should not be at liberty to substitute other
hypotheses for them; that not only “a definition, to be admissible, must
necessarily refer to and agree with some conception which we can
distinctly frame in our thoughts,” but that the straight lines, for
instance, which we define, must be “those by which angles are contained,
those by which triangles are bounded, those of which parallelism may be
predicated, and the like.”(69) And this is true; but this has never been
contradicted. Those who say that the premises of geometry are hypotheses,
are not bound to maintain them to be hypotheses which have no relation
whatever to fact. Since an hypothesis framed for the purpose of scientific
inquiry must relate to something which has real existence (for there can
be no science respecting nonentities), it follows that any hypothesis we
make respecting an object, to facilitate our study of it, must not involve
any thing which is distinctly false, and repugnant to its real nature: we
must not ascribe to the thing any property which it has not; our liberty
extends only to slightly exaggerating some of those which it has (by
assuming it to be completely what it really is very nearly), and
suppressing others, under the indispensable obligation of restoring them
whenever, and in as far as, their presence or absence would make any
material difference in the truth of our conclusions. Of this nature,
accordingly, are the first principles involved in the definitions of
geometry. That the hypotheses should be of this particular character, is,
however, no further necessary, than inasmuch as no others could enable us
to deduce conclusions which, with due corrections, would be true of real
objects: and in fact, when our aim is only to illustrate truths, and not
to investigate them, we are not under any such restriction. We might
suppose an imaginary animal, and work out by deduction, from the known
laws of physiology, its natural history; or an imaginary commonwealth, and
from the elements composing it, might argue what would be its fate. And
the conclusions which we might thus draw from purely arbitrary hypotheses,
might form a highly useful intellectual exercise: but as they could only
teach us what _would_ be the properties of objects which do not really
exist, they would not constitute any addition to our knowledge of nature:
while, on the contrary, if the hypothesis merely divests a real object of
some portion of its properties, without clothing it in false ones, the
conclusions will always express, under known liability to correction,
actual truth.

§ 3. But though Dr. Whewell has not shaken Stewart’s doctrine as to the
hypothetical character of that portion of the first principles of geometry
which are involved in the so-called definitions, he has, I conceive,
greatly the advantage of Stewart on another important point in the theory
of geometrical reasoning; the necessity of admitting, among those first
principles, axioms as well as definitions. Some of the axioms of Euclid
might, no doubt, be exhibited in the form of definitions, or might be
deduced, by reasoning, from propositions similar to what are so called.
Thus, if instead of the axiom, Magnitudes which can be made to coincide
are equal, we introduce a definition, “Equal magnitudes are those which
may be so applied to one another as to coincide;” the three axioms which
follow (Magnitudes which are equal to the same are equal to one another—If
equals are added to equals, the sums are equal—If equals are taken from
equals, the remainders are equal), may be proved by an imaginary
superposition, resembling that by which the fourth proposition of the
first book of Euclid is demonstrated. But though these and several others
may be struck out of the list of first principles, because, though not
requiring demonstration, they are susceptible of it; there will be found
in the list of axioms two or three fundamental truths, not capable of
being demonstrated: among which must be reckoned the proposition that two
straight lines can not inclose a space (or its equivalent, Straight lines
which coincide in two points coincide altogether), and some property of
parallel lines, other than that which constitutes their definition: one of
the most suitable for the purpose being that selected by Professor
Playfair: “Two straight lines which intersect each other can not both of
them be parallel to a third straight line.”(70)

The axioms, as well those which are indemonstrable as those which admit of
being demonstrated, differ from that other class of fundamental principles
which are involved in the definitions, in this, that they are true without
any mixture of hypothesis. That things which are equal to the same thing
are equal to one another, is as true of the lines and figures in nature,
as it would be of the imaginary ones assumed in the definitions. In this
respect, however, mathematics are only on a par with most other sciences.
In almost all sciences there are some general propositions which are
exactly true, while the greater part are only more or less distant
approximations to the truth. Thus in mechanics, the first law of motion
(the continuance of a movement once impressed, until stopped or slackened
by some resisting force) is true without qualification or error. The
rotation of the earth in twenty-four hours, of the same length as in our
time, has gone on since the first accurate observations, without the
increase or diminution of one second in all that period. These are
inductions which require no fiction to make them be received as accurately
true: but along with them there are others, as for instance the
propositions respecting the figure of the earth, which are but
approximations to the truth; and in order to use them for the further
advancement of our knowledge, we must feign that they are exactly true,
though they really want something of being so.

§ 4. It remains to inquire, what is the ground of our belief in
axioms—what is the evidence on which they rest? I answer, they are
experimental truths; generalizations from observation. The proposition,
Two straight lines can not inclose a space—or, in other words, Two
straight lines which have once met, do not meet again, but continue to
diverge—is an induction from the evidence of our senses.

This opinion runs counter to a scientific prejudice of long standing and
great strength, and there is probably no proposition enunciated in this
work for which a more unfavorable reception is to be expected. It is,
however, no new opinion; and even if it were so, would be entitled to be
judged, not by its novelty, but by the strength of the arguments by which
it can be supported. I consider it very fortunate that so eminent a
champion of the contrary opinion as Dr. Whewell has found occasion for a
most elaborate treatment of the whole theory of axioms, in attempting to
construct the philosophy of the mathematical and physical sciences on the
basis of the doctrine against which I now contend. Whoever is anxious that
a discussion should go to the bottom of the subject, must rejoice to see
the opposite side of the question worthily represented. If what is said by
Dr. Whewell, in support of an opinion which he has made the foundation of
a systematic work, can be shown not to be conclusive, enough will have
been done, without going elsewhere in quest of stronger arguments and a
more powerful adversary.

It is not necessary to show that the truths which we call axioms are
originally _suggested_ by observation, and that we should never have known
that two straight lines can not inclose a space if we had never seen a
straight line: thus much being admitted by Dr. Whewell, and by all, in
recent times, who have taken his view of the subject. But they contend,
that it is not experience which _proves_ the axiom; but that its truth is
perceived _a priori_, by the constitution of the mind itself, from the
first moment when the meaning of the proposition is apprehended; and
without any necessity for verifying it by repeated trials, as is requisite
in the case of truths really ascertained by observation.

They can not, however, but allow that the truth of the axiom, Two straight
lines can not inclose a space, even if evident independently of
experience, is also evident from experience. Whether the axiom needs
confirmation or not, it receives confirmation in almost every instant of
our lives; since we can not look at any two straight lines which intersect
one another, without seeing that from that point they continue to diverge
more and more. Experimental proof crowds in upon us in such endless
profusion, and without one instance in which there can be even a suspicion
of an exception to the rule, that we should soon have stronger ground for
believing the axiom, even as an experimental truth, than we have for
almost any of the general truths which we confessedly learn from the
evidence of our senses. Independently of _a priori_ evidence, we should
certainly believe it with an intensity of conviction far greater than we
accord to any ordinary physical truth: and this too at a time of life much
earlier than that from which we date almost any part of our acquired
knowledge, and much too early to admit of our retaining any recollection
of the history of our intellectual operations at that period. Where then
is the necessity for assuming that our recognition of these truths has a
different origin from the rest of our knowledge, when its existence is
perfectly accounted for by supposing its origin to be the same? when the
causes which produce belief in all other instances, exist in this
instance, and in a degree of strength as much superior to what exists in
other cases, as the intensity of the belief itself is superior? The burden
of proof lies on the advocates of the contrary opinion: it is for them to
point out some fact, inconsistent with the supposition that this part of
our knowledge of nature is derived from the same sources as every other
part.(71)

This, for instance, they would be able to do, if they could prove
chronologically that we had the conviction (at least practically) so early
in infancy as to be anterior to those impressions on the senses, upon
which, on the other theory, the conviction is founded. This, however, can
not be proved: the point being too far back to be within the reach of
memory, and too obscure for external observation. The advocates of the _a
priori_ theory are obliged to have recourse to other arguments. These are
reducible to two, which I shall endeavor to state as clearly and as
forcibly as possible.

§ 5. In the first place it is said, that if our assent to the proposition
that two straight lines can not inclose a space, were derived from the
senses, we could only be convinced of its truth by actual trial, that is,
by seeing or feeling the straight lines; whereas, in fact, it is seen to
be true by merely thinking of them. That a stone thrown into water goes to
the bottom, may be perceived by our senses, but mere thinking of a stone
thrown into the water would never have led us to that conclusion: not so,
however, with the axioms relating to straight lines: if I could be made to
conceive what a straight line is, without having seen one, I should at
once recognize that two such lines can not inclose a space. Intuition is
“imaginary looking;”(72) but experience must be real looking: if we see a
property of straight lines to be true by merely fancying ourselves to be
looking at them, the ground of our belief can not be the senses, or
experience; it must be something mental.

To this argument it might be added in the case of this particular axiom
(for the assertion would not be true of all axioms), that the evidence of
it from actual ocular inspection is not only unnecessary, but
unattainable. What says the axiom? That two straight lines _can not_
inclose a space; that after having once intersected, if they are prolonged
to infinity they do not meet, but continue to diverge from one another.
How can this, in any single case, be proved by actual observation? We may
follow the lines to any distance we please; but we can not follow them to
infinity: for aught our senses can testify, they may, immediately beyond
the farthest point to which we have traced them, begin to approach, and at
last meet. Unless, therefore, we had some other proof of the impossibility
than observation affords us, we should have no ground for believing the
axiom at all.

To these arguments, which I trust I can not be accused of understating, a
satisfactory answer will, I conceive, be found, if we advert to one of the
characteristic properties of geometrical forms—their capacity of being
painted in the imagination with a distinctness equal to reality: in other
words, the exact resemblance of our ideas of form to the sensations which
suggest them. This, in the first place, enables us to make (at least with
a little practice) mental pictures of all possible combinations of lines
and angles, which resemble the realities quite as well as any which we
could make on paper; and in the next place, make those pictures just as
fit subjects of geometrical experimentation as the realities themselves;
inasmuch as pictures, if sufficiently accurate, exhibit of course all the
properties which would be manifested by the realities at one given
instant, and on simple inspection: and in geometry we are concerned only
with such properties, and not with that which pictures could not exhibit,
the mutual action of bodies one upon another. The foundations of geometry
would therefore be laid in direct experience, even if the experiments
(which in this case consist merely in attentive contemplation) were
practiced solely upon what we call our ideas, that is, upon the diagrams
in our minds, and not upon outward objects. For in all systems of
experimentation we take some objects to serve as representatives of all
which resemble them; and in the present case the conditions which qualify
a real object to be the representative of its class, are completely
fulfilled by an object existing only in our fancy. Without denying,
therefore, the possibility of satisfying ourselves that two straight lines
can not inclose a space, by merely thinking of straight lines without
actually looking at them; I contend, that we do not believe this truth on
the ground of the imaginary intuition simply, but because we know that the
imaginary lines exactly resemble real ones, and that we may conclude from
them to real ones with quite as much certainty as we could conclude from
one real line to another. The conclusion, therefore, is still an induction
from observation. And we should not be authorized to substitute
observation of the image in our mind, for observation of the reality, if
we had not learned by long-continued experience that the properties of the
reality are faithfully represented in the image; just as we should be
scientifically warranted in describing an animal which we have never seen,
from a picture made of it with a daguerreotype; but not until we had
learned by ample experience, that observation of such a picture is
precisely equivalent to observation of the original.

These considerations also remove the objection arising from the
impossibility of ocularly following the lines in their prolongation to
infinity. For though, in order actually to see that two given lines never
meet, it would be necessary to follow them to infinity; yet without doing
so we may know that if they ever do meet, or if, after diverging from one
another, they begin again to approach, this must take place not at an
infinite, but at a finite distance. Supposing, therefore, such to be the
case, we can transport ourselves thither in imagination, and can frame a
mental image of the appearance which one or both of the lines must present
at that point, which we may rely on as being precisely similar to the
reality. Now, whether we fix our contemplation upon this imaginary
picture, or call to mind the generalizations we have had occasion to make
from former ocular observation, we learn by the evidence of experience,
that a line which, after diverging from another straight line, begins to
approach to it, produces the impression on our senses which we describe by
the expression, “a bent line,” not by the expression, “a straight
line.”(73)

The preceding argument, which is, to my mind unanswerable, merges,
however, in a still more comprehensive one, which is stated most clearly
and conclusively by Professor Bain. The psychological reason why axioms,
and indeed many propositions not ordinarily classed as such, may be
learned from the idea only without referring to the fact, is that in the
process of acquiring the idea we have learned the fact. The proposition is
assented to as soon as the terms are understood, because in learning to
understand the terms we have acquired the experience which proves the
proposition to be true. “We required,” says Mr. Bain,(74) “concrete
experience in the first instance, to attain to the notion of whole and
part; but the notion, once arrived at, implies that the whole is greater.
In fact, we could not have the notion without an experience tantamount to
this conclusion.... When we have mastered the notion of straightness, we
have also mastered that aspect of it expressed by the affirmation that two
straight lines can not inclose a space. No intuitive or innate powers or
perceptions are needed in such case.... We can not have the full meaning
of Straightness, without going through a comparison of straight objects
among themselves, and with their opposites, bent or crooked objects. The
result of this comparison is, _inter alia_, that straightness in two lines
is seen to be incompatible with inclosing a space; the inclosure of space
involves crookedness in at least one of the lines.” And similarly, in the
case of every first principle,(75) “the same knowledge that makes it
understood, suffices to verify it.” The more this observation is
considered the more (I am convinced) it will be felt to go to the very
root of the controversy.

§ 6. The first of the two arguments in support of the theory that axioms
are _a priori_ truths, having, I think, been sufficiently answered; I
proceed to the second, which is usually the most relied on. Axioms (it is
asserted) are conceived by us not only as true, but as universally and
necessarily true. Now, experience can not possibly give to any proposition
this character. I may have seen snow a hundred times, and may have seen
that it was white, but this can not give me entire assurance even that all
snow is white; much less that snow _must_ be white. “However many
instances we may have observed of the truth of a proposition, there is
nothing to assure us that the next case shall not be an exception to the
rule. If it be strictly true that every ruminant animal yet known has
cloven hoofs, we still can not be sure that some creature will not
hereafter be discovered which has the first of these attributes, without
having the other.... Experience must always consist of a limited number of
observations; and, however numerous these may be, they can show nothing
with regard to the infinite number of cases in which the experiment has
not been made.” Besides, Axioms are not only universal, they are also
necessary. Now “experience can not offer the smallest ground for the
necessity of a proposition. She can observe and record what has happened;
but she can not find, in any case, or in any accumulation of cases, any
reason for what _must_ happen. She may see objects side by side; but she
can not see a reason why they must ever be side by side. She finds certain
events to occur in succession; but the succession supplies, in its
occurrence, no reason for its recurrence. She contemplates external
objects; but she can not detect any internal bond, which indissolubly
connects the future with the past, the possible with the real. To learn a
proposition by experience, and to see it to be necessarily true, are two
altogether different processes of thought.”(76) And Dr. Whewell adds, “If
any one does not clearly comprehend this distinction of necessary and
contingent truths, he will not be able to go along with us in our
researches into the foundations of human knowledge; nor, indeed, to pursue
with success any speculation on the subject.”(77)

In the following passage, we are told what the distinction is, the
non-recognition of which incurs this denunciation. “Necessary truths are
those in which we not only learn that the proposition _is_ true, but see
that it _must be_ true; in which the negation of the truth is not only
false, but impossible; in which we can not, even by an effort of
imagination, or in a supposition, conceive the reverse of that which is
asserted. That there are such truths can not be doubted. We may take, for
example, all relations of number. Three and Two added together make Five.
We can not conceive it to be otherwise. We can not, by any freak of
thought, imagine Three and Two to make Seven.”(78)

Although Dr. Whewell has naturally and properly employed a variety of
phrases to bring his meaning more forcibly home, he would, I presume,
allow that they are all equivalent; and that what he means by a necessary
truth, would be sufficiently defined, a proposition the negation of which
is not only false but inconceivable. I am unable to find in any of his
expressions, turn them what way you will, a meaning beyond this, and I do
not believe he would contend that they mean any thing more.

This, therefore, is the principle asserted: that propositions, the
negation of which is inconceivable, or in other words, which we can not
figure to ourselves as being false, must rest on evidence of a higher and
more cogent description than any which experience can afford.

Now I can not but wonder that so much stress should be laid on the
circumstance of inconceivableness, when there is such ample experience to
show, that our capacity or incapacity of conceiving a thing has very
little to do with the possibility of the thing in itself; but is in truth
very much an affair of accident, and depends on the past history and
habits of our own minds. There is no more generally acknowledged fact in
human nature, than the extreme difficulty at first felt in conceiving any
thing as possible, which is in contradiction to long established and
familiar experience; or even to old familiar habits of thought. And this
difficulty is a necessary result of the fundamental laws of the human
mind. When we have often seen and thought of two things together, and have
never in any one instance either seen or thought of them separately, there
is by the primary law of association an increasing difficulty, which may
in the end become insuperable, of conceiving the two things apart. This is
most of all conspicuous in uneducated persons, who are in general utterly
unable to separate any two ideas which have once become firmly associated
in their minds; and if persons of cultivated intellect have any advantage
on the point, it is only because, having seen and heard and read more, and
being more accustomed to exercise their imagination, they have experienced
their sensations and thoughts in more varied combinations, and have been
prevented from forming many of these inseparable associations. But this
advantage has necessarily its limits. The most practiced intellect is not
exempt from the universal laws of our conceptive faculty. If daily habit
presents to any one for a long period two facts in combination, and if he
is not led during that period either by accident or by his voluntary
mental operations to think of them apart, he will probably in time become
incapable of doing so even by the strongest effort; and the supposition
that the two facts can be separated in nature, will at last present itself
to his mind with all the characters of an inconceivable phenomenon.(79)
There are remarkable instances of this in the history of science:
instances in which the most instructed men rejected as impossible, because
inconceivable, things which their posterity, by earlier practice and
longer perseverance in the attempt, found it quite easy to conceive, and
which every body now knows to be true. There was a time when men of the
most cultivated intellects, and the most emancipated from the dominion of
early prejudice, could not credit the existence of antipodes; were unable
to conceive, in opposition to old association, the force of gravity acting
upward instead of downward. The Cartesians long rejected the Newtonian
doctrine of the gravitation of all bodies toward one another, on the faith
of a general proposition, the reverse of which seemed to them to be
inconceivable—the proposition that a body can not act where it is not. All
the cumbrous machinery of imaginary vortices, assumed without the smallest
particle of evidence, appeared to these philosophers a more rational mode
of explaining the heavenly motions, than one which involved what seemed to
them so great an absurdity.(80)

And they no doubt found it as impossible to conceive that a body should
act upon the earth from the distance of the sun or moon, as we find it to
conceive an end to space or time, or two straight lines inclosing a space.
Newton himself had not been able to realize the conception, or we should
not have had his hypothesis of a subtle ether, the occult cause of
gravitation; and his writings prove, that though he deemed the particular
nature of the intermediate agency a matter of conjecture, the necessity of
_some_ such agency appeared to him indubitable.

If, then, it be so natural to the human mind, even in a high state of
culture, to be incapable of conceiving, and on that ground to believe
impossible, what is afterward not only found to be conceivable but proved
to be true; what wonder if in cases where the association is still older,
more confirmed, and more familiar, and in which nothing ever occurs to
shake our conviction, or even suggest to us any conception at variance
with the association, the acquired incapacity should continue, and be
mistaken for a natural incapacity? It is true, our experience of the
varieties in nature enables us, within certain limits, to conceive other
varieties analogous to them. We can conceive the sun or moon falling; for
though we never saw them fall, nor ever, perhaps, imagined them falling,
we have seen so many other things fall, that we have innumerable familiar
analogies to assist the conception; which, after all, we should probably
have some difficulty in framing, were we not well accustomed to see the
sun and moon move (or appear to move), so that we are only called upon to
conceive a slight change in the direction of motion, a circumstance
familiar to our experience. But when experience affords no model on which
to shape the new conception, how is it possible for us to form it? How,
for example, can we imagine an end to space or time? We never saw any
object without something beyond it, nor experienced any feeling without
something following it. When, therefore, we attempt to conceive the last
point of space, we have the idea irresistibly raised of other points
beyond it. When we try to imagine the last instant of time, we can not
help conceiving another instant after it. Nor is there any necessity to
assume, as is done by a modern school of metaphysicians, a peculiar
fundamental law of the mind to account for the feeling of infinity
inherent in our conceptions of space and time; that apparent infinity is
sufficiently accounted for by simpler and universally acknowledged laws.

Now, in the case of a geometrical axiom, such, for example, as that two
straight lines can not inclose a space—a truth which is testified to us by
our very earliest impressions of the external world—how is it possible
(whether those external impressions be or be not the ground of our belief)
that the reverse of the proposition _could_ be otherwise than
inconceivable to us? What analogy have we, what similar order of facts in
any other branch of our experience, to facilitate to us the conception of
two straight lines inclosing a space? Nor is even this all. I have already
called attention to the peculiar property of our impressions of form, that
the ideas or mental images exactly resemble their prototypes, and
adequately represent them for the purposes of scientific observation. From
this, and from the intuitive character of the observation, which in this
case reduces itself to simple inspection, we can not so much as call up in
our imagination two straight lines, in order to attempt to conceive them
inclosing a space, without by that very act repeating the scientific
experiment which establishes the contrary. Will it really be contended
that the inconceivableness of the thing, in such circumstances, proves any
thing against the experimental origin of the conviction? Is it not clear
that in whichever mode our belief in the proposition may have originated,
the impossibility of our conceiving the negative of it must, on either
hypothesis, be the same? As, then, Dr. Whewell exhorts those who have any
difficulty in recognizing the distinction held by him between necessary
and contingent truths, to study geometry—a condition which I can assure
him I have conscientiously fulfilled—I, in return, with equal confidence,
exhort those who agree with him, to study the general laws of association;
being convinced that nothing more is requisite than a moderate familiarity
with those laws, to dispel the illusion which ascribes a peculiar
necessity to our earliest inductions from experience, and measures the
possibility of things in themselves, by the human capacity of conceiving
them.

I hope to be pardoned for adding, that Dr. Whewell himself has both
confirmed by his testimony the effect of habitual association in giving to
an experimental truth the appearance of a necessary one, and afforded a
striking instance of that remarkable law in his own person. In his
_Philosophy of the Inductive Sciences_ he continually asserts, that
propositions which not only are not self-evident, but which we know to
have been discovered gradually, and by great efforts of genius and
patience, have, when once established, appeared so self-evident that, but
for historical proof, it would have been impossible to conceive that they
had not been recognized from the first by all persons in a sound state of
their faculties. “We now despise those who, in the Copernican controversy,
could not conceive the apparent motion of the sun on the heliocentric
hypothesis; or those who, in opposition to Galileo, thought that a uniform
force might be that which generated a velocity proportional to the space;
or those who held there was something absurd in Newton’s doctrine of the
different refrangibility of differently colored rays; or those who
imagined that when elements combine, their sensible qualities must be
manifest in the compound; or those who were reluctant to give up the
distinction of vegetables into herbs, shrubs, and trees. We can not help
thinking that men must have been singularly dull of comprehension, to find
a difficulty in admitting what is to us so plain and simple. We have a
latent persuasion that we in their place should have been wiser and more
clear-sighted; that we should have taken the right side, and given our
assent at once to the truth. Yet in reality such a persuasion is a mere
delusion. The persons who, in such instances as the above, were on the
losing side, were very far, in most cases, from being persons more
prejudiced, or stupid, or narrow-minded, than the greater part of mankind
now are; and the cause for which they fought was far from being a
manifestly bad one, till it had been so decided by the result of the
war.... So complete has been the victory of truth in most of these
instances, that at present we can hardly imagine the struggle to have been
necessary. _The very essence of these triumphs is, that they lead us to
regard the views we reject as not only false but inconceivable._”(81)

This last proposition is precisely what I contend for; and I ask no more,
in order to overthrow the whole theory of its author on the nature of the
evidence of axioms. For what is that theory? That the truth of axioms can
not have been learned from experience, because their falsity is
inconceivable. But Dr. Whewell himself says, that we are continually led,
by the natural progress of thought, to regard as inconceivable what our
forefathers not only conceived but believed, nay even (he might have
added) were unable to conceive the reverse of. He can not intend to
justify this mode of thought: he can not mean to say, that we can be right
in regarding as inconceivable what others have conceived, and as
self-evident what to others did not appear evident at all. After so
complete an admission that inconceivableness is an accidental thing, not
inherent in the phenomenon itself, but dependent on the mental history of
the person who tries to conceive it, how can he ever call upon us to
reject a proposition as impossible on no other ground than its
inconceivableness? Yet he not only does so, but has unintentionally
afforded some of the most remarkable examples which can be cited of the
very illusion which he has himself so clearly pointed out. I select as
specimens, his remarks on the evidence of the three laws of motion, and of
the atomic theory.

With respect to the laws of motion, Dr. Whewell says: “No one can doubt
that, in historical fact, these laws were collected from experience. That
such is the case, is no matter of conjecture. We know the time, the
persons, the circumstances, belonging to each step of each discovery.”(82)
After this testimony, to adduce evidence of the fact would be superfluous.
And not only were these laws by no means intuitively evident, but some of
them were originally paradoxes. The first law was especially so. That a
body, once in motion, would continue forever to move in the same direction
with undiminished velocity unless acted upon by some new force, was a
proposition which mankind found for a long time the greatest difficulty in
crediting. It stood opposed to apparent experience of the most familiar
kind, which taught that it was the nature of motion to abate gradually,
and at last terminate of itself. Yet when once the contrary doctrine was
firmly established, mathematicians, as Dr. Whewell observes, speedily
began to believe that laws, thus contradictory to first appearances, and
which, even after full proof had been obtained, it had required
generations to render familiar to the minds of the scientific world, were
under “a demonstrable necessity, compelling them to be such as they are
and no other;” and he himself, though not venturing “absolutely to
pronounce” that _all_ these laws “can be rigorously traced to an absolute
necessity in the nature of things,”(83) does actually so think of the law
just mentioned; of which he says: “Though the discovery of the first law
of motion was made, historically speaking, by means of experiment, we have
now attained a point of view in which we see that it might have been
certainly known to be true, independently of experience.”(84) Can there be
a more striking exemplification than is here afforded, of the effect of
association which we have described? Philosophers, for generations, have
the most extraordinary difficulty in putting certain ideas together; they
at last succeed in doing so; and after a sufficient repetition of the
process, they first fancy a natural bond between the ideas, then
experience a growing difficulty, which at last, by the continuation of the
same progress, becomes an impossibility, of severing them from one
another. If such be the progress of an experimental conviction of which
the date is of yesterday, and which is in opposition to first appearances,
how must it fare with those which are conformable to appearances familiar
from the first dawn of intelligence, and of the conclusiveness of which,
from the earliest records of human thought, no skeptic has suggested even
a momentary doubt?

The other instance which I shall quote is a truly astonishing one, and may
be called the _reductio ad absurdum_ of the theory of inconceivableness.
Speaking of the laws of chemical composition, Dr. Whewell says:(85) “That
they could never have been clearly understood, and therefore never firmly
established, without laborious and exact experiments, is certain; but yet
we may venture to say, that being once known, they possess an evidence
beyond that of mere experiment. _For how in fact can we conceive
combinations, otherwise than as definite in kind and quality?_ If we were
to suppose each element ready to combine with any other indifferently, and
indifferently in any quantity, we should have a world in which all would
be confusion and indefiniteness. There would be no fixed kinds of bodies.
Salts, and stones, and ores, would approach to and graduate into each
other by insensible degrees. Instead of this, we know that the world
consists of bodies distinguishable from each other by definite
differences, capable of being classified and named, and of having general
propositions asserted concerning them. And as _we can not conceive a world
in which this should not be the case_, it would appear that we can not
conceive a state of things in which the laws of the combination of
elements should not be of that definite and measured kind which we have
above asserted.”

That a philosopher of Dr. Whewell’s eminence should gravely assert that we
can not conceive a world in which the simple elements should combine in
other than definite proportions; that by dint of meditating on a
scientific truth, the original discoverer of which was still living, he
should have rendered the association in his own mind between the idea of
combination and that of constant proportions so familiar and intimate as
to be unable to conceive the one fact without the other; is so signal an
instance of the mental law for which I am contending, that one word more
in illustration must be superfluous.

In the latest and most complete elaboration of his metaphysical system
(the _Philosophy of Discovery_), as well as in the earlier discourse on
the _Fundamental Antithesis of Philosophy_, reprinted as an appendix to
that work, Dr. Whewell, while very candidly admitting that his language
was open to misconception, disclaims having intended to say that mankind
in general can _now_ perceive the law of definite proportions in chemical
combination to be a necessary truth. All he meant was that philosophical
chemists in a future generation may possibly see this. “Some truths may be
seen by intuition, but yet the intuition of them may be a rare and a
difficult attainment.”(86) And he explains that the inconceivableness
which, according to his theory, is the test of axioms, “depends entirely
upon the clearness of the Ideas which the axioms involve. So long as those
ideas are vague and indistinct, the contrary of an axiom may be assented
to, though it can not be distinctly conceived. It may be assented to, not
because it is possible, but because we do not see clearly what is
possible. To a person who is only beginning to think geometrically, there
may appear nothing absurd in the assertion that two straight lines may
inclose a space. And in the same manner, to a person who is only beginning
to think of mechanical truths, it may not appear to be absurd, that in
mechanical processes, Reaction should be greater or less than Action; and
so, again, to a person who has not thought steadily about Substance, it
may not appear inconceivable, that by chemical operations, we should
generate new matter, or destroy matter which already exists.”(87)
Necessary truths, therefore, are not those of which we can not conceive,
but “those of which we can not _distinctly_ conceive, the contrary.”(88)
So long as our ideas are indistinct altogether, we do not know what is or
is not capable of being distinctly conceived; but, by the ever increasing
distinctness with which scientific men apprehend the general conceptions
of science, they in time come to perceive that there are certain laws of
nature, which, though historically and as a matter of fact they were
learned from experience, we can not, now that we know them, distinctly
conceive to be other than they are.

The account which I should give of this progress of the scientific mind is
somewhat different. After a general law of nature has been ascertained,
men’s minds do not at first acquire a complete facility of familiarly
representing to themselves the phenomena of nature in the character which
that law assigns to them. The habit which constitutes the scientific cast
of mind, that of conceiving facts of all descriptions conformably to the
laws which regulate them—phenomena of all descriptions according to the
relations which have been ascertained really to exist between them; this
habit, in the case of newly-discovered relations, comes only by degrees.
So long as it is not thoroughly formed, no necessary character is ascribed
to the new truth. But in time, the philosopher attains a state of mind in
which his mental picture of nature spontaneously represents to him all the
phenomena with which the new theory is concerned, in the exact light in
which the theory regards them: all images or conceptions derived from any
other theory, or from the confused view of the facts which is anterior to
any theory, having entirely disappeared from his mind. The mode of
representing facts which results from the theory, has now become, to his
faculties, the only natural mode of conceiving them. It is a known truth,
that a prolonged habit of arranging phenomena in certain groups, and
explaining them by means of certain principles, makes any other
arrangement or explanation of these facts be felt as unnatural: and it may
at last become as difficult to him to represent the facts to himself in
any other mode, as it often was, originally, to represent them in that
mode.

But, further (if the theory is true, as we are supposing it to be), any
other mode in which he tries, or in which he was formerly accustomed, to
represent the phenomena, will be seen by him to be inconsistent with the
facts that suggested the new theory—facts which now form a part of his
mental picture of nature. And since a contradiction is always
inconceivable, his imagination rejects these false theories, and declares
itself incapable of conceiving them. Their inconceivableness to him does
not, however, result from any thing in the theories themselves,
intrinsically and _a priori_ repugnant to the human faculties; it results
from the repugnance between them and a portion of the facts; which facts
as long as he did not know, or did not distinctly realize in his mental
representations, the false theory did not appear other than conceivable;
it becomes inconceivable, merely from the fact that contradictory elements
can not be combined in the same conception. Although, then, his real
reason for rejecting theories at variance with the true one, is no other
than that they clash with his experience, he easily falls into the belief,
that he rejects them because they are inconceivable, and that he adopts
the true theory because it is self-evident, and does not need the evidence
of experience at all.

This I take to be the real and sufficient explanation of the paradoxical
truth, on which so much stress is laid by Dr. Whewell, that a
scientifically cultivated mind is actually, in virtue of that cultivation,
unable to conceive suppositions which a common man conceives without the
smallest difficulty. For there is nothing inconceivable in the
suppositions themselves; the impossibility is in combining them with facts
inconsistent with them, as part of the same mental picture; an obstacle of
course only felt by those who know the facts, and are able to perceive the
inconsistency. As far as the suppositions themselves are concerned, in the
case of many of Dr. Whewell’s necessary truths the negative of the axiom
is, and probably will be as long as the human race lasts, as easily
conceivable as the affirmative. There is no axiom (for example) to which
Dr. Whewell ascribes a more thorough character of necessity and
self-evidence, than that of the indestructibility of matter. That this is
a true law of nature I fully admit; but I imagine there is no human being
to whom the opposite supposition is inconceivable—who has any difficulty
in imagining a portion of matter annihilated: inasmuch as its apparent
annihilation, in no respect distinguishable from real by our unassisted
senses, takes place every time that water dries up, or fuel is consumed.
Again, the law that bodies combine chemically in definite proportions is
undeniably true; but few besides Dr. Whewell have reached the point which
he seems personally to have arrived at (though he only dares prophesy
similar success to the multitude after the lapse of generations), that of
being unable to conceive a world in which the elements are ready to
combine with one another “indifferently in any quantity;” nor is it likely
that we shall ever rise to this sublime height of inability, so long as
all the mechanical mixtures in our planet, whether solid, liquid, or
aëriform, exhibit to our daily observation the very phenomenon declared to
be inconceivable.

According to Dr. Whewell, these and similar laws of nature can not be
drawn from experience, inasmuch as they are, on the contrary, assumed in
the interpretation of experience. Our inability to “add to or diminish the
quantity of matter in the world,” is a truth which “neither is nor can be
derived from experience; for the experiments which we make to verify it
presuppose its truth.... When men began to use the balance in chemical
analysis, they did not prove by trial, but took for granted, as
self-evident, that the weight of the whole must be found in the aggregate
weight of the elements.”(89) True, it is assumed; but, I apprehend, no
otherwise than as all experimental inquiry assumes provisionally some
theory or hypothesis, which is to be finally held true or not, according
as the experiments decide. The hypothesis chosen for this purpose will
naturally be one which groups together some considerable number of facts
already known. The proposition that the material of the world, as
estimated by weight, is neither increased nor diminished by any of the
processes of nature or art, had many appearances in its favor to begin
with. It expressed truly a great number of familiar facts. There were
other facts which it had the appearance of conflicting with, and which
made its truth, as a universal law of nature, at first doubtful. Because
it was doubtful, experiments were devised to verify it. Men assumed its
truth hypothetically, and proceeded to try whether, on more careful
examination, the phenomena which apparently pointed to a different
conclusion, would not be found to be consistent with it. This turned out
to be the case; and from that time the doctrine took its place as a
universal truth, but as one proved to be such by experience. That the
theory itself preceded the proof of its truth—that it had to be conceived
before it could be proved, and in order that it might be proved—does not
imply that it was self-evident, and did not need proof. Otherwise all the
true theories in the sciences are necessary and self-evident; for no one
knows better than Dr. Whewell that they all began by being assumed, for
the purpose of connecting them by deductions with those facts of
experience on which, as evidence, they now confessedly rest.(90)



                               Chapter VI.


The Same Subject Continued.


§ 1. In the examination which formed the subject of the last chapter, into
the nature of the evidence of those deductive sciences which are commonly
represented to be systems of necessary truth, we have been led to the
following conclusions. The results of those sciences are indeed necessary,
in the sense of necessarily following from certain first principles,
commonly called axioms and definitions; that is, of being certainly true
if those axioms and definitions are so; for the word necessity, even in
this acceptation of it, means no more than certainty. But their claim to
the character of necessity in any sense beyond this, as implying an
evidence independent of and superior to observation and experience, must
depend on the previous establishment of such a claim in favor of the
definitions and axioms themselves. With regard to axioms, we found that,
considered as experimental truths, they rest on superabundant and obvious
evidence. We inquired, whether, since this is the case, it be imperative
to suppose any other evidence of those truths than experimental evidence,
any other origin for our belief of them than an experimental origin. We
decided, that the burden of proof lies with those who maintain the
affirmative, and we examined, at considerable length, such arguments as
they have produced. The examination having led to the rejection of those
arguments, we have thought ourselves warranted in concluding that axioms
are but a class, the most universal class, of inductions from experience;
the simplest and easiest cases of generalization from the facts furnished
to us by our senses or by our internal consciousness.

While the axioms of demonstrative sciences thus appeared to be
experimental truths, the definitions, as they are incorrectly called, in
those sciences, were found by us to be generalizations from experience
which are not even, accurately speaking, truths; being propositions in
which, while we assert of some kind of object, some property or properties
which observation shows to belong to it, we at the same time deny that it
possesses any other properties, though in truth other properties do in
every individual instance accompany, and in almost all instances modify,
the property thus exclusively predicated. The denial, therefore, is a mere
fiction, or supposition, made for the purpose of excluding the
consideration of those modifying circumstances, when their influence is of
too trifling amount to be worth considering, or adjourning it, when
important to a more convenient moment.

From these considerations it would appear that Deductive or Demonstrative
Sciences are all, without exception, Inductive Sciences; that their
evidence is that of experience; but that they are also, in virtue of the
peculiar character of one indispensable portion of the general formulæ
according to which their inductions are made, Hypothetical Sciences. Their
conclusions are only true on certain suppositions, which are, or ought to
be, approximations to the truth, but are seldom, if ever, exactly true;
and to this hypothetical character is to be ascribed the peculiar
certainty, which is supposed to be inherent in demonstration.

What we have now asserted, however, cannot be received as universally true
of Deductive or Demonstrative Sciences, until verified by being applied to
the most remarkable of all those sciences, that of Numbers; the theory of
the Calculus; Arithmetic and Algebra. It is harder to believe of the
doctrines of this science than of any other, either that they are not
truths _a priori_, but experimental truths, or that their peculiar
certainty is owing to their being not absolute but only conditional
truths. This, therefore, is a case which merits examination apart; and the
more so, because on this subject we have a double set of doctrines to
contend with; that of the _a priori_ philosophers on one side; and on the
other, a theory the most opposite to theirs, which was at one time very
generally received, and is still far from being altogether exploded, among
metaphysicians.

§ 2. This theory attempts to solve the difficulty apparently inherent in
the case, by representing the propositions of the science of numbers as
merely verbal, and its processes as simple transformations of language,
substitutions of one expression for another. The proposition, Two and one
is equal to three, according to these writers, is not a truth, is not the
assertion of a really existing fact, but a definition of the word three; a
statement that mankind have agreed to use the name three as a sign exactly
equivalent to two and one; to call by the former name whatever is called
by the other more clumsy phrase. According to this doctrine, the longest
process in algebra is but a succession of changes in terminology, by which
equivalent expressions are substituted one for another; a series of
translations of the same fact, from one into another language; though how,
after such a series of translations, the fact itself comes out changed (as
when we demonstrate a new geometrical theorem by algebra), they have not
explained; and it is a difficulty which is fatal to their theory.

It must be acknowledged that there are peculiarities in the processes of
arithmetic and algebra which render the theory in question very plausible,
and have not unnaturally made those sciences the stronghold of Nominalism.
The doctrine that we can discover facts, detect the hidden processes of
nature, by an artful manipulation of language, is so contrary to common
sense, that a person must have made some advances in philosophy to believe
it: men fly to so paradoxical a belief to avoid, as they think, some even
greater difficulty, which the vulgar do not see. What has led many to
believe that reasoning is a mere verbal process, is, that no other theory
seemed reconcilable with the nature of the Science of Numbers. For we do
not carry any ideas along with us when we use the symbols of arithmetic or
of algebra. In a geometrical demonstration we have a mental diagram, if
not one on paper; AB, AC, are present to our imagination as lines,
intersecting other lines, forming an angle with one another, and the like;
but not so _a_ and _b_. These may represent lines or any other magnitudes,
but those magnitudes are never thought of; nothing is realized in our
imagination but _a_ and _b_. The ideas which, on the particular occasion,
they happen to represent, are banished from the mind during every
intermediate part of the process, between the beginning, when the premises
are translated from things into signs, and the end, when the conclusion is
translated back from signs into things. Nothing, then, being in the
reasoner’s mind but the symbols, what can seem more inadmissible than to
contend that the reasoning process has to do with any thing more? We seem
to have come to one of Bacon’s Prerogative Instances; an _experimentum
crucis_ on the nature of reasoning itself.

Nevertheless, it will appear on consideration, that this apparently so
decisive instance is no instance at all; that there is in every step of an
arithmetical or algebraical calculation a real induction, a real inference
of facts from facts; and that what disguises the induction is simply its
comprehensive nature, and the consequent extreme generality of the
language. All numbers must be numbers of something: there are no such
things as numbers in the abstract. _Ten_ must mean ten bodies, or ten
sounds, or ten beatings of the pulse. But though numbers must be numbers
of something, they may be numbers of any thing. Propositions, therefore,
concerning numbers, have the remarkable peculiarity that they are
propositions concerning all things whatever; all objects, all existences
of every kind, known to our experience. All things possess quantity;
consist of parts which can be numbered; and in that character possess all
the properties which are called properties of numbers. That half of four
is two, must be true whatever the word four represents, whether four
hours, four miles, or four pounds weight. We need only conceive a thing
divided into four equal parts (and all things may be conceived as so
divided), to be able to predicate of it every property of the number four,
that is, every arithmetical proposition in which the number four stands on
one side of the equation. Algebra extends the generalization still
farther: every number represents that particular number of all things
without distinction, but every algebraical symbol does more, it represents
all numbers without distinction. As soon as we conceive a thing divided
into equal parts, without knowing into what number of parts, we may call
it _a_ or _x_, and apply to it, without danger of error, every algebraical
formula in the books. The proposition, 2 (_a_ + _b_)= 2 _a_ + 2 _b_, is a
truth co-extensive with all nature. Since then algebraical truths are true
of all things whatever, and not, like those of geometry, true of lines
only or of angles only, it is no wonder that the symbols should not excite
in our minds ideas of any things in particular. When we demonstrate the
forty-seventh proposition of Euclid, it is not necessary that the words
should raise in us an image of all right-angled triangles, but only of
some one right-angled triangle: so in algebra we need not, under the
symbol _a_, picture to ourselves all things whatever, but only some one
thing; why not, then, the letter itself? The mere written characters, _a_,
_b_, _x_, _y_, _z_, serve as well for representatives of Things in
general, as any more complex and apparently more concrete conception. That
we are conscious of them, however, in their character of things, and not
of mere signs, is evident from the fact that our whole process of
reasoning is carried on by predicating of them the properties of things.
In resolving an algebraic equation, by what rules do we proceed? By
applying at each step to _a_, _b_, and _x_, the proposition that equals
added to equals make equals; that equals taken from equals leave equals;
and other propositions founded on these two. These are not properties of
language, or of signs as such, but of magnitudes, which is as much as to
say, of all things. The inferences, therefore, which are successively
drawn, are inferences concerning things, not symbols; though as any Things
whatever will serve the turn, there is no necessity for keeping the idea
of the Thing at all distinct, and consequently the process of thought may,
in this case, be allowed without danger to do what all processes of
thought, when they have been performed often, will do if permitted,
namely, to become entirely mechanical. Hence the general language of
algebra comes to be used familiarly without exciting ideas, as all other
general language is prone to do from mere habit, though in no other case
than this can it be done with complete safety. But when we look back to
see from whence the probative force of the process is derived, we find
that at every single step, unless we suppose ourselves to be thinking and
talking of the things, and not the mere symbols, the evidence fails.

There is another circumstance, which, still more than that which we have
now mentioned, gives plausibility to the notion that the propositions of
arithmetic and algebra are merely verbal. That is, that when considered as
propositions respecting Things, they all have the appearance of being
identical propositions. The assertion, Two and one is equal to three,
considered as an assertion respecting objects, as for instance, “Two
pebbles and one pebble are equal to three pebbles,” does not affirm
equality between two collections of pebbles, but absolute identity. It
affirms that if we put one pebble to two pebbles, those very pebbles are
three. The objects, therefore, being the very same, and the mere assertion
that “objects are themselves” being insignificant, it seems but natural to
consider the proposition, Two and one is equal to three, as asserting mere
identity of signification between the two names.

This, however, though it looks so plausible, will not bear examination.
The expression “two pebbles and one pebble,” and the expression “three
pebbles,” stand indeed for the same aggregation of objects, but they by no
means stand for the same physical fact. They are names of the same
objects, but of those objects in two different states: though they
_de_note the same things, their _con_notation is different. Three pebbles
in two separate parcels, and three pebbles in one parcel, do not make the
same impression on our senses; and the assertion that the very same
pebbles may by an alteration of place and arrangement be made to produce
either the one set of sensations or the other, though a very familiar
proposition, is not an identical one. It is a truth known to us by early
and constant experience: an inductive truth; and such truths are the
foundation of the science of Number. The fundamental truths of that
science all rest on the evidence of sense; they are proved by showing to
our eyes and our fingers that any given number of objects—ten balls, for
example—may by separation and re-arrangement exhibit to our senses all the
different sets of numbers the sums of which is equal to ten. All the
improved methods of teaching arithmetic to children proceed on a knowledge
of this fact. All who wish to carry the child’s _mind_ along with them in
learning arithmetic; all who wish to teach numbers, and not mere
ciphers—now teach it through the evidence of the senses, in the manner we
have described.

We may, if we please, call the proposition, “Three is two and one,” a
definition of the number three, and assert that arithmetic, as it has been
asserted that geometry, is a science founded on definitions. But they are
definitions in the geometrical sense, not the logical; asserting not the
meaning of a term only, but along with it an observed matter of fact. The
proposition, “A circle is a figure bounded by a line which has all its
points equally distant from a point within it,” is called the definition
of a circle; but the proposition from which so many consequences follow,
and which is really a first principle in geometry, is, that figures
answering to this description exist. And thus we may call “Three is two
and one” a definition of three; but the calculations which depend on that
proposition do not follow from the definition itself, but from an
arithmetical theorem presupposed in it, namely, that collections of
objects exist, which while they impress the senses thus, [Symbol: three
circles, two above one], may be separated into two parts, thus, [Symbol:
two circles, a space, and a third circle]. This proposition being granted,
we term all such parcels Threes, after which the enunciation of the
above-mentioned physical fact will serve also for a definition of the word
Three.

The Science of Number is thus no exception to the conclusion we previously
arrived at, that the processes even of deductive sciences are altogether
inductive, and that their first principles are generalizations from
experience. It remains to be examined whether this science resembles
geometry in the further circumstance, that some of its inductions are not
exactly true; and that the peculiar certainty ascribed to it, on account
of which its propositions are called Necessary Truths, is fictitious and
hypothetical, being true in no other sense than that those propositions
legitimately follow from the hypothesis of the truth of premises which are
avowedly mere approximations to truth.

§ 3. The inductions of arithmetic are of two sorts: first, those which we
have just expounded, such as One and one are two, Two and one are three,
etc., which may be called the definitions of the various numbers, in the
improper or geometrical sense of the word Definition; and secondly, the
two following axioms: The sums of equals are equal, The differences of
equals are equal. These two are sufficient; for the corresponding
propositions respecting unequals may be proved from these by a _reductio
ad absurdum_.

These axioms, and likewise the so-called definitions, are, as has already
been said, results of induction; true of all objects whatever, and, as it
may seem, exactly true, without the hypothetical assumption of unqualified
truth where an approximation to it is all that exists. The conclusions,
therefore, it will naturally be inferred, are exactly true, and the
science of number is an exception to other demonstrative sciences in this,
that the categorical certainty which is predicable of its demonstrations
is independent of all hypothesis.

On more accurate investigation, however, it will be found that, even in
this case, there is one hypothetical element in the ratiocination. In all
propositions concerning numbers, a condition is implied, without which
none of them would be true; and that condition is an assumption which may
be false. The condition is, that 1=1; that all the numbers are numbers of
the same or of equal units. Let this be doubtful, and not one of the
propositions of arithmetic will hold true. How can we know that one pound
and one pound make two pounds, if one of the pounds may be troy, and the
other avoirdupois? They may not make two pounds of either, or of any
weight. How can we know that a forty-horse power is always equal to
itself, unless we assume that all horses are of equal strength? It is
certain that 1 is always equal in _number_ to 1; and where the mere number
of objects, or of the parts of an object, without supposing them to be
equivalent in any other respect, is all that is material, the conclusions
of arithmetic, so far as they go to that alone, are true without mixture
of hypothesis. There are such cases in statistics; as, for instance, an
inquiry into the amount of the population of any country. It is
indifferent to that inquiry whether they are grown people or children,
strong or weak, tall or short; the only thing we want to ascertain is
their number. But whenever, from equality or inequality of number,
equality or inequality in any other respect is to be inferred, arithmetic
carried into such inquiries becomes as hypothetical a science as geometry.
All units must be assumed to be equal in that other respect; and this is
never accurately true, for one actual pound weight is not exactly equal to
another, nor one measured mile’s length to another; a nicer balance, or
more accurate measuring instruments, would always detect some difference.


    What is commonly called mathematical certainty, therefore, which
    comprises the twofold conception of unconditional truth and
    perfect accuracy, is not an attribute of all mathematical truths,
    but of those only which relate to pure Number, as distinguished
    from Quantity in the more enlarged sense; and only so long as we
    abstain from supposing that the numbers are a precise index to
    actual quantities. The certainty usually ascribed to the
    conclusions of geometry, and even to those of mechanics, is
    nothing whatever but certainty of inference. We can have full
    assurance of particular results under particular suppositions, but
    we can not have the same assurance that these suppositions are
    accurately true, nor that they include all the data which may
    exercise an influence over the result in any given instance.


§ 4. It appears, therefore, that the method of all Deductive Sciences is
hypothetical. They proceed by tracing the consequences of certain
assumptions; leaving for separate consideration whether the assumptions
are true or not, and if not exactly true, whether they are a sufficiently
near approximation to the truth. The reason is obvious. Since it is only
in questions of pure number that the assumptions are exactly true, and
even there only so long as no conclusions except purely numerical ones are
to be founded on them; it must, in all other cases of deductive
investigation, form a part of the inquiry, to determine how much the
assumptions want of being exactly true in the case in hand. This is
generally a matter of observation, to be repeated in every fresh case; or
if it has to be settled by argument instead of observation, may require in
every different case different evidence, and present every degree of
difficulty, from the lowest to the highest. But the other part of the
process—namely, to determine what else may be concluded if we find, and in
proportion as we find, the assumptions to be true—may be performed once
for all, and the results held ready to be employed as the occasions turn
up for use. We thus do all beforehand that can be so done, and leave the
least possible work to be performed when cases arise and press for a
decision. This inquiry into the inferences which can be drawn from
assumptions, is what properly constitutes Demonstrative Science.

It is of course quite as practicable to arrive at new conclusions from
facts assumed, as from facts observed; from fictitious, as from real,
inductions. Deduction, as we have seen, consists of a series of inferences
in this form—_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_
is a mark of _d_, which last may be a truth inaccessible to direct
observation. In like manner it is allowable to say, _suppose_ that a were
a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a mark of _d_,
which last conclusion was not thought of by those who laid down the
premises. A system of propositions as complicated as geometry might be
deduced from assumptions which are false; as was done by Ptolemy,
Descartes, and others, in their attempts to explain synthetically the
phenomena of the solar system on the supposition that the apparent motions
of the heavenly bodies were the real motions, or were produced in some way
more or less different from the true one. Sometimes the same thing is
knowingly done, for the purpose of showing the falsity of the assumption;
which is called a _reductio ad absurdum_. In such cases, the reasoning is
as follows: _a_ is a mark of _b_, and _b_ of _c_; now if c were also a
mark of _d, a_ would be a mark of _d_; but _d_ is known to be a mark of
the absence of _a_; consequently _a_ would be a mark of its own absence,
which is a contradiction; therefore _c_ is not a mark of _d_.

§ 5. It has even been held by some writers, that all ratiocination rests
in the last resort on a _reductio ad absurdum_; since the way to enforce
assent to it, in case of obscurity, would be to show that if the
conclusion be denied we must deny some one at least of the premises,
which, as they are all supposed true, would be a contradiction. And in
accordance with this, many have thought that the peculiar nature of the
evidence of ratiocination consisted in the impossibility of admitting the
premises and rejecting the conclusion without a contradiction in terms.
This theory, however, is inadmissible as an explanation of the grounds on
which ratiocination itself rests. If any one denies the conclusion
notwithstanding his admission of the premises, he is not involved in any
direct and express contradiction until he is compelled to deny some
premise; and he can only be forced to do this by a _reductio ad absurdum_,
that is, by another ratiocination: now, if he denies the validity of the
reasoning process itself, he can no more be forced to assent to the second
syllogism than to the first. In truth, therefore, no one is ever forced to
a contradiction in terms: he can only be forced to a contradiction (or
rather an infringement) of the fundamental maxim of ratiocination, namely,
that whatever has a mark, has what it is a mark of; or (in the case of
universal propositions), that whatever is a mark of any thing, is a mark
of whatever else that thing is a mark of. For in the case of every correct
argument, as soon as thrown into the syllogistic form, it is evident
without the aid of any other syllogism, that he who, admitting the
premises, fails to draw the conclusion, does not conform to the above
axiom.

We have now proceeded as far in the theory of Deduction as we can advance
in the present stage of our inquiry. Any further insight into the subject
requires that the foundation shall have been laid of the philosophic
theory of Induction itself; in which theory that of Deduction, as a mode
of Induction, which we have now shown it to be, will assume spontaneously
the place which belongs to it, and will receive its share of whatever
light may be thrown upon the great intellectual operation of which it
forms so important a part.



                               Chapter VII.


Examination Of Some Opinions Opposed To The Preceding Doctrines.


§ 1. Polemical discussion is foreign to the plan of this work. But an
opinion which stands in need of much illustration, can often receive it
most effectually, and least tediously, in the form of a defense against
objections. And on subjects concerning which speculative minds are still
divided, a writer does but half his duty by stating his own doctrine, if
he does not also examine, and to the best of his ability judge, those of
other thinkers.

In the dissertation which Mr. Herbert Spencer has prefixed to his, in many
respects, highly philosophical treatise on the Mind,(91) he criticises
some of the doctrines of the two preceding chapters, and propounds a
theory of his own on the subject of first principles. Mr. Spencer agrees
with me in considering axioms to be “simply our earliest inductions from
experience.” But he differs from me “widely as to the worth of the test of
inconceivableness.” He thinks that it is the ultimate test of all beliefs.
He arrives at this conclusion by two steps. First, we never can have any
stronger ground for believing any thing, than that the belief of it
“invariably exists.” Whenever any fact or proposition is invariably
believed; that is, if I understand Mr. Spencer rightly, believed by all
persons, and by one’s self at all times; it is entitled to be received as
one of the primitive truths, or original premises of our knowledge.
Secondly, the criterion by which we decide whether any thing is invariably
believed to be true, is our inability to conceive it as false. “The
inconceivability of its negation is the test by which we ascertain whether
a given belief invariably exists or not.” “For our primary beliefs, the
fact of invariable existence, tested by an abortive effort to cause their
non-existence, is the only reason assignable.” He thinks this the sole
ground of our belief in our own sensations. If I believe that I feel cold,
I only receive this as true because I can not conceive that I am not
feeling cold. “While the proposition remains true, the negation of it
remains inconceivable.” There are numerous other beliefs which Mr. Spencer
considers to rest on the same basis; being chiefly those, or a part of
those, which the metaphysicians of the Reid and Stewart school consider as
truths of immediate intuition. That there exists a material world; that
this is the very world which we directly and immediately perceive, and not
merely the hidden cause of our perceptions; that Space, Time, Force,
Extension, Figure, are not modes of our consciousness, but objective
realities; are regarded by Mr. Spencer as truths known by the
inconceivableness of their negatives. We can not, he says, by any effort,
conceive these objects of thought as mere states of our mind; as not
having an existence external to us. Their real existence is, therefore, as
certain as our sensations themselves. The truths which are the subject of
direct knowledge, being, according to this doctrine, known to be truths
only by the inconceivability of their negation; and the truths which are
not the object of direct knowledge, being known as inferences from those
which are; and those inferences being believed to follow from the
premises, only because we can not conceive them not to follow;
inconceivability is thus the ultimate ground of all assured beliefs.

Thus far, there is no very wide difference between Mr. Spencer’s doctrine
and the ordinary one of philosophers of the intuitive school, from
Descartes to Dr. Whewell; but at this point Mr. Spencer diverges from
them. For he does not, like them, set up the test of inconceivability as
infallible. On the contrary, he holds that it may be fallacious, not from
any fault in the test itself, but because “men have mistaken for
inconceivable things, some things which were not inconceivable.” And he
himself, in this very book, denies not a few propositions usually regarded
as among the most marked examples of truths whose negations are
inconceivable. But occasional failure, he says, is incident to all tests.
If such failure vitiates “the test of inconceivableness,” it “must
similarly vitiate all tests whatever. We consider an inference logically
drawn from established premises to be true. Yet in millions of cases men
have been wrong in the inferences they have thought thus drawn. Do we
therefore argue that it is absurd to consider an inference true on no
other ground than that it is logically drawn from established premises?
No: we say that though men may have taken for logical inferences,
inferences that were not logical, there nevertheless _are_ logical
inferences, and that we are justified in assuming the truth of what seem
to us such, until better instructed. Similarly, though men may have
thought some things inconceivable which were not so, there may still be
inconceivable things; and the inability to conceive the negation of a
thing, may still be our best warrant for believing it.... Though
occasionally it may prove an imperfect test, yet, as our most certain
beliefs are capable of no better, to doubt any one belief because we have
no higher guarantee for it, is really to doubt all beliefs.” Mr. Spencer’s
doctrine, therefore, does not erect the curable, but only the incurable
limitations of the human conceptive faculty, into laws of the outward
universe.

§ 2. The doctrine, that “a belief which is proved by the inconceivableness
of its negation to invariably exist, is true,” Mr. Spencer enforces by two
arguments, one of which may be distinguished as positive, and the other as
negative.

The positive argument is, that every such belief represents the aggregate
of all past experience. “Conceding the entire truth of” the “position,
that during any phase of human progress, the ability or inability to form
a specific conception wholly depends on the experiences men have had; and
that, by a widening of their experiences, they may, by and by, be enabled
to conceive things before inconceivable to them, it may still be argued
that as, at any time, the best warrant men can have for a belief is the
perfect agreement of all pre-existing experience in support of it, it
follows that, at any time, the inconceivableness of its negation is the
deepest test any belief admits of.... Objective facts are ever impressing
themselves upon us; our experience is a register of these objective facts;
and the inconceivableness of a thing implies that it is wholly at variance
with the register. Even were this all, it is not clear how, if every truth
is primarily inductive, any better test of truth could exist. But it must
be remembered that while many of these facts, impressing themselves upon
us, are occasional; while others again are very general; some are
universal and unchanging. These universal and unchanging facts are, by the
hypothesis, certain to establish beliefs of which the negations are
inconceivable; while the others are not certain to do this; and if they
do, subsequent facts will reverse their action. Hence if, after an immense
accumulation of experiences, there remain beliefs of which the negations
are still inconceivable, most, if not all of them, must correspond to
universal objective facts. If there be ... certain absolute uniformities
in nature; if these uniformities produce, as they must, absolute
uniformities in our experience; and if ... these absolute uniformities in
our experience disable us from conceiving the negations of them; then
answering to each absolute uniformity in nature which we can cognize,
there must exist in us a belief of which the negation is inconceivable,
and which is absolutely true. In this wide range of cases subjective
inconceivableness must correspond to objective impossibility. Further
experience will produce correspondence where it may not yet exist; and we
may expect the correspondence to become ultimately complete. In nearly all
cases this test of inconceivableness must be valid now” (I wish I could
think we were so nearly arrived at omniscience); “and where it is not, it
still expresses the net result of our experience up to the present time;
which is the most that any test can do.”

To this I answer, first, that it is by no means true that the
inconceivability, by us, of the negative of a proposition proves all, or
even any, “pre-existing experience” to be in favor of the affirmative.
There may have been no such pre-existing experiences, but only a mistaken
supposition of experience. How did the inconceivability of antipodes prove
that experience had given any testimony against their possibility? How did
the incapacity men felt of conceiving sunset otherwise than as a motion of
the sun, represent any “net result” of experience in support of its being
the sun and not the earth that moves? It is not experience that is
represented, it is only a superficial semblance of experience. The only
thing proved with regard to real experience, is the negative fact, that
men have _not had_ it of the kind which would have made the inconceivable
proposition conceivable.

Next: Even if it were true that inconceivableness represents the net
result of all past experience, why should we stop at the representative
when we can get at the thing represented? If our incapacity to conceive
the negation of a given supposition is proof of its truth, because proving
that our experience has hitherto been uniform in its favor, the real
evidence for the supposition is not the inconceivableness, but the
uniformity of experience. Now this, which is the substantial and only
proof, is directly accessible. We are not obliged to presume it from an
incidental consequence. If all past experience is in favor of a belief,
let this be stated, and the belief openly rested on that ground: after
which the question arises, what that fact may be worth as evidence of its
truth? For uniformity of experience is evidence in very different degrees:
in some cases it is strong evidence, in others weak, in others it scarcely
amounts to evidence at all. That all metals sink in water, was a uniform
experience, from the origin of the human race to the discovery of
potassium in the present century by Sir Humphry Davy. That all swans are
white, was a uniform experience down to the discovery of Australia. In the
few cases in which uniformity of experience does amount to the strongest
possible proof, as with such propositions as these, Two straight lines can
not inclose a space, Every event has a cause, it is not because their
negations are inconceivable, which is not always the fact; but because the
experience, which has been thus uniform, pervades all nature. It will be
shown in the following Book that none of the conclusions either of
induction or of deduction can be considered certain, except as far as
their truth is shown to be inseparably bound up with truths of this class.

I maintain then, first, that uniformity of past experience is very far
from being universally a criterion of truth. But secondly,
inconceivableness is still further from being a test even of that test.
Uniformity of contrary experience is only one of many causes of
inconceivability. Tradition handed down from a period of more limited
knowledge, is one of the commonest. The mere familiarity of one mode of
production of a phenomenon often suffices to make every other mode appear
inconceivable. Whatever connects two ideas by a strong association may,
and continually does, render their separation in thought impossible; as
Mr. Spencer, in other parts of his speculations, frequently recognizes. It
was not for want of experience that the Cartesians were unable to conceive
that one body could produce motion in another without contact. They had as
much experience of other modes of producing motion as they had of that
mode. The planets had revolved, and heavy bodies had fallen, every hour of
their lives. But they fancied these phenomena to be produced by a hidden
machinery which they did not see, because without it they were unable to
conceive what they did see. The inconceivableness, instead of representing
their experience, dominated and overrode their experience. Without
dwelling further on what I have termed the positive argument of Mr.
Spencer in support of his criterion of truth, I pass to his negative
argument, on which he lays more stress.

§ 3. The negative argument is, that, whether inconceivability be good
evidence or bad, no stronger evidence is to be obtained. That what is
inconceivable can not be true, is postulated in every act of thought. It
is the foundation of all our original premises. Still more it is assumed
in all conclusions from those premises. The invariability of belief,
tested by the inconceivableness of its negation, “is our sole warrant for
every demonstration. Logic is simply a systematization of the process by
which we indirectly obtain this warrant for beliefs that do not directly
possess it. To gain the strongest conviction possible respecting any
complex fact, we either analytically descend from it by successive steps,
each of which we unconsciously test by the inconceivableness of its
negation, until we reach some axiom or truth which we have similarly
tested; or we synthetically ascend from such axiom or truth by such steps.
In either case we connect some isolated belief, with a belief which
invariably exists, by a series of intermediate beliefs which invariably
exist.” The following passage sums up the theory: “When we perceive that
the negation of the belief is inconceivable, we have all possible warrant
for asserting the invariability of its existence: and in asserting this,
we express alike our logical justification of it, and the inexorable
necessity we are under of holding it.... We have seen that this is the
assumption on which every conclusion whatever ultimately rests. We have no
other guarantee for the reality of consciousness, of sensations, of
personal existence; we have no other guarantee for any axiom; we have no
other guarantee for any step in a demonstration. Hence, as being taken for
granted in every act of the understanding, it must be regarded as the
Universal Postulate.” But as this postulate, which we are under an
“inexorable necessity” of holding true, is sometimes false; as “beliefs
that once were shown by the inconceivableness of their negations to
invariably exist, have since been found untrue,” and as “beliefs that now
possess this character may some day share the same fate;” the canon of
belief laid down by Mr. Spencer is, that “the most certain conclusion” is
that “which involves the postulate the fewest times.” Reasoning,
therefore, never ought to prevail against one of the immediate beliefs
(the belief in Matter, in the outward reality of Extension, Space, and the
like), because each of these involves the postulate only once; while an
argument, besides involving it in the premises, involves it again in every
step of the ratiocination, no one of the successive acts of inference
being recognized as valid except because we can not conceive the
conclusion not to follow from the premises.

It will be convenient to take the last part of this argument first. In
every reasoning, according to Mr. Spencer, the assumption of the postulate
is renewed at every step. At each inference we judge that the conclusion
follows from the premises, our sole warrant for that judgment being that
we can not conceive it not to follow. Consequently if the postulate is
fallible, the conclusions of reasoning are more vitiated by that
uncertainty than direct intuitions; and the disproportion is greater, the
more numerous the steps of the argument.

To test this doctrine, let us first suppose an argument consisting only of
a single step, which would be represented by one syllogism. This argument
does rest on an assumption, and we have seen in the preceding chapters
what the assumption is. It is, that whatever has a mark, has what it is a
mark of. The evidence of this axiom I shall not consider at present;(92)
let us suppose it (with Mr. Spencer) to be the inconceivableness of its
reverse.

Let us now add a second step to the argument: we require, what? Another
assumption? No: the same assumption a second time; and so on to a third,
and a fourth. I confess I do not see how, on Mr. Spencer’s own principles,
the repetition of the assumption at all weakens the force of the argument.
If it were necessary the second time to assume some other axiom, the
argument would no doubt be weakened, since it would be necessary to its
validity that both axioms should be true, and it might happen that one was
true and not the other: making two chances of error instead of one. But
since it is the _same_ axiom, if it is true once it is true every time;
and if the argument, being of a hundred links, assumed the axiom a hundred
times, these hundred assumptions would make but one chance of error among
them all. It is satisfactory that we are not obliged to suppose the
deductions of pure mathematics to be among the most uncertain of
argumentative processes, which on Mr. Spencer’s theory they could hardly
fail to be, since they are the longest. But the number of steps in an
argument does not subtract from its reliableness, if no new _premises_, of
an uncertain character, are taken up by the way.(93)

To speak next of the premises. Our assurance of their truth, whether they
be generalities or individual facts, is grounded, in Mr. Spencer’s
opinion, on the inconceivableness of their being false. It is necessary to
advert to a double meaning of the word inconceivable, which Mr. Spencer is
aware of, and would sincerely disclaim founding an argument upon, but from
which his case derives no little advantage notwithstanding. By
inconceivableness is sometimes meant, inability to form or get rid of an
_idea_; sometimes, inability to form or get rid of a _belief_. The former
meaning is the most conformable to the analogy of language; for a
conception always means an idea, and never a belief. The wrong meaning of
“inconceivable” is, however, fully as frequent in philosophical discussion
as the right meaning, and the intuitive school of metaphysicians could not
well do without either. To illustrate the difference, we will take two
contrasted examples. The early physical speculators considered antipodes
incredible, because inconceivable. But antipodes were not inconceivable in
the primitive sense of the word. An idea of them could be formed without
difficulty: they could be completely pictured to the mental eye. What was
difficult, and, as it then seemed, impossible, was to apprehend them as
believable. The idea could be put together, of men sticking on by their
feet to the under side of the earth; but the belief _would_ follow, that
they must fall off. Antipodes were not unimaginable, but they were
unbelievable.

On the other hand, when I endeavor to conceive an end to extension, the
two ideas refuse to come together. When I attempt to form a conception of
the last point of space, I can not help figuring to myself a vast space
beyond that last point. The combination is, under the conditions of our
experience, unimaginable. This double meaning of inconceivable it is very
important to bear in mind, for the argument from inconceivableness almost
always turns on the alternate substitution of each of those meanings for
the other.

In which of these two senses does Mr. Spencer employ the term, when he
makes it a test of the truth of a proposition that its negation is
inconceivable? Until Mr. Spencer expressly stated the contrary, I inferred
from the course of his argument, that he meant unbelievable. He has,
however, in a paper published in the fifth number of the _Fortnightly
Review_, disclaimed this meaning, and declared that by an inconceivable
proposition he means, now and always, “one of which the terms can not, by
any effort, be brought before consciousness in that relation which the
proposition asserts between them—a proposition of which the subject and
predicate offer an insurmountable resistance to union in thought.” We now,
therefore, know positively that Mr. Spencer always endeavors to use the
word inconceivable in this, its proper, sense: but it may yet be
questioned whether his endeavor is always successful; whether the other,
and popular use of the word, does not sometimes creep in with its
associations, and prevent him from maintaining a clear separation between
the two. When, for example, he says, that when I feel cold, I can not
conceive that I am not feeling cold, this expression can not be translated
into “I can not conceive myself not feeling cold,” for it is evident that
I can: the word conceive, therefore, is here used to express the
recognition of a matter of fact—the perception of truth or falsehood;
which I apprehend to be exactly the meaning of an act of belief, as
distinguished from simple conception. Again, Mr. Spencer calls the attempt
to conceive something which is inconceivable “an abortive effort to cause
the non-existence,” not of a conception or mental representation, but of a
belief. There is need, therefore, to revise a considerable part of Mr.
Spencer’s language, if it is to be kept always consistent with his
definition of inconceivability. But in truth the point is of little
importance; since inconceivability, in Mr. Spencer’s theory, is only a
test of truth, inasmuch as it is a test of believability. The
inconceivableness of a supposition is the extreme case of its
unbelievability. This is the very foundation of Mr. Spencer’s doctrine.
The invariability of the belief is with him the real guarantee. The
attempt to conceive the negative is made in order to test the
inevitableness of the belief. It should be called, an attempt to _believe_
the negative. When Mr. Spencer says that while looking at the sun a man
can not conceive that he is looking into darkness, he should have said
that a man can not _believe_ that he is doing so. For it is surely
possible, in broad daylight, to _imagine_ one’s self looking into
darkness.(94) As Mr. Spencer himself says, speaking of the belief of our
own existence, “That he _might_ not exist, he can conceive well enough;
but that he _does_ not exist, he finds it impossible to conceive,” _i.e._,
to believe. So that the statement resolves itself into this: That I exist,
and that I have sensations, I believe, because I can not believe
otherwise. And in this case every one will admit that the impossibility is
real. Any one’s present sensations, or other states of subjective
consciousness, that one person inevitably believes. They are facts known
_per se_: it is impossible to ascend beyond them. Their negative is really
unbelievable, and therefore there is never any question about believing
it. Mr. Spencer’s theory is not needed for these truths.

But according to Mr. Spencer there are other beliefs, relating to other
things than our own subjective feelings, for which we have the same
guarantee—which are, in a similar manner, invariable and necessary. With
regard to these other beliefs, they can not be necessary, since they do
not always exist. There have been, and are, many persons who do not
believe the reality of an external world, still less the reality of
extension and figure as the forms of that external world; who do not
believe that space and time have an existence independent of the mind—nor
any other of Mr. Spencer’s objective intuitions. The negations of these
alleged invariable beliefs are not unbelievable, for they are believed. It
may be maintained, without obvious error, that we can not _imagine_
tangible objects as mere states of our own and other people’s
consciousness; that the perception of them irresistibly suggests to us the
_idea_ of something external to ourselves: and I am not in a condition to
say that this is not the fact (though I do not think any one is entitled
to affirm it of any person besides himself). But many thinkers have
believed, whether they could conceive it or not, that what we represent to
ourselves as material objects, are mere modifications of consciousness;
complex feelings of touch and of muscular action. Mr. Spencer may think
the inference correct from the unimaginable to the unbelievable, because
he holds that belief itself is but the persistence of an idea, and that
what we can succeed in imagining we can not at the moment help
apprehending as believable. But of what consequence is it what we
apprehend at the moment, if the moment is in contradiction to the
permanent state of our mind? A person who has been frightened when an
infant by stories of ghosts, though he disbelieves them in after years
(and perhaps never believed them), may be unable all his life to be in a
dark place, in circumstances stimulating to the imagination, without
mental discomposure. The idea of ghosts, with all its attendant terrors,
is irresistibly called up in his mind by the outward circumstances. Mr.
Spencer may say, that while he is under the influence of this terror he
does not disbelieve in ghosts, but has a temporary and uncontrollable
belief in them. Be it so; but allowing it to be so, which would it be
truest to say of this man on the whole—that he believes in ghosts, or that
he does not believe in them? Assuredly that he does not believe in them.
The case is similar with those who disbelieve a material world. Though
they can not get rid of the idea; though while looking at a solid object
they can not help having the conception, and therefore, according to Mr.
Spencer’s metaphysics, the momentary belief, of its externality; even at
that moment they would sincerely deny holding that belief: and it would be
incorrect to call them other than disbelievers of the doctrine. The belief
therefore is not invariable; and the test of inconceivableness fails in
the only cases to which there could ever be any occasion to apply it.

That a thing may be perfectly believable, and yet may not have become
conceivable, and that we may habitually believe one side of an
alternative, and conceive only in the other, is familiarly exemplified in
the state of mind of educated persons respecting sunrise and sunset. All
educated persons either know by investigation, or believe on the authority
of science, that it is the earth and not the sun which moves: but there
are probably few who habitually _conceive_ the phenomenon otherwise than
as the ascent or descent of the sun. Assuredly no one can do so without a
prolonged trial; and it is probably not easier now than in the first
generation after Copernicus. Mr. Spencer does not say, “In looking at
sunrise it is impossible not to conceive that it is the sun which moves,
therefore this is what every body believes, and we have all the evidence
for it that we can have for any truth.” Yet this would be an exact
parallel to his doctrine about the belief in matter.

The existence of matter, and other Noumena, as distinguished from the
phenomenal world, remains a question of argument, as it was before; and
the very general, but neither necessary nor universal, belief in them,
stands as a psychological phenomenon to be explained, either on the
hypothesis of its truth, or on some other. The belief is not a conclusive
proof of its own truth, unless there are no such things as _idola tribûs_;
but being a fact, it calls on antagonists to show, from what except the
real existence of the thing believed, so general and apparently
spontaneous a belief can have originated. And its opponents have never
hesitated to accept this challenge.(95) The amount of their success in
meeting it will probably determine the ultimate verdict of philosophers on
the question.

§ 4. In the revision, or rather reconstruction, of his “Principles of
Psychology,” as one of the stages or platforms in the imposing structure
of his System of Philosophy, Mr. Spencer has resumed what he justly
terms(96) the “amicable controversy that has been long pending between
us;” expressing at the same time a regret, which I cordially share, that
“this lengthened exposition of a single point of difference, unaccompanied
by an exposition of the numerous points of concurrence, unavoidably
produces an appearance of dissent very far greater than that which
exists.” I believe, with Mr. Spencer, that the difference between us, if
measured by our conclusions, is “superficial rather than substantial;” and
the value I attach to so great an amount of agreement, in the field of
analytic psychology, with a thinker of his force and depth, is such as I
can hardly overstate. But I also agree with him that the difference which
exists in our premises is one of “profound importance, philosophically
considered;” and not to be dismissed while any part of the case of either
of us has not been fully examined and discussed.

In his present statement of the Universal Postulate, Mr. Spencer has
exchanged his former expression, “beliefs which invariably exist,” for the
following: “cognitions of which the predicates invariably exist along with
their subjects.” And he says that “an abortive effort to conceive the
negation of a proposition, shows that the cognition expressed is one of
which the predicate invariably exists along with its subject; and the
discovery that the predicate invariably exists along with its subject, is
the discovery that this cognition is one we are compelled to accept.” Both
these premises of Mr. Spencer’s syllogism I am able to assent to, but in
different senses of the middle term. If the invariable existence of the
predicate along with its subject, is to be understood in the most obvious
meaning, as an existence in actual Nature, or in other words, in our
objective, or sensational, experience, I of course admit that this, once
ascertained, compels us to accept the proposition: but then I do not admit
that the failure of an attempt to conceive the negative, proves the
predicate to be always co-existent with the subject in actual Nature. If,
on the other hand (which I believe to be Mr. Spencer’s meaning) the
invariable existence of the predicate along with the subject is to be
understood only of our conceptive faculty, _i.e._, that the one is
inseparable from the other in our thoughts; then, indeed, the inability to
separate the two ideas proves their inseparable conjunction, here and now,
in the mind which has failed in the attempt; but this inseparability in
thought does not prove a corresponding inseparability in fact; nor even in
the thoughts of other people, or of the same person in a possible future.

“That some propositions have been wrongly accepted as true, because their
negations were supposed inconceivable when they were not,” does not, in
Mr. Spencer’s opinion, “disprove the validity of the test;” not only
because any test whatever “is liable to yield untrue results, either from
incapacity or from carelessness in those who use it,” but because the
propositions in question “were complex propositions, not to be established
by a test applicable to propositions no further decomposable.” “A test
legitimately applicable to a simple proposition, the subject and predicate
of which are in direct relation, can not be legitimately applied to a
complex proposition, the subject and predicate of which are indirectly
related through the many simple propositions implied.” “That things which
are equal to the same thing are equal to one another, is a fact which can
be known by direct comparison of actual or ideal relations.... But that
the square of the hypothenuse of a right-angled triangle equals the sum of
the squares of the other two sides, can not be known immediately by
comparison of two states of consciousness: here the truth can be reached
only mediately, through a series of simple judgments respecting the
likenesses or unlikenesses of certain relations.” Moreover, even when the
proposition admits of being tested by immediate consciousness, people
often neglect to do it. A school-boy, in adding up a column of figures,
will say “35 and 9 are 46,” though this is contrary to the verdict which
consciousness gives when 35 and 9 are really called up before it; but this
is not done. And not only school-boys, but men and thinkers, do not always
“distinctly translate into their equivalent states of consciousness the
words they use.”

It is but just to give Mr. Spencer’s doctrine the benefit of the
limitation he claims—viz., that it is only applicable to propositions
which are assented to on simple inspection, without any intervening media
of proof. But this limitation does not exclude some of the most marked
instances of propositions now known to be false or groundless, but whose
negative was once found inconceivable: such as, that in sunrise and sunset
it is the sun which moves; that gravitation may exist without an
intervening medium; and even the case of antipodes. The distinction drawn
by Mr. Spencer is real; but, in the case of the propositions classed by
him as complex, consciousness, until the media of proof are supplied,
gives no verdict at all: it neither declares the equality of the square of
the hypothenuse with the sum of the squares of the sides to be
inconceivable, nor their inequality to be inconceivable. But in all the
three cases which I have just cited, the inconceivability seems to be
apprehended directly; no train of argument was needed, as in the case of
the square of the hypothenuse, to obtain the verdict of consciousness on
the point. Neither is any of the three a case like that of the
school-boy’s mistake, in which the mind was never really brought into
contact with the proposition. They are cases in which one of two opposite
predicates, _mero adspectu_, seemed to be incompatible with the subject,
and the other, therefore, to be proved always to exist with it.(97)

As now limited by Mr. Spencer, the ultimate cognitions fit to be submitted
to his test are only those of so universal and elementary a character as
to be represented in the earliest and most unvarying experience, or
apparent experience, of all mankind. In such cases the inconceivability of
the negative, if real, is accounted for by the experience: and why (I have
asked) should the truth be tested by the inconceivability, when we can go
further back for proof—namely, to the experience itself? To this Mr.
Spencer answers, that the experiences can not be all recalled to mind, and
if recalled, would be of unmanageable multitude. To test a proposition by
experience seems to him to mean that “before accepting as certain the
proposition that any rectilineal figure must have as many angles as it has
sides,” I have “to think of every triangle, square, pentagon, hexagon,
etc., which I have ever seen, and to verify the asserted relation in each
case.” I can only say, with surprise, that I do not understand this to be
the meaning of an appeal to experience. It is enough to know that one has
been seeing the fact all one’s life, and has never remarked any instance
to the contrary, and that other people, with every opportunity of
observation, unanimously declare the same thing. It is true, even this
experience may be insufficient, and so it might be even if I could recall
to mind every instance of it; but its insufficiency, instead of being
brought to light, is disguised, if instead of sifting the experience
itself, I appeal to a test which bears no relation to the sufficiency of
the experience, but, at the most, only to its familiarity. These remarks
do not lose their force even if we believe, with Mr. Spencer, that mental
tendencies originally derived from experience impress themselves
permanently on the cerebral structure and are transmitted by inheritance,
so that modes of thinking which are acquired by the race become innate and
_a priori_ in the individual, thus representing, in Mr. Spencer’s opinion,
the experience of his progenitors, in addition to his own. All that would
follow from this is, that a conviction might be really innate, _i.e._,
prior to individual experience, and yet not be true, since the inherited
tendency to accept it may have been originally the result of other causes
than its truth.

Mr. Spencer would have a much stronger case, if he could really show that
the evidence of Reasoning rests on the Postulate, or, in other words, that
we believe that a conclusion follows from premises only because we can not
conceive it not to follow. But this statement seems to me to be of the
same kind as one I have previously commented on, viz., that I believe I
see light, because I can not, while the sensation remains, conceive that I
am looking into darkness. Both these statements seem to me incompatible
with the meaning (as very rightly limited by Mr. Spencer) of the verb to
conceive. To say that when I apprehend that A is B and that B is C, I can
not conceive that A is not C, is to my mind merely to say that I am
compelled to _believe_ that A is C. If to conceive be taken in its proper
meaning, viz., to form a mental representation, I _may_ be able to
conceive A as not being C. After assenting, with full understanding, to
the Copernican proof that it is the earth and not the sun that moves, I
not only can conceive, or represent to myself, sunset as a motion of the
sun, but almost every one finds this conception of sunset easier to form,
than that which they nevertheless know to be the true one.

§ 5. Sir William Hamilton holds as I do, that inconceivability is no
criterion of impossibility. “There is no ground for inferring a certain
fact to be impossible, merely from our inability to conceive its
possibility.” “Things there are which _may_, nay _must_, be true, of which
the understanding is wholly unable to construe to itself the
possibility.”(98) Sir William Hamilton is, however, a firm believer in the
_a priori_ character of many axioms, and of the sciences deduced from
them; and is so far from considering those axioms to rest on the evidence
of experience, that he declares certain of them to be true even of
Noumena—of the Unconditioned—of which it is one of the principal aims of
his philosophy to prove that the nature of our faculties debars us from
having any knowledge. The axioms to which he attributes this exceptional
emancipation from the limits which confine all our other possibilities of
knowledge; the chinks through which, as he represents, one ray of light
finds its way to us from behind the curtain which veils from us the
mysterious world of Things in themselves—are the two principles, which he
terms, after the school-men, the Principle of Contradiction, and the
Principle of Excluded Middle: the first, that two contradictory
propositions can not both be true; the second, that they can not both be
false. Armed with these logical weapons, we may boldly face Things in
themselves, and tender to them the double alternative, sure that they must
absolutely elect one or the other side, though we may be forever precluded
from discovering which. To take his favorite example, we can not conceive
the infinite divisibility of matter, and we can not conceive a minimum, or
end to divisibility: yet one or the other must be true.

As I have hitherto said nothing of the two axioms in question, those of
Contradiction and of Excluded Middle, it is not unseasonable to consider
them here. The former asserts that an affirmative proposition and the
corresponding negative proposition can not both be true; which has
generally been held to be intuitively evident. Sir William Hamilton and
the Germans consider it to be the statement in words of a form or law of
our thinking faculty. Other philosophers, not less deserving of
consideration, deem it to be an identical proposition; an assertion
involved in the meaning of terms; a mode of defining Negation, and the
word Not.

I am able to go one step with these last. An affirmative assertion and its
negative are not two independent assertions, connected with each other
only as mutually incompatible. That if the negative be true, the
affirmative must be false, really is a mere identical proposition; for the
negative proposition asserts nothing but the falsity of the affirmative,
and has no other sense or meaning whatever. The Principium Contradictionis
should therefore put off the ambitious phraseology which gives it the air
of a fundamental antithesis pervading nature, and should be enunciated in
the simpler form, that the same proposition can not at the same time be
false and true. But I can go no further with the Nominalists; for I can
not look upon this last as a merely verbal proposition. I consider it to
be, like other axioms, one of our first and most familiar generalizations
from experience. The original foundation of it I take to be, that Belief
and Disbelief are two different mental states, excluding one another. This
we know by the simplest observation of our own minds. And if we carry our
observation outward, we also find that light and darkness, sound and
silence, motion and quiescence, equality and inequality, preceding and
following, succession and simultaneousness, any positive phenomenon
whatever and its negative, are distinct phenomena, pointedly contrasted,
and the one always absent where the other is present. I consider the maxim
in question to be a generalization from all these facts.

In like manner as the Principle of Contradiction (that one of two
contradictories must be false) means that an assertion can not be _both_
true and false, so the Principle of Excluded Middle, or that one of two
contradictories must be true, means that an assertion must be _either_
true or false: either the affirmative is true, or otherwise the negative
is true, which means that the affirmative is false. I can not help
thinking this principle a surprising specimen of a so-called necessity of
Thought, since it is not even true, unless with a large qualification. A
proposition must be either true or false, _provided_ that the predicate be
one which can in any intelligible sense be attributed to the subject; (and
as this is always assumed to be the case in treatises on logic, the axiom
is always laid down there as of absolute truth). “Abracadabra is a second
intention” is neither true nor false. Between the true and the false there
is a third possibility, the Unmeaning: and this alternative is fatal to
Sir William Hamilton’s extension of the maxim to Noumena. That Matter must
either have a minimum of divisibility or be infinitely divisible, is more
than we can ever know. For in the first place, Matter, in any other than
the phenomenal sense of the term, may not exist: and it will scarcely be
said that a nonentity must be either infinitely or finitely divisible. In
the second place, though matter, considered as the occult cause of our
sensations, do really exist, yet what we call divisibility may be an
attribute only of our sensations of sight and touch, and not of their
uncognizable cause. Divisibility may not be predicable at all, in any
intelligible sense, of Things in themselves, nor therefore of Matter in
itself; and the assumed necessity of being either infinitely or finitely
divisible, may be an inapplicable alternative.

On this question I am happy to have the full concurrence of Mr. Herbert
Spencer, from whose paper in the _Fortnightly Review_ I extract the
following passage. The germ of an idea identical with that of Mr. Spencer
may be found in the present chapter, on a preceding page; but in Mr.
Spencer it is not an undeveloped thought, but a philosophical theory.

“When remembering a certain thing as in a certain place, the place and the
thing are mentally represented together; while to think of the
non-existence of the thing in that place implies a consciousness in which
the place is represented, but not the thing. Similarly, if instead of
thinking of an object as colorless, we think of its having color, the
change consists in the addition to the concept of an element that was
before absent from it—the object can not be thought of first as red and
then as not red, without one component of the thought being totally
expelled from the mind by another. The law of the Excluded Middle, then,
is simply a generalization of the universal experience that some mental
states are directly destructive of other states. It formulates a certain
absolutely constant law, that the appearance of any positive mode of
consciousness can not occur without excluding a correlative negative mode;
and that the negative mode can not occur without excluding the correlative
positive mode: the antithesis of positive and negative being, indeed,
merely an expression of this experience. Hence it follows that if
consciousness is not in one of the two modes it must be in the other.”(99)

I must here close this supplementary chapter, and with it the Second Book.
The theory of Induction, in the most comprehensive sense of the term, will
form the subject of the Third.



                                Book III.


OF INDUCTION.


    “According to the doctrine now stated, the highest, or rather the
    only proper object of physics, is to ascertain those established
    conjunctions of successive events, which constitute the order of
    the universe; to record the phenomena which it exhibits to our
    observations, or which it discloses to our experiments; and to
    refer these phenomena to their general laws.”—D. STEWART,
    _Elements of the Philosophy of the Human Mind_, vol. ii., chap.
    iv., sect. 1.

    “In such cases the inductive and deductive methods of inquiry may
    be said to go hand in hand, the one verifying the conclusions
    deduced by the other; and the combination of experiment and
    theory, which may thus be brought to bear in such cases, forms an
    engine of discovery infinitely more powerful than either taken
    separately. This state of any department of science is perhaps of
    all others the most interesting, and that which promises the most
    to research.”—SIR J. HERSCHEL, _Discourse on the Study of Natural
    Philosophy_.



                                Chapter I.


Preliminary Observations On Induction In General.


§ 1. The portion of the present inquiry upon which we are now about to
enter, may be considered as the principal, both from its surpassing in
intricacy all the other branches, and because it relates to a process
which has been shown in the preceding Book to be that in which the
investigation of nature essentially consists. We have found that all
Inference, consequently all Proof, and all discovery of truths not
self-evident, consists of inductions, and the interpretation of
inductions: that all our knowledge, not intuitive, comes to us exclusively
from that source. What Induction is, therefore, and what conditions render
it legitimate, can not but be deemed the main question of the science of
logic—the question which includes all others. It is, however, one which
professed writers on logic have almost entirely passed over. The
generalities of the subject have not been altogether neglected by
metaphysicians; but, for want of sufficient acquaintance with the
processes by which science has actually succeeded in establishing general
truths, their analysis of the inductive operation, even when
unexceptionable as to correctness, has not been specific enough to be made
the foundation of practical rules, which might be for induction itself
what the rules of the syllogism are for the interpretation of induction:
while those by whom physical science has been carried to its present state
of improvement—and who, to arrive at a complete theory of the process,
needed only to generalize, and adapt to all varieties of problems, the
methods which they themselves employed in their habitual pursuits—never
until very lately made any serious attempt to philosophize on the subject,
nor regarded the mode in which they arrived at their conclusions as
deserving of study, independently of the conclusions themselves.

§ 2. For the purposes of the present inquiry, Induction may be defined,
the operation of discovering and proving general propositions. It is true
that (as already shown) the process of indirectly ascertaining individual
facts, is as truly inductive as that by which we establish general truths.
But it is not a different kind of induction; it is a form of the very same
process: since, on the one hand, generals are but collections of
particulars, definite in kind but indefinite in number; and on the other
hand, whenever the evidence which we derive from observation of known
cases justifies us in drawing an inference respecting even one unknown
case, we should on the same evidence be justified in drawing a similar
inference with respect to a whole class of cases. The inference either
does not hold at all, or it holds in all cases of a certain description;
in all cases which, in certain definable respects, resemble those we have
observed.

If these remarks are just; if the principles and rules of inference are
the same whether we infer general propositions or individual facts; it
follows that a complete logic of the sciences would be also a complete
logic of practical business and common life. Since there is no case of
legitimate inference from experience, in which the conclusion may not
legitimately be a general proposition; an analysis of the process by which
general truths are arrived at, is virtually an analysis of all induction
whatever. Whether we are inquiring into a scientific principle or into an
individual fact, and whether we proceed by experiment or by ratiocination,
every step in the train of inferences is essentially inductive, and the
legitimacy of the induction depends in both cases on the same conditions.

True it is that in the case of the practical inquirer, who is endeavoring
to ascertain facts not for the purposes of science but for those of
business, such, for instance, as the advocate or the judge, the chief
difficulty is one in which the principles of induction will afford him no
assistance. It lies not in making his inductions, but in the selection of
them; in choosing from among all general propositions ascertained to be
true, those which furnish marks by which he may trace whether the given
subject possesses or not the predicate in question. In arguing a doubtful
question of fact before a jury, the general propositions or principles to
which the advocate appeals are mostly, in themselves, sufficiently trite,
and assented to as soon as stated: his skill lies in bringing his case
under those propositions or principles; in calling to mind such of the
known or received maxims of probability as admit of application to the
case in hand, and selecting from among them those best adapted to his
object. Success is here dependent on natural or acquired sagacity, aided
by knowledge of the particular subject, and of subjects allied with it.
Invention, though it can be cultivated, can not be reduced to rule; there
is no science which will enable a man to bethink himself of that which
will suit his purpose.

But when he _has_ thought of something, science can tell him whether that
which he has thought of will suit his purpose or not. The inquirer or
arguer must be guided by his own knowledge and sagacity in the choice of
the inductions out of which he will construct his argument. But the
validity of the argument when constructed, depends on principles, and must
be tried by tests which are the same for all descriptions of inquiries,
whether the result be to give A an estate, or to enrich science with a new
general truth. In the one case and in the other, the senses, or testimony,
must decide on the individual facts; the rules of the syllogism will
determine whether, those facts being supposed correct, the case really
falls within the formulæ of the different inductions under which it has
been successively brought; and finally, the legitimacy of the inductions
themselves must be decided by other rules, and these it is now our purpose
to investigate. If this third part of the operation be, in many of the
questions of practical life, not the most, but the least arduous portion
of it, we have seen that this is also the case in some great departments
of the field of science; in all those which are principally deductive, and
most of all in mathematics; where the inductions themselves are few in
number, and so obvious and elementary that they seem to stand in no need
of the evidence of experience, while to combine them so as to prove a
given theorem or solve a problem, may call for the utmost powers of
invention and contrivance with which our species is gifted.

If the identity of the logical processes which prove particular facts and
those which establish general scientific truths, required any additional
confirmation, it would be sufficient to consider that in many branches of
science, single facts have to be proved, as well as principles; facts as
completely individual as any that are debated in a court of justice; but
which are proved in the same manner as the other truths of the science,
and without disturbing in any degree the homogeneity of its method. A
remarkable example of this is afforded by astronomy. The individual facts
on which that science grounds its most important deductions, such facts as
the magnitudes of the bodies of the solar system, their distances from one
another, the figure of the earth, and its rotation, are scarcely any of
them accessible to our means of direct observation: they are proved
indirectly, by the aid of inductions founded on other facts which we can
more easily reach. For example, the distance of the moon from the earth
was determined by a very circuitous process. The share which direct
observation had in the work consisted in ascertaining, at one and the same
instant, the zenith distances of the moon, as seen from two points very
remote from one another on the earth’s surface. The ascertainment of these
angular distances ascertained their supplements; and since the angle at
the earth’s centre subtended by the distance between the two places of
observation was deducible by spherical trigonometry from the latitude and
longitude of those places, the angle at the moon subtended by the same
line became the fourth angle of a quadrilateral of which the other three
angles were known. The four angles being thus ascertained, and two sides
of the quadrilateral being radii of the earth; the two remaining sides and
the diagonal, or, in other words, the moon’s distance from the two places
of observation and from the centre of the earth, could be ascertained, at
least in terms of the earth’s radius, from elementary theorems of
geometry. At each step in this demonstration a new induction is taken in,
represented in the aggregate of its results by a general proposition.

Not only is the process by which an individual astronomical fact was thus
ascertained, exactly similar to those by which the same science
establishes its general truths, but also (as we have shown to be the case
in all legitimate reasoning) a general proposition might have been
concluded instead of a single fact. In strictness, indeed, the result of
the reasoning _is_ a general proposition; a theorem respecting the
distance, not of the moon in particular, but of any inaccessible object;
showing in what relation that distance stands to certain other quantities.
And although the moon is almost the only heavenly body the distance of
which from the earth can really be thus ascertained, this is merely owing
to the accidental circumstances of the other heavenly bodies, which render
them incapable of affording such data as the application of the theorem
requires; for the theorem itself is as true of them as it is of the
moon.(100)

We shall fall into no error, then, if in treating of Induction, we limit
our attention to the establishment of general propositions. The principles
and rules of Induction as directed to this end, are the principles and
rules of all Induction; and the logic of Science is the universal Logic,
applicable to all inquiries in which man can engage.



                               Chapter II.


Of Inductions Improperly So Called.


§ 1. Induction, then, is that operation of the mind, by which we infer
that what we know to be true in a particular case or cases, will be true
in all cases which resemble the former in certain assignable respects. In
other words, Induction is the process by which we conclude that what is
true of certain individuals of a class is true of the whole class, or that
what is true at certain times will be true in similar circumstances at all
times.

This definition excludes from the meaning of the term Induction, various
logical operations, to which it is not unusual to apply that name.

Induction, as above defined, is a process of inference; it proceeds from
the known to the unknown; and any operation involving no inference, any
process in which what seems the conclusion is no wider than the premises
from which it is drawn, does not fall within the meaning of the term. Yet
in the common books of Logic we find this laid down as the most perfect,
indeed the only quite perfect, form of induction. In those books, every
process which sets out from a less general and terminates in a more
general expression—which admits of being stated in the form, “This and
that A are B, therefore every A is B”—is called an induction, whether any
thing be really concluded or not: and the induction is asserted not to be
perfect, unless every single individual of the class A is included in the
antecedent, or premise: that is, unless what we affirm of the class has
already been ascertained to be true of every individual in it, so that the
nominal conclusion is not really a conclusion, but a mere re-assertion of
the premises. If we were to say, All the planets shine by the sun’s light,
from observation of each separate planet, or All the Apostles were Jews,
because this is true of Peter, Paul, John, and every other apostle—these,
and such as these, would, in the phraseology in question, be called
perfect, and the only perfect, Inductions. This, however, is a totally
different kind of induction from ours; it is not an inference from facts
known to facts unknown, but a mere short-hand registration of facts known.
The two simulated arguments which we have quoted, are not generalizations;
the propositions purporting to be conclusions from them, are not really
general propositions. A general proposition is one in which the predicate
is affirmed or denied of an unlimited number of individuals; namely, all,
whether few or many, existing or capable of existing, which possess the
properties connoted by the subject of the proposition. “All men are
mortal” does not mean all now living, but all men past, present, and to
come. When the signification of the term is limited so as to render it a
name not for any and every individual falling under a certain general
description, but only for each of a number of individuals, designated as
such, and as it were counted off individually, the proposition, though it
may be general in its language, is no general proposition, but merely that
number of singular propositions, written in an abridged character. The
operation may be very useful, as most forms of abridged notation are; but
it is no part of the investigation of truth, though often bearing an
important part in the preparation of the materials for that investigation.

As we may sum up a definite number of singular propositions in one
proposition, which will be apparently, but not really, general, so we may
sum up a definite number of general propositions in one proposition, which
will be apparently, but not really, more general. If by a separate
induction applied to every distinct species of animals, it has been
established that each possesses a nervous system, and we affirm thereupon
that all animals have a nervous system; this looks like a generalization,
though as the conclusion merely affirms of all what has already been
affirmed of each, it seems to tell us nothing but what we knew before. A
distinction, however, must be made. If in concluding that all animals have
a nervous system, we mean the same thing and no more as if we had said
“all known animals,” the proposition is not general, and the process by
which it is arrived at is not induction. But if our meaning is that the
observations made of the various species of animals have discovered to us
a law of animal nature, and that we are in a condition to say that a
nervous system will be found even in animals yet undiscovered, this indeed
is an induction; but in this case the general proposition contains more
than the sum of the special propositions from which it is inferred. The
distinction is still more forcibly brought out when we consider, that if
this real generalization be legitimate at all, its legitimacy probably
does not require that we should have examined without exception every
known species. It is the number and nature of the instances, and not their
being the whole of those which happen to be known, that makes them
sufficient evidence to prove a general law: while the more limited
assertion, which stops at all known animals, can not be made unless we
have rigorously verified it in every species. In like manner (to return to
a former example) we might have inferred, not that all _the_ planets, but
that all _planets_, shine by reflected light: the former is no induction;
the latter is an induction, and a bad one, being disproved by the case of
double stars—self-luminous bodies which are properly planets, since they
revolve round a centre.

§ 2. There are several processes used in mathematics which require to be
distinguished from Induction, being not unfrequently called by that name,
and being so far similar to Induction properly so called, that the
propositions they lead to are really general propositions. For example,
when we have proved with respect to the circle, that a straight line can
not meet it in more than two points, and when the same thing has been
successively proved of the ellipse, the parabola, and the hyperbola, it
may be laid down as a universal property of the sections of the cone. The
distinction drawn in the two previous examples can have no place here,
there being no difference between all _known_ sections of the cone and
_all_ sections, since a cone demonstrably can not be intersected by a
plane except in one of these four lines. It would be difficult, therefore,
to refuse to the proposition arrived at, the name of a generalization,
since there is no room for any generalization beyond it. But there is no
induction, because there is no inference: the conclusion is a mere summing
up of what was asserted in the various propositions from which it is
drawn. A case somewhat, though not altogether, similar, is the proof of a
geometrical theorem by means of a diagram. Whether the diagram be on paper
or only in the imagination, the demonstration (as formerly observed(101))
does not prove directly the general theorem; it proves only that the
conclusion, which the theorem asserts generally, is true of the particular
triangle or circle exhibited in the diagram; but since we perceive that in
the same way in which we have proved it of that circle, it might also be
proved of any other circle, we gather up into one general expression all
the singular propositions susceptible of being thus proved, and embody
them in a universal proposition. Having shown that the three angles of the
triangle ABC are together equal to two right angles, we conclude that this
is true of every other triangle, not because it is true of ABC, but for
the same reason which proved it to be true of ABC. If this were to be
called Induction, an appropriate name for it would be, induction by parity
of reasoning. But the term can not properly belong to it; the
characteristic quality of Induction is wanting, since the truth obtained,
though really general, is not believed on the evidence of particular
instances. We do not conclude that all triangles have the property because
some triangles have, but from the ulterior demonstrative evidence which
was the ground of our conviction in the particular instances.

There are nevertheless, in mathematics, some examples of so-called
Induction, in which the conclusion does bear the appearance of a
generalization grounded on some of the particular cases included in it. A
mathematician, when he has calculated a sufficient number of the terms of
an algebraical or arithmetical series to have ascertained what is called
the _law_ of the series, does not hesitate to fill up any number of the
succeeding terms without repeating the calculations. But I apprehend he
only does so when it is apparent from _a priori_ considerations (which
might be exhibited in the form of demonstration) that the mode of
formation of the subsequent terms, each from that which preceded it, must
be similar to the formation of the terms which have been already
calculated. And when the attempt has been hazarded without the sanction of
such general considerations, there are instances on record in which it has
led to false results.

It is said that Newton discovered the binomial theorem by induction; by
raising a binomial successively to a certain number of powers, and
comparing those powers with one another until he detected the relation in
which the algebraic formula of each power stands to the exponent of that
power, and to the two terms of the binomial. The fact is not improbable:
but a mathematician like Newton, who seemed to arrive _per saltum_ at
principles and conclusions that ordinary mathematicians only reached by a
succession of steps, certainly could not have performed the comparison in
question without being led by it to the _a priori_ ground of the law;
since any one who understands sufficiently the nature of multiplication to
venture upon multiplying several lines of symbols at one operation, can
not but perceive that in raising a binomial to a power, the co-efficients
must depend on the laws of permutation and combination: and as soon as
this is recognized, the theorem is demonstrated. Indeed, when once it was
seen that the law prevailed in a few of the lower powers, its identity
with the law of permutation would at once suggest the considerations which
prove it to obtain universally. Even, therefore, such cases as these, are
but examples of what I have called Induction by parity of reasoning, that
is, not really Induction, because not involving inference of a general
proposition from particular instances.

§ 3. There remains a third improper use of the term Induction, which it is
of real importance to clear up, because the theory of Induction has been,
in no ordinary degree, confused by it, and because the confusion is
exemplified in the most recent and elaborate treatise on the inductive
philosophy which exists in our language. The error in question is that of
confounding a mere description, by general terms, of a set of observed
phenomena, with an induction from them.

Suppose that a phenomenon consists of parts, and that these parts are only
capable of being observed separately, and as it were piecemeal. When the
observations have been made, there is a convenience (amounting for many
purposes to a necessity) in obtaining a representation of the phenomenon
as a whole, by combining, or as we may say, piecing these detached
fragments together. A navigator sailing in the midst of the ocean
discovers land: he can not at first, or by any one observation, determine
whether it is a continent or an island; but he coasts along it, and after
a few days finds himself to have sailed completely round it: he then
pronounces it an island. Now there was no particular time or place of
observation at which he could perceive that this land was entirely
surrounded by water: he ascertained the fact by a succession of partial
observations, and then selected a general expression which summed up in
two or three words the whole of what he so observed. But is there any
thing of the nature of an induction in this process? Did he infer any
thing that had not been observed, from something else which had? Certainly
not. He had observed the whole of what the proposition asserts. That the
land in question is an island, is not an inference from the partial facts
which the navigator saw in the course of his circumnavigation; it is the
facts themselves; it is a summary of those facts; the description of a
complex fact, to which those simpler ones are as the parts of a whole.

Now there is, I conceive, no difference in kind between this simple
operation, and that by which Kepler ascertained the nature of the
planetary orbits: and Kepler’s operation, all at least that was
characteristic in it, was not more an inductive act than that of our
supposed navigator.

The object of Kepler was to determine the real path described by each of
the planets, or let us say by the planet Mars (since it was of that body
that he first established the two of his three laws which did not require
a comparison of planets). To do this there was no other mode than that of
direct observation: and all which observation could do was to ascertain a
great number of the successive places of the planet; or rather, of its
apparent places. That the planet occupied successively all these
positions, or at all events, positions which produced the same impressions
on the eye, and that it passed from one of these to another insensibly,
and without any apparent breach of continuity; thus much the senses, with
the aid of the proper instruments, could ascertain. What Kepler did more
than this, was to find what sort of a curve these different points would
make, supposing them to be all joined together. He expressed the whole
series of the observed places of Mars by what Dr. Whewell calls the
general conception of an ellipse. This operation was far from being as
easy as that of the navigator who expressed the series of his observations
on successive points of the coast by the general conception of an island.
But it is the very same sort of operation; and if the one is not an
induction but a description, this must also be true of the other.

The only real induction concerned in the case, consisted in inferring that
because the observed places of Mars were correctly represented by points
in an imaginary ellipse, therefore Mars would continue to revolve in that
same ellipse; and in concluding (before the gap had been filled up by
further observations) that the positions of the planet during the time
which intervened between two observations, must have coincided with the
intermediate points of the curve. For these were facts which had not been
directly observed. They were inferences from the observations; facts
inferred, as distinguished from facts seen. But these inferences were so
far from being a part of Kepler’s philosophical operation, that they had
been drawn long before he was born. Astronomers had long known that the
planets periodically returned to the same places. When this had been
ascertained, there was no induction left for Kepler to make, nor did he
make any further induction. He merely applied his new conception to the
facts inferred, as he did to the facts observed. Knowing already that the
planets continued to move in the same paths; when he found that an ellipse
correctly represented the past path, he knew that it would represent the
future path. In finding a compendious expression for the one set of facts,
he found one for the other: but he found the expression only, not the
inference; nor did he (which is the true test of a general truth) add any
thing to the power of prediction already possessed.

§ 4. The descriptive operation which enables a number of details to be
summed up in a single proposition, Dr. Whewell, by an aptly chosen
expression, has termed the Colligation of Facts. In most of his
observations concerning that mental process I fully agree, and would
gladly transfer all that portion of his book into my own pages. I only
think him mistaken in setting up this kind of operation, which according
to the old and received meaning of the term, is not induction at all, as
the type of induction generally; and laying down, throughout his work, as
principles of induction, the principles of mere colligation.

Dr. Whewell maintains that the general proposition which binds together
the particular facts, and makes them, as it were, one fact, is not the
mere sum of those facts, but something more, since there is introduced a
conception of the mind, which did not exist in the facts themselves. “The
particular facts,” says he,(102) “are not merely brought together, but
there is a new element added to the combination by the very act of thought
by which they are combined.... When the Greeks, after long observing the
motions of the planets, saw that these motions might be rightly considered
as produced by the motion of one wheel revolving in the inside of another
wheel, these wheels were creations of their minds, added to the facts
which they perceived by sense. And even if the wheels were no longer
supposed to be material, but were reduced to mere geometrical spheres or
circles, they were not the less products of the mind alone—something
additional to the facts observed. The same is the case in all other
discoveries. The facts are known, but they are insulated and unconnected,
till the discoverer supplies from his own store a principle of connection.
The pearls are there, but they will not hang together till some one
provides the string.”

Let me first remark that Dr. Whewell, in this passage, blends together,
indiscriminately, examples of both the processes which I am endeavoring to
distinguish from one another. When the Greeks abandoned the supposition
that the planetary motions were produced by the revolution of material
wheels, and fell back upon the idea of “mere geometrical spheres or
circles,” there was more in this change of opinion than the mere
substitution of an ideal curve for a physical one. There was the
abandonment of a theory, and the replacement of it by a mere description.
No one would think of calling the doctrine of material wheels a mere
description. That doctrine was an attempt to point out the force by which
the planets were acted upon, and compelled to move in their orbits. But
when, by a great step in philosophy, the materiality of the wheels was
discarded, and the geometrical forms alone retained, the attempt to
account for the motions was given up, and what was left of the theory was
a mere description of the orbits. The assertion that the planets were
carried round by wheels revolving in the inside of other wheels, gave
place to the proposition, that they moved in the same lines which would be
traced by bodies so carried: which was a mere mode of representing the sum
of the observed facts; as Kepler’s was another and a better mode of
representing the same observations.

It is true that for these simply descriptive operations, as well as for
the erroneous inductive one, a conception of the mind was required. The
conception of an ellipse must have presented itself to Kepler’s mind,
before he could identify the planetary orbits with it. According to Dr.
Whewell, the conception was something added to the facts. He expresses
himself as if Kepler had put something into the facts by his mode of
conceiving them. But Kepler did no such thing. The ellipse was in the
facts before Kepler recognized it; just as the island was an island before
it had been sailed round. Kepler did not _put_ what he had conceived into
the facts, but _saw_ it in them. A conception implies, and corresponds to,
something conceived: and though the conception itself is not in the facts,
but in our mind, yet if it is to convey any knowledge relating to them, it
must be a conception _of_ something which really is in the facts, some
property which they actually possess, and which they would manifest to our
senses, if our senses were able to take cognizance of it. If, for
instance, the planet left behind it in space a visible track, and if the
observer were in a fixed position at such a distance from the plane of the
orbit as would enable him to see the whole of it at once, he would see it
to be an ellipse; and if gifted with appropriate instruments and powers of
locomotion, he could prove it to be such by measuring its different
dimensions. Nay, further: if the track were visible, and he were so placed
that he could see all parts of it in succession, but not all of them at
once, he might be able, by piecing together his successive observations,
to discover both that it was an ellipse and that the planet moved in it.
The case would then exactly resemble that of the navigator who discovers
the land to be an island by sailing round it. If the path was visible, no
one I think would dispute that to identify it with an ellipse is to
describe it: and I can not see why any difference should be made by its
not being directly an object of sense, when every point in it is as
exactly ascertained as if it were so.

Subject to the indispensable condition which has just been stated, I do
not conceive that the part which conceptions have in the operation of
studying facts, has ever been overlooked or undervalued. No one ever
disputed that in order to reason about any thing we must have a conception
of it; or that when we include a multitude of things under a general
expression, there is implied in the expression a conception of something
common to those things. But it by no means follows that the conception is
necessarily pre-existent, or constructed by the mind out of its own
materials. If the facts are rightly classed under the conception, it is
because there is in the facts themselves something of which the conception
is itself a copy; and which if we can not directly perceive, it is because
of the limited power of our organs, and not because the thing itself is
not there. The conception itself is often obtained by abstraction from the
very facts which, in Dr. Whewell’s language, it is afterward called in to
connect. This he himself admits, when he observes (which he does on
several occasions), how great a service would be rendered to the science
of physiology by the philosopher “who should establish a precise, tenable,
and consistent conception of life.”(103) Such a conception can only be
abstracted from the phenomena of life itself; from the very facts which it
is put in requisition to connect. In other cases, no doubt, instead of
collecting the conception from the very phenomena which we are attempting
to colligate, we select it from among those which have been previously
collected by abstraction from other facts. In the instance of Kepler’s
laws, the latter was the case. The facts being out of the reach of being
observed, in any such manner as would have enabled the senses to identify
directly the path of the planet, the conception requisite for framing a
general description of that path could not be collected by abstraction
from the observations themselves; the mind had to supply hypothetically,
from among the conceptions it had obtained from other portions of its
experience, some one which would correctly represent the series of the
observed facts. It had to frame a supposition respecting the general
course of the phenomenon, and ask itself, If this be the general
description, what will the details be? and then compare these with the
details actually observed. If they agreed, the hypothesis would serve for
a description of the phenomenon: if not, it was necessarily abandoned, and
another tried. It is such a case as this which gives rise to the doctrine
that the mind, in framing the descriptions, adds something of its own
which it does not find in the facts.

Yet it is a fact surely, that the planet does describe an ellipse; and a
fact which we could see, if we had adequate visual organs and a suitable
position. Not having these advantages, but possessing the conception of an
ellipse, or (to express the meaning in less technical language) knowing
what an ellipse was, Kepler tried whether the observed places of the
planet were consistent with such a path. He found they were so; and he,
consequently, asserted as a fact that the planet moved in an ellipse. But
this fact, which Kepler did not add to, but found in, the motions of the
planet, namely, that it occupied in succession the various points in the
circumference of a given ellipse, was the very fact, the separate parts of
which had been separately observed; it was the sum of the different
observations.

Having stated this fundamental difference between my opinion and that of
Dr. Whewell, I must add, that his account of the manner in which a
conception is selected, suitable to express the facts, appears to me
perfectly just. The experience of all thinkers will, I believe, testify
that the process is tentative; that it consists of a succession of
guesses; many being rejected, until one at last occurs fit to be chosen.
We know from Kepler himself that before hitting upon the “conception” of
an ellipse, he tried nineteen other imaginary paths, which, finding them
inconsistent with the observations, he was obliged to reject. But as Dr.
Whewell truly says, the successful hypothesis, though a guess, ought
generally to be called, not a lucky, but a skillful guess. The guesses
which serve to give mental unity and wholeness to a chaos of scattered
particulars, are accidents which rarely occur to any minds but those
abounding in knowledge and disciplined in intellectual combinations.

How far this tentative method, so indispensable as a means to the
colligation of facts for purposes of description, admits of application to
Induction itself, and what functions belong to it in that department, will
be considered in the chapter of the present Book which relates to
Hypotheses. On the present occasion we have chiefly to distinguish this
process of Colligation from Induction properly so called; and that the
distinction may be made clearer, it is well to advert to a curious and
interesting remark, which is as strikingly true of the former operation,
as it appears to me unequivocally false of the latter.

In different stages of the progress of knowledge, philosophers have
employed, for the colligation of the same order of facts, different
conceptions. The early rude observations of the heavenly bodies, in which
minute precision was neither attained nor sought, presented nothing
inconsistent with the representation of the path of a planet as an exact
circle, having the earth for its centre. As observations increased in
accuracy, facts were disclosed which were not reconcilable with this
simple supposition: for the colligation of those additional facts, the
supposition was varied; and varied again and again as facts became more
numerous and precise. The earth was removed from the centre to some other
point within the circle; the planet was supposed to revolve in a smaller
circle called an epicycle, round an imaginary point which revolved in a
circle round the earth: in proportion as observation elicited fresh facts
contradictory to these representations, other epicycles and other
eccentrics were added, producing additional complication; until at last
Kepler swept all these circles away, and substituted the conception of an
exact ellipse. Even this is found not to represent with complete
correctness the accurate observations of the present day, which disclose
many slight deviations from an orbit exactly elliptical. Now Dr. Whewell
has remarked that these successive general expressions, though apparently
so conflicting, were all correct: they all answered the purpose of
colligation; they all enabled the mind to represent to itself with
facility, and by a simultaneous glance, the whole body of facts at the
time ascertained: each in its turn served as a correct description of the
phenomena, so far as the senses had up to that time taken cognizance of
them. If a necessity afterward arose for discarding one of these general
descriptions of the planet’s orbit, and framing a different imaginary
line, by which to express the series of observed positions, it was because
a number of new facts had now been added, which it was necessary to
combine with the old facts into one general description. But this did not
affect the correctness of the former expression, considered as a general
statement of the only facts which it was intended to represent. And so
true is this, that, as is well remarked by M. Comte, these ancient
generalizations, even the rudest and most imperfect of them, that of
uniform movement in a circle, are so far from being entirely false, that
they are even now habitually employed by astronomers when only a rough
approximation to correctness is required. “L’astronomie moderne, en
détruisant sans retour les hypothèses primitives, envisagées comme lois
réelles du monde, a soigneusement maintenu leur valeur positive et
permanente, la propriété de représenter commodément les phénomènes quand
il s’agit d’une première ébauche. Nos ressources à cet égard sont même
bien plus étendues, précisément à cause que nous ne nous faisons aucune
illusion sur la réalité des hypothèses; ce qui nous permet d’employer sans
scrupule, en chaque cas, celle que nous jugeons la plus avantageuse.”(104)

Dr. Whewell’s remark, therefore, is philosophically correct. Successive
expressions for the colligation of observed facts, or, in other words,
successive descriptions of a phenomenon as a whole, which has been
observed only in parts, may, though conflicting, be all correct as far as
they go. But it would surely be absurd to assert this of conflicting
inductions.

The scientific study of facts may be undertaken for three different
purposes: the simple description of the facts; their explanation; or their
prediction: meaning by prediction, the determination of the conditions
under which similar facts may be expected again to occur. To the first of
these three operations the name of Induction does not properly belong: to
the other two it does. Now, Dr. Whewell’s observation is true of the first
alone. Considered as a mere description, the circular theory of the
heavenly motions represents perfectly well their general features: and by
adding epicycles without limit, those motions, even as now known to us,
might be expressed with any degree of accuracy that might be required. The
elliptical theory, as a mere description, would have a great advantage in
point of simplicity, and in the consequent facility of conceiving it and
reasoning about it; but it would not really be more true than the other.
Different descriptions, therefore, may be all true: but not, surely,
different explanations. The doctrine that the heavenly bodies moved by a
virtue inherent in their celestial nature; the doctrine that they were
moved by impact (which led to the hypothesis of vortices as the only
impelling force capable of whirling bodies in circles), and the Newtonian
doctrine, that they are moved by the composition of a centripetal with an
original projectile force; all these are explanations, collected by real
induction from supposed parallel cases; and they were all successively
received by philosophers, as scientific truths on the subject of the
heavenly bodies. Can it be said of these, as was said of the different
descriptions, that they are all true as far as they go? Is it not clear
that only one can be true in any degree, and the other two must be
altogether false? So much for explanations: let us now compare different
predictions: the first, that eclipses will occur when one planet or
satellite is so situated as to cast its shadow upon another; the second,
that they will occur when some great calamity is impending over mankind.
Do these two doctrines only differ in the degree of their truth, as
expressing real facts with unequal degrees of accuracy? Assuredly the one
is true, and the other absolutely false.(105)

In every way, therefore, it is evident that to explain induction as the
colligation of facts by means of appropriate conceptions, that is,
conceptions which will really express them, is to confound mere
description of the observed facts with inference from those facts, and
ascribe to the latter what is a characteristic property of the former.

There is, however, between Colligation and Induction, a real correlation,
which it is important to conceive correctly. Colligation is not always
induction; but induction is always colligation. The assertion that the
planets move in ellipses, was but a mode of representing observed facts;
it was but a colligation; while the assertion that they are drawn, or
tend, toward the sun, was the statement of a new fact, inferred by
induction. But the induction, once made, accomplishes the purposes of
colligation likewise. It brings the same facts, which Kepler had connected
by his conception of an ellipse, under the additional conception of bodies
acted upon by a central force, and serves, therefore, as a new bond of
connection for those facts; a new principle for their classification.

Further, the descriptions which are improperly confounded with induction,
are nevertheless a necessary preparation for induction; no less necessary
than correct observation of the facts themselves. Without the previous
colligation of detached observations by means of one general conception,
we could never have obtained any basis for an induction, except in the
case of phenomena of very limited compass. We should not be able to affirm
any predicates at all, of a subject incapable of being observed otherwise
than piecemeal: much less could we extend those predicates by induction to
other similar subjects. Induction, therefore, always presupposes, not only
that the necessary observations are made with the necessary accuracy, but
also that the results of these observations are, so far as practicable,
connected together by general descriptions, enabling the mind to represent
to itself as wholes whatever phenomena are capable of being so
represented.

§ 5. Dr. Whewell has replied at some length to the preceding observations,
restating his opinions, but without (as far as I can perceive) adding any
thing material to his former arguments. Since, however, mine have not had
the good fortune to make any impression upon him, I will subjoin a few
remarks, tending to show more clearly in what our difference of opinion
consists, as well as, in some measure, to account for it.

Nearly all the definitions of induction, by writers of authority, make it
consist in drawing inferences from known cases to unknown; affirming of a
class, a predicate which has been found true of some cases belonging to
the class; concluding because some things have a certain property, that
other things which resemble them have the same property—or because a thing
has manifested a property at a certain time, that it has and will have
that property at other times.

It will scarcely be contended that Kepler’s operation was an Induction in
this sense of the term. The statement, that Mars moves in an elliptical
orbit, was no generalization from individual cases to a class of cases.
Neither was it an extension to all time, of what had been found true at
some particular time. The whole amount of generalization which the case
admitted of, was already completed, or might have been so. Long before the
elliptic theory was thought of, it had been ascertained that the planets
returned periodically to the same apparent places; the series of these
places was, or might have been, completely determined, and the apparent
course of each planet marked out on the celestial globe in an
uninterrupted line. Kepler did not extend an observed truth to other cases
than those in which it had been observed: he did not widen the _subject_
of the proposition which expressed the observed facts. The alteration he
made was in the predicate. Instead of saying, the successive places of
Mars are so and so, he summed them up in the statement, that the
successive places of Mars are points in an ellipse. It is true, this
statement, as Dr. Whewell says, was not the sum of the observations
_merely_; it was the sum of the observations _seen under a new point of
view_.(106) But it was not the sum of _more_ than the observations, as a
real induction is. It took in no cases but those which had been actually
observed, or which could have been inferred from the observations before
the new point of view presented itself. There was not that transition from
known cases to unknown, which constitutes Induction in the original and
acknowledged meaning of the term.

Old definitions, it is true, can not prevail against new knowledge: and if
the Keplerian operation, as a logical process, be really identical with
what takes place in acknowledged induction, the definition of induction
ought to be so widened as to take it in; since scientific language ought
to adapt itself to the true relations which subsist between the things it
is employed to designate. Here then it is that I am at issue with Dr.
Whewell. He does think the operations identical. He allows of no logical
process in any case of induction, other than what there was in Kepler’s
case, namely, guessing until a guess is found which tallies with the
facts; and accordingly, as we shall see hereafter, he rejects all canons
of induction, because it is not by means of them that we guess. Dr.
Whewell’s theory of the logic of science would be very perfect if it did
not pass over altogether the question of Proof. But in my apprehension
there is such a thing as proof, and inductions differ altogether from
descriptions in their relation to that element. Induction is proof; it is
inferring something unobserved from something observed: it requires,
therefore, an appropriate test of proof; and to provide that test, is the
special purpose of inductive logic. When, on the contrary, we merely
collate known observations, and, in Dr. Whewell’s phraseology, connect
them by means of a new conception; if the conception does serve to connect
the observations, we have all we want. As the proposition in which it is
embodied pretends to no other truth than what it may share with many other
modes of representing the same facts, to be consistent with the facts is
all it requires: it neither needs nor admits of proof; though it may serve
to prove other things, inasmuch as, by placing the facts in mental
connection with other facts, not previously seen to resemble them, it
assimilates the case to another class of phenomena, concerning which real
Inductions have already been made. Thus Kepler’s so-called law brought the
orbit of Mars into the class ellipse, and by doing so, proved all the
properties of an ellipse to be true of the orbit: but in this proof
Kepler’s law supplied the minor premise, and not (as is the case with real
Inductions) the major.

Dr. Whewell calls nothing Induction where there is not a new mental
conception introduced, and every thing induction where there is. But this
is to confound two very different things, Invention and Proof. The
introduction of a new conception belongs to Invention: and invention may
be required in any operation, but is the essence of none. A new conception
may be introduced for descriptive purposes, and so it may for inductive
purposes. But it is so far from constituting induction, that induction
does not necessarily stand in need of it. Most inductions require no
conception but what was present in every one of the particular instances
on which the induction is grounded. That all men are mortal is surely an
inductive conclusion; yet no new conception is introduced by it. Whoever
knows that any man has died, has all the conceptions involved in the
inductive generalization. But Dr. Whewell considers the process of
invention which consists in framing a new conception consistent with the
facts, to be not merely a necessary part of all induction, but the whole
of it.

The mental operation which extracts from a number of detached observations
certain general characters in which the observed phenomena resemble one
another, or resemble other known facts, is what Bacon, Locke, and most
subsequent metaphysicians, have understood by the word Abstraction. A
general expression obtained by abstraction, connecting known facts by
means of common characters, but without concluding from them to unknown,
may, I think, with strict logical correctness, be termed a Description;
nor do I know in what other way things can ever be described. My position,
however, does not depend on the employment of that particular word; I am
quite content to use Dr. Whewell’s term Colligation, or the more general
phrases, “mode of representing, or of expressing, phenomena:” provided it
be clearly seen that the process is not Induction, but something radically
different.

What more may usefully be said on the subject of Colligation, or of the
correlative expression invented by Dr. Whewell, the Explication of
Conceptions, and generally on the subject of ideas and mental
representations as connected with the study of facts, will find a more
appropriate place in the Fourth Book, on the Operations Subsidiary to
Induction: to which I must refer the reader for the removal of any
difficulty which the present discussion may have left.



                               Chapter III.


Of The Ground Of Induction.


§ 1. Induction properly so called, as distinguished from those mental
operations, sometimes, though improperly, designated by the name, which I
have attempted in the preceding chapter to characterize, may, then, be
summarily defined as Generalization from Experience. It consists in
inferring from some individual instances in which a phenomenon is observed
to occur, that it occurs in all instances of a certain class; namely, in
all which _resemble_ the former, in what are regarded as the material
circumstances.

In what way the material circumstances are to be distinguished from those
which are immaterial, or why some of the circumstances are material and
others not so, we are not yet ready to point out. We must first observe,
that there is a principle implied in the very statement of what Induction
is; an assumption with regard to the course of nature and the order of the
universe; namely, that there are such things in nature as parallel cases;
that what happens once, will, under a sufficient degree of similarity of
circumstances, happen again, and not only again, but as often as the same
circumstances recur. This, I say, is an assumption, involved in every case
of induction. And, if we consult the actual course of nature, we find that
the assumption is warranted. The universe, so far as known to us, is so
constituted, that whatever is true in any one case, is true in all cases
of a certain description; the only difficulty is, to find what
description.

This universal fact, which is our warrant for all inferences from
experience, has been described by different philosophers in different
forms of language: that the course of nature is uniform; that the universe
is governed by general laws; and the like. One of the most usual of these
modes of expression, but also one of the most inadequate, is that which
has been brought into familiar use by the metaphysicians of the school of
Reid and Stewart. The disposition of the human mind to generalize from
experience—a propensity considered by these philosophers as an instinct of
our nature—they usually describe under some such name as “our intuitive
conviction that the future will resemble the past.” Now it has been well
pointed out by Mr. Bailey,(107) that (whether the tendency be or not an
original and ultimate element of our nature), Time, in its modifications
of past, present, and future, has no concern either with the belief
itself, or with the grounds of it. We believe that fire will burn
to-morrow, because it burned to-day and yesterday; but we believe, on
precisely the same grounds, that it burned before we were born, and that
it burns this very day in Cochin-China. It is not from the past to the
future, as past and future, that we infer, but from the known to the
unknown; from facts observed to facts unobserved; from what we have
perceived, or been directly conscious of, to what has not come within our
experience. In this last predicament is the whole region of the future;
but also the vastly greater portion of the present and of the past.

Whatever be the most proper mode of expressing it, the proposition that
the course of nature is uniform, is the fundamental principle, or general
axiom of Induction. It would yet be a great error to offer this large
generalization as any explanation of the inductive process. On the
contrary, I hold it to be itself an instance of induction, and induction
by no means of the most obvious kind. Far from being the first induction
we make, it is one of the last, or at all events one of those which are
latest in attaining strict philosophical accuracy. As a general maxim,
indeed, it has scarcely entered into the minds of any but philosophers;
nor even by them, as we shall have many opportunities of remarking, have
its extent and limits been always very justly conceived. The truth is,
that this great generalization is itself founded on prior generalizations.
The obscurer laws of nature were discovered by means of it, but the more
obvious ones must have been understood and assented to as general truths
before it was ever heard of. We should never have thought of affirming
that all phenomena take place according to general laws, if we had not
first arrived, in the case of a great multitude of phenomena, at some
knowledge of the laws themselves; which could be done no otherwise than by
induction. In what sense, then, can a principle, which is so far from
being our earliest induction, be regarded as our warrant for all the
others? In the only sense, in which (as we have already seen) the general
propositions which we place at the head of our reasonings when we throw
them into syllogisms, ever really contribute to their validity. As
Archbishop Whately remarks, every induction is a syllogism with the major
premise suppressed; or (as I prefer expressing it) every induction may be
thrown into the form of a syllogism, by supplying a major premise. If this
be actually done, the principle which we are now considering, that of the
uniformity of the course of nature, will appear as the ultimate major
premise of all inductions, and will, therefore, stand to all inductions in
the relation in which, as has been shown at so much length, the major
proposition of a syllogism always stands to the conclusion; not
contributing at all to prove it, but being a necessary condition of its
being proved; since no conclusion is proved, for which there can not be
found a true major premise.(108)

The statement, that the uniformity of the course of nature is the ultimate
major premise in all cases of induction, may be thought to require some
explanation. The immediate major premise in every inductive argument, it
certainly is not. Of that, Archbishop Whately’s must be held to be the
correct account. The induction, “John, Peter, etc., are mortal, therefore
all mankind are mortal,” may, as he justly says, be thrown into a
syllogism by prefixing as a major premise (what is at any rate a necessary
condition of the validity of the argument), namely, that what is true of
John, Peter, etc., is true of all mankind. But how came we by this major
premise? It is not self-evident; nay, in all cases of unwarranted
generalization, it is not true. How, then, is it arrived at? Necessarily
either by induction or ratiocination; and if by induction, the process,
like all other inductive arguments, may be thrown into the form of a
syllogism. This previous syllogism it is, therefore, necessary to
construct. There is, in the long run, only one possible construction. The
real proof that what is true of John, Peter, etc., is true of all mankind,
can only be, that a different supposition would be inconsistent with the
uniformity which we know to exist in the course of nature. Whether there
would be this inconsistency or not, may be a matter of long and delicate
inquiry; but unless there would, we have no sufficient ground for the
major of the inductive syllogism. It hence appears, that if we throw the
whole course of any inductive argument into a series of syllogisms, we
shall arrive by more or fewer steps at an ultimate syllogism, which will
have for its major premise the principle, or axiom, of the uniformity of
the course of nature.(109)

It was not to be expected that in the case of this axiom, any more than of
other axioms, there should be unanimity among thinkers with respect to the
grounds on which it is to be received as true. I have already stated that
I regard it as itself a generalization from experience. Others hold it to
be a principle which, antecedently to any verification by experience, we
are compelled by the constitution of our thinking faculty to assume as
true. Having so recently, and at so much length, combated a similar
doctrine as applied to the axioms of mathematics, by arguments which are
in a great measure applicable to the present case, I shall defer the more
particular discussion of this controverted point in regard to the
fundamental axiom of induction, until a more advanced period of our
inquiry.(110) At present it is of more importance to understand thoroughly
the import of the axiom itself. For the proposition, that the course of
nature is uniform, possesses rather the brevity suitable to popular, than
the precision requisite in philosophical language: its terms require to be
explained, and a stricter than their ordinary signification given to them,
before the truth of the assertion can be admitted.

§ 2. Every person’s consciousness assures him that he does not always
expect uniformity in the course of events; he does not always believe that
the unknown will be similar to the known, that the future will resemble
the past. Nobody believes that the succession of rain and fine weather
will be the same in every future year as in the present. Nobody expects to
have the same dreams repeated every night. On the contrary, every body
mentions it as something extraordinary, if the course of nature is
constant, and resembles itself, in these particulars. To look for
constancy where constancy is not to be expected, as for instance that a
day which has once brought good fortune will always be a fortunate day, is
justly accounted superstition.

The course of nature, in truth, is not only uniform, it is also infinitely
various. Some phenomena are always seen to recur in the very same
combinations in which we met with them at first; others seem altogether
capricious; while some, which we had been accustomed to regard as bound
down exclusively to a particular set of combinations, we unexpectedly find
detached from some of the elements with which we had hitherto found them
conjoined, and united to others of quite a contrary description. To an
inhabitant of Central Africa, fifty years ago, no fact probably appeared
to rest on more uniform experience than this, that all human beings are
black. To Europeans, not many years ago, the proposition, All swans are
white, appeared an equally unequivocal instance of uniformity in the
course of nature. Further experience has proved to both that they were
mistaken; but they had to wait fifty centuries for this experience. During
that long time, mankind believed in a uniformity of the course of nature
where no such uniformity really existed.

According to the notion which the ancients entertained of induction, the
foregoing were cases of as legitimate inference as any inductions
whatever. In these two instances, in which, the conclusion being false,
the ground of inference must have been insufficient, there was,
nevertheless, as much ground for it as this conception of induction
admitted of. The induction of the ancients has been well described by
Bacon, under the name of “Inductio per enumerationem simplicem, ubi non
reperitur instantia contradictoria.” It consists in ascribing the
character of general truths to all propositions which are true in every
instance that we happen to know of. This is the kind of induction which is
natural to the mind when unaccustomed to scientific methods. The tendency,
which some call an instinct, and which others account for by association,
to infer the future from the past, the known from the unknown, is simply a
habit of expecting that what has been found true once or several times,
and never yet found false, will be found true again. Whether the instances
are few or many, conclusive or inconclusive, does not much affect the
matter: these are considerations which occur only on reflection; the
unprompted tendency of the mind is to generalize its experience, provided
this points all in one direction; provided no other experience of a
conflicting character comes unsought. The notion of seeking it, of
experimenting for it, of _interrogating_ nature (to use Bacon’s
expression) is of much later growth. The observation of nature, by
uncultivated intellects, is purely passive: they accept the facts which
present themselves, without taking the trouble of searching for more: it
is a superior mind only which asks itself what facts are needed to enable
it to come to a safe conclusion, and then looks out for these.

But though we have always a propensity to generalize from unvarying
experience, we are not always warranted in doing so. Before we can be at
liberty to conclude that something is universally true because we have
never known an instance to the contrary, we must have reason to believe
that if there were in nature any instances to the contrary, we should have
known of them. This assurance, in the great majority of cases, we can not
have, or can have only in a very moderate degree. The possibility of
having it, is the foundation on which we shall see hereafter that
induction by simple enumeration may in some remarkable cases amount
practically to proof.(111) No such assurance, however, can be had, on any
of the ordinary subjects of scientific inquiry. Popular notions are
usually founded on induction by simple enumeration; in science it carries
us but a little way. We are forced to begin with it; we must often rely on
it provisionally, in the absence of means of more searching investigation.
But, for the accurate study of nature, we require a surer and a more
potent instrument.

It was, above all, by pointing out the insufficiency of this rude and
loose conception of Induction, that Bacon merited the title so generally
awarded to him, of Founder of the Inductive Philosophy. The value of his
own contributions to a more philosophical theory of the subject has
certainly been exaggerated. Although (along with some fundamental errors)
his writings contain, more or less fully developed, several of the most
important principles of the Inductive Method, physical investigation has
now far outgrown the Baconian conception of Induction. Moral and political
inquiry, indeed, are as yet far behind that conception. The current and
approved modes of reasoning on these subjects are still of the same
vicious description against which Bacon protested; the method almost
exclusively employed by those professing to treat such matters
inductively, is the very _inductio per enumerationem simplicem_ which he
condemns; and the experience which we hear so confidently appealed to by
all sects, parties, and interests, is still, in his own emphatic words,
_mera palpatio_.

§ 3. In order to a better understanding of the problem which the logician
must solve if he would establish a scientific theory of Induction, let us
compare a few cases of incorrect inductions with others which are
acknowledged to be legitimate. Some, we know, which were believed for
centuries to be correct, were nevertheless incorrect. That all swans are
white, can not have been a good induction, since the conclusion has turned
out erroneous. The experience, however, on which the conclusion rested,
was genuine. From the earliest records, the testimony of the inhabitants
of the known world was unanimous on the point. The uniform experience,
therefore, of the inhabitants of the known world, agreeing in a common
result, without one known instance of deviation from that result, is not
always sufficient to establish a general conclusion.

But let us now turn to an instance apparently not very dissimilar to this.
Mankind were wrong, it seems, in concluding that all swans were white: are
we also wrong, when we conclude that all men’s heads grow above their
shoulders, and never below, in spite of the conflicting testimony of the
naturalist Pliny? As there were black swans, though civilized people had
existed for three thousand years on the earth without meeting with them,
may there not also be “men whose heads do grow beneath their shoulders,”
notwithstanding a rather less perfect unanimity of negative testimony from
observers? Most persons would answer No; it was more credible that a bird
should vary in its color, than that men should vary in the relative
position of their principal organs. And there is no doubt that in so
saying they would be right: but to say why they are right, would be
impossible, without entering more deeply than is usually done, into the
true theory of Induction.

Again, there are cases in which we reckon with the most unfailing
confidence upon uniformity, and other cases in which we do not count upon
it at all. In some we feel complete assurance that the future will
resemble the past, the unknown be precisely similar to the known. In
others, however invariable may be the result obtained from the instances
which have been observed, we draw from them no more than a very feeble
presumption that the like result will hold in all other cases. That a
straight line is the shortest distance between two points, we do not doubt
to be true even in the region of the fixed stars.(112) When a chemist
announces the existence and properties of a newly-discovered substance, if
we confide in his accuracy, we feel assured that the conclusions he has
arrived at will hold universally, though the induction be founded but on a
single instance. We do not withhold our assent, waiting for a repetition
of the experiment; or if we do, it is from a doubt whether the one
experiment was properly made, not whether if properly made it would be
conclusive. Here, then, is a general law of nature, inferred without
hesitation from a single instance; a universal proposition from a singular
one. Now mark another case, and contrast it with this. Not all the
instances which have been observed since the beginning of the world, in
support of the general proposition that all crows are black, would be
deemed a sufficient presumption of the truth of the proposition, to
outweigh the testimony of one unexceptionable witness who should affirm
that in some region of the earth not fully explored, he had caught and
examined a crow, and had found it to be gray.

Why is a single instance, in some cases, sufficient for a complete
induction, while in others, myriads of concurring instances, without a
single exception known or presumed, go such a very little way toward
establishing a universal proposition? Whoever can answer this question
knows more of the philosophy of logic than the wisest of the ancients, and
has solved the problem of induction.



                               Chapter IV.


Of Laws Of Nature.


§ 1. In the contemplation of that uniformity in the course of nature,
which is assumed in every inference from experience, one of the first
observations that present themselves is, that the uniformity in question
is not properly uniformity, but uniformities. The general regularity
results from the co-existence of partial regularities. The course of
nature in general is constant, because the course of each of the various
phenomena that compose it is so. A certain fact invariably occurs whenever
certain circumstances are present, and does not occur when they are
absent; the like is true of another fact; and so on. From these separate
threads of connection between parts of the great whole which we term
nature, a general tissue of connection unavoidably weaves itself, by which
the whole is held together. If A is always accompanied by D, B by E, and C
by F, it follows that A B is accompanied by D E, A C by D F, B C by E F,
and finally A B C by D E F; and thus the general character of regularity
is produced, which, along with and in the midst of infinite diversity,
pervades all nature.

The first point, therefore, to be noted in regard to what is called the
uniformity of the course of nature, is, that it is itself a complex fact,
compounded of all the separate uniformities which exist in respect to
single phenomena. These various uniformities, when ascertained by what is
regarded as a sufficient induction, we call, in common parlance, Laws of
Nature. Scientifically speaking, that title is employed in a more
restricted sense, to designate the uniformities when reduced to their most
simple expression. Thus in the illustration already employed, there were
seven uniformities; all of which, if considered sufficiently certain,
would, in the more lax application of the term, be called laws of nature.
But of the seven, three alone are properly distinct and independent: these
being presupposed, the others follow of course. The first three,
therefore, according to the stricter acceptation, are called laws of
nature; the remainder not; because they are in truth mere _cases_ of the
first three; virtually included in them; said, therefore, to _result_ from
them: whoever affirms those three has already affirmed all the rest.

To substitute real examples for symbolical ones, the following are three
uniformities, or call them laws of nature: the law that air has weight,
the law that pressure on a fluid is propagated equally in all directions,
and the law that pressure in one direction, not opposed by equal pressure
in the contrary direction, produces motion, which does not cease until
equilibrium is restored. From these three uniformities we should be able
to predict another uniformity, namely, the rise of the mercury in the
Torricellian tube. This, in the stricter use of the phrase, is not a law
of nature. It is the result of laws of nature. It is a _case_ of each and
every one of the three laws: and is the only occurrence by which they
could all be fulfilled. If the mercury were not sustained in the
barometer, and sustained at such a height that the column of mercury were
equal in weight to a column of the atmosphere of the same diameter; here
would be a case, either of the air not pressing upon the surface of the
mercury with the force which is called its weight, or of the downward
pressure on the mercury not being propagated equally in an upward
direction, or of a body pressed in one direction and not in the direction
opposite, either not moving in the direction in which it is pressed, or
stopping before it had attained equilibrium. If we knew, therefore, the
three simple laws, but had never tried the Torricellian experiment, we
might _deduce_ its result from those laws. The known weight of the air,
combined with the position of the apparatus, would bring the mercury
within the first of the three inductions; the first induction would bring
it within the second, and the second within the third, in the manner which
we characterized in treating of Ratiocination. We should thus come to know
the more complex uniformity, independently of specific experience, through
our knowledge of the simpler ones from which it results; though, for
reasons which will appear hereafter, _verification_ by specific experience
would still be desirable, and might possibly be indispensable.

Complex uniformities which, like this, are mere cases of simpler ones, and
have, therefore, been virtually affirmed in affirming those, may with
propriety be called _laws_, but can scarcely, in the strictness of
scientific speech, be termed Laws of Nature. It is the custom in science,
wherever regularity of any kind can be traced, to call the general
proposition which expresses the nature of that regularity, a law; as when,
in mathematics, we speak of the law of decrease of the successive terms of
a converging series. But the expression _law of nature_ has generally been
employed with a sort of tacit reference to the original sense of the word
law, namely, the expression of the will of a superior. When, therefore, it
appeared that any of the uniformities which were observed in nature, would
result spontaneously from certain other uniformities, no separate act of
creative will being supposed necessary for the production of the
derivative uniformities, these have not usually been spoken of as laws of
nature. According to one mode of expression, the question, What are the
laws of nature? may be stated thus: What are the fewest and simplest
assumptions, which being granted, the whole existing order of nature would
result? Another mode of stating it would be thus: What are the fewest
general propositions from which all the uniformities which exist in the
universe might be deductively inferred?

Every great advance which marks an epoch in the progress of science, has
consisted in a step made toward the solution of this problem. Even a
simple colligation of inductions already made, without any fresh extension
of the inductive inference, is already an advance in that direction. When
Kepler expressed the regularity which exists in the observed motions of
the heavenly bodies, by the three general propositions called his laws,
he, in so doing, pointed out three simple suppositions which, instead of a
much greater number, would suffice to construct the whole scheme of the
heavenly motions, so far as it was known up to that time. A similar and
still greater step was made when these laws, which at first did not seem
to be included in any more general truths, were discovered to be cases of
the three laws of motion, as obtaining among bodies which mutually tend
toward one another with a certain force, and have had a certain
instantaneous impulse originally impressed upon them. After this great
discovery, Kepler’s three propositions, though still called laws, would
hardly, by any person accustomed to use language with precision, be termed
laws of nature: that phrase would be reserved for the simpler and more
general laws into which Newton is said to have resolved them.

According to this language, every well-grounded inductive generalization
is either a law of nature, or a result of laws of nature, capable, if
those laws are known, of being predicted from them. And the problem of
Inductive Logic may be summed up in two questions: how to ascertain the
laws of nature; and how, after having ascertained them, to follow them
into their results. On the other hand, we must not suffer ourselves to
imagine that this mode of statement amounts to a real analysis, or to any
thing but a mere verbal transformation of the problem; for the expression,
Laws of Nature, _means_ nothing but the uniformities which exist among
natural phenomena (or, in other words, the results of induction), when
reduced to their simplest expression. It is, however, something to have
advanced so far, as to see that the study of nature is the study of laws,
not _a_ law; of uniformities, in the plural number: that the different
natural phenomena have their separate rules or modes of taking place,
which, though much intermixed and entangled with one another, may, to a
certain extent, be studied apart: that (to resume our former metaphor) the
regularity which exists in nature is a web composed of distinct threads,
and only to be understood by tracing each of the threads separately; for
which purpose it is often necessary to unravel some portion of the web,
and exhibit the fibres apart. The rules of experimental inquiry are the
contrivances for unraveling the web.

§ 2. In thus attempting to ascertain the general order of nature by
ascertaining the particular order of the occurrence of each one of the
phenomena of nature, the most scientific proceeding can be no more than an
improved form of that which was primitively pursued by the human
understanding, while undirected by science. When mankind first formed the
idea of studying phenomena according to a stricter and surer method than
that which they had in the first instance spontaneously adopted, they did
not, conformably to the well-meant but impracticable precept of Descartes,
set out from the supposition that nothing had been already ascertained.
Many of the uniformities existing among phenomena are so constant, and so
open to observation, as to force themselves upon involuntary recognition.
Some facts are so perpetually and familiarly accompanied by certain
others, that mankind learned, as children learn, to expect the one where
they found the other, long before they knew how to put their expectation
into words by asserting, in a proposition, the existence of a connection
between those phenomena. No science was needed to teach that food
nourishes, that water drowns, or quenches thirst, that the sun gives light
and heat, that bodies fall to the ground. The first scientific inquirers
assumed these and the like as known truths, and set out from them to
discover others which were unknown: nor were they wrong in so doing,
subject, however, as they afterward began to see, to an ulterior revision
of these spontaneous generalizations themselves, when the progress of
knowledge pointed out limits to them, or showed their truth to be
contingent on some circumstance not originally attended to. It will
appear, I think, from the subsequent part of our inquiry, that there is no
logical fallacy in this mode of proceeding; but we may see already that
any other mode is rigorously impracticable: since it is impossible to
frame any scientific method of induction, or test of the correctness of
inductions, unless on the hypothesis that some inductions deserving of
reliance have been already made.

Let us revert, for instance, to one of our former illustrations, and
consider why it is that, with exactly the same amount of evidence, both
negative and positive, we did not reject the assertion that there are
black swans, while we should refuse credence to any testimony which
asserted that there were men wearing their heads underneath their
shoulders. The first assertion was more credible than the latter. But why
more credible? So long as neither phenomenon had been actually witnessed,
what reason was there for finding the one harder to be believed than the
other? Apparently because there is less constancy in the colors of
animals, than in the general structure of their anatomy. But how do we
know this? Doubtless, from experience. It appears, then, that we need
experience to inform us, in what degree, and in what cases, or sorts of
cases, experience is to be relied on. Experience must be consulted in
order to learn from it under what circumstances arguments from it will be
valid. We have no ulterior test to which we subject experience in general;
but we make experience its own test. Experience testifies, that among the
uniformities which it exhibits or seems to exhibit, some are more to be
relied on than others; and uniformity, therefore, may be presumed, from
any given number of instances, with a greater degree of assurance, in
proportion as the case belongs to a class in which the uniformities have
hitherto been found more uniform.

This mode of correcting one generalization by means of another, a narrower
generalization by a wider, which common sense suggests and adopts in
practice, is the real type of scientific Induction. All that art can do is
but to give accuracy and precision to this process, and adapt it to all
varieties of cases, without any essential alteration in its principle.

There are of course no means of applying such a test as that above
described, unless we already possess a general knowledge of the prevalent
character of the uniformities existing throughout nature. The
indispensable foundation, therefore, of a scientific formula of induction,
must be a survey of the inductions to which mankind have been conducted in
unscientific practice; with the special purpose of ascertaining what kinds
of uniformities have been found perfectly invariable, pervading all
nature, and what are those which have been found to vary with difference
of time, place, or other changeable circumstances.

§ 3. The necessity of such a survey is confirmed by the consideration,
that the stronger inductions are the touch-stone to which we always
endeavor to bring the weaker. If we find any means of deducing one of the
less strong inductions from stronger ones, it acquires, at once, all the
strength of those from which it is deduced; and even adds to that
strength; since the independent experience on which the weaker induction
previously rested, becomes additional evidence of the truth of the better
established law in which it is now found to be included. We may have
inferred, from historical evidence, that the uncontrolled power of a
monarch, of an aristocracy, or of the majority, will often be abused: but
we are entitled to rely on this generalization with much greater assurance
when it is shown to be a corollary from still better established facts;
the very low degree of elevation of character ever yet attained by the
average of mankind, and the little efficacy, for the most part, of the
modes of education hitherto practiced, in maintaining the predominance of
reason and conscience over the selfish propensities. It is at the same
time obvious that even these more general facts derive an accession of
evidence from the testimony which history bears to the effects of
despotism. The strong induction becomes still stronger when a weaker one
has been bound up with it.

On the other hand, if an induction conflicts with stronger inductions, or
with conclusions capable of being correctly deduced from them, then,
unless on reconsideration it should appear that some of the stronger
inductions have been expressed with greater universality than their
evidence warrants, the weaker one must give way. The opinion so long
prevalent that a comet, or any other unusual appearance in the heavenly
regions, was the precursor of calamities to mankind, or to those at least
who witnessed it; the belief in the veracity of the oracles of Delphi or
Dodona; the reliance on astrology, or on the weather-prophecies in
almanacs, were doubtless inductions supposed to be grounded on
experience:(113) and faith in such delusions seems quite capable of
holding out against a great multitude of failures, provided it be
nourished by a reasonable number of casual coincidences between the
prediction and the event. What has really put an end to these insufficient
inductions, is their inconsistency with the stronger inductions
subsequently obtained by scientific inquiry, respecting the causes on
which terrestrial events really depend; and where those scientific truths
have not yet penetrated, the same or similar delusions still prevail.

It may be affirmed as a general principle, that all inductions, whether
strong or weak, which can be connected by ratiocination, are confirmatory
of one another; while any which lead deductively to consequences that are
incompatible, become mutually each other’s test, showing that one or other
must be given up, or at least more guardedly expressed. In the case of
inductions which confirm each other, the one which becomes a conclusion
from ratiocination rises to at least the level of certainty of the weakest
of those from which it is deduced; while in general all are more or less
increased in certainty. Thus the Torricellian experiment, though a mere
case of three more general laws, not only strengthened greatly the
evidence on which those laws rested, but converted one of them (the weight
of the atmosphere) from a still doubtful generalization into a completely
established doctrine.

If, then, a survey of the uniformities which have been ascertained to
exist in nature, should point out some which, as far as any human purpose
requires certainty, may be considered quite certain and quite universal;
then by means of these uniformities we may be able to raise multitudes of
other inductions to the same point in the scale. For if we can show, with
respect to any inductive inference, that either it must be true, or one of
these certain and universal inductions must admit of an exception; the
former generalization will attain the same certainty, and indefeasibleness
within the bounds assigned to it, which are the attributes of the latter.
It will be proved to be a law; and if not a result of other and simpler
laws, it will be a law of nature.

There are such certain and universal inductions; and it is because there
are such, that a Logic of Induction is possible.



                                Chapter V.


Of The Law Of Universal Causation.


§ 1. The phenomena of nature exist in two distinct relations to one
another; that of simultaneity, and that of succession. Every phenomenon is
related, in a uniform manner, to some phenomena that co-exist with it, and
to some that have preceded and will follow it.

Of the uniformities which exist among synchronous phenomena, the most
important, on every account, are the laws of number; and next to them
those of space, or, in other words, of extension and figure. The laws of
number are common to synchronous and successive phenomena. That two and
two make four, is equally true whether the second two follow the first two
or accompany them. It is as true of days and years as of feet and inches.
The laws of extension and figure (in other words, the theorems of
geometry, from its lowest to its highest branches) are, on the contrary,
laws of simultaneous phenomena only. The various parts of space, and of
the objects which are said to fill space, co-exist; and the unvarying laws
which are the subject of the science of geometry, are an expression of the
mode of their co-existence.

This is a class of laws, or in other words, of uniformities, for the
comprehension and proof of which it is not necessary to suppose any lapse
of time, any variety of facts or events succeeding one another. The
propositions of geometry are independent of the succession of events. All
things which possess extension, or, in other words, which fill space, are
subject to geometrical laws. Possessing extension, they possess figure;
possessing figure, they must possess some figure in particular, and have
all the properties which geometry assigns to that figure. If one body be a
sphere and another a cylinder, of equal height and diameter, the one will
be exactly two-thirds of the other, let the nature and quality of the
material be what it will. Again, each body, and each point of a body, must
occupy some place or position among other bodies; and the position of two
bodies relatively to each other, of whatever nature the bodies be, may be
unerringly inferred from the position of each of them relatively to any
third body.

In the laws of number, then, and in those of space, we recognize in the
most unqualified manner, the rigorous universality of which we are in
quest. Those laws have been in all ages the type of certainty, the
standard of comparison for all inferior degrees of evidence. Their
invariability is so perfect, that it renders us unable even to conceive
any exception to them; and philosophers have been led, though (as I have
endeavored to show) erroneously, to consider their evidence as lying not
in experience, but in the original constitution of the intellect. If,
therefore, from the laws of space and number, we were able to deduce
uniformities of any other description, this would be conclusive evidence
to us that those other uniformities possessed the same rigorous certainty.
But this we can not do. From laws of space and number alone, nothing can
be deduced but laws of space and number.

Of all truths relating to phenomena, the most valuable to us are those
which relate to the order of their succession. On a knowledge of these is
founded every reasonable anticipation of future facts, and whatever power
we possess of influencing those facts to our advantage. Even the laws of
geometry are chiefly of practical importance to us as being a portion of
the premises from which the order of the succession of phenomena may be
inferred. Inasmuch as the motion of bodies, the action of forces, and the
propagation of influences of all sorts, take place in certain lines and
over definite spaces, the properties of those lines and spaces are an
important part of the laws to which those phenomena are themselves
subject. Again, motions, forces, or other influences, and times, are
numerable quantities; and the properties of number are applicable to them
as to all other things. But though the laws of number and space are
important elements in the ascertainment of uniformities of succession,
they can do nothing toward it when taken by themselves. They can only be
made instrumental to that purpose when we combine with them additional
premises, expressive of uniformities of succession already known. By
taking, for instance, as premises these propositions, that bodies acted
upon by an instantaneous force move with uniform velocity in straight
lines; that bodies acted upon by a continuous force move with accelerated
velocity in straight lines; and that bodies acted upon by two forces in
different directions move in the diagonal of a parallelogram, whose sides
represent the direction and quantity of those forces; we may by combining
these truths with propositions relating to the properties of straight
lines and of parallelograms (as that a triangle is half a parallelogram of
the same base and altitude), deduce another important uniformity of
succession, viz., that a body moving round a centre of force describes
areas proportional to the times. But unless there had been laws of
succession in our premises, there could have been no truths of succession
in our conclusions. A similar remark might be extended to every other
class of phenomena really peculiar; and, had it been attended to, would
have prevented many chimerical attempts at demonstrations of the
indemonstrable, and explanations which do not explain.

It is not, therefore, enough for us that the laws of space, which are only
laws of simultaneous phenomenon, and the laws of number, which though true
of successive phenomena do not relate to their succession, possess the
rigorous certainty and universality of which we are in search. We must
endeavor to find some law of succession which has those same attributes,
and is therefore fit to be made the foundation of processes for
discovering, and of a test for verifying, all other uniformities of
succession. This fundamental law must resemble the truths of geometry in
their most remarkable peculiarity, that of never being, in any instance
whatever, defeated or suspended by any change of circumstances.

Now among all those uniformities in the succession of phenomena, which
common observation is sufficient to bring to light, there are very few
which have any, even apparent, pretension to this rigorous
indefeasibility: and of those few, one only has been found capable of
completely sustaining it. In that one, however, we recognize a law which
is universal also in another sense; it is co-extensive with the entire
field of successive phenomena, all instances whatever of succession being
examples of it. This law is the Law of Causation. The truth that every
fact which has a beginning has a cause, is co-extensive with human
experience.

This generalization may appear to some minds not to amount to much, since
after all it asserts only this: “it is a law, that every event depends on
some law:” “it is a law, that there is a law for every thing.” We must
not, however, conclude that the generality of the principle is merely
verbal; it will be found on inspection to be no vague or unmeaning
assertion, but a most important and really fundamental truth.

§ 2. The notion of Cause being the root of the whole theory of Induction,
it is indispensable that this idea should, at the very outset of our
inquiry, be, with the utmost practicable degree of precision, fixed and
determined. If, indeed, it were necessary for the purpose of inductive
logic that the strife should be quelled, which has so long raged among the
different schools of metaphysicians, respecting the origin and analysis of
our idea of causation; the promulgation, or at least the general
reception, of a true theory of induction, might be considered desperate
for a long time to come. But the science of the Investigation of Truth by
means of Evidence, is happily independent of many of the controversies
which perplex the science of the ultimate constitution of the human mind,
and is under no necessity of pushing the analysis of mental phenomenon to
that extreme limit which alone ought to satisfy a metaphysician.

I premise, then, that when in the course of this inquiry I speak of the
cause of any phenomenon, I do not mean a cause which is not itself a
phenomenon; I make no research into the ultimate or ontological cause of
any thing. To adopt a distinction familiar in the writings of the Scotch
metaphysicians, and especially of Reid, the causes with which I concern
myself are not _efficient_, but _physical_ causes. They are causes in that
sense alone, in which one physical fact is said to be the cause of
another. Of the efficient causes of phenomena, or whether any such causes
exist at all, I am not called upon to give an opinion. The notion of
causation is deemed, by the schools of metaphysics most in vogue at the
present moment, to imply a mysterious and most powerful tie, such as can
not, or at least does not, exist between any physical fact and that other
physical fact on which it is invariably consequent, and which is popularly
termed its cause: and thence is deduced the supposed necessity of
ascending higher, into the essences and inherent constitution of things,
to find the true cause, the cause which is not only followed by, but
actually produces, the effect. No such necessity exists for the purposes
of the present inquiry, nor will any such doctrine be found in the
following pages. The only notion of a cause, which the theory of induction
requires, is such a notion as can be gained from experience. The Law of
Causation, the recognition of which is the main pillar of inductive
science, is but the familiar truth, that invariability of succession is
found by observation to obtain between every fact in nature and some other
fact which has preceded it; independently of all considerations respecting
the ultimate mode of production of phenomena, and of every other question
regarding the nature of “Things in themselves.”

Between the phenomena, then, which exist at any instant, and the phenomena
which exist at the succeeding instant, there is an invariable order of
succession; and, as we said in speaking of the general uniformity of the
course of nature, this web is composed of separate fibres; this collective
order is made up of particular sequences, obtaining invariably among the
separate parts. To certain facts, certain facts always do, and, as we
believe, will continue to, succeed. The invariable antecedent is termed
the cause; the invariable consequent, the effect. And the universality of
the law of causation consists in this, that every consequent is connected
in this manner with some particular antecedent, or set of antecedents. Let
the fact be what it may, if it has begun to exist, it was preceded by some
fact or facts, with which it is invariably connected. For every event
there exists some combination of objects or events, some given concurrence
of circumstances, positive and negative, the occurrence of which is always
followed by that phenomenon. We may not have found out what this
concurrence of circumstances may be; but we never doubt that there is such
a one, and that it never occurs without having the phenomenon in question
as its effect or consequence. On the universality of this truth depends
the possibility of reducing the inductive process to rules. The undoubted
assurance we have that there is a law to be found if we only knew how to
find it, will be seen presently to be the source from which the canons of
the Inductive Logic derive their validity.

§ 3. It is seldom, if ever, between a consequent and a single antecedent,
that this invariable sequence subsists. It is usually between a consequent
and the sum of several antecedents; the concurrence of all of them being
requisite to produce, that is, to be certain of being followed by, the
consequent. In such cases it is very common to single out one only of the
antecedents under the denomination of Cause, calling the others merely
Conditions. Thus, if a person eats of a particular dish, and dies in
consequence, that is, would not have died if he had not eaten of it,
people would be apt to say that eating of that dish was the cause of his
death. There needs not, however, be any invariable connection between
eating of the dish and death; but there certainly is, among the
circumstances which took place, some combination or other on which death
is invariably consequent: as, for instance, the act of eating of the dish,
combined with a particular bodily constitution, a particular state of
present health, and perhaps even a certain state of the atmosphere; the
whole of which circumstances perhaps constituted in this particular case
the _conditions_ of the phenomenon, or, in other words, the set of
antecedents which determined it, and but for which it would not have
happened. The real Cause, is the whole of these antecedents; and we have,
philosophically speaking, no right to give the name of cause to one of
them, exclusively of the others. What, in the case we have supposed,
disguises the incorrectness of the expression, is this: that the various
conditions, except the single one of eating the food, were not _events_
(that is, instantaneous changes, or successions of instantaneous changes)
but _states_, possessing more or less of permanency; and might therefore
have preceded the effect by an indefinite length of duration, for want of
the event which was requisite to complete the required concurrence of
conditions: while as soon as that event, eating the food, occurs, no other
cause is waited for, but the effect begins immediately to take place: and
hence the appearance is presented of a more immediate and close connection
between the effect and that one antecedent, than between the effect and
the remaining conditions. But though we may think proper to give the name
of cause to that one condition, the fulfillment of which completes the
tale, and brings about the effect without further delay; this condition
has really no closer relation to the effect than any of the other
conditions has. All the conditions were equally indispensable to the
production of the consequent; and the statement of the cause is
incomplete, unless in some shape or other we introduce them all. A man
takes mercury, goes out-of-doors, and catches cold. We say, perhaps, that
the cause of his taking cold was exposure to the air. It is clear,
however, that his having taken mercury may have been a necessary condition
of his catching cold; and though it might consist with usage to say that
the cause of his attack was exposure to the air, to be accurate we ought
to say that the cause was exposure to the air while under the effect of
mercury.

If we do not, when aiming at accuracy, enumerate all the conditions, it is
only because some of them will in most cases be understood without being
expressed, or because for the purpose in view they may without detriment
be overlooked. For example, when we say, the cause of a man’s death was
that his foot slipped in climbing a ladder, we omit as a thing unnecessary
to be stated the circumstance of his weight, though quite as indispensable
a condition of the effect which took place. When we say that the assent of
the crown to a bill makes it law, we mean that the assent, being never
given until all the other conditions are fulfilled, makes up the sum of
the conditions, though no one now regards it as the principal one. When
the decision of a legislative assembly has been determined by the casting
vote of the chairman, we sometimes say that this one person was the cause
of all the effects which resulted from the enactment. Yet we do not really
suppose that his single vote contributed more to the result than that of
any other person who voted in the affirmative; but, for the purpose we
have in view, which is to insist on his individual responsibility, the
part which any other person had in the transaction is not material.

In all these instances the fact which was dignified with the name of
cause, was the one condition which came last into existence. But it must
not be supposed that in the employment of the term this or any other rule
is always adhered to. Nothing can better show the absence of any
scientific ground for the distinction between the cause of a phenomenon
and its conditions, than the capricious manner in which we select from
among the conditions that which we choose to denominate the cause. However
numerous the conditions may be, there is hardly any of them which may not,
according to the purpose of our immediate discourse, obtain that nominal
pre-eminence. This will be seen by analyzing the conditions of some one
familiar phenomenon. For example, a stone thrown into water falls to the
bottom. What are the conditions of this event? In the first place there
must be a stone, and water, and the stone must be thrown into the water;
but these suppositions forming part of the enunciation of the phenomenon
itself, to include them also among the conditions would be a vicious
tautology; and this class of conditions, therefore, have never received
the name of cause from any but the Aristotelians, by whom they were called
the _material_ cause, _causa materialis_. The next condition is, there
must be an earth: and accordingly it is often said, that the fall of a
stone is caused by the earth; or by a power or property of the earth, or a
force exerted by the earth, all of which are merely roundabout ways of
saying that it is caused by the earth; or, lastly, the earth’s attraction;
which also is only a technical mode of saying that the earth causes the
motion, with the additional particularity that the motion is toward the
earth, which is not a character of the cause, but of the effect. Let us
now pass to another condition. It is not enough that the earth should
exist; the body must be within that distance from it, in which the earth’s
attraction preponderates over that of any other body. Accordingly we may
say, and the expression would be confessedly correct, that the cause of
the stone’s falling is its being _within the sphere_ of the earth’s
attraction. We proceed to a further condition. The stone is immersed in
water: it is therefore a condition of its reaching the ground, that its
specific gravity exceed that of the surrounding fluid, or in other words
that it surpass in weight an equal volume of water. Accordingly any one
would be acknowledged to speak correctly who said, that the cause of the
stone’s going to the bottom is its exceeding in specific gravity the fluid
in which it is immersed.

Thus we see that each and every condition of the phenomenon may be taken
in its turn, and, with equal propriety in common parlance, but with equal
impropriety in scientific discourse, may be spoken of as if it were the
entire cause. And in practice, that particular condition is usually styled
the cause, whose share in the matter is superficially the most
conspicuous, or whose requisiteness to the production of the effect we
happen to be insisting on at the moment. So great is the force of this
last consideration, that it sometimes induces us to give the name of cause
even to one of the negative conditions. We say, for example, The army was
surprised because the sentinel was off his post. But since the sentinel’s
absence was not what created the enemy, or put the soldiers asleep, how
did it cause them to be surprised? All that is really meant is, that the
event would not have happened if he had been at his duty. His being off
his post was no producing cause, but the mere absence of a preventing
cause: it was simply equivalent to his non-existence. From nothing, from a
mere negation, no consequences can proceed. All effects are connected, by
the law of causation, with some set of _positive_ conditions; negative
ones, it is true, being almost always required in addition. In other
words, every fact or phenomenon which has a beginning, invariably arises
when some certain combination of positive facts exists, provided certain
other positive facts do not exist.

There is, no doubt, a tendency (which our first example, that of death
from taking a particular food, sufficiently illustrates) to associate the
idea of causation with the proximate antecedent _event_, rather than with
any of the antecedent _states_, or permanent facts, which may happen also
to be conditions of the phenomenon; the reason being that the event not
only exists, but begins to exist immediately previous; while the other
conditions may have pre-existed for an indefinite time. And this tendency
shows itself very visibly in the different logical fictions which are
resorted to, even by men of science, to avoid the necessity of giving the
name of cause to any thing which had existed for an indeterminate length
of time before the effect. Thus, rather than say that the earth causes the
fall of bodies, they ascribe it to a _force_ exerted by the earth, or an
_attraction_ by the earth, abstractions which they can represent to
themselves as exhausted by each effort, and therefore constituting at each
successive instant a fresh fact, simultaneous with, or only immediately
preceding, the effect. Inasmuch as the coming of the circumstance which
completes the assemblage of conditions, is a change or event, it thence
happens that an event is always the antecedent in closest apparent
proximity to the consequent: and this may account for the illusion which
disposes us to look upon the proximate event as standing more peculiarly
in the position of a cause than any of the antecedent states. But even
this peculiarity, of being in closer proximity to the effect than any
other of its conditions, is, as we have already seen, far from being
necessary to the common notion of a cause; with which notion, on the
contrary, any one of the conditions, either positive or negative, is
found, on occasion, completely to accord.(114)

The cause, then, philosophically speaking, is the sum total of the
conditions, positive and negative taken together; the whole of the
contingencies of every description, which being realized, the consequent
invariably follows. The negative conditions, however, of any phenomenon, a
special enumeration of which would generally be very prolix, may be all
summed up under one head, namely, the absence of preventing or
counteracting causes. The convenience of this mode of expression is mainly
grounded on the fact, that the effects of any cause in counteracting
another cause may in most cases be, with strict scientific exactness,
regarded as a mere extension of its own proper and separate effects. If
gravity retards the upward motion of a projectile, and deflects it into a
parabolic trajectory, it produces, in so doing, the very same kind of
effect, and even (as mathematicians know) the same quantity of effect, as
it does in its ordinary operation of causing the fall of bodies when
simply deprived of their support. If an alkaline solution mixed with an
acid destroys its sourness, and prevents it from reddening vegetable
blues, it is because the specific effect of the alkali is to combine with
the acid, and form a compound with totally different qualities. This
property, which causes of all descriptions possess, of preventing the
effects of other causes by virtue (for the most part) of the same laws
according to which they produce their own,(115) enables us, by
establishing the general axiom that all causes are liable to be
counteracted in their effects by one another, to dispense with the
consideration of negative conditions entirely, and limit the notion of
cause to the assemblage of the positive conditions of the phenomenon: one
negative condition invariably understood, and the same in all instances
(namely, the absence of counteracting causes) being sufficient, along with
the sum of the positive conditions, to make up the whole set of
circumstances on which the phenomenon is dependent.

§ 4. Among the positive conditions, as we have seen that there are some to
which, in common parlance, the term cause is more readily and frequently
awarded, so there are others to which it is, in ordinary circumstances,
refused. In most cases of causation a distinction is commonly drawn
between something which acts, and some other thing which is acted upon;
between an _agent_ and a _patient_. Both of these, it would be universally
allowed, are conditions of the phenomenon; but it would be thought absurd
to call the latter the cause, that title being reserved for the former.
The distinction, however, vanishes on examination, or rather is found to
be only verbal; arising from an incident of mere expression, namely, that
the object said to be acted upon, and which is considered as the scene in
which the effect takes place, is commonly included in the phrase by which
the effect is spoken of, so that if it were also reckoned as part of the
cause, the seeming incongruity would arise of its being supposed to cause
itself. In the instance which we have already had, of falling bodies, the
question was thus put: What is the cause which makes a stone fall? and if
the answer had been “the stone itself,” the expression would have been in
apparent contradiction to the meaning of the word cause. The stone,
therefore, is conceived as the patient, and the earth (or, according to
the common and most unphilosophical practice, an occult quality of the
earth) is represented as the agent or cause. But that there is nothing
fundamental in the distinction may be seen from this, that it is quite
possible to conceive the stone as causing its own fall, provided the
language employed be such as to save the mere verbal incongruity. We might
say that the stone moves toward the earth by the properties of the matter
composing it; and according to this mode of presenting the phenomenon, the
stone itself might without impropriety be called the agent; though, to
save the established doctrine of the inactivity of matter, men usually
prefer here also to ascribe the effect to an occult quality, and say that
the cause is not the stone itself, but the _weight_ or _gravitation_ of
the stone.

Those who have contended for a radical distinction between agent and
patient, have generally conceived the agent as that which causes some
state of, or some change in the state of, another object which is called
the patient. But a little reflection will show that the license we assume
of speaking of phenomena as _states_ of the various objects which take
part in them (an artifice of which so much use has been made by some
philosophers, Brown in particular, for the apparent explanation of
phenomena), is simply a sort of logical fiction, useful sometimes as one
among several modes of expression, but which should never be supposed to
be the enunciation of a scientific truth. Even those attributes of an
object which might seem with greatest propriety to be called states of the
object itself, its sensible qualities, its color, hardness, shape, and the
like, are in reality (as no one has pointed out more clearly than Brown
himself) phenomena of causation, in which the substance is distinctly the
agent, or producing cause, the patient being our own organs, and those of
other sentient beings. What we call states of objects, are always
sequences into which the objects enter, generally as antecedents or
causes; and things are never more active than in the production of those
phenomena in which they are said to be acted upon. Thus, in the example of
a stone falling to the earth, according to the theory of gravitation the
stone is as much an agent as the earth, which not only attracts, but is
itself attracted by, the stone. In the case of a sensation produced in our
organs, the laws of our organization, and even those of our minds, are as
directly operative in determining the effect produced, as the laws of the
outward object. Though we call prussic acid the agent of a person’s death,
the whole of the vital and organic properties of the patient are as
actively instrumental as the poison, in the chain of effects which so
rapidly terminates his sentient existence. In the process of education, we
may call the teacher the agent, and the scholar only the material acted
upon; yet in truth all the facts which pre-existed in the scholar’s mind
exert either co-operating or counteracting agencies in relation to the
teacher’s efforts. It is not light alone which is the agent in vision, but
light coupled with the active properties of the eye and brain, and with
those of the visible object. The distinction between agent and patient is
merely verbal: patients are always agents; in a great proportion, indeed,
of all natural phenomena, they are so to such a degree as to react
forcibly on the causes which acted upon them: and even when this is not
the case, they contribute, in the same manner as any of the other
conditions, to the production of the effect of which they are vulgarly
treated as the mere theatre. All the positive conditions of a phenomenon
are alike agents, alike active; and in any expression of the cause which
professes to be complete, none of them can with reason be excluded, except
such as have already been implied in the words used for describing the
effect; nor by including even these would there be incurred any but a
merely verbal impropriety.

§ 5. There is a case of causation which calls for separate notice, as it
possesses a peculiar feature, and presents a greater degree of complexity
than the common case. It often happens that the effect, or one of the
effects, of a cause, is, not to produce of itself a certain phenomenon,
but to fit something else for producing it. In other words, there is a
case of causation in which the effect is to invest an object with a
certain property. When sulphur, charcoal, and nitre are put together in
certain proportions and in a certain manner, the effect is, not an
explosion, but that the mixture acquires a property by which, in given
circumstances, it will explode. The various causes, natural and
artificial, which educate the human body or the human mind, have for their
principal effect, not to make the body or mind immediately do any thing,
but to endow it with certain properties—in other words, to give assurance
that in given circumstances certain results will take place in it, or as
consequences of it. Physiological agencies often have for the chief part
of their operation to _predispose_ the constitution to some mode of
action. To take a simpler instance than all these: putting a coat of white
paint upon a wall does not merely produce in those who see it done, the
sensation of white; it confers on the wall the permanent property of
giving that kind of sensation. Regarded in reference to the sensation, the
putting on of the paint is a condition of a condition; it is a condition
of the wall’s causing that particular fact. The wall may have been painted
years ago, but it has acquired a property which has lasted till now, and
will last longer; the antecedent condition necessary to enable the wall to
become in its turn a condition, has been fulfilled once for all. In a case
like this, where the immediate consequent in the sequence is a property
produced in an object, no one now supposes the property to be a
substantive entity “inherent” in the object. What has been produced is
what, in other language, may be called a state of preparation in an object
for producing an effect. The ingredients of the gunpowder have been
brought into a state of preparation for exploding as soon as the other
conditions of an explosion shall have occurred. In the case of the
gunpowder, this state of preparation consists in a certain collocation of
its particles relatively to one another. In the example of the wall, it
consists in a new collocation of two things relatively to each other—the
wall and the paint. In the example of the molding influences on the human
mind, its being a collocation at all is only conjectural; for, even on the
materialistic hypothesis, it would remain to be proved that the increased
facility with which the brain sums up a column of figures when it has been
long trained to calculation, is the result of a permanent new arrangement
of some of its material particles. We must, therefore, content ourselves
with what we know, and must include among the effects of causes, the
capacities given to objects of being causes of other effects. This
capacity is not a real thing existing in the objects; it is but a name for
our conviction that they will act in a particular manner when certain new
circumstances arise. We may invest this assurance of future events with a
fictitious objective existence, by calling it a state of the object. But
unless the state consists, as in the case of the gunpowder it does, in a
collocation of particles, it expresses no present fact; it is but the
contingent future fact brought back under another name.

It may be thought that this form of causation requires us to admit an
exception to the doctrine that the conditions of a phenomenon—the
antecedents required for calling it into existence—must all be found among
the facts immediately, not remotely, preceding its commencement. But what
we have arrived at is not a correction, it is only an explanation, of that
doctrine. In the enumeration of the conditions required for the occurrence
of any phenomenon, it always has to be included that objects must be
present, possessed of given properties. It is a condition of the
phenomenon explosion that an object should be present, of one or other of
certain kinds, which for that reason are called explosive. The presence of
one of these objects is a condition immediately precedent to the
explosion. The condition which is not immediately precedent is the cause
which produced, not the explosion, but the explosive property. The
conditions of the explosion itself were all present immediately before it
took place, and the general law, therefore, remains intact.

§ 6. It now remains to advert to a distinction which is of first-rate
importance both for clearing up the notion of cause, and for obviating a
very specious objection often made against the view which we have taken of
the subject.

When we define the cause of any thing (in the only sense in which the
present inquiry has any concern with causes) to be “the antecedent which
it invariably follows,” we do not use this phrase as exactly synonymous
with “the antecedent which it invariably _has_ followed in our past
experience.” Such a mode of conceiving causation would be liable to the
objection very plausibly urged by Dr. Reid, namely, that according to this
doctrine night must be the cause of day, and day the cause of night; since
these phenomena have invariably succeeded one another from the beginning
of the world. But it is necessary to our using the word cause, that we
should believe not only that the antecedent always _has_ been followed by
the consequent, but that, as long as the present constitution of
things(116) endures, it always _will_ be so. And this would not be true of
day and night. We do not believe that night will be followed by day under
all imaginable circumstances, but only that it will be so _provided_ the
sun rises above the horizon. If the sun ceased to rise, which, for aught
we know, may be perfectly compatible with the general laws of matter,
night would be, or might be, eternal. On the other hand, if the sun is
above the horizon, his light not extinct, and no opaque body between us
and him, we believe firmly that unless a change takes place in the
properties of matter, this combination of antecedents will be followed by
the consequent, day; that if the combination of antecedents could be
indefinitely prolonged, it would be always day; and that if the same
combination had always existed, it would always have been day, quite
independently of night as a previous condition. Therefore is it that we do
not call night the cause, nor even a condition, of day. The existence of
the sun (or some such luminous body), and there being no opaque medium in
a straight line(117) between that body and the part of the earth where we
are situated, are the sole conditions; and the union of these, without the
addition of any superfluous circumstance, constitutes the cause. This is
what writers mean when they say that the notion of cause involves the idea
of necessity. If there be any meaning which confessedly belongs to the
term necessity, it is _unconditionalness_. That which is necessary, that
which _must_ be, means that which will be, whatever supposition we may
make in regard to all other things. The succession of day and night
evidently is not necessary in this sense. It is conditional on the
occurrence of other antecedents. That which will be followed by a given
consequent when, and only when, some third circumstance also exists, is
not the cause, even though no case should ever have occurred in which the
phenomenon took place without it.

Invariable sequence, therefore, is not synonymous with causation, unless
the sequence, besides being invariable, is unconditional. There are
sequences, as uniform in past experience as any others whatever, which yet
we do not regard as cases of causation, but as conjunctions in some sort
accidental. Such, to an accurate thinker, is that of day and night. The
one might have existed for any length of time, and the other not have
followed the sooner for its existence; it follows only if certain other
antecedents exist; and where those antecedents existed, it would follow in
any case. No one, probably, ever called night the cause of day; mankind
must so soon have arrived at the very obvious generalization, that the
state of general illumination which we call day would follow from the
presence of a sufficiently luminous body, whether darkness had preceded or
not.

We may define, therefore, the cause of a phenomenon, to be the antecedent,
or the concurrence of antecedents, on which it is invariably and
_unconditionally_ consequent. Or if we adopt the convenient modification
of the meaning of the word cause, which confines it to the assemblage of
positive conditions without the negative, then instead of
“unconditionally,” we must say, “subject to no other than negative
conditions.”

To some it may appear, that the sequence between night and day being
invariable in our experience, we have as much ground in this case as
experience can give in any case, for recognizing the two phenomena as
cause and effect; and that to say that more is necessary—to require a
belief that the succession is unconditional, or, in other words, that it
would be invariable under all changes of circumstances, is to acknowledge
in causation an element of belief not derived from experience. The answer
to this is, that it is experience itself which teaches us that one
uniformity of sequence is conditional and another unconditional. When we
judge that the succession of night and day is a derivative sequence,
depending on something else, we proceed on grounds of experience. It is
the evidence of experience which convinces us that day could equally exist
without being followed by night, and that night could equally exist
without being followed by day. To say that these beliefs are “not
generated by our mere observation of sequence,”(118) is to forget that
twice in every twenty-four hours, when the sky is clear, we have an
_experimentum crucis_ that the cause of day is the sun. We have an
experimental knowledge of the sun which justifies us on experimental
grounds in concluding, that if the sun were always above the horizon there
would be day, though there had been no night, and that if the sun were
always below the horizon there would be night, though there had been no
day. We thus know from experience that the succession of night and day is
not unconditional. Let me add, that the antecedent which is only
conditionally invariable, is not the invariable antecedent. Though a fact
may, in experience, have always been followed by another fact, yet if the
remainder of our experience teaches us that it might not always be so
followed, or if the experience itself is such as leaves room for a
possibility that the known cases may not correctly represent all possible
cases, the hitherto invariable antecedent is not accounted the cause; but
why? Because we are not sure that it _is_ the invariable antecedent.

Such cases of sequence as that of day and night not only do not contradict
the doctrine which resolves causation into invariable sequence, but are
necessarily implied in that doctrine. It is evident, that from a limited
number of unconditional sequences, there will result a much greater number
of conditional ones. Certain causes being given, that is, certain
antecedents which are unconditionally followed by certain consequents; the
mere co-existence of these causes will give rise to an unlimited number of
additional uniformities. If two causes exist together, the effects of both
will exist together; and if many causes co-exist, these causes (by what we
shall term hereafter the intermixture of their laws) will give rise to new
effects, accompanying or succeeding one another in some particular order,
which order will be invariable while the causes continue to co-exist, but
no longer. The motion of the earth in a given orbit round the sun, is a
series of changes which follow one another as antecedents and consequents,
and will continue to do so while the sun’s attraction, and the force with
which the earth tends to advance in a direct line through space, continue
to co-exist in the same quantities as at present. But vary either of these
causes, and this particular succession of motions would cease to take
place. The series of the earth’s motions, therefore, though a case of
sequence invariable within the limits of human experience, is not a case
of causation. It is not unconditional.

This distinction between the relations of succession which, so far as we
know, are unconditional, and those relations, whether of succession or of
co-existence, which, like the earth’s motions, or the succession of day
and night, depend on the existence or on the co-existence of other
antecedent facts—corresponds to the great division which Dr. Whewell and
other writers have made of the field of science, into the investigation of
what they term the Laws of Phenomena, and the investigation of causes; a
phraseology, as I conceive, not philosophically sustainable, inasmuch as
the ascertainment of causes, such causes as the human faculties can
ascertain, namely, causes which are themselves phenomena, is, therefore,
merely the ascertainment of other and more universal Laws of Phenomena.
And let me here observe, that Dr. Whewell, and in some degree even Sir
John Herschel, seem to have misunderstood the meaning of those writers
who, like M. Comté, limit the sphere of scientific investigation to Laws
of Phenomena, and speak of the inquiry into causes as vain and futile. The
causes which M. Comté designates as inaccessible, are efficient causes.
The investigation of physical, as opposed to efficient, causes (including
the study of all the active forces in Nature, considered as facts of
observation) is as important a part of M. Comté’s conception of science as
of Dr. Whewell’s. His objection to the _word_ cause is a mere matter of
nomenclature, in which, as a matter of nomenclature, I consider him to be
entirely wrong. “Those,” it is justly remarked by Mr. Bailey,(119) “who,
like M. Comté, object to designate _events_ as causes, are objecting
without any real ground to a mere but extremely convenient generalization,
to a very useful common name, the employment of which involves, or needs
involve, no particular theory.” To which it may be added, that by
rejecting this form of expression, M. Comté leaves himself without any
term for marking a distinction which, however incorrectly expressed, is
not only real, but is one of the fundamental distinctions in science;
indeed it is on this alone, as we shall hereafter find, that the
possibility rests of framing a rigorous Canon of Induction. And as things
left without a name are apt to be forgotten, a Canon of that description
is not one of the many benefits which the philosophy of Induction has
received from M. Comté’s great powers.

§ 7. Does a cause always stand with its effect in the relation of
antecedent and consequent? Do we not often say of two simultaneous facts
that they are cause and effect—as when we say that fire is the cause of
warmth, the sun and moisture the cause of vegetation, and the like? Since
a cause does not necessarily perish because its effect has been produced,
the two things do very generally co-exist; and there are some appearances,
and some common expressions, seeming to imply not only that causes may,
but that they must, be contemporaneous with their effects. _Cessante causâ
cessat et effectus_, has been a dogma of the schools: the necessity for
the continued existence of the cause in order to the continuance of the
effect, seems to have been once a generally received doctrine. Kepler’s
numerous attempts to account for the motions of the heavenly bodies on
mechanical principles, were rendered abortive by his always supposing that
the agency which set those bodies in motion must continue to operate in
order to keep up the motion which it at first produced. Yet there were at
all times many familiar instances of the continuance of effects, long
after their causes had ceased. A _coup de soleil_ gives a person
brain-fever: will the fever go off as soon as he is moved out of the
sunshine? A sword is run through his body: must the sword remain in his
body in order that he may continue dead? A plowshare once made, remains a
plowshare, without any continuance of heating and hammering, and even
after the man who heated and hammered it has been gathered to his fathers.
On the other hand, the pressure which forces up the mercury in an
exhausted tube must be continued in order to sustain it in the tube. This
(it may be replied) is because another force is acting without
intermission, the force of gravity, which would restore it to its level,
unless counterpoised by a force equally constant. But again: a tight
bandage causes pain, which pain will sometimes go off as soon as the
bandage is removed. The illumination which the sun diffuses over the earth
ceases when the sun goes down.

There is, therefore, a distinction to be drawn. The conditions which are
necessary for the first production of a phenomenon, are occasionally also
necessary for its continuance; though more commonly its continuance
requires no condition except negative ones. Most things, once produced,
continue as they are, until something changes or destroys them; but some
require the permanent presence of the agencies which produced them at
first. These may, if we please, be considered as instantaneous phenomena,
requiring to be renewed at each instant by the cause by which they were at
first generated. Accordingly, the illumination of any given point of space
has always been looked upon as an instantaneous fact, which perishes and
is perpetually renewed as long as the necessary conditions subsist. If we
adopt this language we avoid the necessity of admitting that the
continuance of the cause is ever required to maintain the effect. We may
say, it is not required to maintain, but to reproduce, the effect, or else
to counteract some force tending to destroy it. And this may be a
convenient phraseology. But it is only a phraseology. The fact remains,
that in some cases (though those are a minority) the continuance of the
conditions which produced an effect is necessary to the continuance of the
effect.

As to the ulterior question, whether it is strictly necessary that the
cause, or assemblage of conditions, should precede, by ever so short an
instant, the production of the effect (a question raised and argued with
much ingenuity by Sir John Herschel in an Essay already quoted),(120) the
inquiry is of no consequence for our present purpose. There certainly are
cases in which the effect follows without any interval perceptible by our
faculties; and when there is an interval, we can not tell by how many
intermediate links imperceptible to us that interval may really be filled
up. But even granting that an effect may commence simultaneously with its
cause, the view I have taken of causation is in no way practically
affected. Whether the cause and its effect be necessarily successive or
not, the beginning of a phenomenon is what implies a cause, and causation
is the law of the succession of phenomena. If these axioms be granted, we
can afford, though I see no necessity for doing so, to drop the words
antecedent and consequent as applied to cause and effect. I have no
objection to define a cause, the assemblage of phenomena, which occurring,
some other phenomenon invariably commences, or has its origin. Whether the
effect coincides in point of time with, or immediately follows, the
hindmost of its conditions, is immaterial. At all events, it does not
precede it; and when we are in doubt, between two co-existent phenomena,
which is cause and which effect, we rightly deem the question solved if we
can ascertain which of them preceded the other.

§ 8. It continually happens that several different phenomena, which are
not in the slightest degree dependent or conditional on one another, are
found all to depend, as the phrase is, on one and the same agent; in other
words, one and the same phenomenon is seen to be followed by several sorts
of effects quite heterogeneous, but which go on simultaneously one with
another; provided, of course, that all other conditions requisite for each
of them also exist. Thus, the sun produces the celestial motions; it
produces daylight, and it produces heat. The earth causes the fall of
heavy bodies, and it also, in its capacity of a great magnet, causes the
phenomena of the magnetic needle. A crystal of galena causes the
sensations of hardness, of weight, of cubical form, of gray color, and
many others between which we can trace no interdependence. The purpose to
which the phraseology of Properties and Powers is specially adapted, is
the expression of this sort of cases. When the same phenomenon is followed
(either subject or not to the presence of other conditions) by effects of
different and dissimilar orders, it is usual to say that each different
sort of effect is produced by a different property of the cause. Thus we
distinguish the attractive or gravitative property of the earth, and its
magnetic property: the gravitative, luminiferous, and calorific properties
of the sun: the color, shape, weight, and hardness of a crystal. These are
mere phrases, which explain nothing, and add nothing to our knowledge of
the subject; but, considered as abstract names denoting the connection
between the different effects produced and the object which produces them,
they are a very powerful instrument of abridgment, and of that
acceleration of the process of thought which abridgment accomplishes.

This class of considerations leads to a conception which we shall find to
be of great importance, that of a Permanent Cause, or original natural
agent. There exist in nature a number of permanent causes, which have
subsisted ever since the human race has been in existence, and for an
indefinite and probably an enormous length of time previous. The sun, the
earth, and planets, with their various constituents, air, water, and other
distinguishable substances, whether simple or compound, of which nature is
made up, are such Permanent Causes. These have existed, and the effects or
consequences which they were fitted to produce have taken place (as often
as the other conditions of the production met), from the very beginning of
our experience. But we can give no account of the origin of the Permanent
Causes themselves. Why these particular natural agents existed originally
and no others, or why they are commingled in such and such proportions,
and distributed in such and such a manner throughout space, is a question
we can not answer. More than this: we can discover nothing regular in the
distribution itself; we can reduce it to no uniformity, to no law. There
are no means by which, from the distribution of these causes or agents in
one part of space, we could conjecture whether a similar distribution
prevails in another. The co-existence, therefore, of Primeval Causes
ranks, to us, among merely casual concurrences: and all those sequences or
co-existences among the effects of several such causes, which, though
invariable while those causes co-exist, would, if the co-existence
terminated, terminate along with it, we do not class as cases of
causation, or laws of nature: we can only calculate on finding these
sequences or co-existences where we know by direct evidence, that the
natural agents on the properties of which they ultimately depend, are
distributed in the requisite manner. These Permanent Causes are not always
objects; they are sometimes events, that is to say, periodical cycles of
events, that being the only mode in which events can possess the property
of permanence. Not only, for instance, is the earth itself a permanent
cause, or primitive natural agent, but the earth’s rotation is so too: it
is a cause which has produced, from the earliest period (by the aid of
other necessary conditions), the succession of day and night, the ebb and
flow of the sea, and many other effects, while, as we can assign no cause
(except conjecturally) for the rotation itself, it is entitled to be
ranked as a primeval cause. It is, however, only the _origin_ of the
rotation which is mysterious to us: once begun, its continuance is
accounted for by the first law of motion (that of the permanence of
rectilinear motion once impressed) combined with the gravitation of the
parts of the earth toward one another.

All phenomena without exception which begin to exist, that is, all except
the primeval causes, are effects either immediate or remote of those
primitive facts, or of some combination of them. There is no Thing
produced, no event happening, in the known universe, which is not
connected by a uniformity, or invariable sequence, with some one or more
of the phenomena which preceded it; insomuch that it will happen again as
often as those phenomena occur again, and as no other phenomenon having
the character of a counteracting cause shall co-exist. These antecedent
phenomena, again, were connected in a similar manner with some that
preceded them; and so on, until we reach, as the ultimate step attainable
by us, either the properties of some one primeval cause, or the
conjunction of several. The whole of the phenomena of nature were
therefore the necessary, or, in other words, the unconditional,
consequences of some former collocation of the Permanent Causes.

The state of the whole universe at any instant, we believe to be the
consequence of its state at the previous instant; insomuch that one who
knew all the agents which exist at the present moment, their collocation
in space, and all their properties, in other words, the laws of their
agency, could predict the whole subsequent history of the universe, at
least unless some new volition of a power capable of controlling the
universe should supervene.(121) And if any particular state of the entire
universe could ever recur a second time, all subsequent states would
return too, and history would, like a circulating decimal of many figures,
periodically repeat itself:


    Jam redit et virgo, redeunt Saturnia regna....
    Alter erit tum Tiphys, et altera quæ vehat Argo
    Delectos heroas; erunt quoque altera bella,
    Atque iterum ad Trojam magnus mittetur Achilles.


And though things do not really revolve in this eternal round, the whole
series of events in the history of the universe, past and future, is not
the less capable, in its own nature, of being constructed _a priori_ by
any one whom we can suppose acquainted with the original distribution of
all natural agents, and with the whole of their properties, that is, the
laws of succession existing between them and their effects: saving the far
more than human powers of combination and calculation which would be
required, even in one possessing the data, for the actual performance of
the task.

§ 9. Since every thing which occurs is determined by laws of causation and
collocations of the original causes, it follows that the co-existences
which are observable among effects can not be themselves the subject of
any similar set of laws, distinct from laws of causation. Uniformities
there are, as well of co-existence as of succession, among effects; but
these must in all cases be a mere result either of the identity or of the
co-existence of their causes: if the causes did not co-exist, neither
could the effects. And these causes being also effects of prior causes,
and these of others, until we reach the primeval causes, it follows that
(except in the case of effects which can be traced immediately or remotely
to one and the same cause) the co-existences of phenomena can in no case
be universal, unless the co-existences of the primeval causes to which the
effects are ultimately traceable can be reduced to a universal law: but we
have seen that they can not. There are, accordingly, no original and
independent, in other words no unconditional, uniformities of
co-existence, between effects of different causes; if they co-exist, it is
only because the causes have casually co-existed. The only independent and
unconditional co-existences which are sufficiently invariable to have any
claim to the character of laws, are between different and mutually
independent effects of the same cause; in other words, between different
properties of the same natural agent. This portion of the Laws of Nature
will be treated of in the latter part of the present Book, under the name
of the Specific Properties of Kinds.

§ 10. Since the first publication of the present treatise, the sciences of
physical nature have made a great advance in generalization, through the
doctrine known as the Conservation or Persistence of Force. This imposing
edifice of theory, the building and laying out of which has for some time
been the principal occupation of the most systematic minds among physical
inquirers, consists of two stages: one, of ascertained fact, the other
containing a large element of hypothesis.

To begin with the first. It is proved by numerous facts, both natural and
of artificial production, that agencies which had been regarded as
distinct and independent sources of force—heat, electricity, chemical
action, nervous and muscular action, momentum of moving bodies—are
interchangeable, in definite and fixed quantities, with one another. It
had long been known that these dissimilar phenomena had the power, under
certain conditions, of producing one another: what is new in the theory is
a more accurate estimation of what this production consists in. What
happens is, that the whole or part of the one kind of phenomena
disappears, and is replaced by phenomena of one of the other descriptions,
and that there is an equivalence in quantity between the phenomena that
have disappeared and those which have been produced, insomuch that if the
process be reversed, the very same quantity which had disappeared will
re-appear, without increase or diminution. Thus the amount of heat which
will raise the temperature of a pound of water one degree of the
thermometer, will, if expended, say in the expansion of steam, lift a
weight of 772 pounds one foot, or a weight of one pound 772 feet: and the
same exact quantity of heat can, by certain means, be recovered, through
the expenditure of exactly that amount of mechanical motion.

The establishment of this comprehensive law has led to a change in the
language in which the scientific world had been accustomed to speak of
what are called the Forces of nature. Before this correlation between
phenomena most unlike one another had been ascertained, their unlikeness
had caused them to be referred to so many distinct forces. Now that they
are known to be convertible into one another without loss, they are spoken
of as all of them results of one and the same force, manifesting itself in
different modes. This force (it is said) can only produce a limited and
definite quantity of effect, but always does produce that definite
quantity; and produces it, according to circumstances, in one or another
of the forms, or divides it among several, but so as (according to a scale
of numerical equivalents established by experiment) always to make up the
same sum; and no one of the manifestations can be produced, save by the
disappearance of the equivalent quantity of another, which in its turn, in
appropriate circumstances, will re-appear undiminished. This mutual
interchangeability of the forces of nature, according to fixed numerical
equivalents, is the part of the new doctrine which rests on irrefragable
fact.

To make the statement true, however, it is necessary to add, that an
indefinite and perhaps immense interval of time may elapse between the
disappearance of the force in one form and its re-appearance in another. A
stone thrown up into the air with a given force, and falling back
immediately, will, by the time it reaches the earth, recover the exact
amount of mechanical momentum which was expended in throwing it up,
deduction being made of a small portion of motion which has been
communicated to the air. But if the stone has lodged on a height, it may
not fall back for years, or perhaps ages, and until it does, the force
expended in raising it is temporarily lost, being represented only by
what, in the language of the new theory, is called potential energy. The
coal imbedded in the earth is considered by the theory as a vast reservoir
of force, which has remained dormant for many geological periods, and will
so remain until, by being burned, it gives out the stored-up force in the
form of heat. Yet it is not supposed that this force is a material thing
which can be confined by bounds, as used to be thought of latent heat when
that important phenomenon was first discovered. What is meant is that when
the coal does at last, by combustion, generate a quantity of heat
(transformable like all other heat into mechanical momentum, and the other
forms of force), this extrication of heat is the re-appearance of a force
derived from the sun’s rays, expended myriads of ages ago in the
vegetation of the organic substances which were the material of the coal.

Let us now pass to the higher stage of the theory of Conservation of
Force; the part which is no longer a generalization of proved fact, but a
combination of fact and hypothesis. Stated in few words, it is as follows:
That the Conservation of Force is really the Conservation of Motion; that
in the various interchanges between the forms of force, it is always
motion that is transformed into motion. To establish this, it is necessary
to assume motions which are hypothetical. The supposition is, that there
are motions which manifest themselves to our senses only as heat,
electricity, etc., being molecular motions; oscillations, invisible to us,
among the minute particles of bodies; and that these molecular motions are
transmutable into molar motions (motions of masses), and molar motions
into molecular. Now there is a real basis of fact for this supposition: we
have positive evidence of the existence of molecular motion in these
manifestations of force. In the case of chemical action, for instance, the
particles separate and form new combinations, often with a great visible
disturbance of the mass. In the case of heat, the evidence is equally
conclusive, since heat expands bodies (that is, causes their particles to
move _from_ one another); and if of sufficient amount, changes their mode
of aggregation from solid to liquid, or from liquid to gaseous. Again, the
mechanical actions which produce heat—friction, and the collision of
bodies—must from the nature of the case produce a shock, that is, an
internal motion of particles, which indeed, we find, is often so violent
as to break them permanently asunder. Such facts are thought to warrant
the inference, that it is not, as was supposed, heat that causes the
motion of particles, but the motion of particles that causes heat; the
original cause of both being the previous motion (whether molar or
molecular—collision of bodies or combustion of fuel) which formed the
heating agency. This inference already contains hypothesis; but at least
the supposed cause, the intestine motion of molecules, is a _vera causa_.
But in order to reduce the Conservation of Force to Conservation of
Motion, it was necessary to attribute to motion the heat propagated,
through apparently empty space, from the sun. This required the
supposition (already made for the explanation of the laws of light) of a
subtle ether pervading space, which, though impalpable to us, must have
the property which constitutes matter, that of resistance, since waves are
propagated through it by an impulse from a given point. The ether must be
supposed (a supposition not required by the theory of light) to penetrate
into the minute interstices of all bodies. The vibratory motion supposed
to be taking place in the heated mass of the sun, is considered as
imparted from that mass to the particles of the surrounding ether, and
through them to the particles of the same ether in the interstices of
terrestrial bodies; and this, too, with a sufficient mechanical force to
throw the particles of those bodies into a state of similar vibration,
producing the expansion of their mass, and the sensation of heat in
sentient creatures. All this is hypothesis, though, of its legitimacy as
hypothesis, I do not mean to express any doubt. It would seem to follow as
a consequence from this theory, that Force may and should be defined,
matter in motion. This definition, however, will not stand, for, as has
already been seen, the matter needs not be in _actual_ motion. It is not
necessary to suppose that the motion afterward manifested, is actually
taking place among the molecules of the coal during its sojourn in the
earth;(122) certainly not in the stone which is at rest on the eminence to
which it has been raised. The true definition of Force must be, not
motion, but Potentiality of Motion; and what the doctrine, if established,
amounts to, is, not that there is at all times the same quantity of actual
motion in the universe; but that the possibilities of motion are limited
to a definite quantity, which can not be added to, but which can not be
exhausted; and that all actual motion which takes place in Nature is a
draft upon this limited stock. It needs not all of it have ever existed as
actual motion. There is a vast amount of potential motion in the universe
in the form of gravitation, which it would be a great abuse of hypothesis
to suppose to have been stored up by the expenditure of an equal amount of
actual motion in some former state of the universe. Nor does the motion
produced by gravity take place, so far as we know, at the expense of any
other motion, either molar or molecular.

It is proper to consider whether the adoption of this theory as a
scientific truth, involving as it does a change in the conception hitherto
entertained of the most general physical agencies, requires any
modification in the view I have taken of Causation as a law of nature. As
it appears to me, none whatever. The manifestations which the theory
regards as modes of motion, are as much distinct and separate phenomena
when referred to a single force, as when attributed to several. Whether
the phenomenon is called a transformation of force or the generation of
one, it has its own set or sets of antecedents, with which it is connected
by invariable and unconditional sequence; and that set, or those sets, of
antecedents are its cause. The relation of the Conservation theory to the
principle of Causation is discussed in much detail, and very
instructively, by Professor Bain, in the second volume of his Logic. The
chief practical conclusion drawn by him, bearing on Causation, is, that we
must distinguish in the assemblage of conditions which constitutes the
Cause of a phenomenon, two elements: one, the presence of a force; the
other, the collocation or position of objects which is required in order
that the force may undergo the particular transmutation which constitutes
the phenomenon. Now, it might always have been said with acknowledged
correctness, that a force and a collocation were both of them necessary to
produce any phenomenon. The law of causation is, that change can only be
produced by change. Along with any number of stationary antecedents, which
are collocations, there must be at least one changing antecedent, which is
a force. To produce a bonfire, there must not only be fuel, and air, and a
spark, which are collocations, but chemical action between the air and the
materials, which is a force. To grind corn, there must be a certain
collocation of the parts composing a mill, relatively to one another and
to the corn; but there must also be the gravitation of water, or the
motion of wind, to supply a force. But as the force in these cases was
regarded as a property of the objects in which it is embodied, it seemed
tautology to say that there must be the collocation _and_ the force. As
the collocation must be a collocation of objects possessing the
force-giving property, the collocation, so understood, included the force.

How, then, shall we have to express these facts, if the theory be finally
substantiated that all Force is reducible to a previous Motion? We shall
have to say, that one of the conditions of every phenomenon is an
antecedent Motion. But it will have to be explained that this needs not be
_actual_ motion. The coal which supplies the force exerted in combustion
is not shown to have been exerting that force in the form of molecular
motion in the pit; it was not even exerting pressure. The stone on the
eminence _is_ exerting a pressure, but only equivalent to its weight, not
to the additional momentum it would acquire by falling. The antecedent,
therefore, is not a force in action; and we can still only call it a
property of the objects, by which they would exert a force on the
occurrence of a fresh collocation. The collocation, therefore, still
includes the force. The force said to be stored up, is simply a particular
property which the object has acquired. The cause we are in search of, is
a collocation of objects possessing that particular property. When,
indeed, we inquire further into the cause from which they derive that
property, the new conception introduced by the Conservation theory comes
in: the property is itself an effect, and its cause, according to the
theory, is a former motion of exactly equivalent amount, which has been
impressed on the particles of the body, perhaps at some very distant
period. But the case is simply one of those we have already considered, in
which the efficacy of a cause consists in its investing an object with a
property. The force said to be laid up, and merely potential, is no more a
really existing thing than any other properties of objects are really
existing things. The expression is a mere artifice of language, convenient
for describing the phenomena: it is unnecessary to suppose that any thing
has been in continuous existence except an abstract potentiality. A force
suspended in its operation, neither manifesting itself by motion nor by
pressure, is not an existing fact, but a name for our conviction that in
appropriate circumstances a fact would take place. We know that a pound
weight, were it to fall from the earth into the sun, would acquire in
falling a momentum equal to millions of pounds; but we do not credit the
pound weight with more of actually existing force than is equal to the
pressure it is now exerting on the earth, and that is exactly a pound. We
might as well say that a force of millions of pounds exists in a pound, as
that the force which will manifest itself when the coal is burned is a
real thing existing in the coal. What is fixed in the coal is only a
certain property: it has become fit to be the antecedent of an effect
called combustion, which partly consists in giving out, under certain
conditions, a given definite quantity of heat.

We thus see that no new general conception of Causation is introduced by
the Conservation theory. The indestructibility of Force no more interferes
with the theory of Causation than the indestructibility of Matter, meaning
by matter the element of resistance in the sensible world. It only enables
us to understand better than before the nature and laws of some of the
sequences.

This better understanding, however, enables us, with Mr. Bain, to admit,
as one of the tests for distinguishing causation from mere concomitance,
the expenditure or transfer of energy. If the effect, or any part of the
effect, to be accounted for, consists in putting matter in motion, then
any of the objects present which has lost motion has contributed to the
effect; and this is the true meaning of the proposition that the cause is
that one of the antecedents which exerts active force.

§ 11. It is proper in this place to advert to a rather ancient doctrine
respecting causation, which has been revived during the last few years in
many quarters, and at present gives more signs of life than any other
theory of causation at variance with that set forth in the preceding
pages.

According to the theory in question, Mind, or to speak move precisely,
Will, is the only cause of phenomena. The type of Causation, as well as
the exclusive source from which we derive the idea, is our own voluntary
agency. Here, and here only (it is said), we have direct evidence of
causation. We know that we can move our bodies. Respecting the phenomena
of inanimate nature, we have no other direct knowledge than that of
antecedence and sequence. But in the case of our voluntary actions, it is
affirmed that we are conscious of power before we have experience of
results. An act of volition, whether followed by an effect or not, is
accompanied by a consciousness of effort, “of force exerted, of power in
action, which is necessarily causal, or causative.” This feeling of energy
or force, inherent in an act of will, is knowledge _a priori_; assurance,
prior to experience, that we have the power of causing effects. Volition,
therefore, it is asserted, is something more than an unconditional
antecedent; it is a cause, in a different sense from that in which
physical phenomena are said to cause one another: it is an Efficient
Cause. From this the transition is easy to the further doctrine, that
Volition is the _sole_ Efficient Cause of all phenomena. “It is
inconceivable that dead force could continue unsupported for a moment
beyond its creation. We can not even conceive of change or phenomena
without the energy of a mind.” “The word _action_” itself, says another
writer of the same school, “has no real significance except when applied
to the doings of an intelligent agent. Let any one conceive, if he can, of
any power, energy, or force inherent in a lump of matter.” Phenomena may
have the semblance of being produced by physical causes, but they are in
reality produced, say these writers, by the immediate agency of mind. All
things which do not proceed from a human (or, I suppose, an animal) will
proceed, they say, directly from divine will. The earth is not moved by
the combination of a centripetal and a projectile force; this is but a
mode of speaking, which serves to facilitate our conceptions. It is moved
by the direct volition of an omnipotent Being, in a path coinciding with
that which we deduce from the hypothesis of these two forces.

As I have so often observed, the general question of the existence of
Efficient Causes does not fall within the limits of our subject; but a
theory which represents them as capable of being subjects of human
knowledge, and which passes off as efficient causes what are only physical
or phenomenal causes, belongs as much to Logic as to metaphysics, and is a
fit subject for discussion here.

To my apprehension, a volition is not an efficient, but simply a physical
cause. Our will causes our bodily actions in the same sense, and in no
other, in which cold causes ice, or a spark causes an explosion of
gunpowder. The volition, a state of our mind, is the antecedent; the
motion of our limbs in conformity to the volition, is the consequent. This
sequence I conceive to be not a subject of direct consciousness, in the
sense intended by the theory. The antecedent, indeed, and the consequent,
are subjects of consciousness. But the connection between them is a
subject of experience. I can not admit that our consciousness of the
volition contains in itself any _a priori_ knowledge that the muscular
motion will follow. If our nerves of motion were paralyzed, or our muscles
stiff and inflexible, and had been so all our lives, I do not see the
slightest ground for supposing that we should ever (unless by information
from other people) have known any thing of volition as a physical power,
or been conscious of any tendency in feelings of our mind to produce
motions of our body, or of other bodies. I will not undertake to say
whether we should in that case have had the physical feeling which I
suppose is meant when these writers speak of “consciousness of effort:” I
see no reason why we should not; since that physical feeling is probably a
state of nervous sensation beginning and ending in the brain, without
involving the motory apparatus: but we certainly should not have
designated it by any term equivalent to effort, since effort implies
consciously aiming at an end, which we should not only in that case have
had no reason to do, but could not even have had the idea of doing. If
conscious at all of this peculiar sensation, we should have been conscious
of it, I conceive, only as a kind of uneasiness, accompanying our feelings
of desire.

It is well argued by Sir William Hamilton against the theory in question,
that it “is refuted by the consideration that between the overt fact of
corporeal movement of which we are cognizant, and the internal act of
mental determination of which we are also cognizant, there intervenes a
numerous series of intermediate agencies of which we have no knowledge;
and, consequently, that we can have no consciousness of any causal
connection between the extreme links of this chain, the volition to move
and the limb moving, as this hypothesis asserts. No one is immediately
conscious, for example, of moving his arm through his volition. Previously
to this ultimate movement, muscles, nerves, a multitude of solid and fluid
parts, must be set in motion by the will, but of this motion we know, from
consciousness, absolutely nothing. A person struck with paralysis is
conscious of no inability in his limb to fulfill the determinations of his
will; and it is only after having willed, and finding that his limbs do
not obey his volition, that he learns by this experience, that the
external movement does not follow the internal act. But as the paralytic
learns after the volition that his limbs do not obey his mind; so it is
only after volition that the man in health learns, that his limbs do obey
the mandates of his will.”(123)

Those against whom I am contending have never produced, and do not pretend
to produce, any positive evidence(124) that the power of our will to move
our bodies would be known to us independently of experience. What they
have to say on the subject is, that the production of physical events by a
will seems to carry its own explanation with it, while the action of
matter upon matter seems to require something else to explain it; and is
even, according to them, “inconceivable” on any other supposition than
that some will intervenes between the apparent cause and its apparent
effect. They thus rest their case on an appeal to the inherent laws of our
conceptive faculty; mistaking, as I apprehend, for the laws of that
faculty its acquired habits, grounded on the spontaneous tendencies of its
uncultured state. The succession between the will to move a limb and the
actual motion is one of the most direct and instantaneous of all sequences
which come under our observation, and is familiar to every moment’s
experience from our earliest infancy; more familiar than any succession of
events exterior to our bodies, and especially more so than any other case
of the apparent origination (as distinguished from the mere communication)
of motion. Now, it is the natural tendency of the mind to be always
attempting to facilitate its conception of unfamiliar facts by
assimilating them to others which are familiar. Accordingly, our voluntary
acts, being the most familiar to us of all cases of causation, are, in the
infancy and early youth of the human race, spontaneously taken as the type
of causation in general, and all phenomena are supposed to be directly
produced by the will of some sentient being. This original Fetichism I
shall not characterize in the words of Hume, or of any follower of Hume,
but in those of a religious metaphysician, Dr. Reid, in order more
effectually to show the unanimity which exists on the subject among all
competent thinkers.

“When we turn our attention to external objects, and begin to exercise our
rational faculties about them, we find that there are some motions and
changes in them which we have power to produce, and that there are many
which must have some other cause. Either the objects must have life and
active power, as we have, or they must be moved or changed by something
that has life and active power, as external objects are moved by us.

“Our first thoughts seem to be, that the objects in which we perceive such
motion have understanding and active power as we have. ‘Savages,’ says the
Abbé Raynal, ‘wherever they see motion which they can not account for,
there they suppose a soul.’ All men may be considered as savages in this
respect, until they are capable of instruction, and of using their
faculties in a more perfect manner than savages do.

“The Abbé Raynal’s observation is sufficiently confirmed, both from fact,
and from the structure of all languages.

“Rude nations do really believe sun, moon, and stars, earth, sea, and air,
fountains, and lakes, to have understanding and active power. To pay
homage to them, and implore their favor, is a kind of idolatry natural to
savages.

“All languages carry in their structure the marks of their being formed
when this belief prevailed. The distinction of verbs and participles into
active and passive, which is found in all languages, must have been
originally intended to distinguish what is really active from what is
merely passive; and in all languages, we find active verbs applied to
those objects, in which, according to the Abbé Raynal’s observation,
savages suppose a soul.

“Thus we say the sun rises and sets, and comes to the meridian, the moon
changes, the sea ebbs and flows, the winds blow. Languages were formed by
men who believed these objects to have life and active power in
themselves. It was therefore proper and natural to express their motions
and changes by active verbs.

“There is no surer way of tracing the sentiments of nations before they
have records, than by the structure of their language, which,
notwithstanding the changes produced in it by time, will always retain
some signatures of the thoughts of those by whom it was invented. When we
find the same sentiments indicated in the structure of all languages,
those sentiments must have been common to the human species when languages
were invented.

“When a few, of superior intellectual abilities, find leisure for
speculation, they begin to philosophize, and soon discover, that many of
those objects which at first they believed to be intelligent and active
are really lifeless and passive. This is a very important discovery. It
elevates the mind, emancipates from many vulgar superstitions, and invites
to further discoveries of the same kind.

“As philosophy advances, life and activity in natural objects retires, and
leaves them dead and inactive. Instead of moving voluntarily, we find them
to be moved necessarily; instead of acting, we find them to be acted upon;
and Nature appears as one great machine, where one wheel is turned by
another, that by a third; and how far this necessary succession may reach,
the philosopher does not know.”(125)

There is, then, a spontaneous tendency of the intellect to account to
itself for all cases of causation by assimilating them to the intentional
acts of voluntary agents like itself. This is the instinctive philosophy
of the human mind in its earliest stage, before it has become familiar
with any other invariable sequences than those between its own volitions
or those of other human beings and their voluntary acts. As the notion of
fixed laws of succession among external phenomena gradually establishes
itself, the propensity to refer all phenomena to voluntary agency slowly
gives way before it. The suggestions, however, of daily life continuing to
be more powerful than those of scientific thought, the original
instinctive philosophy maintains its ground in the mind, underneath the
growths obtained by cultivation, and keeps up a constant resistance to
their throwing their roots deep into the soil. The theory against which I
am contending derives its nourishment from that substratum. Its strength
does not lie in argument, but in its affinity to an obstinate tendency of
the infancy of the human mind.

That this tendency, however, is not the result of an inherent mental law,
is proved by superabundant evidence. The history of science, from its
earliest dawn, shows that mankind have not been unanimous in thinking
either that the action of matter upon matter was not conceivable, or that
the action of mind upon matter was. To some thinkers, and some schools of
thinkers, both in ancient and in modern times, this last has appeared much
more inconceivable than the former. Sequences entirely physical and
material, as soon as they had become sufficiently familiar to the human
mind, came to be thought perfectly natural, and were regarded not only as
needing no explanation themselves, but as being capable of affording it to
others, and even of serving as the ultimate explanation of things in
general.

One of the ablest recent supporters of the Volitional theory has furnished
an explanation, at once historically true and philosophically acute, of
the failure of the Greek philosophers in physical inquiry, in which, as I
conceive, he unconsciously depicts his own state of mind. “Their
stumbling-block was one as to the nature of the evidence they had to
expect for their conviction.... They had not seized the idea that they
must not expect to understand the processes of outward causes, but only
their results; and consequently, the whole physical philosophy of the
Greeks was an attempt to identify mentally the effect with its cause, to
feel after some not only necessary but natural connection, where they
meant by natural that which would _per se_ carry some presumption to their
own mind.... They wanted to see some _reason_ why the physical antecedent
should produce this particular consequent, and their only attempts were in
directions where they could find such reasons.”(126) In other words, they
were not content merely to know that one phenomenon was always followed by
another; they thought that they had not attained the true aim of science,
unless they could perceive something in the nature of the one phenomenon
from which it might have been known or presumed _previous to trial_ that
it would be followed by the other: just what the writer, who has so
clearly pointed out their error, thinks that he perceives in the nature of
the phenomenon Volition. And to complete the statement of the case, he
should have added that these early speculators not only made this their
aim, but were quite satisfied with their success in it; not only sought
for causes which should carry in their mere statement evidence of their
efficiency, but fully believed that they had found such causes. The
reviewer can see plainly that this was an error, because _he_ does not
believe that there exist any relations between material phenomena which
can account for their producing one another; but the very fact of the
persistency of the Greeks in this error, shows that their minds were in a
very different state: they were able to derive from the assimilation of
physical facts to other physical facts, the kind of mental satisfaction
which we connect with the word explanation, and which the reviewer would
have us think can only be found in referring phenomena to a will. When
Thales and Hippo held that moisture was the universal cause, and external
element, of which all other things were but the infinitely various
sensible manifestations; when Anaximenes predicated the same thing of air,
Pythagoras of numbers, and the like, they all thought that they had found
a real explanation; and were content to rest in this explanation as
ultimate. The ordinary sequences of the external universe appeared to
them, no less than to their critic, to be inconceivable without the
supposition of some universal agency to connect the antecedents with the
consequents; but they did not think that Volition, exerted by minds, was
the only agency which fulfilled this requirement. Moisture, or air, or
numbers, carried to their minds a precisely similar impression of making
intelligible what was otherwise inconceivable, and gave the same full
satisfaction to the demands of their conceptive faculty.

It was not the Greeks alone, who “wanted to see some reason why the
physical antecedent should produce this particular consequent,” some
connection “which would _per se_ carry some presumption to their own
mind.” Among modern philosophers, Leibnitz laid it down as a self-evident
principle that all physical causes without exception must contain in their
own nature something which makes it intelligible that they should be able
to produce the effects which they do produce. Far from admitting Volition
as the only kind of cause which carried internal evidence of its own
power, and as the real bond of connection between physical antecedents and
their consequents, he demanded some naturally and _per se_ efficient
physical antecedent as the bond of connection between Volition itself and
its effects. He distinctly refused to admit the will of God as a
sufficient explanation of any thing except miracles; and insisted upon
finding something that would account _better_ for the phenomena of nature
than a mere reference to divine volition.(127)

Again, and conversely, the action of mind upon matter (which, we are now
told, not only needs no explanation itself, but is the explanation of all
other effects), has appeared to some thinkers to be itself the grand
inconceivability. It was to get over this very difficulty that the
Cartesians invented the system of Occasional Causes. They could not
conceive that thoughts in a mind could produce movements in a body, or
that bodily movements could produce thoughts. They could see no necessary
connection, no relation _a priori_, between a motion and a thought. And as
the Cartesians, more than any other school of philosophical speculation
before or since, made their own minds the measure of all things, and
refused, on principle, to believe that Nature had done what they were
unable to see any reason why she must do, they affirmed it to be
impossible that a material and a mental fact could be causes one of
another. They regarded them as mere Occasions on which the real agent,
God, thought fit to exert his power as a Cause. When a man wills to move
his foot, it is not his will that moves it, but God (they said) moves it
on the occasion of his will. God, according to this system, is the only
efficient cause, not _quâ_ mind, or _quâ_ endowed with volition, but _quâ_
omnipotent. This hypothesis was, as I said, originally suggested by the
supposed inconceivability of any real mutual action between Mind and
Matter; but it was afterward extended to the action of Matter upon Matter,
for on a nicer examination they found this inconceivable too, and
therefore, according to their logic, impossible. The _deus ex machinâ_ was
ultimately called in to produce a spark on the occasion of a flint and
steel coming together, or to break an egg on the occasion of its falling
on the ground.

All this, undoubtedly, shows that it is the disposition of mankind in
general, not to be satisfied with knowing that one fact is invariably
antecedent and another consequent, but to look out for something which may
seem to explain their being so. But we also see that this demand may be
completely satisfied by an agency purely physical, provided it be much
more familiar than that which it is invoked to explain. To Thales and
Anaximenes, it appeared inconceivable that the antecedents which we see in
nature should produce the consequents; but perfectly natural that water,
or air, should produce them. The writers whom I oppose declare this
inconceivable, but can conceive that mind, or volition, is _per se_ an
efficient cause: while the Cartesians could not conceive even that, but
peremptorily declared that no mode of production of any fact whatever was
conceivable, except the direct agency of an omnipotent being; thus giving
additional proof of what finds new confirmation in every stage of the
history of science: that both what persons can, and what they can not,
conceive, is very much an affair of accident, and depends altogether on
their experience, and their habits of thought; that by cultivating the
requisite associations of ideas, people may make themselves unable to
conceive any given thing; and may make themselves able to conceive most
things, however inconceivable these may at first appear; and the same
facts in each person’s mental history which determine what is or is not
conceivable to him, determine also which among the various sequences in
nature will appear to him so natural and plausible, as to need no other
proof of their existence; to be evident by their own light, independent
equally of experience and of explanation.

By what rule is any one to decide between one theory of this description
and another? The theorists do not direct us to any external evidence; they
appeal each to his own subjective feelings. One says, the succession C B
appears to me more natural, conceivable, and credible _per se_, than the
succession A B; you are therefore mistaken in thinking that B depends upon
A; I am certain, though I can give no other evidence of it, that C comes
in between A and B, and is the real and only cause of B. The other
answers, the successions C B and A B appear to me equally natural and
conceivable, or the latter more so than the former: A is quite capable of
producing B without any other intervention. A third agrees with the first
in being unable to conceive that A can produce B, but finds the sequence D
B still more natural than C B, or of nearer kin to the subject-matter, and
prefers his D theory to the C theory. It is plain that there is no
universal law operating here, except the law that each person’s
conceptions are governed and limited by his individual experiences and
habits of thought. We are warranted in saying of all three, what each of
them already believes of the other two, namely, that they exalt into an
original law of the human intellect and of outward nature one particular
sequence of phenomena, which appears to them more natural and more
conceivable than other sequences, only because it is more familiar. And
from this judgment I am unable to except the theory, that Volition is an
Efficient Cause.

I am unwilling to leave the subject without adverting to the additional
fallacy contained in the corollary from this theory; in the inference that
because Volition is an efficient cause, therefore it is the only cause,
and the direct agent in producing even what is apparently produced by
something else. Volitions are not known to produce any thing directly
except nervous action, for the will influences even the muscles only
through the nerves. Though it were granted, then, that every phenomenon
has an efficient, and not merely a phenomenal cause, and that volition, in
the case of the peculiar phenomena which are known to be produced by it,
is that efficient cause; are we therefore to say, with these writers, that
since we know of no other efficient cause, and ought not to assume one
without evidence, there _is_ no other, and volition is the direct cause of
all phenomena? A more outrageous stretch of inference could hardly be
made. Because among the infinite variety of the phenomena of nature there
is one, namely, a particular mode of action of certain nerves, which has
for its cause, and as we are now supposing for its efficient cause, a
state of our mind; and because this is the only efficient cause of which
we are conscious, being the only one of which in the nature of the case we
_can_ be conscious, since it is the only one which exists within
ourselves; does this justify us in concluding that all other phenomena
must have the same kind of efficient cause with that one eminently
special, narrow, and peculiarly human or animal, phenomenon? The nearest
parallel to this specimen of generalization is suggested by the recently
revived controversy on the old subject of Plurality of Worlds, in which
the contending parties have been so conspicuously successful in
overthrowing one another. Here also we have experience only of a single
case, that of the world in which we live, but that this is inhabited we
know absolutely, and without possibility of doubt. Now if on this evidence
any one were to infer that every heavenly body without exception, sun,
planet, satellite, comet, fixed star or nebula, is inhabited, and must be
so from the inherent constitution of things, his inference would exactly
resemble that of the writers who conclude that because volition is the
efficient cause of our own bodily motions, it must be the efficient cause
of every thing else in the universe. It is true there are cases in which,
with acknowledged propriety, we generalize from a single instance to a
multitude of instances. But they must be instances which resemble the one
known instance, and not such as have no circumstance in common with it
except that of being instances. I have, for example, no direct evidence
that any creature is alive except myself, yet I attribute, with full
assurance, life and sensation to other human beings and animals. But I do
not conclude that all other things are alive merely because I am. I
ascribe to certain other creatures a life like my own, because they
manifest it by the same sort of indications by which mine is manifested. I
find that their phenomena and mine conform to the same laws, and it is for
this reason that I believe both to arise from a similar cause. Accordingly
I do not extend the conclusion beyond the grounds for it. Earth, fire,
mountains, trees, are remarkable agencies, but their phenomena do not
conform to the same laws as my actions do, and I therefore do not believe
earth or fire, mountains or trees, to possess animal life. But the
supporters of the Volition Theory ask us to infer that volition causes
every thing, for no reason except that it causes one particular thing;
although that one phenomenon, far from being a type of all natural
phenomena, is eminently peculiar; its laws bearing scarcely any
resemblance to those of any other phenomenon, whether of inorganic or of
organic nature.

NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.


    The author of the Second Burnett Prize Essay (Dr. Tulloch), who
    has employed a considerable number of pages in controverting the
    doctrines of the preceding chapter, has somewhat surprised me by
    denying a fact, which I imagined too well known to require
    proof—that there have been philosophers who found in physical
    explanations of phenomena the same complete mental satisfaction
    which we are told is only given by volitional explanation, and
    others who denied the Volitional Theory on the same ground of
    inconceivability on which it is defended. The assertion of the
    Essayist is countersigned still more positively by an able
    reviewer of the Essay:(128) “Two illustrations,” says the
    reviewer, “are advanced by Mr. Mill: the case of Thales and
    Anaximenes, stated by him to have maintained, the one Moisture and
    the other Air to be the origin of all things; and that of
    Descartes and Leibnitz, whom he asserts to have found the action
    of Mind upon Matter the grand inconceivability. In
    counter-statement as to the first of these cases the author
    shows—what we believe now hardly admits of doubt—that the Greek
    philosophers distinctly recognized as beyond and above their
    primal material source, the νοῦς, or Divine Intelligence, as the
    efficient and originating Source of all; and as to the second, by
    proof that it was the _mode_, not the _fact_, of that action on
    matter, which was represented as inconceivable.”

    A greater quantity of historical error has seldom been comprised
    in a single sentence. With regard to Thales, the assertion that he
    considered water as a mere material in the hands of νοῦς rests on
    a passage of Cicero _de Naturâ Deorum_; and whoever will refer to
    any of the accurate historians of philosophy, will find that they
    treat this as a mere fancy of Cicero, resting on no authority,
    opposed to all the evidence; and make surmises as to the manner in
    which Cicero may have been led into the error. (See Rutter, vol.
    i., p. 211, 2d ed.; Brandis, vol. i., pp. 118-9, 1st ed.; Preller,
    _Historia Philosophiæ Græco-Romanæ_, p. 10. “Schiefe Ansicht,
    durchaus zu verwerfen;” “augenscheinlich folgernd statt zu
    berichten;” “quibus vera sententia Thaletis plane detorquetur,”
    are the expressions of these writers.) As for Anaximenes, he even
    according to Cicero, maintained, not that air was the material out
    of which God made the world, but that the air was a god:
    “Anaximenes aëra deum statuit;” or, according to St. Augustine,
    that it was the material out of which the gods were made; “non
    tamen ab ipsis [Diis] aërem factum, sed ipsos ex aëre ortos
    credidit.” Those who are not familiar with the metaphysical
    terminology of antiquity, must not be misled by finding it stated
    that Anaximenes attributed ψυχὴ (translated _soul_, or _life_) to
    his universal element, the air. The Greek philosophers
    acknowledged several kinds of ψυχὴ, the nutritive, the sensitive,
    and the intellective.(129) Even the moderns, with admitted
    correctness, attribute life to plants. As far as we can make out
    the meaning of Anaximenes, he made choice of Air as the universal
    agent, on the ground that it is perpetually in motion, without any
    apparent cause external to itself: so that he conceived it as
    exercising spontaneous force, and as the principle of life and
    activity in all things, men and gods inclusive. If this be not
    representing it as the Efficient Cause the dispute altogether has
    no meaning.

    If either Anaximenes, or Thales, or any of their contemporaries,
    had held the doctrine that νοῦς was the Efficient Cause, that
    doctrine could not have been reputed, as it was throughout
    antiquity, to have originated with Anaxagoras. The testimony of
    Aristotle, in the first book of his Metaphysics, is perfectly
    decisive with respect to these early speculations. After
    enumerating four kinds of causes, or rather four different
    meanings of the word Cause, viz., the Essence of a thing, the
    Matter of it, the Origin of Motion (Efficient Cause), and the End
    or Final Cause, he proceeds to say, that most of the early
    philosophers recognized only the second kind of Cause, the Matter
    of a thing, τὰς ἐν ὕλης εἶδει μόνας ᾠήθησαν ἀρχὰς εἷναι πάντων. As
    his first example he specifies Thales, whom he describes as taking
    the lead in this view of the subject, ὁ τῆς τοιαύτης ἀρχηγὸς
    φιλοσοφίας, and goes on to Hippon, Anaximenes, Diogenes (of
    Apollonia), Hippasus of Metapontum, Heraclitus, and Empedocles.
    Anaxagoras, however (he proceeds to say), taught a different
    doctrine, as we _know_, and it is _alleged_ that Hermotimus of
    Clazomenæ taught it before him. Anaxagoras represented, that even
    if these various theories of the universal material were true,
    there would be need of some other cause to account for the
    transformations of the materials, since the material can not
    originate its own changes: οὐ γὰρ δὴ τό γε ὑποκείμενον αὐτὸ ποιεὶ
    μεταβάλλειν ἑαῦτο; λέγω δ᾽ οἰον οὐτε τὸ ξύλον οὔτε ὁ χαλκὸς αἴτιος
    τοῦ μεταβάλλειν ἑκάτερον αὐτῶν, οὐδὲ ποιεῖ τὸ μὲν ξύλον κλίνην ὁ
    δέ χαλκὸς ἀνδριάντα, ἀλλ᾽ ἑτερόν τι τῆς μεταβολῆς αἴτιον, viz.,
    the other kind of cause, ὄθεν ἡ ἀρχὴ τῆς κινήσεως—an Efficient
    Cause. Aristotle expresses great approbation of this doctrine
    (which he says made its author appear the only sober man among
    persons raving, οἰον νήφων ἐφάνη παρ᾽ εἰκῆ λέγοντας τοῦς
    πρότερον); but while describing the influence which it exercised
    over subsequent speculation, he remarks that the philosophers
    against whom this, as he thinks, insuperable difficulty was urged,
    had not felt it to be any difficulty: οὐδέν ἐδυσχεράναν ἐν
    ἑαυτοῖς. It is surely unnecessary to say more in proof of the
    matter of fact which Dr. Tulloch and his reviewer disbelieve.

    Having pointed out what he thinks the error of these early
    speculators in not recognizing the need of an efficient cause,
    Aristotle goes on to mention two other efficient causes to which
    they might have had recourse, instead of intelligence: τύχη,
    chance, and τὸ αὐτομάτον, spontaneity. He indeed puts these aside
    as not sufficiently worthy causes for the order in the universe,
    οὐδ᾽ αὑ τωῷ αὐτομάτῳ καὶ τῇ τύχῃ τοσοῦτον ἐπιτρέψαι πρᾶγμα καλῶς
    εἰχεν; but he does not reject them as incapable of producing _any_
    effect, but only as incapable of producing _that_ effect. He
    himself recognizes τύχη and τὸ αὐτομάτον as co-ordinate agents
    with Mind in producing the phenomena of the universe; the
    department allotted to them being composed of all the classes of
    phenomena which are not supposed to follow any uniform law. By
    thus including Chance among efficient causes, Aristotle fell into
    an error which philosophy has now outgrown, but which is by no
    means so alien to the spirit even of modern speculation as it may
    at first sight appear. Up to quite a recent period philosophers
    went on ascribing, and many of them have not yet ceased to
    ascribe, a real existence to the results of abstraction. Chance
    could make out as good a title to that dignity as many other of
    the mind’s abstract creations: it had had a name given to it, and
    why should it not be a reality? As for τὸ αὐτομάτον, it is
    recognized even yet as one of the modes of origination of
    phenomena by all those thinkers who maintain what is called the
    Freedom of the Will. The same self-determining power which that
    doctrine attributes to volitions, was supposed by the ancients to
    be possessed also by some other natural phenomena: a circumstance
    which throws considerable light on more than one of the supposed
    invincible necessities of belief. I have introduced it here,
    because this belief of Aristotle, or rather of the Greek
    philosophers generally, is as fatal as the doctrines of Thales and
    the Ionic school to the theory that the human mind is compelled by
    its constitution to conceive volition as the origin of all force,
    and the efficient cause of all phenomena.(130)

    With regard to the modern philosophers (Leibnitz and the
    Cartesians) whom I had cited as having maintained that the action
    of mind upon matter, so far from being the only conceivable origin
    of material phenomena, is itself inconceivable; the attempt to
    rebut this argument by asserting that the mode, not the fact, of
    the action of mind on matter was represented as inconceivable, is
    an abuse of the privilege of writing confidently about authors
    without reading them; for any knowledge whatever of Leibnitz would
    have taught those who thus speak of him, that the inconceivability
    of the mode, and the impossibility of the thing, were in his mind
    convertible expressions. What was his famous Principle of the
    Sufficient Reason, the very corner-stone of his Philosophy, from
    which the Pre-established Harmony, the doctrine of Monads, and all
    the opinions most characteristic of Leibnitz, were corollaries? It
    was, that nothing exists, the existence of which is not capable of
    being proved and explained _a priori_; the proof and explanation
    in the case of contingent facts being derived from the nature of
    their causes; which could not be the causes unless there was
    something in their nature showing them to be capable of producing
    those particular effects. And this “something” which accounts for
    the production of physical effects, he was able to find in many
    physical causes, but could not find it in any finite minds, which
    therefore he unhesitatingly asserted to be incapable of producing
    any physical effects whatever. “On ne saurait concevoir,” he says,
    “une action réciproque de la matière et de l’intelligence l’une
    sur l’autre,” and there is therefore (he contends) no choice but
    between the Occasional Causes of the Cartesians and his own
    Pre-established Harmony, according to which there is no more
    connection between our volitions and our muscular actions than
    there is between two clocks which are wound up to strike at the
    same instant. But he felt no similar difficulty as to physical
    causes; and throughout his speculations, as in the passage I have
    already cited respecting gravitation, he distinctly refuses to
    consider as part of the order of nature any fact which is not
    explicable from the nature of its physical cause.

    With regard to the Cartesians (not Descartes; I did not make that
    mistake, though the reviewer of Dr. Tulloch’s Essay attributes it
    to me) I take a passage almost at random from Malebranche, who is
    the best known of the Cartesians, and, though not the inventor of
    the system of Occasional Causes, is its principal expositor. In
    Part II., chap. iii., of his Sixth Book, having first said that
    matter can not have the power of moving itself, he proceeds to
    argue that neither can mind have the power of moving it. “Quand on
    examine l’idée que l’on a de tous les esprits finis, on ne voit
    point de liaison nécessaire entre leur volonté et le mouvement de
    quelque corps que ce soit, on voit au contraire qu’il n’y en a
    point, et qu’il n’y en peut avoir” (there is nothing in the idea
    of finite mind which can account for its causing the motion of a
    body); “on doit aussi conclure, si on vent raisonner selon ses
    lumières, qu’il n’y a aucun esprit créé qui puisse remuer quelque
    corps que ce soit comme cause véritable on principale, de même que
    l’on a dit qu’aucun corps ne se pouvait remuer soi-même:” thus the
    idea of Mind is according to him as incompatible as the idea of
    Matter with the exercise of active force. But when, he continues,
    we consider not a created but a Divine Mind, the case is altered;
    for the idea of a Divine Mind includes omnipotence; and the idea
    of omnipotence does contain the idea of being able to move bodies.
    Thus it is the nature of omnipotence which renders the motion of
    bodies even by the Divine Mind credible or conceivable, while, so
    far as depended on the mere nature of mind, it would have been
    inconceivable and incredible. If Malebranche had not believed in
    an omnipotent Being, he would have held all action of mind on body
    to be a demonstrated impossibility.(131)

    A doctrine more precisely the reverse of the Volitional theory of
    causation can not well be imagined. The Volitional theory is, that
    we know by intuition or by direct experience the action of our own
    mental volitions on matter; that we may hence infer all other
    action upon matter to be that of volition, and might thus know,
    without any other evidence, that matter is under the government of
    a Divine Mind. Leibnitz and the Cartesians, on the contrary,
    maintain that our volitions do not and can not act upon matter,
    and that it is only the existence of an all-governing Being, and
    that Being omnipotent, which can account for the sequence between
    our volitions and our bodily actions. When we consider that each
    of these two theories, which, as theories of causation, stand at
    the opposite extremes of possible divergence from one another,
    invokes not only as its evidence, but as its sole evidence, the
    absolute inconceivability of any theory but itself, we are enabled
    to measure the worth of this kind of evidence: and when we find
    the Volitional theory entirely built upon the assertion that by
    our mental constitution we are compelled to recognize our
    volitions as efficient causes, and then find other thinkers
    maintaining that we know that they are not and can not be such
    causes, and can not conceive them to be so, I think we have a
    right to say that this supposed law of our mental constitution
    does not exist.

    Dr. Tulloch (pp. 45-47) thinks it a sufficient answer to this,
    that Leibnitz and the Cartesians were Theists, and believed the
    will of God to be an efficient cause. Doubtless they did, and the
    Cartesians even believed (though Leibnitz did not) that it is the
    only such cause. Dr. Tulloch mistakes the nature of the question.
    I was not writing on Theism, as Dr. Tulloch is, but against a
    particular theory of causation, which, if it be unfounded, can
    give no effective support to Theism or to any thing else. I found
    it asserted that volition is the only efficient cause, on the
    ground that no other efficient cause is conceivable. To this
    assertion I oppose the instances of Leibnitz and of the
    Cartesians, who affirmed with equal positiveness that volition as
    an efficient cause is itself not conceivable, and that
    omnipotence, which renders all things conceivable, can alone take
    away the impossibility. This I thought, and think, a conclusive
    answer to the argument on which this theory of causation avowedly
    depends. But I certainly did not imagine that Theism was bound up
    with that theory; nor expected to be charged with denying Leibnitz
    and the Cartesians to be Theists because I denied that they held
    the theory.



                               Chapter VI.


On The Composition Of Causes.


§ 1. To complete the general notion of causation on which the rules of
experimental inquiry into the laws of nature must be founded, one
distinction still remains to be pointed out: a distinction so radical, and
of so much importance, as to require a chapter to itself.

The preceding discussions have rendered us familiar with the case in which
several agents, or causes, concur as conditions to the production of an
effect; a case, in truth, almost universal, there being very few effects
to the production of which no more than one agent contributes. Suppose,
then, that two different agents, operating jointly, are followed, under a
certain set of collateral conditions, by a given effect. If either of
these agents, instead of being joined with the other, had operated alone,
under the same set of conditions in all other respects, some effect would
probably have followed, which would have been different from the joint
effect of the two, and more or less dissimilar to it. Now, if we happen to
know what would be the effect of each cause when acting separately from
the other, we are often able to arrive deductively, or _a priori_, at a
correct prediction of what will arise from their conjunct agency. To
render this possible, it is only necessary that the same law which
expresses the effect of each cause acting by itself, shall also correctly
express the part due to that cause of the effect which follows from the
two together. This condition is realized in the extensive and important
class of phenomena commonly called mechanical, namely the phenomena of the
communication of motion (or of pressure, which is tendency to motion) from
one body to another. In this important class of cases of causation, one
cause never, properly speaking, defeats or frustrates another; both have
their full effect. If a body is propelled in two directions by two forces,
one tending to drive it to the north and the other to the east, it is
caused to move in a given time exactly as far in both directions as the
two forces would separately have carried it; and is left precisely where
it would have arrived if it had been acted upon first by one of the two
forces, and afterward by the other. This law of nature is called, in
dynamics, the principle of the Composition of Forces; and in imitation of
that well-chosen expression, I shall give the name of the Composition of
Causes to the principle which is exemplified in all cases in which the
joint effect of several causes is identical with the sum of their separate
effects.

This principle, however, by no means prevails in all departments of the
field of nature. The chemical combination of two substances produces, as
is well known, a third substance, with properties different from those of
either of the two substances separately, or of both of them taken
together. Not a trace of the properties of hydrogen or of oxygen is
observable in those of their compound, water. The taste of sugar of lead
is not the sum of the tastes of its component elements, acetic acid and
lead or its oxide; nor is the color of blue vitriol a mixture of the
colors of sulphuric acid and copper. This explains why mechanics is a
deductive or demonstrative science, and chemistry not. In the one, we can
compute the effects of combinations of causes, whether real or
hypothetical, from the laws which we know to govern those causes when
acting separately, because they continue to observe the same laws when in
combination which they observe when separate: whatever would have happened
in consequence of each cause taken by itself, happens when they are
together, and we have only to cast up the results. Not so in the phenomena
which are the peculiar subject of the science of chemistry. There most of
the uniformities to which the causes conform when separate, cease
altogether when they are conjoined; and we are not, at least in the
present state of our knowledge, able to foresee what result will follow
from any new combination until we have tried the specific experiment.

If this be true of chemical combinations, it is still more true of those
far more complex combinations of elements which constitute organized
bodies; and in which those extraordinary new uniformities arise which are
called the laws of life. All organized bodies are composed of parts
similar to those composing inorganic nature, and which have even
themselves existed in an inorganic state; but the phenomena of life, which
result from the juxtaposition of those parts in a certain manner, bear no
analogy to any of the effects which would be produced by the action of the
component substances considered as mere physical agents. To whatever
degree we might imagine our knowledge of the properties of the several
ingredients of a living body to be extended and perfected, it is certain
that no mere summing up of the separate actions of those elements will
ever amount to the action of the living body itself. The tongue, for
instance, is, like all other parts of the animal frame, composed of
gelatine, fibrine, and other products of the chemistry of digestion; but
from no knowledge of the properties of those substances could we ever
predict that it could taste, unless gelatine or fibrine could themselves
taste; for no elementary fact can be in the conclusion which was not in
the premises.

There are thus two different modes of the conjunct action of causes; from
which arise two modes of conflict, or mutual interference, between laws of
nature. Suppose, at a given point of time and space, two or more causes,
which, if they acted separately, would produce effects contrary, or at
least conflicting with each other; one of them tending to undo, wholly or
partially, what the other tends to do. Thus the expansive force of the
gases generated by the ignition of gunpowder tends to project a bullet
toward the sky, while its gravity tends to make it fall to the ground. A
stream running into a reservoir at one end tends to fill it higher and
higher, while a drain at the other extremity tends to empty it. Now, in
such cases as these, even if the two causes which are in joint action
exactly annul one another, still the laws of both are fulfilled; the
effect is the same as if the drain had been open for half an hour
first,(132) and the stream had flowed in for as long afterward. Each agent
produces the same amount of effect as if it had acted separately, though
the contrary effect which was taking place during the same time
obliterated it as fast as it was produced. Here, then, are two causes,
producing by their joint operations an effect which at first seems quite
dissimilar to those which they produce separately, but which on
examination proves to be really the sum of those separate effects. It will
be noticed that we here enlarge the idea of the sum of two effects, so as
to include what is commonly called their difference, but which is in
reality the result of the addition of opposites; a conception to which
mankind are indebted for that admirable extension of the algebraical
calculus, which has so vastly increased its powers as an instrument of
discovery, by introducing into its reasonings (with the sign of
subtraction prefixed, and under the name of Negative Quantities) every
description whatever of positive phenomena, provided they are of such a
quality in reference to those previously introduced, that to add the one
is equivalent to subtracting an equal quantity of the other.

There is, then, one mode of the mutual interference of laws of nature, in
which, even when the concurrent causes annihilate each other’s effects,
each exerts its full efficacy according to its own law—its law as a
separate agent. But in the other description of cases, the agencies which
are brought together cease entirely, and a totally different set of
phenomena arise: as in the experiment of two liquids which, when mixed in
certain proportions, instantly become, not a larger amount of liquid, but
a solid mass.

§ 2. This difference between the case in which the joint effect of causes
is the sum of their separate effects, and the case in which it is
heterogeneous to them—between laws which work together without alteration,
and laws which, when called upon to work together, cease and give place to
others—is one of the fundamental distinctions in nature. The former case,
that of the Composition of Causes, is the general one; the other is always
special and exceptional. There are no objects which do not, as to some of
their phenomena, obey the principle of the Composition of Causes; none
that have not some laws which are rigidly fulfilled in every combination
into which the objects enter. The weight of a body, for instance, is a
property which it retains in all the combinations in which it is placed.
The weight of a chemical compound, or of an organized body, is equal to
the sum of the weights of the elements which compose it. The weight either
of the elements or of the compound will vary, if they be carried farther
from their centre of attraction, or brought nearer to it; but whatever
effects the one effects the other. They always remain precisely equal. So,
again, the component parts of a vegetable or animal substance do not lose
their mechanical and chemical properties as separate agents, when, by a
peculiar mode of juxtaposition, they, as an aggregate whole, acquire
physiological or vital properties in addition. Those bodies continue, as
before, to obey mechanical and chemical laws, in so far as the operation
of those laws is not counteracted by the new laws which govern them as
organized beings; when, in short, a concurrence of causes takes place
which calls into action new laws bearing no analogy to any that we can
trace in the separate operation of the causes, the new laws, while they
supersede one portion of the previous laws, may co-exist with another
portion, and may even compound the effect of those previous laws with
their own.

Again, laws which were themselves generated in the second mode, may
generate others in the first. Though there are laws which, like those of
chemistry and physiology, owe their existence to a breach of the principle
of Composition of Causes, it does not follow that these peculiar, or, as
they might be termed, _heteropathic_ laws, are not capable of composition
with one another. The causes which by one combination have had their laws
altered, may carry their new laws with them unaltered into their ulterior
combinations. And hence there is no reason to despair of ultimately
raising chemistry and physiology to the condition of deductive sciences;
for though it is impossible to deduce all chemical and physiological
truths from the laws or properties of simple substances or elementary
agents, they may possibly be deducible from laws which commence when these
elementary agents are brought together into some moderate number of not
very complex combinations. The Laws of Life will never be deducible from
the mere laws of the ingredients, but the prodigiously complex Facts of
Life may all be deducible from comparatively simple laws of life; which
laws (depending indeed on combinations, but on comparatively simple
combinations, of antecedents) may, in more complex circumstances, be
strictly compounded with one another, and with the physical and chemical
laws of the ingredients. The details of the vital phenomena, even now,
afford innumerable exemplifications of the Composition of Causes; and in
proportion as these phenomena are more accurately studied, there appears
more reason to believe that the same laws which operate in the simpler
combinations of circumstances do, in fact, continue to be observed in the
more complex. This will be found equally true in the phenomena of mind;
and even in social and political phenomena, the results of the laws of
mind. It is in the case of chemical phenomena that the least progress has
yet been made in bringing the special laws under general ones from which
they may be deduced; but there are even in chemistry many circumstances to
encourage the hope that such general laws will hereafter be discovered.
The different actions of a chemical compound will never, undoubtedly, be
found to be the sums of the actions of its separate elements; but there
may exist, between the properties of the compound and those of its
elements, some constant relation, which, if discoverable by a sufficient
induction, would enable us to foresee the sort of compound which will
result from a new combination before we have actually tried it, and to
judge of what sort of elements some new substance is compounded before we
have analyzed it. The law of definite proportions, first discovered in its
full generality by Dalton, is a complete solution of this problem in one,
though but a secondary aspect, that of quantity; and in respect to
quality, we have already some partial generalizations, sufficient to
indicate the possibility of ultimately proceeding farther. We can
predicate some common properties of the kind of compounds which result
from the combination, in each of the small number of possible proportions,
of any acid whatever with any base. We have also the curious law,
discovered by Berthollet, that two soluble salts mutually decompose one
another whenever the new combinations which result produce an insoluble
compound, or one less soluble than the two former. Another uniformity is
that called the law of isomorphism; the identity of the crystalline forms
of substances which possess in common certain peculiarities of chemical
composition.(133) Thus it appears that even heteropathic laws, such laws
of combined agency as are not compounded of the laws of the separate
agencies, are yet, at least in some cases, derived from them according to
a fixed principle. There may, therefore, be laws of the generation of laws
from others dissimilar to them; and in chemistry, these undiscovered laws
of the dependence of the properties of the compound on the properties of
its elements, may, together with the laws of the elements themselves,
furnish the premises by which the science is perhaps destined one day to
be rendered deductive.

It would seem, therefore, that there is no class of phenomena in which the
Composition of Causes does not obtain: that as a general rule, causes in
combination produce exactly the same effects as when acting singly: but
that this rule, though general, is not universal: that in some instances,
at some particular points in the transition from separate to united
action, the laws change, and an entirely new set of effects are either
added to, or take the place of, those which arise from the separate agency
of the same causes: the laws of these new effects being again susceptible
of composition, to an indefinite extent, like the laws which they
superseded.

§ 3. That effects are proportional to their causes is laid down by some
writers as an axiom in the theory of causation; and great use is sometimes
made of this principle in reasonings respecting the laws of nature, though
it is encumbered with many difficulties and apparent exceptions, which
much ingenuity has been expended in showing not to be real ones. This
proposition, in so far as it is true, enters as a particular case into the
general principle of the Composition of Causes; the causes compounded
being, in this instance, homogeneous; in which case, if in any, their
joint effect might be expected to be identical with the sum of their
separate effects. If a force equal to one hundred weight will raise a
certain body along an inclined plane, a force equal to two hundred weight
will raise two bodies exactly similar, and thus the effect is proportional
to the cause. But does not a force equal to two hundred weight actually
contain in itself two forces each equal to one hundred weight, which, if
employed apart, would separately raise the two bodies in question? The
fact, therefore, that when exerted jointly they raise both bodies at once,
results from the Composition of Causes, and is a mere instance of the
general fact that mechanical forces are subject to the law of Composition.
And so in every other case which can be supposed. For the doctrine of the
proportionality of effects to their causes can not of course be applicable
to cases in which the augmentation of the cause alters the kind of effect;
that is, in which the surplus quantity superadded to the cause does not
become compounded with it, but the two together generate an altogether new
phenomenon. Suppose that the application of a certain quantity of heat to
a body merely increases its bulk, that a double quantity melts it, and a
triple quantity decomposes it: these three effects being heterogeneous, no
ratio, whether corresponding or not to that of the quantities of heat
applied, can be established between them. Thus the supposed axiom of the
proportionality of effects to their causes fails at the precise point
where the principle of the Composition of Causes also fails; viz., where
the concurrence of causes is such as to determine a change in the
properties of the body generally, and render it subject to new laws, more
or less dissimilar to those to which it conformed in its previous state.
The recognition, therefore, of any such law of proportionality is
superseded by the more comprehensive principle, in which as much of it as
is true is implicitly asserted.(134)

The general remarks on causation, which seemed necessary as an
introduction to the theory of the inductive process, may here terminate.
That process is essentially an inquiry into cases of causation. All the
uniformities which exist in the succession of phenomena, and most of the
uniformities in their co-existence, are either, as we have seen,
themselves laws of causation, or consequences resulting from, and
corollaries capable of being deduced from, such laws. If we could
determine what causes are correctly assigned to what effects, and what
effects to what causes, we should be virtually acquainted with the whole
course of nature. All those uniformities which are mere results of
causation might then be explained and accounted for; and every individual
fact or event might be predicted, provided we had the requisite data, that
is, the requisite knowledge of the circumstances which, in the particular
instance, preceded it.

To ascertain, therefore, what are the laws of causation which exist in
nature; to determine the effect of every cause, and the causes of all
effects, is the main business of Induction; and to point out how this is
done is the chief object of Inductive Logic.



                               Chapter VII.


On Observation And Experiment.


§ 1. It results from the preceding exposition, that the process of
ascertaining what consequents, in nature, are invariably connected with
what antecedents, or in other words what phenomena are related to each
other as causes and effects, is in some sort a process of analysis. That
every fact which begins to exist has a cause, and that this cause must be
found in some fact or concourse of facts which immediately preceded the
occurrence, may be taken for certain. The whole of the present facts are
the infallible result of all past facts, and more immediately of all the
facts which existed at the moment previous. Here, then, is a great
sequence, which we know to be uniform. If the whole prior state of the
entire universe could again recur, it would again be followed by the
present state. The question is, how to resolve this complex uniformity
into the simpler uniformities which compose it, and assign to each portion
of the vast antecedent the portion of the consequent which is attendant on
it.

This operation, which we have called analytical, inasmuch as it is the
resolution of a complex whole into the component elements, is more than a
merely mental analysis. No mere contemplation of the phenomena, and
partition of them by the intellect alone, will of itself accomplish the
end we have now in view. Nevertheless, such a mental partition is an
indispensable first step. The order of nature, as perceived at a first
glance, presents at every instant a chaos followed by another chaos. We
must decompose each chaos into single facts. We must learn to see in the
chaotic antecedent a multitude of distinct antecedents, in the chaotic
consequent a multitude of distinct consequents. This, supposing it done,
will not of itself tell us on which of the antecedents each consequent is
invariably attendant. To determine that point, we must endeavor to effect
a separation of the facts from one another, not in our minds only, but in
nature. The mental analysis, however, must take place first. And every one
knows that in the mode of performing it, one intellect differs immensely
from another. It is the essence of the act of observing; for the observer
is not he who merely sees the thing which is before his eyes, but he who
sees what parts that thing is composed of. To do this well is a rare
talent. One person, from inattention, or attending only in the wrong
place, overlooks half of what he sees; another sets down much more than he
sees, confounding it with what he imagines, or with what he infers;
another takes note of the _kind_ of all the circumstances, but being
inexpert in estimating their degree, leaves the quantity of each vague and
uncertain; another sees indeed the whole, but makes such an awkward
division of it into parts, throwing things into one mass which require to
be separated, and separating others which might more conveniently be
considered as one, that the result is much the same, sometimes even worse,
than if no analysis had been attempted at all. It would be possible to
point out what qualities of mind, and modes of mental culture, fit a
person for being a good observer: that, however, is a question not of
Logic, but of the Theory of Education, in the most enlarged sense of the
term. There is not properly an Art of Observing. There may be rules for
observing. But these, like rules for inventing, are properly instructions
for the preparation of one’s own mind; for putting it into the state in
which it will be most fitted to observe, or most likely to invent. They
are, therefore, essentially rules of self-education, which is a different
thing from Logic. They do not teach how to do the thing, but how to make
ourselves capable of doing it. They are an art of strengthening the limbs,
not an art of using them.

The extent and minuteness of observation which may be requisite, and the
degree of decomposition to which it may be necessary to carry the mental
analysis, depend on the particular purpose in view. To ascertain the state
of the whole universe at any particular moment is impossible, but would
also be useless. In making chemical experiments, we do not think it
necessary to note the position of the planets; because experience has
shown, as a very superficial experience is sufficient to show, that in
such cases that circumstance is not material to the result: and
accordingly, in the ages when men believed in the occult influences of the
heavenly bodies, it might have been unphilosophical to omit ascertaining
the precise condition of those bodies at the moment of the experiment. As
to the degree of minuteness of the mental subdivision, if we were obliged
to break down what we observe into its very simplest elements, that is,
literally into single facts, it would be difficult to say where we should
find them; we can hardly ever affirm that our divisions of any kind have
reached the ultimate unit. But this, too, is fortunately unnecessary. The
only object of the mental separation is to suggest the requisite physical
separation, so that we may either accomplish it ourselves, or seek for it
in nature; and we have done enough when we have carried the subdivision as
far as the point at which we are able to see what observations or
experiments we require. It is only essential, at whatever point our mental
decomposition of facts may for the present have stopped, that we should
hold ourselves ready and able to carry it further as occasion requires,
and should not allow the freedom of our discriminating faculty to be
imprisoned by the swathes and bands of ordinary classification; as was the
case with all early speculative inquirers, not excepting the Greeks, to
whom it seldom occurred that what was called by one abstract name might,
in reality, be several phenomena, or that there was a possibility of
decomposing the facts of the universe into any elements but those which
ordinary language already recognized.

§ 2. The different antecedents and consequents being, then, supposed to
be, so far as the case requires, ascertained and discriminated from one
another, we are to inquire which is connected with which. In every
instance which comes under our observation, there are many antecedents and
many consequents. If those antecedents could not be severed from one
another except in thought, or if those consequents never were found apart,
it would be impossible for us to distinguish (_a posteriori_ at least) the
real laws, or to assign to any cause its effect, or to any effect its
cause. To do so, we must be able to meet with some of the antecedents
apart from the rest, and observe what follows from them; or some of the
consequents, and observe by what they are preceded. We must, in short,
follow the Baconian rule of _varying the circumstances_. This is, indeed,
only the first rule of physical inquiry, and not, as some have thought,
the sole rule; but it is the foundation of all the rest.

For the purpose of varying the circumstances, we may have recourse
(according to a distinction commonly made) either to observation or to
experiment; we may either _find_ an instance in nature suited to our
purposes, or, by an artificial arrangement of circumstances, _make_ one.
The value of the instance depends on what it is in itself, not on the mode
in which it is obtained: its employment for the purposes of induction
depends on the same principles in the one case and in the other; as the
uses of money are the same whether it is inherited or acquired. There is,
in short, no difference in kind, no real logical distinction, between the
two processes of investigation. There are, however, practical distinctions
to which it is of considerable importance to advert.

§ 3. The first and most obvious distinction between Observation and
Experiment is, that the latter is an immense extension of the former. It
not only enables us to produce a much greater number of variations in the
circumstances than nature spontaneously offers, but also, in thousands of
cases, to produce the precise _sort_ of variation which we are in want of
for discovering the law of the phenomenon; a service which nature, being
constructed on a quite different scheme from that of facilitating our
studies, is seldom so friendly as to bestow upon us. For example, in order
to ascertain what principle in the atmosphere enables it to sustain life,
the variation we require is that a living animal should be immersed in
each component element of the atmosphere separately. But nature does not
supply either oxygen or azote in a separate state. We are indebted to
artificial experiment for our knowledge that it is the former, and not the
latter, which supports respiration; and for our knowledge of the very
existence of the two ingredients.

Thus far the advantage of experimentation over simple observation is
universally recognized: all are aware that it enables us to obtain
innumerable combinations of circumstances which are not to be found in
nature, and so add to nature’s experiments a multitude of experiments of
our own. But there is another superiority (or, as Bacon would have
expressed it, another prerogative) of instances artificially obtained over
spontaneous instances—of our own experiments over even the same
experiments when made by nature—which is not of less importance, and which
is far from being felt and acknowledged in the same degree.

When we can produce a phenomenon artificially, we can take it, as it were,
home with us, and observe it in the midst of circumstances with which in
all other respects we are accurately acquainted. If we desire to know what
are the effects of the cause A, and are able to produce A by means at our
disposal, we can generally determine at our own discretion, so far as is
compatible with the nature of the phenomenon A, the whole of the
circumstances which shall be present along with it: and thus, knowing
exactly the simultaneous state of every thing else which is within the
reach of A’s influence, we have only to observe what alteration is made in
that state by the presence of A.

For example, by the electric machine we can produce, in the midst of known
circumstances, the phenomena which nature exhibits on a grander scale in
the form of lightning and thunder. Now let any one consider what amount of
knowledge of the effects and laws of electric agency mankind could have
obtained from the mere observation of thunder-storms, and compare it with
that which they have gained, and may expect to gain, from electrical and
galvanic experiments. This example is the more striking, now that we have
reason to believe that electric action is of all natural phenomena (except
heat) the most pervading and universal, which, therefore, it might
antecedently have been supposed could stand least in need of artificial
means of production to enable it to be studied; while the fact is so much
the contrary, that without the electric machine, the Leyden jar, and the
voltaic battery, we probably should never have suspected the existence of
electricity as one of the great agents in nature; the few electric
phenomena we should have known of would have continued to be regarded
either as supernatural, or as a sort of anomalies and eccentricities in
the order of the universe.

When we have succeeded in insulating the phenomenon which is the subject
of inquiry, by placing it among known circumstances, we may produce
further variations of circumstances to any extent, and of such kinds as we
think best calculated to bring the laws of the phenomenon into a clear
light. By introducing one well-defined circumstance after another into the
experiment, we obtain assurance of the manner in which the phenomenon
behaves under an indefinite variety of possible circumstances. Thus,
chemists, after having obtained some newly-discovered substance in a pure
state (that is, having made sure that there is nothing present which can
interfere with and modify its agency), introduce various other substances,
one by one, to ascertain whether it will combine with them, or decompose
them, and with what result; and also apply heat, or electricity, or
pressure, to discover what will happen to the substance under each of
these circumstances.

But if, on the other hand, it is out of our power to produce the
phenomenon, and we have to seek for instances in which nature produces it,
the task before us is very different.

Instead of being able to choose what the concomitant circumstances shall
be, we now have to discover what they are; which, when we go beyond the
simplest and most accessible cases, it is next to impossible to do with
any precision and completeness. Let us take, as an exemplification of a
phenomenon which we have no means of fabricating artificially, a human
mind. Nature produces many; but the consequence of our not being able to
produce them by art is, that in every instance in which we see a human
mind developing itself, or acting upon other things, we see it surrounded
and obscured by an indefinite multitude of unascertainable circumstances,
rendering the use of the common experimental methods almost delusive. We
may conceive to what extent this is true, if we consider, among other
things, that whenever Nature produces a human mind, she produces, in close
connection with it, a body; that is, a vast complication of physical
facts, in no two cases perhaps exactly similar, and most of which (except
the mere structure, which we can examine in a sort of coarse way after it
has ceased to act), are radically out of the reach of our means of
exploration. If, instead of a human mind, we suppose the subject of
investigation to be a human society or State, all the same difficulties
recur in a greatly augmented degree.

We have thus already come within sight of a conclusion, which the progress
of the inquiry will, I think, bring before us with the clearest evidence:
namely, that in the sciences which deal with phenomena in which artificial
experiments are impossible (as in the case of astronomy), or in which they
have a very limited range (as in mental philosophy, social science, and
even physiology), induction from direct experience is practiced at a
disadvantage in most cases equivalent to impracticability; from which it
follows that the methods of those sciences, in order to accomplish any
thing worthy of attainment, must be to a great extent, if not principally,
deductive. This is already known to be the case with the first of the
sciences we have mentioned, astronomy; that it is not generally recognized
as true of the others, is probably one of the reasons why they are not in
a more advanced state.

§ 4. If what is called pure observation is at so great a disadvantage,
compared with artificial experimentation, in one department of the direct
exploration of phenomena, there is another branch in which the advantage
is all on the side of the former.

Inductive inquiry having for its object to ascertain what causes are
connected with what effects, we may begin this search at either end of the
road which leads from the one point to the other: we may either inquire
into the effects of a given cause or into the causes of a given effect.
The fact that light blackens chloride of silver might have been discovered
either by experiments on light, trying what effect it would produce on
various substances, or by observing that portions of the chloride had
repeatedly become black, and inquiring into the circumstances. The effect
of the urali poison might have become known either by administering it to
animals, or by examining how it happened that the wounds which the Indians
of Guiana inflict with their arrows prove so uniformly mortal. Now it is
manifest from the mere statement of the examples, without any theoretical
discussion, that artificial experimentation is applicable only to the
former of these modes of investigation. We can take a cause, and try what
it will produce; but we can not take an effect, and try what it will be
produced by. We can only watch till we see it produced, or are enabled to
produce it by accident.

This would be of little importance, if it always depended on our choice
from which of the two ends of the sequence we would undertake our
inquiries. But we have seldom any option. As we can only travel from the
known to the unknown, we are obliged to commence at whichever end we are
best acquainted with. If the agent is more familiar to us than its
effects, we watch for, or contrive, instances of the agent, under such
varieties of circumstances as are open to us, and observe the result. If,
on the contrary, the conditions on which a phenomenon depends are obscure,
but the phenomenon itself familiar, we must commence our inquiry from the
effect. If we are struck with the fact that chloride of silver has been
blackened, and have no suspicion of the cause, we have no resource but to
compare instances in which the fact has chanced to occur, until by that
comparison we discover that in all those instances the substances had been
exposed to light. If we knew nothing of the Indian arrows but their fatal
effect, accident alone could turn our attention to experiments on the
urali; in the regular course of investigation, we could only inquire, or
try to observe, what had been done to the arrows in particular instances.

Wherever, having nothing to guide us to the cause, we are obliged to set
out from the effect, and to apply the rule of varying the circumstances to
the consequents, not the antecedents, we are necessarily destitute of the
resource of artificial experimentation. We can not, at our choice, obtain
consequents, as we can antecedents, under any set of circumstances
compatible with their nature. There are no means of producing effects but
through their causes, and by the supposition the causes of the effect in
question are not known to us. We have, therefore, no expedient but to
study it where it offers itself spontaneously. If nature happens to
present us with instances sufficiently varied in their circumstances, and
if we are able to discover, either among the proximate antecedents or
among some other order of antecedents, something which is always found
when the effect is found, however various the circumstances, and never
found when it is not, we may discover, by mere observation without
experiment, a real uniformity in nature.

But though this is certainly the most favorable case for sciences of pure
observation, as contrasted with those in which artificial experiments are
possible, there is in reality no case which more strikingly illustrates
the inherent imperfection of direct induction when not founded on
experimentation. Suppose that, by a comparison of cases of the effect, we
have found an antecedent which appears to be, and perhaps is, invariably
connected with it: we have not yet proved that antecedent to be the cause
until we have reversed the process, and produced the effect by means of
that antecedent. If we can produce the antecedent artificially, and if,
when we do so, the effect follows, the induction is complete; that
antecedent is the cause of that consequent.(135) But we have then added
the evidence of experiment to that of simple observation. Until we had
done so, we had only proved _invariable_ antecedence within the limits of
experience, but not _unconditional_ antecedence, or causation. Until it
had been shown by the actual production of the antecedent under known
circumstances, and the occurrence thereupon of the consequent, that the
antecedent was really the condition on which it depended; the uniformity
of succession which was proved to exist between them might, for aught we
knew, be (like the succession of day and night) not a case of causation at
all; both antecedent and consequent might be successive stages of the
effect of an ulterior cause. Observation, in short, without experiment
(supposing no aid from deduction) can ascertain sequences and
co-existences, but can not prove causation.

In order to see these remarks verified by the actual state of the
sciences, we have only to think of the condition of natural history. In
zoology, for example, there is an immense number of uniformities
ascertained, some of co-existence, others of succession, to many of which,
notwithstanding considerable variations of the attendant circumstances, we
know not any exception: but the antecedents, for the most part, are such
as we can not artificially produce; or if we can, it is only by setting in
motion the exact process by which nature produces them; and this being to
us a mysterious process, of which the main circumstances are not only
unknown but unobservable, we do not succeed in obtaining the antecedents
under known circumstances. What is the result? That on this vast subject,
which affords so much and such varied scope for observation, we have made
most scanty progress in ascertaining any laws of causation. We know not
with certainty, in the case of most of the phenomena that we find
conjoined, which is the condition of the other; which is cause, and which
effect, or whether either of them is so, or they are not rather conjunct
effects of causes yet to be discovered, complex results of laws hitherto
unknown.

Although some of the foregoing observations may be, in technical
strictness of arrangement, premature in this place, it seemed that a few
general remarks on the difference between sciences of mere observation and
sciences of experimentation, and the extreme disadvantage under which
directly inductive inquiry is necessarily carried on in the former, were
the best preparation for discussing the methods of direct induction; a
preparation rendering superfluous much that must otherwise have been
introduced, with some inconvenience, into the heart of that discussion. To
the consideration of these methods we now proceed.



                              Chapter VIII.


Of The Four Methods Of Experimental Inquiry.


§ 1. The simplest and most obvious modes of singling out from among the
circumstances which precede or follow a phenomenon, those with which it is
really connected by an invariable law, are two in number. One is, by
comparing together different instances in which the phenomenon occurs. The
other is, by comparing instances in which the phenomenon does occur, with
instances in other respects similar in which it does not. These two
methods may be respectively denominated, the Method of Agreement, and the
Method of Difference.

In illustrating these methods, it will be necessary to bear in mind the
twofold character of inquiries into the laws of phenomena; which may be
either inquiries into the cause of a given effect, or into the effects or
properties of a given cause. We shall consider the methods in their
application to either order of investigation, and shall draw our examples
equally from both.

We shall denote antecedents by the large letters of the alphabet, and the
consequents corresponding to them by the small. Let A, then, be an agent
or cause, and let the object of our inquiry be to ascertain what are the
effects of this cause. If we can either find, or produce, the agent A in
such varieties of circumstances that the different cases have no
circumstance in common except A; then whatever effect we find to be
produced in all our trials, is indicated as the effect of A. Suppose, for
example, that A is tried along with B and C, and that the effect is _a b
c_; and suppose that A is next tried with D and E, but without B and C,
and that the effect is _a d e_. Then we may reason thus: _b_ and _c_ are
not effects of A, for they were not produced by it in the second
experiment; nor are _d_ and _e_, for they were not produced in the first.
Whatever is really the effect of A must have been produced in both
instances; now this condition is fulfilled by no circumstance except _a_.
The phenomenon _a_ can not have been the effect of B or C, since it was
produced where they were not; nor of D or E, since it was produced where
they were not. Therefore it is the effect of A.

For example, let the antecedent A be the contact of an alkaline substance
and an oil. This combination being tried under several varieties of
circumstances, resembling each other in nothing else, the results agree in
the production of a greasy and detersive or saponaceous substance: it is
therefore concluded that the combination of an oil and an alkali causes
the production of a soap. It is thus we inquire, by the Method of
Agreement, into the effect of a given cause.

In a similar manner we may inquire into the cause of a given effect. Let
_a_ be the effect. Here, as shown in the last chapter, we have only the
resource of observation without experiment: we can not take a phenomenon
of which we know not the origin, and try to find its mode of production by
producing it: if we succeeded in such a random trial it could only be by
accident. But if we can observe a in two different combinations, _a b c_
and _a d e_; and if we know, or can discover, that the antecedent
circumstances in these cases respectively were A B C and A D E, we may
conclude by a reasoning similar to that in the preceding example, that A
is the antecedent connected with the consequent _a_ by a law of causation.
B and C, we may say, can not be causes of _a_, since on its second
occurrence they were not present; nor are D and E, for they were not
present on its first occurrence. A, alone of the five circumstances, was
found among the antecedents of _a_ in both instances.

For example, let the effect _a_ be crystallization. We compare instances
in which bodies are known to assume crystalline structure, but which have
no other point of agreement; and we find them to have one, and as far as
we can observe, only one, antecedent in common: the deposition of a solid
matter from a liquid state, either a state of fusion or of solution. We
conclude, therefore, that the solidification of a substance from a liquid
state is an invariable antecedent of its crystallization.

In this example we may go further, and say, it is not only the invariable
antecedent but the cause; or at least the proximate event which completes
the cause. For in this case we are able, after detecting the antecedent A,
to produce it artificially, and by finding that _a_ follows it, verify the
result of our induction. The importance of thus reversing the proof was
strikingly manifested when, by keeping a phial of water charged with
siliceous particles undisturbed for years, a chemist (I believe Dr.
Wollaston) succeeded in obtaining crystals of quartz; and in the equally
interesting experiment in which Sir James Hall produced artificial marble
by the cooling of its materials from fusion under immense pressure: two
admirable examples of the light which may be thrown upon the most secret
processes of Nature by well-contrived interrogation of her.

But if we can not artificially produce the phenomenon A, the conclusion
that it is the cause of _a_ remains subject to very considerable doubt.
Though an invariable, it may not be the unconditional antecedent of _a_,
but may precede it as day precedes night or night day. This uncertainty
arises from the impossibility of assuring ourselves that A is the _only_
immediate antecedent common to both the instances. If we could be certain
of having ascertained all the invariable antecedents, we might be sure
that the unconditional invariable antecedent, or cause, must be found
somewhere among them. Unfortunately it is hardly ever possible to
ascertain all the antecedents, unless the phenomenon is one which we can
produce artificially. Even then, the difficulty is merely lightened, not
removed: men knew how to raise water in pumps long before they adverted to
what was really the operating circumstance in the means they employed,
namely, the pressure of the atmosphere on the open surface of the water.
It is, however, much easier to analyze completely a set of arrangements
made by ourselves, than the whole complex mass of the agencies which
nature happens to be exerting at the moment of the production of a given
phenomenon. We may overlook some of the material circumstances in an
experiment with an electrical machine; but we shall, at the worst, be
better acquainted with them than with those of a thunder-storm.

The mode of discovering and proving laws of nature, which we have now
examined, proceeds on the following axiom: Whatever circumstances can be
excluded, without prejudice to the phenomenon, or can be absent
notwithstanding its presence, is not connected with it in the way of
causation. The casual circumstances being thus eliminated, if only one
remains, that one is the cause which we are in search of: if more than
one, they either are, or contain among them, the cause; and so, _mutatis
mutandis_, of the effect. As this method proceeds by comparing different
instances to ascertain in what they agree, I have termed it the Method of
Agreement; and we may adopt as its regulating principal the following
canon:

FIRST CANON.

_If two or more instances of the phenomenon under investigation have only
one circumstance in common, the circumstance in which alone all the
instances agree, is the cause (or effect) of the given phenomenon._

Quitting for the present the Method of Agreement, to which we shall almost
immediately return, we proceed to a still more potent instrument of the
investigation of nature, the Method of Difference.

§ 2. In the Method of Agreement, we endeavored to obtain instances which
agreed in the given circumstance but differed in every other: in the
present method we require, on the contrary, two instances resembling one
another in every other respect, but differing in the presence or absence
of the phenomenon we wish to study. If our object be to discover the
effects of an agent A, we must procure A in some set of ascertained
circumstances, as A B C, and having noted the effects produced, compare
them with the effect of the remaining circumstances B C, when A is absent.
If the effect of A B C is _a b c_, and the effect of B C _b c_, it is
evident that the effect of A is _a_. So again, if we begin at the other
end, and desire to investigate the cause of an effect _a_, we must select
an instance, as _a b c_, in which the effect occurs, and in which the
antecedents were A B C, and we must look out for another instance in which
the remaining circumstances, _b c_, occur without _a_. If the antecedents,
in that instance, are B C, we know that the cause of _a_ must be A: either
A alone, or A in conjunction with some of the other circumstances present.

It is scarcely necessary to give examples of a logical process to which we
owe almost all the inductive conclusions we draw in daily life. When a man
is shot through the heart, it is by this method we know that it was the
gunshot which killed him: for he was in the fullness of life immediately
before, all circumstances being the same, except the wound.

The axioms implied in this method are evidently the following. Whatever
antecedent can not be excluded without preventing the phenomenon, is the
cause, or a condition, of that phenomenon: whatever consequent can be
excluded, with no other difference in the antecedents than the absence of
a particular one, is the effect of that one. Instead of comparing
different instances of a phenomenon, to discover in what they agree, this
method compares an instance of its occurrence with an instance of its
non-occurrence, to discover in what they differ. The canon which is the
regulating principle of the Method of Difference may be expressed as
follows:

SECOND CANON.

_If an instance in which the phenomenon under investigation occurs, and an
instance in which it does not occur, have every circumstance in common
save one, that one occurring only in the former; the circumstance in which
alone the two instances differ, is the effect, or the cause, or an
indispensable part of the cause, of the phenomenon._

§ 3. The two methods which we have now stated have many features of
resemblance, but there are also many distinctions between them. Both are
methods of _elimination_. This term (employed in the theory of equations
to denote the process by which one after another of the elements of a
question is excluded, and the solution made to depend on the relation
between the remaining elements only) is well suited to express the
operation, analogous to this, which has been understood since the time of
Bacon to be the foundation of experimental inquiry: namely, the successive
exclusion of the various circumstances which are found to accompany a
phenomenon in a given instance, in order to ascertain what are those among
them which can be absent consistently with the existence of the
phenomenon. The Method of Agreement stands on the ground that whatever can
be eliminated, is not connected with the phenomenon by any law. The Method
of Difference has for its foundation, that whatever can not be eliminated,
is connected with the phenomenon by a law.

Of these methods, that of Difference is more particularly a method of
artificial experiment; while that of Agreement is more especially the
resource employed where experimentation is impossible. A few reflections
will prove the fact, and point out the reason of it.

It is inherent in the peculiar character of the Method of Difference, that
the nature of the combinations which it requires is much more strictly
defined than in the Method of Agreement. The two instances which are to be
compared with one another must be exactly similar, in all circumstances
except the one which we are attempting to investigate: they must be in the
relation of A B C and B C, or of _a b c_ and _b c_. It is true that this
similarity of circumstances needs not extend to such as are already known
to be immaterial to the result. And in the case of most phenomena we learn
at once, from the commonest experience, that most of the co-existent
phenomena of the universe may be either present or absent without
affecting the given phenomenon; or, if present, are present indifferently
when the phenomenon does not happen and when it does. Still, even limiting
the identity which is required between the two instances, A B C and B C,
to such circumstances as are not already known to be indifferent, it is
very seldom that nature affords two instances, of which we can be assured
that they stand in this precise relation to one another. In the
spontaneous operations of nature there is generally such complication and
such obscurity, they are mostly either on so overwhelmingly large or on so
inaccessibly minute a scale, we are so ignorant of a great part of the
facts which really take place, and even those of which we are not ignorant
are so multitudinous, and therefore so seldom exactly alike in any two
cases, that a spontaneous experiment, of the kind required by the Method
of Difference, is commonly not to be found. When, on the contrary, we
obtain a phenomenon by an artificial experiment, a pair of instances such
as the method requires is obtained almost as a matter of course, provided
the process does not last a long time. A certain state of surrounding
circumstances existed before we commenced the experiment; this is B C. We
then introduce A; say, for instance, by merely bringing an object from
another part of the room, before there has been time for any change in the
other elements. It is, in short (as M. Comté observes), the very nature of
an experiment, to introduce into the pre-existing state of circumstances a
change perfectly definite. We choose a previous state of things with which
we are well acquainted, so that no unforeseen alteration in that state is
likely to pass unobserved; and into this we introduce, as rapidly as
possible, the phenomenon which we wish to study; so that in general we are
entitled to feel complete assurance that the pre-existing state, and the
state which we have produced, differ in nothing except the presence or
absence of that phenomenon. If a bird is taken from a cage, and instantly
plunged into carbonic acid gas, the experimentalist may be fully assured
(at all events after one or two repetitions) that no circumstance capable
of causing suffocation had supervened in the interim, except the change
from immersion in the atmosphere to immersion in carbonic acid gas. There
is one doubt, indeed, which may remain in some cases of this description;
the effect may have been produced not by the change, but by the means
employed to produce the change. The possibility, however, of this last
supposition generally admits of being conclusively tested by other
experiments. It thus appears that in the study of the various kinds of
phenomena which we can, by our voluntary agency, modify or control, we can
in general satisfy the requisitions of the Method of Difference; but that
by the spontaneous operations of nature those requisitions are seldom
fulfilled.

The reverse of this is the case with the Method of Agreement. We do not
here require instances of so special and determinate a kind. Any instances
whatever, in which nature presents us with a phenomenon, may be examined
for the purposes of this method; and if all such instances agree in any
thing, a conclusion of considerable value is already attained. We can
seldom, indeed, be sure that the one point of agreement is the only one;
but this ignorance does not, as in the Method of Difference, vitiate the
conclusion; the certainty of the result, as far as it goes, is not
affected. We have ascertained one invariable antecedent or consequent,
however many other invariable antecedents or consequents may still remain
unascertained. If A B C, A D E, A F G, are all equally followed by a, then
a is an invariable consequent of A. If _a b c_, _a d e_, _a f g_, all
number A among their antecedents, then A is connected as an antecedent, by
some invariable law, with _a_. But to determine whether this invariable
antecedent is a cause, or this invariable consequent an effect, we must be
able, in addition, to produce the one by means of the other; or, at least,
to obtain that which alone constitutes our assurance of having produced
any thing, namely, an instance in which the effect, _a_, has come into
existence, with no other change in the pre-existing circumstances than the
addition of A. And this, if we can do it, is an application of the Method
of Difference, not of the Method of Agreement.

It thus appears to be by the Method of Difference alone that we can ever,
in the way of direct experience, arrive with certainty at causes. The
Method of Agreement leads only to laws of phenomena (as some writers call
them, but improperly, since laws of causation are also laws of phenomena):
that is, to uniformities, which either are not laws of causation, or in
which the question of causation must for the present remain undecided. The
Method of Agreement is chiefly to be resorted to, as a means of suggesting
applications of the Method of Difference (as in the last example the
comparison of A B C, A D E, A F G, suggested that A was the antecedent on
which to try the experiment whether it could produce _a_); or as an
inferior resource, in case the Method of Difference is impracticable;
which, as we before showed, generally arises from the impossibility of
artificially producing the phenomena. And hence it is that the Method of
Agreement, though applicable in principle to either case, is more
emphatically the method of investigation on those subjects where
artificial experimentation is impossible; because on those it is,
generally, our only resource of a directly inductive nature; while, in the
phenomena which we can produce at pleasure, the Method of Difference
generally affords a more efficacious process, which will ascertain causes
as well as mere laws.

§ 4. There are, however, many cases in which, though our power of
producing the phenomenon is complete, the Method of Difference either can
not be made available at all, or not without a previous employment of the
Method of Agreement. This occurs when the agency by which we can produce
the phenomenon is not that of one single antecedent, but a combination of
antecedents, which we have no power of separating from each other, and
exhibiting apart. For instance, suppose the subject of inquiry to be the
cause of the double refraction of light. We can produce this phenomenon at
pleasure, by employing any one of the many substances which are known to
refract light in that peculiar manner. But if, taking one of those
substances, as Iceland spar, for example, we wish to determine on which of
the properties of Iceland spar this remarkable phenomenon depends, we can
make no use, for that purpose, of the Method of Difference; for we can not
find another substance precisely resembling Iceland spar except in some
one property. The only mode, therefore, of prosecuting this inquiry is
that afforded by the Method of Agreement; by which, in fact, through a
comparison of all the known substances which have the property of doubly
refracting light, it was ascertained that they agree in the circumstance
of being crystalline substances; and though the converse does not hold,
though all crystalline substances have not the property of double
refraction, it was concluded, with reason, that there is a real connection
between these two properties; that either crystalline structure, or the
cause which gives rise to that structure, is one of the conditions of
double refraction.

Out of this employment of the Method of Agreement arises a peculiar
modification of that method, which is sometimes of great avail in the
investigation of nature. In cases similar to the above, in which it is not
possible to obtain the precise pair of instances which our second canon
requires—instances agreeing in every antecedent except A, or in every
consequent except _a_, we may yet be able, by a double employment of the
Method of Agreement, to discover in what the instances which contain A or
_a_ differ from those which do not.

If we compare various instances in which _a_ occurs, and find that they
all have in common the circumstance A, and (as far as can be observed) no
other circumstance, the Method of Agreement, so far, bears testimony to a
connection between A and _a_. In order to convert this evidence of
connection into proof of causation by the direct Method of Difference, we
ought to be able, in some one of these instances, as for example, A B C,
to leave out A, and observe whether by doing so, _a_ is prevented. Now
supposing (what is often the case) that we are not able to try this
decisive experiment; yet, provided we can by any means discover what would
be its result if we could try it, the advantage will be the same. Suppose,
then, that as we previously examined a variety of instances in which _a_
occurred, and found them to agree in containing A, so we now observe a
variety of instances in which _a_ does not occur, and find them agree in
not containing A; which establishes, by the Method of Agreement, the same
connection between the absence of A and the absence of _a_, which was
before established between their presence. As, then, it had been shown
that whenever A is present _a_ is present, so, it being now shown that
when A is taken away a is removed along with it, we have by the one
proposition A B C, _a b c_, by the other B C, _b c_, the positive and
negative instances which the Method of Difference requires.

This method may be called the Indirect Method of Difference, or the Joint
Method of Agreement and Difference; and consists in a double employment of
the Method of Agreement, each proof being independent of the other, and
corroborating it. But it is not equivalent to a proof by the direct Method
of Difference. For the requisitions of the Method of Difference are not
satisfied, unless we can be quite sure either that the instances
affirmative of _a_ agree in no antecedent whatever but A, or that the
instances negative of _a_ agree in nothing but the negation of A. Now, if
it were possible, which it never is, to have this assurance, we should not
need the joint method; for either of the two sets of instances separately
would then be sufficient to prove causation. This indirect method,
therefore, can only be regarded as a great extension and improvement of
the Method of Agreement, but not as participating in the more cogent
nature of the Method of Difference. The following may be stated as its
canon:

THIRD CANON.

_If two or more instances in which the phenomenon occurs have only one
circumstance in common, while two or more instances in which it does not
occur have nothing in common save the absence of that circumstance, the
circumstance in which alone the two sets of instances differ, is the
effect, or the cause, or an indispensable part of the cause, of the
phenomenon._

We shall presently see that the Joint Method of Agreement and Difference
constitutes, in another respect not yet adverted to, an improvement upon
the common Method of Agreement, namely, in being unaffected by a
characteristic imperfection of that method, the nature of which still
remains to be pointed out. But as we can not enter into this exposition
without introducing a new element of complexity into this long and
intricate discussion, I shall postpone it to a subsequent chapter, and
shall at once proceed to a statement of two other methods, which will
complete the enumeration of the means which mankind possess for exploring
the laws of nature by specific observation and experience.

§ 5. The first of these has been aptly denominated the Method of Residues.
Its principle is very simple. Subducting from any given phenomenon all the
portions which, by virtue of preceding inductions, can be assigned to
known causes, the remainder will be the effect of the antecedents which
had been overlooked, or of which the effect was as yet an unknown
quantity.

Suppose, as before, that we have the antecedents A B C, followed by the
consequents _a b c_, and that by previous inductions (founded, we will
suppose, on the Method of Difference) we have ascertained the causes of
some of these effects, or the effects of some of these causes; and are
thence apprised that the effect of A is _a_, and that the effect of B is
_b_. Subtracting the sum of these effects from the total phenomenon, there
remains _c_, which now, without any fresh experiments, we may know to be
the effect of C. This Method of Residues is in truth a peculiar
modification of the Method of Difference. If the instance A B C, _a b c_,
could have been compared with a single instance A B, _a b_, we should have
proved C to be the cause of _c_, by the common process of the Method of
Difference. In the present case, however, instead of a single instance A
B, we have had to study separately the causes A and B, and to infer from
the effects which they produce separately what effect they must produce in
the case A B C, where they act together. Of the two instances, therefore,
which the Method of Difference requires—the one positive, the other
negative—the negative one, or that in which the given phenomenon is
absent, is not the direct result of observation and experiment, but has
been arrived at by deduction. As one of the forms of the Method of
Difference, the Method of Residues partakes of its rigorous certainty,
provided the previous inductions, those which gave the effects of A and B,
were obtained by the same infallible method, and provided we are certain
that C is the _only_ antecedent to which the residual phenomenon _c_ can
be referred; the only agent of which we had not already calculated and
subducted the effect. But as we can never be quite certain of this, the
evidence derived from the Method of Residues is not complete unless we can
obtain C artificially, and try it separately, or unless its agency, when
once suggested, can be accounted for, and proved deductively from known
laws.

Even with these reservations, the Method of Residues is one of the most
important among our instruments of discovery. Of all the methods of
investigating laws of nature, this is the most fertile in unexpected
results: often informing us of sequences in which neither the cause nor
the effect were sufficiently conspicuous to attract of themselves the
attention of observers. The agent C may be an obscure circumstance, not
likely to have been perceived unless sought for, nor likely to have been
sought for until attention had been awakened by the insufficiency of the
obvious causes to account for the whole of the effect. And _c_ may be so
disguised by its intermixture with _a_ and _b_, that it would scarcely
have presented itself spontaneously as a subject of separate study. Of
these uses of the method, we shall presently cite some remarkable
examples. The canon of the Method of Residues is as follows:

FOURTH CANON.

_Subduct from any phenomenon such part as is known by previous inductions
to be the effect of certain antecedents, and the residue of the phenomenon
is the effect of the remaining antecedents._

§ 6. There remains a class of laws which it is impracticable to ascertain
by any of the three methods which I have attempted to characterize:
namely, the laws of those Permanent Causes, or indestructible natural
agents, which it is impossible either to exclude or to isolate; which we
can neither hinder from being present, nor contrive that they shall be
present alone. It would appear at first sight that we could by no means
separate the effects of these agents from the effects of those other
phenomena with which they can not be prevented from co-existing. In
respect, indeed, to most of the permanent causes, no such difficulty
exists; since, though we can not eliminate them as co-existing facts, we
can eliminate them as influencing agents, by simply trying our experiment
in a local situation beyond the limits of their influence. The pendulum,
for example, has its oscillations disturbed by the vicinity of a mountain:
we remove the pendulum to a sufficient distance from the mountain, and the
disturbance ceases: from these data we can determine by the Method of
Difference, the amount of effect due to the mountain; and beyond a certain
distance every thing goes on precisely as it would do if the mountain
exercised no influence whatever, which, accordingly, we, with sufficient
reason, conclude to be the fact.

The difficulty, therefore, in applying the methods already treated of to
determine the effects of Permanent Causes, is confined to the cases in
which it is impossible for us to get out of the local limits of their
influence. The pendulum can be removed from the influence of the mountain,
but it can not be removed from the influence of the earth: we can not take
away the earth from the pendulum, nor the pendulum from the earth, to
ascertain whether it would continue to vibrate if the action which the
earth exerts upon it were withdrawn. On what evidence, then, do we ascribe
its vibrations to the earth’s influence? Not on any sanctioned by the
Method of Difference; for one of the two instances, the negative instance,
is wanting. Nor by the Method of Agreement; for though all pendulums agree
in this, that during their oscillations the earth is always present, why
may we not as well ascribe the phenomenon to the sun, which is equally a
co-existent fact in all the experiments? It is evident that to establish
even so simple a fact of causation as this, there was required some method
over and above those which we have yet examined.

As another example, let us take the phenomenon Heat. Independently of all
hypothesis as to the real nature of the agency so called, this fact is
certain, that we are unable to exhaust any body of the whole of its heat.
It is equally certain that no one ever perceived heat not emanating from a
body. Being unable, then, to separate Body and Heat, we can not effect
such a variation of circumstances as the foregoing three methods require;
we can not ascertain, by those methods, what portion of the phenomena
exhibited by any body is due to the heat contained in it. If we could
observe a body with its heat, and the same body entirely divested of heat,
the Method of Difference would show the effect due to the heat, apart from
that due to the body. If we could observe heat under circumstances
agreeing in nothing but heat, and therefore not characterized also by the
presence of a body, we could ascertain the effects of heat, from an
instance of heat with a body and an instance of heat without a body, by
the Method of Agreement; or we could determine by the Method of Difference
what effect was due to the body, when the remainder which was due to the
heat would be given by the Method of Residues. But we can do none of these
things; and without them the application of any of the three methods to
the solution of this problem would be illusory. It would be idle, for
instance, to attempt to ascertain the effect of heat by subtracting from
the phenomena exhibited by a body all that is due to its other properties;
for as we have never been able to observe any bodies without a portion of
heat in them, effects due to that heat might form a part of the very
results which we were affecting to subtract, in order that the effect of
heat might be shown by the residue.

If, therefore, there were no other methods of experimental investigation
than these three, we should be unable to determine the effects due to heat
as a cause. But we have still a resource. Though we can not exclude an
antecedent altogether, we may be able to produce, or nature may produce
for us some modification in it. By a modification is here meant, a change
in it not amounting to its total removal. If some modification in the
antecedent A is always followed by a change in the consequent _a_, the
other consequents _b_ and _c_ remaining the same; or _vicè versa_, if
every change in _a_ is found to have been preceded by some modification in
A, none being observable in any of the other antecedents, we may safely
conclude that _a_ is, wholly or in part, an effect traceable to A, or at
least in some way connected with it through causation. For example, in the
case of heat, though we can not expel it altogether from any body, we can
modify it in quantity, we can increase or diminish it; and doing so, we
find by the various methods of experimentation or observation already
treated of, that such increase or diminution of heat is followed by
expansion or contraction of the body. In this manner we arrive at the
conclusion, otherwise unattainable by us, that one of the effects of heat
is to enlarge the dimensions of bodies; or, what is the same thing in
other words, to widen the distances between their particles.

A change in a thing, not amounting to its total removal, that is, a change
which leaves it still the same thing it was, must be a change either in
its quantity, or in some of its variable relations to other things, of
which variable relations the principal is its position in space. In the
previous example, the modification which was produced in the antecedent
was an alteration in its quantity. Let us now suppose the question to be,
what influence the moon exerts on the surface of the earth. We can not try
an experiment in the absence of the moon, so as to observe what
terrestrial phenomena her annihilation would put an end to; but when we
find that all the variations in the _position_ of the moon are followed by
corresponding variations in the time and place of high water, the place
being always either the part of the earth which is nearest to, or that
which is most remote from, the moon, we have ample evidence that the moon
is, wholly or partially, the cause which determines the tides. It very
commonly happens, as it does in this instance, that the variations of an
effect are correspondent, or analogous, to those of its cause; as the moon
moves farther toward the east, the high-water point does the same: but
this is not an indispensable condition, as may be seen in the same
example, for along with that high-water point there is at the same instant
another high-water point diametrically opposite to it, and which,
therefore, of necessity, moves toward the west, as the moon, followed by
the nearer of the tide waves, advances toward the east: and yet both these
motions are equally effects of the moon’s motion.

That the oscillations of the pendulum are caused by the earth, is proved
by similar evidence. Those oscillations take place between equidistant
points on the two sides of a line, which, being perpendicular to the
earth, varies with every variation in the earth’s position, either in
space or relatively to the object. Speaking accurately, we only know by
the method now characterized, that all terrestrial bodies tend to the
earth, and not to some unknown fixed point lying in the same direction. In
every twenty-four hours, by the earth’s rotation, the line drawn from the
body at right angles to the earth coincides successively with all the
radii of a circle, and in the course of six months the place of that
circle varies by nearly two hundred millions of miles; yet in all these
changes of the earth’s position, the line in which bodies tend to fall
continues to be directed toward it: which proves that terrestrial gravity
is directed to the earth, and not, as was once fancied by some, to a fixed
point of space.

The method by which these results were obtained may be termed the Method
of Concomitant Variations; it is regulated by the following canon:

FIFTH CANON.

_Whatever phenomenon varies in any manner whenever another phenomenon
varies in some particular manner, is either a cause or an effect of that
phenomenon, or is connected with it through some fact of causation._

The last clause is subjoined, because it by no means follows when two
phenomena accompany each other in their variations, that the one is cause
and the other effect. The same thing may, and indeed must happen,
supposing them to be two different effects of a common cause: and by this
method alone it would never be possible to ascertain which of the
suppositions is the true one. The only way to solve the doubt would be
that which we have so often adverted to, viz., by endeavoring to ascertain
whether we can produce the one set of variations by means of the other. In
the case of heat, for example, by increasing the temperature of a body we
increase its bulk, but by increasing its bulk we do not increase its
temperature; on the contrary (as in the rarefaction of air under the
receiver of an air-pump), we generally diminish it: therefore heat is not
an effect, but a cause, of increase of bulk. If we can not ourselves
produce the variations, we must endeavor, though it is an attempt which is
seldom successful, to find them produced by nature in some case in which
the pre-*existing circumstances are perfectly known to us.

It is scarcely necessary to say, that in order to ascertain the uniform
concomitance of variations in the effect with variations in the cause, the
same precautions must be used as in any other case of the determination of
an invariable sequence. We must endeavor to retain all the other
antecedents unchanged, while that particular one is subjected to the
requisite series of variations; or, in other words, that we may be
warranted in inferring causation from concomitance of variations, the
concomitance itself must be proved by the Method of Difference.

It might at first appear that the Method of Concomitant Variations assumes
a new axiom, or law of causation in general, namely, that every
modification of the cause is followed by a change in the effect. And it
does usually happen that when a phenomenon A causes a phenomenon _a_, any
variation in the quantity or in the various relations of A, is uniformly
followed by a variation in the quantity or relations of _a_. To take a
familiar instance, that of gravitation. The sun causes a certain tendency
to motion in the earth; here we have cause and effect; but that tendency
is _toward_ the sun, and therefore varies in direction as the sun varies
in the relation of position; and, moreover, the tendency varies in
intensity, in a certain numerical correspondence to the sun’s distance
from the earth, that is, according to another relation of the sun. Thus we
see that there is not only an invariable connection between the sun and
the earth’s gravitation, but that two of the relations of the sun, its
position with respect to the earth and its distance from the earth, are
invariably connected as antecedents with the quantity and direction of the
earth’s gravitation. The cause of the earth’s gravitating at all, is
simply the sun; but the cause of its gravitating with a given intensity
and in a given direction, is the existence of the sun in a given direction
and at a given distance. It is not strange that a modified cause, which is
in truth a different cause, should produce a different effect.

Although it is for the most part true that a modification of the cause is
followed by a modification of the effect, the Method of Concomitant
Variations does not, however, presuppose this as an axiom. It only
requires the converse proposition: that any thing on whose modifications,
modifications of an effect are invariably consequent, must be the cause
(or connected with the cause) of that effect; a proposition, the truth of
which is evident; for if the thing itself had no influence on the effect,
neither could the modifications of the thing have any influence. If the
stars have no power over the fortunes of mankind, it is implied in the
very terms that the conjunctions or oppositions of different stars can
have no such power.

Although the most striking applications of the Method of Concomitant
Variations take place in the cases in which the Method of Difference,
strictly so called, is impossible, its use is not confined to those cases;
it may often usefully follow after the Method of Difference, to give
additional precision to a solution which that has found. When by the
Method of Difference it has first been ascertained that a certain object
produces a certain effect, the Method of Concomitant Variations may be
usefully called in, to determine according to what law the quantity or the
different relations of the effect follow those of the cause.

§ 7. The case in which this method admits of the most extensive
employment, is that in which the variations of the cause are variations of
quantity. Of such variations we may in general affirm with safety, that
they will be attended not only with variations, but with similar
variations, of the effect: the proposition that more of the cause is
followed by more of the effect, being a corollary from the principle of
the Composition of Causes, which, as we have seen, is the general rule of
causation; cases of the opposite description, in which causes change their
properties on being conjoined with one another, being, on the contrary,
special and exceptional. Suppose, then, that when A changes in quantity,
_a_ also changes in quantity, and in such a manner that we can trace the
numerical relation which the changes of the one bear to such changes of
the other as take place within our limits of observation. We may then,
with certain precautions, safely conclude that the same numerical relation
will hold beyond those limits. If, for instance, we find that when A is
double, _a_ is double; that when A is treble or quadruple, _a_ is treble
or quadruple; we may conclude that if A were a half or a third, _a_ would
be a half or a third, and finally, that if A were annihilated, _a_ would
be annihilated; and that _a_ is wholly the effect of A, or wholly the
effect of the same cause with A. And so with any other numerical relation
according to which A and _a_ would vanish simultaneously; as, for
instance, if _a_ were proportional to the square of A. If, on the other
hand, _a_ is not wholly the effect of A, but yet varies when A varies, it
is probably a mathematical function not of A alone, but of A and something
else: its changes, for example, may be such as would occur if part of it
remained constant, or varied on some other principle, and the remainder
varied in some numerical relations to the variations of A. In that case,
when A diminishes, _a_ will be seen to approach not toward zero, but
toward some other limit; and when the series of variations is such as to
indicate what that limit is, if constant, or the law of its variation, if
variable, the limit will exactly measure how much of _a_ is the effect of
some other and independent cause, and the remainder will be the effect of
A (or of the cause of A).

These conclusions, however, must not be drawn without certain precautions.
In the first place, the possibility of drawing them at all, manifestly
supposes that we are acquainted not only with the variations, but with the
absolute quantities both of A and _a_. If we do not know the total
quantities, we can not, of course, determine the real numerical relation
according to which those quantities vary. It is, therefore, an error to
conclude, as some have concluded, that because increase of heat expands
bodies, that is, increases the distance between their particles, therefore
the distance is wholly the effect of heat, and that if we could entirely
exhaust the body of its heat, the particles would be in complete contact.
This is no more than a guess, and of the most hazardous sort, not a
legitimate induction: for since we neither know how much heat there is in
any body, nor what is the real distance between any two of its particles,
we can not judge whether the contraction of the distance does or does not
follow the diminution of the quantity of heat according to such a
numerical relation that the two quantities would vanish simultaneously.

In contrast with this, let us consider a case in which the absolute
quantities are known; the case contemplated in the first law of motion:
viz., that all bodies in motion continue to move in a straight line with
uniform velocity until acted upon by some new force. This assertion is in
open opposition to first appearances; all terrestrial objects, when in
motion, gradually abate their velocity, and at last stop; which
accordingly the ancients, with their _inductio per enumerationem
simplicem_, imagined to be the law. Every moving body, however, encounters
various obstacles, as friction, the resistance of the atmosphere, etc.,
which we know by daily experience to be causes capable of destroying
motion. It was suggested that the whole of the retardation might be owing
to these causes. How was this inquired into? If the obstacles could have
been entirely removed, the case would have been amenable to the Method of
Difference. They could not be removed, they could only be diminished, and
the case, therefore, admitted only of the Method of Concomitant
Variations. This accordingly being employed, it was found that every
diminution of the obstacles diminished the retardation of the motion: and
inasmuch as in this case (unlike the case of heat) the total quantities
both of the antecedent and of the consequent were known, it was
practicable to estimate, with an approach to accuracy, both the amount of
the retardation and the amount of the retarding causes, or resistances,
and to judge how near they both were to being exhausted; and it appeared
that the effect dwindled as rapidly, and at each step was as far on the
road toward annihilation, as the cause was. The simple oscillation of a
weight suspended from a fixed point, and moved a little out of the
perpendicular, which in ordinary circumstances lasts but a few minutes,
was prolonged in Borda’s experiments to more than thirty hours, by
diminishing as much as possible the friction at the point of suspension,
and by making the body oscillate in a space exhausted as nearly as
possible of its air. There could therefore be no hesitation in assigning
the whole of the retardation of motion to the influence of the obstacles;
and since, after subducting this retardation from the total phenomenon,
the remainder was a uniform velocity, the result was the proposition known
as the first law of motion.

There is also another characteristic uncertainty affecting the inference
that the law of variation which the quantities observe within our limits
of observation, will hold beyond those limits. There is, of course, in the
first instance, the possibility that beyond the limits, and in
circumstances therefore of which we have no direct experience, some
counteracting cause might develop itself; either a new agent or a new
property of the agents concerned, which lies dormant in the circumstances
we are able to observe. This is an element of uncertainty which enters
largely into all our predictions of effects; but it is not peculiarly
applicable to the Method of Concomitant Variations. The uncertainty,
however, of which I am about to speak, is characteristic of that method;
especially in the cases in which the extreme limits of our observation are
very narrow, in comparison with the possible variations in the quantities
of the phenomena. Any one who has the slightest acquaintance with
mathematics, is aware that very different laws of variation may produce
numerical results which differ but slightly from one another within narrow
limits; and it is often only when the absolute amounts of variation are
considerable, that the difference between the results given by one law and
by another becomes appreciable. When, therefore, such variations in the
quantity of the antecedents as we have the means of observing are small in
comparison with the total quantities, there is much danger lest we should
mistake the numerical law, and be led to miscalculate the variations which
would take place beyond the limits; a miscalculation which would vitiate
any conclusion respecting the dependence of the effect upon the cause,
that could be founded on those variations. Examples are not wanting of
such mistakes. “The formulæ,” says Sir John Herschel,(136) “which have
been empirically deduced for the elasticity of steam (till very recently),
and those for the resistance of fluids, and other similar subjects,” when
relied on beyond the limits of the observations from which they were
deduced, "have almost invariably failed to support the theoretical
structures which have been erected on them."

In this uncertainty, the conclusion we may draw from the concomitant
variations of _a_ and A, to the existence of an invariable and exclusive
connection between them, or to the permanency of the same numerical
relation between their variations when the quantities are much greater or
smaller than those which we have had the means of observing, can not be
considered to rest on a complete induction. All that in such a case can be
regarded as proved on the subject of causation is, that there is some
connection between the two phenomena; that A, or something which can
influence A, must be _one_ of the causes which collectively determine _a_.
We may, however, feel assured that the relation which we have observed to
exist between the variations of A and _a_, will hold true in all cases
which fall between the same extreme limits; that is, wherever the utmost
increase or diminution in which the result has been found by observation
to coincide with the law, is not exceeded.

The four methods which it has now been attempted to describe, are the only
possible modes of experimental inquiry—of direct induction _a posteriori_,
as distinguished from deduction: at least, I know not, nor am able to
imagine any others. And even of these, the Method of Residues, as we have
seen, is not independent of deduction; though, as it also requires
specific experience, it may, without impropriety, be included among
methods of direct observation and experiment.

These, then, with such assistance as can be obtained from Deduction,
compose the available resources of the human mind for ascertaining the
laws of the succession of phenomena. Before proceeding to point out
certain circumstances by which the employment of these methods is
subjected to an immense increase of complication and of difficulty, it is
expedient to illustrate the use of the methods, by suitable examples drawn
from actual physical investigations. These, accordingly, will form the
subject of the succeeding chapter.



                               Chapter IX.


Miscellaneous Examples Of The Four Methods.


§ 1. I shall select, as a first example, an interesting speculation of one
of the most eminent of theoretical chemists, Baron Liebig. The object in
view is to ascertain the immediate cause of the death produced by metallic
poisons.

Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
introduced into the animal organism, except in the smallest doses, destroy
life. These facts have long been known, as insulated truths of the lowest
order of generalization; but it was reserved for Liebig, by an apt
employment of the first two of our methods of experimental inquiry, to
connect these truths together by a higher induction, pointing out what
property, common to all these deleterious substances, is the really
operating cause of their fatal effect.

When solutions of these substances are placed in sufficiently close
contact with many animal products, albumen, milk, muscular fibre, and
animal membranes, the acid or salt leaves the water in which it was
dissolved, and enters into combination with the animal substance, which
substance, after being thus acted upon, is found to have lost its tendency
to spontaneous decomposition, or putrefaction.

Observation also shows, in cases where death has been produced by these
poisons, that the parts of the body with which the poisonous substances
have been brought into contact, do not afterward putrefy.

And, finally, when the poison has been supplied in too small a quantity to
destroy life, eschars are produced, that is, certain superficial portions
of the tissues are destroyed, which are afterward thrown off by the
reparative process taking place in the healthy parts.

These three sets of instances admit of being treated according to the
Method of Agreement. In all of them the metallic compounds are brought
into contact with the substances which compose the human or animal body;
and the instances do not seem to agree in any other circumstance. The
remaining antecedents are as different, and even opposite, as they could
possibly be made; for in some the animal substances exposed to the action
of the poisons are in a state of life, in others only in a state of
organization, in others not even in that. And what is the result which
follows in all the cases? The conversion of the animal substance (by
combination with the poison) into a chemical compound, held together by so
powerful a force as to resist the subsequent action of the ordinary causes
of decomposition. Now, organic life (the necessary condition of sensitive
life) consisting in a continual state of decomposition and recomposition
of the different organs and tissues, whatever incapacitates them for this
decomposition destroys life. And thus the proximate cause of the death
produced by this description of poisons is ascertained, as far as the
Method of Agreement can ascertain it.

Let us now bring our conclusion to the test of the Method of Difference.
Setting out from the cases already mentioned, in which the antecedent is
the presence of substances forming with the tissues a compound incapable
of putrefaction, (and _a fortiori_ incapable of the chemical actions which
constitute life), and the consequent is death, either of the whole
organism, or of some portion of it; let us compare with these cases other
cases, as much resembling them as possible, but in which that effect is
not produced. And, first, “many insoluble basic salts of arsenious acid
are known not to be poisonous. The substance called alkargen, discovered
by Bunsen, which contains a very large quantity of arsenic, and approaches
very closely in composition to the organic arsenious compounds found in
the body, has not the slightest injurious action upon the organism.” Now
when these substances are brought into contact with the tissues in any
way, they do not combine with them; they do not arrest their progress to
decomposition. As far, therefore, as these instances go, it appears that
when the effect is absent, it is by reason of the absence of that
antecedent which we had already good ground for considering as the
proximate cause.

But the rigorous conditions of the Method of Difference are not yet
satisfied; for we can not be sure that these unpoisonous bodies agree with
the poisonous substances in every property, except the particular one of
entering into a difficultly decomposable compound with the animal tissues.
To render the method strictly applicable, we need an instance, not of a
different substance, but of one of the very same substances, in
circumstances which would prevent it from forming, with the tissues, the
sort of compound in question; and then, if death does not follow, our case
is made out. Now such instances are afforded by the antidotes to these
poisons. For example, in case of poisoning by arsenious acid, if hydrated
peroxide of iron is administered, the destructive agency is instantly
checked. Now this peroxide is known to combine with the acid, and form a
compound, which, being insoluble, can not act at all on animal tissues.
So, again, sugar is a well-known antidote to poisoning by salts of copper;
and sugar reduces those salts either into metallic copper, or into the red
sub-oxide, neither of which enters into combination with animal matter.
The disease called painter’s colic, so common in manufactories of
white-lead, is unknown where the workmen are accustomed to take, as a
preservative, sulphuric acid lemonade (a solution of sugar rendered acid
by sulphuric acid). Now diluted sulphuric acid has the property of
decomposing all compounds of lead with organic matter, or of preventing
them from being formed.

There is another class of instances, of the nature required by the Method
of Difference, which seem at first sight to conflict with the theory.
Soluble salts of silver, such for instance as the nitrate, have the same
stiffening antiseptic effect on decomposing animal substances as corrosive
sublimate and the most deadly metallic poisons; and when applied to the
external parts of the body, the nitrate is a powerful caustic, depriving
those parts of all active vitality, and causing them to be thrown off by
the neighboring living structures, in the form of an eschar. The nitrate
and the other salts of silver ought, then, it would seem, if the theory be
correct, to be poisonous; yet they may be administered internally with
perfect impunity. From this apparent exception arises the strongest
confirmation which the theory has yet received. Nitrate of silver, in
spite of its chemical properties, does not poison when introduced into the
stomach; but in the stomach, as in all animal liquids, there is common
salt; and in the stomach there is also free muriatic acid. These
substances operate as natural antidotes, combining with the nitrate, and
if its quantity is not too great, immediately converting it into chloride
of silver, a substance very slightly soluble, and therefore incapable of
combining with the tissues, although to the extent of its solubility it
has a medicinal influence, though an entirely different class of organic
actions.

The preceding instances have afforded an induction of a high order of
conclusiveness, illustrative of the two simplest of our four methods;
though not rising to the maximum of certainty which the Method of
Difference, in its most perfect exemplification, is capable of affording.
For (let us not forget) the positive instance and the negative one which
the rigor of that method requires, ought to differ only in the presence or
absence of one single circumstance. Now, in the preceding argument, they
differ in the presence or absence not of a single _circumstance_, but of a
single _substance_: and as every substance has innumerable properties,
there is no knowing what number of real differences are involved in what
is nominally and apparently only one difference. It is conceivable that
the antidote, the peroxide of iron for example, may counteract the poison
through some other of its properties than that of forming an insoluble
compound with it; and if so, the theory would fall to the ground, so far
as it is supported by that instance. This source of uncertainty, which is
a serious hinderance to all extensive generalizations in chemistry, is,
however, reduced in the present case to almost the lowest degree possible,
when we find that not only one substance, but many substances, possess the
capacity of acting as antidotes to metallic poisons, and that all these
agree in the property of forming insoluble compounds with the poisons,
while they can not be ascertained to agree in any other property
whatsoever. We have thus, in favor of the theory, all the evidence which
can be obtained by what we termed the Indirect Method of Difference, or
the Joint Method of Agreement and Difference; the evidence of which,
though it never can amount to that of the Method of Difference properly so
called, may approach indefinitely near to it.

§ 2. Let the object be(137) to ascertain the law of what is termed
_induced_ electricity; to find under what conditions any electrified body,
whether positively or negatively electrified, gives rise to a contrary
electric state in some other body adjacent to it.

The most familiar exemplification of the phenomenon to be investigated is
the following. Around the prime conductors of an electrical machine the
atmosphere to some distance, or any conducting surface suspended in that
atmosphere, is found to be in an electric condition opposite to that of
the prime conductor itself. Near and around the positive prime conductor
there is negative electricity, and near and around the negative prime
conductor there is positive electricity. When pith balls are brought near
to either of the conductors, they become electrified with the opposite
electricity to it; either receiving a share from the already electrified
atmosphere by conduction, or acted upon by the direct inductive influence
of the conductor itself: they are then attracted by the conductor to which
they are in opposition; or, if withdrawn in their electrified state, they
will be attracted by any other oppositely charged body. In like manner the
hand, if brought near enough to the conductor, receives or gives an
electric discharge; now we have no evidence that a charged conductor can
be suddenly discharged unless by the approach of a body oppositely
electrified. In the case, therefore, of the electric machine, it appears
that the accumulation of electricity in an insulated conductor is always
accompanied by the excitement of the contrary electricity in the
surrounding atmosphere, and in every conductor placed near the former
conductor. It does not seem possible, in this case, to produce one
electricity by itself.

Let us now examine all the other instances which we can obtain, resembling
this instance in the given consequent, namely, the evolution of an
opposite electricity in the neighborhood of an electrified body. As one
remarkable instance we have the Leyden jar; and after the splendid
experiments of Faraday in complete and final establishment of the
substantial identity of magnetism and electricity, we may cite the magnet,
both the natural and the electro-magnet, in neither of which it is
possible to produce one kind of electricity by itself, or to charge one
pole without charging an opposite pole with the contrary electricity at
the same time. We can not have a magnet with one pole: if we break a
natural loadstone into a thousand pieces, each piece will have its two
oppositely electrified poles complete within itself. In the voltaic
circuit, again, we can not have one current without its opposite. In the
ordinary electric machine, the glass cylinder or plate, and the rubber,
acquire opposite electricities.

From all these instances, treated by the Method of Agreement, a general
law appears to result. The instances embrace all the known modes in which
a body can become charged with electricity; and in all of them there is
found, as a concomitant or consequent, the excitement of the opposite
electric state in some other body or bodies. It seems to follow that the
two facts are invariably connected, and that the excitement of electricity
in any body has for one of its necessary conditions the possibility of a
simultaneous excitement of the opposite electricity in some neighboring
body.

As the two contrary electricities can only be produced together, so they
can only cease together. This may be shown by an application of the Method
of Difference to the example of the Leyden jar. It needs scarcely be here
remarked that in the Leyden jar, electricity can be accumulated and
retained in considerable quantity, by the contrivance of having two
conducting surfaces of equal extent, and parallel to each other through
the whole of that extent, with a non-conducting substance such as glass
between them. When one side of the jar is charged positively, the other is
charged negatively, and it was by virtue of this fact that the Leyden jar
served just now as an instance in our employment of the Method of
Agreement. Now it is impossible to discharge one of the coatings unless
the other can be discharged at the same time. A conductor held to the
positive side can not convey away any electricity unless an equal quantity
be allowed to pass from the negative side: if one coating be perfectly
insulated, the charge is safe. The dissipation of one must proceed _pari
passu_ with that of the other.

The law thus strongly indicated admits of corroboration by the Method of
Concomitant Variations. The Leyden jar is capable of receiving a much
higher charge than can ordinarily be given to the conductor of an
electrical machine. Now in the case of the Leyden jar, the metallic
surface which receives the induced electricity is a conductor exactly
similar to that which receives the primary charge, and is therefore as
susceptible of receiving and retaining the one electricity, as the
opposite surface of receiving and retaining the other; but in the machine,
the neighboring body which is to be oppositely electrified is the
surrounding atmosphere, or any body casually brought near to the
conductor; and as these are generally much inferior in their capacity of
becoming electrified, to the conductor itself, their limited power imposes
a corresponding limit to the capacity of the conductor for being charged.
As the capacity of the neighboring body for supporting the opposition
increases, a higher charge becomes possible: and to this appears to be
owing the great superiority of the Leyden jar.

A further and most decisive confirmation by the Method of Difference, is
to be found in one of Faraday’s experiments in the course of his
researches on the subject of Induced Electricity.

Since common or machine electricity, and voltaic electricity, may be
considered for the present purpose to be identical, Faraday wished to know
whether, as the prime conductor develops opposite electricity upon a
conductor in its vicinity, so a voltaic current running along a wire would
induce an opposite current upon another wire laid parallel to it at a
short distance. Now this case is similar to the cases previously examined,
in every circumstance except the one to which we have ascribed the effect.
We found in the former instances that whenever electricity of one kind was
excited in one body, electricity of the opposite kind must be excited in a
neighboring body. But in Faraday’s experiment this indispensable
opposition exists within the wire itself. From the nature of a voltaic
charge, the two opposite currents necessary to the existence of each other
are both accommodated in one wire; and there is no need of another wire
placed beside it to contain one of them, in the same way as the Leyden jar
must have a positive and a negative surface. The exciting cause can and
does produce all the effect which its laws require, independently of any
electric excitement of a neighboring body. Now the result of the
experiment with the second wire was, that no opposite current was
produced. There was an instantaneous effect at the closing and breaking of
the voltaic circuit; electric inductions appeared when the two wires were
moved to and from one another; but these are phenomena of a different
class. There was no induced electricity in the sense in which this is
predicated of the Leyden jar; there was no sustained current running up
the one wire while an opposite current ran down the neighboring wire; and
this alone would have been a true parallel case to the other.

It thus appears by the combined evidence of the Method of Agreement, the
Method of Concomitant Variations, and the most rigorous form of the Method
of Difference, that neither of the two kinds of electricity can be excited
without an equal excitement of the other and opposite kind: that both are
effects of the same cause; that the possibility of the one is a condition
of the possibility of the other, and the quantity of the one an impassable
limit to the quantity of the other. A scientific result of considerable
interest in itself, and illustrating those three methods in a manner both
characteristic and easily intelligible.(138)

§ 3. Our third example shall be extracted from Sir John Herschel’s
_Discourse __ course on the Study of Natural Philosophy_, a work replete
with happily-selected exemplifications of inductive processes from almost
every department of physical science, and in which alone, of all books
which I have met with, the four methods of induction are distinctly
recognized, though not so clearly characterized and defined, nor their
correlation so fully shown, as has appeared to me desirable. The present
example is described by Sir John Herschel as “one of the most beautiful
specimens” which can be cited “of inductive experimental inquiry lying
within a moderate compass;” the theory of dew, first promulgated by the
late Dr. Wells, and now universally adopted by scientific authorities. The
passages in inverted commas are extracted verbatim from the
Discourse.(139)

“Suppose _dew_ were the phenomenon proposed, whose cause we would know. In
the first place” we must determine precisely what we mean by dew: what the
fact really is whose cause we desire to investigate. “We must separate dew
from rain, and the moisture of fogs, and limit the application of the term
to what is really meant, which is the spontaneous appearance of moisture
on substances exposed in the open air when no rain or _visible_ wet is
falling.” This answers to a preliminary operation which will be
characterized in the ensuing book, treating of operations subsidiary to
induction.(140)

“Now, here we have analogous phenomena in the moisture which bedews a cold
metal or stone when we breathe upon it; that which appears on a glass of
water fresh from the well in hot weather; that which appears on the inside
of windows when sudden rain or hail chills the external air; that which
runs down our walls when, after a long frost, a warm, moist thaw comes
on.” Comparing these cases, we find that they all contain the phenomenon
which was proposed as the subject of investigation. Now “all these
instances agree in one point, the coldness of the object dewed, in
comparison with the air in contact with it.” But there still remains the
most important case of all, that of nocturnal dew: does the same
circumstance exist in this case? “Is it a fact that the object dewed _is_
colder than the air? Certainly not, one would at first be inclined to say;
for what is to _make_ it so? But ... the experiment is easy: we have only
to lay a thermometer in contact with the dewed substance, and hang one at
a little distance above it, out of reach of its influence. The experiment
has been therefore made, the question has been asked, and the answer has
been invariably in the affirmative. Whenever an object contracts dew, it
_is_ colder than the air.”

Here, then, is a complete application of the Method of Agreement,
establishing the fact of an invariable connection between the deposition
of dew on a surface, and the coldness of that surface compared with the
external air. But which of these is cause, and which effect? or are they
both effects of something else? On this subject the Method of Agreement
can afford us no light: we must call in a more potent method. “We must
collect more facts, or, which comes to the same thing, vary the
circumstances; since every instance in which the circumstances differ is a
fresh fact: and especially, we must note the contrary or negative cases,
_i.e._, where no dew is produced:” a comparison between instances of dew
and instances of no dew, being the condition necessary to bring the Method
of Difference into play.

“Now, first, no dew is produced on the surface of polished metals, but it
_is_ very copiously on glass, both exposed with their faces upward, and in
some cases the under side of a horizontal plate of glass is also dewed.”
Here is an instance in which the effect is produced, and another instance
in which it is not produced; but we can not yet pronounce, as the canon of
the Method of Difference requires, that the latter instance agrees with
the former in all its circumstances except one; for the differences
between glass and polished metals are manifold, and the only thing we can
as yet be sure of is, that the cause of dew will be found among the
circumstances by which the former substance is distinguished from the
latter. But if we could be sure that glass, and the various other
substances on which dew is deposited, have only one quality in common, and
that polished metals and the other substances on which dew is not
deposited, have also nothing in common but the one circumstance of not
having the one quality which the others have; the requisitions of the
Method of Difference would be completely satisfied, and we should
recognize, in that quality of the substances, the cause of dew. This,
accordingly, is the path of inquiry which is next to be pursued.

“In the cases of polished metal and polished glass, the contrast shows
evidently that the _substance_ has much to do with the phenomenon;
therefore let the substance _alone_ be diversified as much as possible, by
exposing polished surfaces of various kinds. This done, a _scale of
intensity_ becomes obvious. Those polished substances are found to be most
strongly dewed which conduct heat worst; while those which conduct heat
well, resist dew most effectually.” The complication increases; here is
the Method of Concomitant Variations called to our assistance; and no
other method was practicable on this occasion; for the quality of
conducting heat could not be excluded, since all substances conduct heat
in some degree. The conclusion obtained is, that _cæteris paribus_ the
deposition of dew is in some proportion to the power which the body
possesses of resisting the passage of heat; and that this, therefore (or
something connected with this), must be at least one of the causes which
assist in producing the deposition of dew on the surface.

“But if we expose rough surfaces instead of polished, we sometimes find
this law interfered with. Thus, roughened iron, especially if painted over
or blackened, becomes dewed sooner than varnished paper; the kind of
_surface_, therefore, has a great influence. Expose, then, the _same_
material in very diversified states, as to surface” (that is, employ the
Method of Difference to ascertain concomitance of variations), “and
another scale of intensity becomes at once apparent; those _surfaces_
which _part with their heat_ most readily by radiation are found to
contract dew most copiously.” Here, therefore, are the requisites for a
second employment of the Method of Concomitant Variations; which in this
case also is the only method available, since all substances radiate heat
in some degree or other. The conclusion obtained by this new application
of the method is, that _cæteris paribus_ the deposition of dew is also in
some proportion to the power of radiating heat; and that the quality of
doing this abundantly (or some cause on which that quality depends) is
another of the causes which promote the deposition of dew on the
substance.

“Again, the influence ascertained to exist of _substance_ and _surface_
leads us to consider that of _texture_: and here, again, we are presented
on trial with remarkable differences, and with a third scale of intensity,
pointing out substances of a close, firm texture, such as stones, metals,
etc., as unfavorable, but those of a loose one, as cloth, velvet, wool,
eider-down, cotton, etc., as eminently favorable to the contraction of
dew." The Method of Concomitant Variations is here, for the third time,
had recourse to; and, as before, from necessity, since the texture of no
substance is absolutely firm or absolutely loose. Looseness of texture,
therefore, or something which is the cause of that quality, is another
circumstance which promotes the deposition of dew; but this third course
resolves itself into the first, viz., the quality of resisting the passage
of heat: for substances of loose texture "are precisely those which are
best adapted for clothing, or for impeding the free passage of heat from
the skin into the air, so as to allow their outer surfaces to be very
cold, while they remain warm within;” and this last is, therefore, an
induction (from fresh instances) simply _corroborative_ of a former
induction.

It thus appears that the instances in which much dew is deposited, which
are very various, agree in this, and, so far as we are able to observe, in
this only, that they either radiate heat rapidly or conduct it slowly:
qualities between which there is no other circumstance of agreement than
that by virtue of either, the body tends to lose heat from the surface
more rapidly than it can be restored from within. The instances, on the
contrary, in which no dew, or but a small quantity of it, is formed, and
which are also extremely various, agree (as far as we can observe) in
nothing except in _not_ having this same property. We seem, therefore, to
have detected the characteristic difference between the substances on
which dew is produced and those on which it is not produced. And thus have
been realized the requisitions of what we have termed the Indirect Method
of Difference, or the Joint Method of Agreement and Difference. The
example afforded of this indirect method, and of the manner in which the
data are prepared for it by the Methods of Agreement and of Concomitant
Variations, is the most important of all the illustrations of induction
afforded by this interesting speculation.

We might now consider the question, on what the deposition of dew depends,
to be completely solved, if we could be quite sure that the substances on
which dew is produced differ from those on which it is not, in _nothing_
but in the property of losing heat from the surface faster than the loss
can be repaired from within. And though we never can have that complete
certainty, this is not of so much importance as might at first be
supposed; for we have, at all events, ascertained that even if there be
any other quality hitherto unobserved which is present in all the
substances which contract dew, and absent in those which do not, this
other property must be one which, in all that great number of substances,
is present or absent exactly where the property of being a better radiator
than conductor is present or absent; an extent of coincidence which
affords a strong presumption of a community of cause, and a consequent
invariable co-existence between the two properties; so that the property
of being a better radiator than conductor, if not itself the cause, almost
certainly always accompanies the cause, and for purposes of prediction, no
error is likely to be committed by treating it as if it were really such.

Reverting now to an earlier stage of the inquiry, let us remember that we
had ascertained that, in every instance where dew is formed, there is
actual coldness of the surface below the temperature of the surrounding
air; but we were not sure whether this coldness was the cause of dew, or
its effect. This doubt we are now able to resolve. We have found that, in
every such instance, the substance is one which, by its own properties or
laws, would, if exposed in the night, become colder than the surrounding
air. The coldness, therefore, being accounted for independently of the
dew, while it is proved that there is a connection between the two, it
must be the dew which depends on the coldness; or, in other words, the
coldness is the cause of the dew.

This law of causation, already so amply established, admits, however, of
efficient additional corroboration in no less than three ways. First, by
deduction from the known laws of aqueous vapor when diffused through air
or any other gas; and though we have not yet come to the Deductive Method,
we will not omit what is necessary to render this speculation complete. It
is known by direct experiment that only a limited quantity of water can
remain suspended in the state of vapor at each degree of temperature, and
that this maximum grows less and less as the temperature diminishes. From
this it follows, deductively, that if there is already as much vapor
suspended as the air will contain at its existing temperature, any
lowering of that temperature will cause a portion of the vapor to be
condensed, and become water. But again, we know deductively, from the laws
of heat, that the contact of the air with a body colder than itself will
necessarily lower the temperature of the stratum of air immediately
applied to its surface; and will, therefore, cause it to part with a
portion of its water, which accordingly will, by the ordinary laws of
gravitation or cohesion, attach itself to the surface of the body, thereby
constituting dew. This deductive proof, it will have been seen, has the
advantage of at once proving causation as well as co-existence; and it has
the additional advantage that it also accounts for the exceptions to the
occurrence of the phenomenon, the cases in which, although the body is
colder than the air, yet no dew is deposited; by showing that this will
necessarily be the case when the air is so under-supplied with aqueous
vapor, comparatively to its temperature, that even when somewhat cooled by
the contact of the colder body it can still continue to hold in suspension
all the vapor which was previously suspended in it: thus in a very dry
summer there are no dews, in a very dry winter no hoar-frost. Here,
therefore, is an additional condition of the production of dew, which the
methods we previously made use of failed to detect, and which might have
remained still undetected, if recourse had not been had to the plan of
deducing the effect from the ascertained properties of the agents known to
be present.

The second corroboration of the theory is by direct experiment, according
to the canon of the Method of Difference. We can, by cooling the surface
of any body, find in all cases some temperature (more or less inferior to
that of the surrounding air, according to its hygrometric condition) at
which dew will begin to be deposited. Here, too, therefore, the causation
is directly proved. We can, it is true, accomplish this only on a small
scale, but we have ample reason to conclude that the same operation, if
conducted in nature’s great laboratory, would equally produce the effect.

And, finally, even on that great scale we are able to verify the result.
The case is one of those rare cases, as we have shown them to be, in which
nature works the experiment for us in the same manner in which we
ourselves perform it; introducing into the previous state of things a
single and perfectly definite new circumstance, and manifesting the effect
so rapidly that there is not time for any other material change in the
pre-existing circumstances. “It is observed that dew is never copiously
deposited in situations much screened from the open sky, and not at all in
a cloudy night; but _if the clouds withdraw even for a few minutes, and
leave a clear opening, a deposition of dew presently begins_, and goes on
increasing... Dew formed in clear intervals will often even evaporate
again when the sky becomes thickly overcast.” The proof, therefore, is
complete, that the presence or absence of an uninterrupted communication
with the sky causes the deposition or non-deposition of dew. Now, since a
clear sky is nothing but the absence of clouds, and it is a known property
of clouds, as of all other bodies between which and any given object
nothing intervenes but an elastic fluid, that they tend to raise or keep
up the superficial temperature of the object by radiating heat to it, we
see at once that the disappearance of clouds will cause the surface to
cool; so that nature, in this case, produces a change in the antecedent by
definite and known means, and the consequent follows accordingly: a
natural experiment which satisfies the requisitions of the Method of
Difference.(141)

The accumulated proof of which the Theory of Dew has been found
susceptible, is a striking instance of the fullness of assurance which the
inductive evidence of laws of causation may attain, in cases in which the
invariable sequence is by no means obvious to a superficial view.

§ 4. The admirable physiological investigations of Dr. Brown-Séquard
afford brilliant examples of the application of the Inductive Methods to a
class of inquiries in which, for reasons which will presently be given,
direct induction takes place under peculiar difficulties and
disadvantages. As one of the most apt instances, I select his speculation
(in the proceedings of the Royal Society for May 16, 1861) on the
relations between muscular irritability, cadaveric rigidity, and
putrefaction.

The law which Dr. Brown-Séquard’s investigation tends to establish, is the
following: “The greater the degree of muscular irritability at the time of
death, the later the cadaveric rigidity sets in, and the longer it lasts,
and the later also putrefaction appears, and the slower it progresses.”
One would say at first sight that the method here required must be that of
Concomitant Variations. But this is a delusive appearance, arising from
the circumstance that the conclusion to be tested is itself a fact of
concomitant variations. For the establishment of that fact any of the
Methods may be put in requisition, and it will be found that the fourth
Method, though really employed, has only a subordinate place in this
particular investigation.

The evidences by which Dr. Brown-Séquard establishes the law may be
enumerated as follows:

1st. Paralyzed muscles have greater irritability than healthy muscles.
Now, paralyzed muscles are later in assuming the cadaveric rigidity than
healthy muscles, the rigidity lasts longer, and putrefaction sets in
later, and proceeds more slowly.

Both these propositions had to be proved by experiment; and for the
experiments which prove them, science is also indebted to Dr.
Brown-Séquard. The former of the two—that paralyzed muscles have greater
irritability than healthy muscles—he ascertained in various ways, but most
decisively by “comparing the duration of irritability in a paralyzed
muscle and in the corresponding healthy one of the opposite side, while
they are both submitted to the same excitation.” He “often found, in
experimenting in that way, that the paralyzed muscle remained irritable
twice, three times, or even four times as long as the healthy one.” This
is a case of induction by the Method of Difference. The two limbs, being
those of the same animal, were presumed to differ in no circumstance
material to the case except the paralysis, to the presence and absence of
which, therefore, the difference in the muscular irritability was to be
attributed. This assumption of complete resemblance in all material
circumstances save one, evidently could not be safely made in any one pair
of experiments, because the two legs of any given animal might be
accidentally in very different pathological conditions; but if, besides
taking pains to avoid any such difference, the experiment was repeated
sufficiently often in different animals to exclude the supposition that
any abnormal circumstance could be present in them all, the conditions of
the Method of Difference were adequately secured.

In the same manner in which Dr. Brown-Séquard proved that paralyzed
muscles have greater irritability, he also proved the correlative
proposition respecting cadaveric rigidity and putrefaction. Having, by
section of the roots of the sciatic nerve, and again of a lateral half of
the spinal cord, produced paralysis in one hind leg of an animal while the
other remained healthy, he found that not only did muscular irritability
last much longer in the paralyzed limb, but rigidity set in later and
ended later, and putrefaction began later and was less rapid than on the
healthy side. This is a common case of the Method of Difference, requiring
no comment. A further and very important corroboration was obtained by the
same method. When the animal was killed, not shortly after the section of
the nerve, but a month later, the effect was reversed; rigidity set in
sooner, and lasted a shorter time, than in the healthy muscles. But after
this lapse of time, the paralyzed muscles, having been kept by the
paralysis in a state of rest, had lost a great part of their irritability,
and instead of more, had become less irritable than those on the healthy
side. This gives the A B C, _a b c_, and B C, b c, of the Method of
Difference. One antecedent, increased irritability, being changed, and the
other circumstances being the same, the consequence did not follow; and,
moreover, when a new antecedent, contrary to the first, was supplied, it
was followed by a contrary consequent. This instance is attended with the
special advantage of proving that the retardation and prolongation of the
rigidity do not depend directly on the paralysis, since that was the same
in both the instances; but specifically on one effect of the paralysis,
namely, the increased irritability; since they ceased when it ceased, and
were reversed when it was reversed.

2d. Diminution of the temperature of muscles before death increases their
irritability. But diminution of their temperature also retards cadaveric
rigidity and putrefaction.

Both these truths were first made known by Dr. Brown-Séquard himself,
through experiments which conclude according to the Method of Difference.
There is nothing in the nature of the process requiring specific analysis.

3d. Muscular exercise, prolonged to exhaustion, diminishes the muscular
irritability. This is a well-known truth, dependent on the most general
laws of muscular action, and proved by experiments under the Method of
Difference, constantly repeated. Now, it has been shown by observation
that overdriven cattle, if killed before recovery from their fatigue,
become rigid and putrefy in a surprisingly short time. A similar fact has
been observed in the case of animals hunted to death; cocks killed during
or shortly after a fight; and soldiers slain in the field of battle. These
various cases agree in no circumstance, directly connected with the
muscles, except that these have just been subjected to exhausting
exercise. Under the canon, therefore, of the Method of Agreement, it may
be inferred that there is a connection between the two facts. The Method
of Agreement, indeed, as has been shown, is not competent to prove
causation. The present case, however, is already known to be a case of
causation, it being certain that the state of the body after death must
somehow depend upon its state at the time of death. We are, therefore,
warranted in concluding that the single circumstance in which all the
instances agree, is the part of the antecedent which is the cause of that
particular consequent.

4th. In proportion as the nutrition of muscles is in a good state, their
irritability is high. This fact also rests on the general evidence of the
laws of physiology, grounded on many familiar applications of the Method
of Difference. Now, in the case of those who die from accident or
violence, with their muscles in a good state of nutrition, the muscular
irritability continues long after death, rigidity sets in late, and
persists long without the putrefactive change. On the contrary, in cases
of disease in which nutrition has been diminished for a long time before
death, all these effects are reversed. These are the conditions of the
Joint Method of Agreement and Difference. The cases of retarded and long
continued rigidity here in question agree only in being preceded by a high
state of nutrition of the muscles; the cases of rapid and brief rigidity
agree only in being preceded by a low state of muscular nutrition; a
connection is, therefore, inductively proved between the degree of the
nutrition, and the slowness and prolongation of the rigidity.

5th. Convulsions, like exhausting exercise, but in a still greater degree,
diminish the muscular irritability. Now, when death follows violent and
prolonged convulsions, as in tetanus, hydrophobia, some cases of cholera,
and certain poisons, rigidity sets in very rapidly, and after a very brief
duration, gives place to putrefaction. This is another example of the
Method of Agreement, of the same character with No. 3.

6th. The series of instances which we shall take last, is of a more
complex character, and requires a more minute analysis.

It has long been observed that in some cases of death by lightning,
cadaveric rigidity either does not take place at all, or is of such
extremely brief duration as to escape notice, and that in these cases
putrefaction is very rapid. In other cases, however, the usual cadaveric
rigidity appears. There must be some difference in the cause, to account
for this difference in the effect. Now, “death by lightning may be the
result of, 1st, a syncope by fright, or in consequence of a direct or
reflex influence of lightning on the par vagum; 2d, hemorrhage in or
around the brain, or in the lungs, the pericardium, etc.; 3d, concussion,
or some other alteration in the brain;” none of which phenomena have any
known property capable of accounting for the suppression, or almost
suppression, of the cadaveric rigidity. But the cause of death may also be
that the lightning produces “a violent convulsion of every muscle in the
body,” of which, if of sufficient intensity, the known effect would be
that “muscular irritability ceases almost at once.” If Dr. Brown-Séquard’s
generalization is a true law, these will be the very cases in which
rigidity is so much abridged as to escape notice; and the cases in which,
on the contrary, rigidity takes place as usual, will be those in which the
stroke of lightning operates in some of the other modes which have been
enumerated. How, then, is this brought to the test? By experiments, not on
lightning, which can not be commanded at pleasure, but on the same natural
agency in a manageable form, that of artificial galvanism. Dr.
Brown-Séquard galvanized the entire bodies of animals immediately after
death. Galvanism can not operate in any of the modes in which the stroke
of lightning may have operated, except the single one of producing
muscular convulsions. If, therefore, after the bodies have been
galvanized, the duration of rigidity is much shortened and putrefaction
much accelerated, it is reasonable to ascribe the same effects when
produced by lightning to the property which galvanism shares with
lightning, and not to those which it does not. Now this Dr. Brown-Séquard
found to be the fact. The galvanic experiment was tried with charges of
very various degrees of strength; and the more powerful the charge, the
shorter was found to be the duration of rigidity, and the more speedy and
rapid the putrefaction. In the experiment in which the charge was
strongest, and the muscular irritability most promptly destroyed, the
rigidity only lasted fifteen minutes. On the principle, therefore, of the
Method of Concomitant Variations, it may be inferred that the duration of
the rigidity depends on the degree of the irritability; and that if the
charge had been as much stronger than Dr. Brown-Séquard’s strongest, as a
stroke of lightning must be stronger than any electric shock which we can
produce artificially, the rigidity would have been shortened in a
corresponding ratio, and might have disappeared altogether. This
conclusion having been arrived at, the case of an electric shock, whether
natural or artificial, becomes an instance, in addition to all those
already ascertained, of correspondence between the irritability of the
muscle and the duration of rigidity.

All these instances are summed up in the following statement: “That when
the degree of muscular irritability at the time of death is considerable,
either in consequence of a good state of nutrition, as in persons who die
in full health from an accidental cause, or in consequence of rest, as in
cases of paralysis, or on account of the influence of cold, cadaveric
rigidity in all these cases sets in late and lasts long, and putrefaction
appears late, and progresses slowly;” but “that when the degree of
muscular irritability at the time of death is slight, either in
consequence of a bad state of nutrition, or of exhaustion from
overexertion, or from convulsions caused by disease or poison, cadaveric
rigidity sets in and ceases soon, and putrefaction appears and progresses
quickly.” These facts present, in all their completeness, the conditions
of the Joint Method of Agreement and Difference. Early and brief rigidity
takes place in cases which agree only in the circumstance of a low state
of muscular irritability. Rigidity begins late and lasts long in cases
which agree only in the contrary circumstance, of a muscular irritability
high and unusually prolonged. It follows that there is a connection
through causation between the degree of muscular irritability after death,
and the tardiness and prolongation of the cadaveric rigidity.

This investigation places in a strong light the value and efficacy of the
Joint Method. For, as we have already seen, the defect of that Method is,
that like the Method of Agreement, of which it is only an improved form,
it can not prove causation. But in the present case (as in one of the
steps in the argument which led up to it) causation is already proved;
since there could never be any doubt that the rigidity altogether, and the
putrefaction which follows it, are caused by the fact of death: the
observations and experiments on which this rests are too familiar to need
analysis, and fall under the Method of Difference. It being, therefore,
beyond doubt that the aggregate antecedent, the death, is the actual cause
of the whole train of consequents, whatever of the circumstances attending
the death can be shown to be followed in all its variations by variations
in the effect under investigation, must be the particular feature of the
fact of death on which that effect depends. The degree of muscular
irritability at the time of death fulfills this condition. The only point
that could be brought into question, would be whether the effect depended
on the irritability itself, or on something which always accompanied the
irritability: and this doubt is set at rest by establishing, as the
instances do, that by whatever cause the high or low irritability is
produced, the effect equally follows; and can not, therefore, depend upon
the causes of irritability, nor upon the other effects of those causes,
which are as various as the causes themselves, but upon the irritability,
solely.

§ 5. The last two examples will have conveyed to any one by whom they have
been duly followed, so clear a conception of the use and practical
management of three of the four methods of experimental inquiry, as to
supersede the necessity of any further exemplification of them. The
remaining method, that of Residues, not having found a place in any of the
preceding investigations, I shall quote from Sir John Herschel some
examples of that method, with the remarks by which they are introduced.

“It is by this process, in fact, that science, in its present advanced
state, is chiefly promoted. Most of the phenomena which Nature presents
are very complicated; and when the effects of all known causes are
estimated with exactness, and subducted, the residual facts are constantly
appearing in the form of phenomena altogether new, and leading to the most
important conclusions.

“For example: the return of the comet predicted by Professor Eucke a great
many times in succession, and the general good agreement of its calculated
with its observed place during any one of its periods of visibility, would
lead us to say that its gravitation toward the sun and planets is the sole
and sufficient cause of all the phenomena of its orbitual motion; but when
the effect of this cause is strictly calculated and subducted from the
observed motion, there is found to remain behind a _residual phenomenon_,
which would never have been otherwise ascertained to exist, which is a
small anticipation of the time of its re-appearance, or a diminution of
its periodic time, which can not be accounted for by gravity, and whose
cause is therefore to be inquired into. Such an anticipation would be
caused by the resistance of a medium disseminated through the celestial
regions; and as there are other good reasons for believing this to be a
_vera causa_” (an actually existing antecedent), “it has therefore been
ascribed to such a resistance.(142)

“M. Arago, having suspended a magnetic needle by a silk thread, and set it
in vibration, observed, that it came much sooner to a state of rest when
suspended over a plate of copper, than when no such plate was beneath it.
Now, in both cases there were two _veræ causæ_” (antecedents known to
exist) “why it _should_ come at length to rest, viz., the resistance of
the air, which opposes, and at length destroys, all motions performed in
it; and the want of perfect mobility in the silk thread. But the effect of
these causes being exactly known by the observation made in the absence of
the copper, and being thus allowed for and subducted, a residual
phenomenon appeared, in the fact that a retarding influence was exerted by
the copper itself; and this fact, once ascertained, speedily led to the
knowledge of an entirely new and unexpected class of relations.” This
example belongs, however, not to the Method of Residues but to the Method
of Difference, the law being ascertained by a direct comparison of the
results of two experiments, which differed in nothing but the presence or
absence of the plate of copper. To have made it exemplify the Method of
Residues, the effect of the resistance of the air and that of the rigidity
of the silk should have been calculated _a priori_, from the laws obtained
by separate and foregone experiments.

“Unexpected and peculiarly striking confirmations of inductive laws
frequently occur in the form of residual phenomena, in the course of
investigations of a widely different nature from those which gave rise to
the inductions themselves. A very elegant example may be cited in the
unexpected confirmation of the law of the development of heat in elastic
fluids by compression, which is afforded by the phenomena of sound. The
inquiry into the cause of sound had led to conclusions respecting its mode
of propagation, from which its velocity in the air could be precisely
calculated. The calculations were performed; but, when compared with fact,
though the agreement was quite sufficient to show the general correctness
of the cause and mode of propagation assigned, yet the _whole_ velocity
could not be shown to arise from this theory. There was still a residual
velocity to be accounted for, which placed dynamical philosophers for a
long time in great dilemma. At length Laplace struck on the happy idea,
that this might arise from the _heat_ developed in the act of that
condensation which necessarily takes place at every vibration by which
sound is conveyed. The matter was subjected to exact calculation, and the
result was at once the complete explanation of the residual phenomenon,
and a striking confirmation of the general law of the development of heat
by compression, under circumstances beyond artificial imitation.”

“Many of the new elements of chemistry have been detected in the
investigation of residual phenomena. Thus Arfwedson discovered lithia by
perceiving an excess of weight in the sulphate produced from a small
portion of what he considered as magnesia present in a mineral he had
analyzed. It is on this principle, too, that the small concentrated
residues of great operations in the arts are almost sure to be the
lurking-places of new chemical ingredients: witness iodine, brome,
selenium, and the new metals accompanying platina in the experiments of
Wollaston and Tennant. It was a happy thought of Glauber to examine what
every body else threw away.”(143)

“Almost all the greatest discoveries in Astronomy,” says the same
author,(144) “have resulted from the consideration of residual phenomena
of a quantitative or numerical kind.... It was thus that the grand
discovery of the precession of the equinoxes resulted as a residual
phenomenon, from the imperfect explanation of the return of the seasons by
the return of the sun to the same apparent place among the fixed stars.
Thus, also, aberration and nutation resulted as residual phenomena from
that portion of the changes of the apparent places of the fixed stars
which was left unaccounted for by precession. And thus again the apparent
proper motions of the stars are the observed residues of their apparent
movements outstanding and unaccounted for by strict calculation of the
effects of precession, nutation, and aberration. The nearest approach
which human theories can make to perfection is to diminish this residue,
this _caput mortuum_ of observation, as it may be considered, as much as
practicable, and, if possible, to reduce it to nothing, either by showing
that something has been neglected in our estimation of known causes, or by
reasoning upon it as a new fact, and on the principle of the inductive
philosophy ascending from the effect to its cause or causes.”

The disturbing effects mutually produced by the earth and planets upon
each other’s motions were first brought to light as residual phenomena, by
the difference which appeared between the observed places of those bodies,
and the places calculated on a consideration solely of their gravitation
toward the sun. It was this which determined astronomers to consider the
law of gravitation as obtaining between all bodies whatever, and therefore
between all particles of matter; their first tendency having been to
regard it as a force acting only between each planet or satellite and the
central body to whose system it belonged. Again, the catastrophists, in
geology, be their opinion right or wrong, support it on the plea, that
after the effect of all causes now in operation has been allowed for,
there remains in the existing constitution of the earth a large residue of
facts, proving the existence at former periods either of other forces, or
of the same forces in a much greater degree of intensity. To add one more
example: those who assert, what no one has shown any real ground for
believing, that there is in one human individual, one sex, or one race of
mankind over another, an inherent and inexplicable superiority in mental
faculties, could only substantiate their proposition by subtracting from
the differences of intellect which we in fact see, all that can be traced
by known laws either to the ascertained differences of physical
organization, or to the differences which have existed in the outward
circumstances in which the subjects of the comparison have hitherto been
placed. What these causes might fail to account for would constitute a
residual phenomenon, which and which alone would be evidence of an
ulterior original distinction, and the measure of its amount. But the
asserters of such supposed differences have not provided themselves with
these necessary logical conditions of the establishment of their doctrine.

The spirit of the Method of Residues being, it is hoped, sufficiently
intelligible from these examples, and the other three methods having
already been so fully exemplified, we may here close our exposition of the
four methods, considered as employed in the investigation of the simpler
and more elementary order of the combinations of phenomena.

§ 6. Dr. Whewell has expressed a very unfavorable opinion of the utility
of the Four Methods, as well as of the aptness of the examples by which I
have attempted to illustrate them. His words are these:(145)

“Upon these methods, the obvious thing to remark is, that they take for
granted the very thing which is most difficult to discover, the reduction
of the phenomena to formulæ such as are here presented to us. When we have
any set of complex facts offered to us; for instance, those which were
offered in the cases of discovery which I have mentioned—the facts of the
planetary paths, of falling bodies, of refracted rays, of cosmical
motions, of chemical analysis; and when, in any of these cases, we would
discover the law of nature which governs them, or, if any one chooses so
to term it, the feature in which all the cases agree, where are we to look
for our A, B, C, and _a_, _b_, _c_? Nature does not present to us the
cases in this form; and how are we to reduce them to this form? You say
_when_ we find the combination of A B C with _a b c_ and A B D with _a b
d_, then we may draw our inference. Granted; but when and where are we to
find such combinations? Even now that the discoveries are made, who will
point out to us what are the A, B, C, and _a_, _b_, _c_, elements of the
cases which have just been enumerated? Who will tell us which of the
methods of inquiry those historically real and successful inquiries
exemplify? Who will carry these formulæ through the history of the
sciences, as they have really grown up, and show us that these four
methods have been operative in their formation; or that any light is
thrown upon the steps of their progress by reference to these formulæ?”

He adds that, in this work, the methods have not been applied “to a large
body of conspicuous and undoubted examples of discovery, extending along
the whole history of science;” which ought to have been done in order that
the methods might be shown to possess the “advantage” (which he claims as
belonging to his own) of being those “by which all great discoveries in
science have really been made.”—(P. 277.)

There is a striking similarity between the objections here made against
Canons of Induction, and what was alleged, in the last century, by as able
men as Dr. Whewell, against the acknowledged Canon of Ratiocination. Those
who protested against the Aristotelian Logic said of the Syllogism, what
Dr. Whewell says of the Inductive Methods, that it “takes for granted the
very thing which is most difficult to discover, the reduction of the
argument to formulæ such as are here presented to us.” The grand
difficulty, they said, is to obtain your syllogism, not to judge of its
correctness when obtained. On the matter of fact, both they and Dr.
Whewell are right. The greatest difficulty in both cases is, first, that
of obtaining the evidence, and next, of reducing it to the form which
tests its conclusiveness. But if we try to reduce it without knowing what
it is to be reduced to, we are not likely to make much progress. It is a
more difficult thing to solve a geometrical problem, than to judge whether
a proposed solution is correct: but if people were not able to judge of
the solution when found, they would have little chance of finding it. And
it can not be pretended that to judge of an induction when found is
perfectly easy, is a thing for which aids and instruments are superfluous;
for erroneous inductions, false inferences from experience, are quite as
common, on some subjects much commoner than true ones. The business of
Inductive Logic is to provide rules and models (such as the Syllogism and
its rules are for ratiocination) to which if inductive arguments conform,
those arguments are conclusive, and not otherwise. This is what the Four
Methods profess to be, and what I believe they are universally considered
to be by experimental philosophers, who had practiced all of them long
before any one sought to reduce the practice to theory.

The assailants of the Syllogism had also anticipated Dr. Whewell in the
other branch of his argument. They said that no discoveries were ever made
by syllogism; and Dr. Whewell says, or seems to say, that none were ever
made by the Four Methods of Induction. To the former objectors, Archbishop
Whately very pertinently answered, that their argument, if good at all,
was good against the reasoning process altogether; for whatever can not be
reduced to syllogism, is not reasoning. And Dr. Whewell’s argument, if
good at all, is good against all inferences from experience. In saying
that no discoveries were ever made by the Four Methods, he affirms that
none were ever made by observation and experiment; for assuredly if any
were, it was by processes reducible to one or other of those methods.

This difference between us accounts for the dissatisfaction which my
examples give him; for I did not select them with a view to satisfy any
one who required to be convinced that observation and experiment are modes
of acquiring knowledge: I confess that in the choice of them I thought
only of illustration, and of facilitating the _conception_ of the Methods
by concrete instances. If it had been my object to justify the processes
themselves as means of investigation, there would have been no need to
look far off, or make use of recondite or complicated instances. As a
specimen of a truth ascertained by the Method of Agreement, I might have
chosen the proposition, “Dogs bark.” This dog, and that dog, and the other
dog, answer to A B C, A D E, A F G. The circumstance of being a dog
answers to A. Barking answers to _a_. As a truth made known by the Method
of Difference, “Fire burns” might have sufficed. Before I touch the fire I
am not burned; this is B C: I touch it, and am burned; this is A B C, _a_
B C.

Such familiar experimental processes are not regarded as inductions by Dr.
Whewell; but they are perfectly homogeneous with those by which, even on
his own showing, the pyramid of science is supplied with its base. In vain
he attempts to escape from this conclusion by laying the most arbitrary
restrictions on the choice of examples admissible as instances of
Induction: they must neither be such as are still matter of discussion (p.
265), nor must any of them be drawn from mental and social subjects (p.
269), nor from ordinary observation and practical life (pp. 241-247). They
must be taken exclusively from the generalizations by which scientific
thinkers have ascended to great and comprehensive laws of natural
phenomena. Now it is seldom possible, in these complicated inquiries, to
go much beyond the initial steps, without calling in the instrument of
Deduction, and the temporary aid of hypothesis; as I myself, in common
with Dr. Whewell, have maintained against the purely empirical school.
Since, therefore, such cases could not conveniently be selected to
illustrate the principles of mere observation and experiment, Dr. Whewell
is misled by their absence into representing the Experimental Methods as
serving no purpose in scientific investigation; forgetting that if those
methods had not supplied the first generalizations, there would have been
no materials for his own conception of Induction to work upon.

His challenge, however, to point out which of the four methods are
exemplified in certain important cases of scientific inquiry, is easily
answered. “The planetary paths,” as far as they are a case of induction at
all,(146) fall under the Method of Agreement. The law of “falling bodies,”
namely, that they describe spaces proportional to the squares of the
times, was historically a deduction from the first law of motion; but the
experiments by which it was verified, and by which it might have been
discovered, were examples of the Method of Agreement; and the apparent
variation from the true law, caused by the resistance of the air, was
cleared up by experiments _in vacuo_, constituting an application of the
Method of Difference. The law of “refracted rays” (the constancy of the
ratio between the sines of incidence and of refraction for each refracting
substance) was ascertained by direct measurement, and therefore by the
Method of Agreement. The “cosmical motions” were determined by highly
complex processes of thought, in which Deduction was predominant, but the
Methods of Agreement and of Concomitant Variations had a large part in
establishing the empirical laws. Every case without exception of “chemical
analysis” constitutes a well-marked example of the Method of Difference.
To any one acquainted with the subjects—to Dr. Whewell himself, there
would not be the smallest difficulty in setting out “the A B C and _a b c_
elements” of these cases.

If discoveries are ever made by observation and experiment without
Deduction, the four methods are methods of discovery: but even if they
were not methods of discovery, it would not be the less true that they are
the sole methods of Proof; and in that character, even the results of
deduction are amenable to them. The great generalizations which begin as
Hypotheses, must end by being proved, and are in reality (as will be shown
hereafter) proved, by the Four Methods. Now it is with Proof, as such,
that Logic is principally concerned. This distinction has indeed no chance
of finding favor with Dr. Whewell; for it is the peculiarity of his
system, not to recognize, in cases of Induction, any necessity for proof.
If, after assuming an hypothesis and carefully collating it with facts,
nothing is brought to light inconsistent with it, that is, if experience
does not _dis_prove it, he is content: at least until a simpler
hypothesis, equally consistent with experience, presents itself. If this
be Induction, doubtless there is no necessity for the four methods. But to
suppose that it is so, appears to me a radical misconception of the nature
of the evidence of physical truths.

So real and practical is the need of a test for induction, similar to the
syllogistic test of ratiocination, that inferences which bid defiance to
the most elementary notions of inductive logic are put forth without
misgiving by persons eminent in physical science, as soon as they are off
the ground on which they are conversant with the facts, and not reduced to
judge only by the arguments; and as for educated persons in general, it
may be doubted if they are better judges of a good or a bad induction than
they were before Bacon wrote. The improvement in the results of thinking
has seldom extended to the processes; or has reached, if any process, that
of investigation only, not that of proof. A knowledge of many laws of
nature has doubtless been arrived at, by framing hypotheses and finding
that the facts corresponded to them; and many errors have been got rid of
by coming to a knowledge of facts which were inconsistent with them, but
not by discovering that the mode of thought which led to the errors was
itself faulty, and might have been known to be such independently of the
facts which disproved the specific conclusion. Hence it is, that while the
thoughts of mankind have on many subjects worked themselves practically
right, the thinking power remains as weak as ever: and on all subjects on
which the facts which would check the result are not accessible, as in
what relates to the invisible world, and even, as has been seen lately, to
the visible world of the planetary regions, men of the greatest scientific
acquirements argue as pitiably as the merest ignoramus. For though they
have made many sound inductions, they have not learned from them (and Dr.
Whewell thinks there is no necessity that they should learn) the
principles of inductive _evidence_.



                                Chapter X.


Of Plurality Of Causes, And Of The Intermixture Of Effects.


§ 1. In the preceding exposition of the four methods of observation and
experiment, by which we contrive to distinguish among a mass of
co-existent phenomena the particular effect due to a given cause, or the
particular cause which gave birth to a given effect, it has been necessary
to suppose, in the first instance, for the sake of simplification, that
this analytical operation is encumbered by no other difficulties than what
are essentially inherent in its nature; and to represent to ourselves,
therefore, every effect, on the one hand as connected exclusively with a
single cause, and on the other hand as incapable of being mixed and
confounded with any other co-existent effect. We have regarded _a b c d
e_, the aggregate of the phenomena existing at any moment, as consisting
of dissimilar facts, _a_, _b_, _c_, _d_, and _e_, for each of which one,
and only one, cause needs be sought; the difficulty being only that of
singling out this one cause from the multitude of antecedent
circumstances, A, B, C, D, and E. The cause indeed may not be simple; it
may consist of an assemblage of conditions; but we have supposed that
there was only one possible assemblage of conditions from which the given
effect could result.

If such were the fact, it would be comparatively an easy task to
investigate the laws of nature. But the supposition does not hold in
either of its parts. In the first place, it is not true that the same
phenomenon is always produced by the same cause: the effect _a_ may
sometimes arise from A, sometimes from B. And, secondly, the effects of
different causes are often not dissimilar, but homogeneous, and marked out
by no assignable boundaries from one another: A and B may produce not _a_
and _b_, but different portions of an effect _a_. The obscurity and
difficulty of the investigation of the laws of phenomena is singularly
increased by the necessity of adverting to these two circumstances:
Intermixture of Effects, and Plurality of Causes. To the latter, being the
simpler of the two considerations, we shall first direct our attention.

It is not true, then, that one effect must be connected with only one
cause, or assemblage of conditions; that each phenomenon can be produced
only in one way. There are often several independent modes in which the
same phenomenon could have originated. One fact may be the consequent in
several invariable sequences; it may follow, with equal uniformity, any
one of several antecedents, or collections of antecedents. Many causes may
produce mechanical motion; many causes may produce some kinds of
sensation; many causes may produce death. A given effect may really be
produced by a certain cause, and yet be perfectly capable of being
produced without it.

§ 2. One of the principal consequences of this fact of Plurality of Causes
is, to render the first of the inductive methods, that of Agreement,
uncertain. To illustrate that method, we supposed two instances, A B C
followed by _a b c_, and A D E followed by _a d e_. From these instances
it might apparently be concluded that A is an invariable antecedent of
_a_, and even that it is the unconditional invariable antecedent, or
cause, if we could be sure that there is no other antecedent common to the
two cases. That this difficulty may not stand in the way, let us suppose
the two cases positively ascertained to have no antecedent in common
except A. The moment, however, that we let in the possibility of a
plurality of causes, the conclusion fails. For it involves a tacit
supposition, that _a_ must have been produced in both instances by the
same cause. If there can possibly have been two causes, those two may, for
example, be C and E: the one may have been the cause of _a_ in the former
of the instances, the other in the latter, A having no influence in either
case.

Suppose, for example, that two great artists or great philosophers, that
two extremely selfish or extremely generous characters, were compared
together as to the circumstances of their education and history, and the
two cases were found to agree only in one circumstance: would it follow
that this one circumstance was the cause of the quality which
characterized both those individuals? Not at all; for the causes which may
produce any type of character are very numerous; and the two persons might
equally have agreed in their character, though there had been no manner of
resemblance in their previous history.

This, therefore, is a characteristic imperfection of the Method of
Agreement, from which imperfection the Method of Difference is free. For
if we have two instances, A B C and B C, of which B C gives _b c_, and A
being added converts it into _a b c_, it is certain that in this instance
at least, A was either the cause of _a_, or an indispensable portion of
its cause, even though the cause which produces it in other instances may
be altogether different. Plurality of Causes, therefore, not only does not
diminish the reliance due to the Method of Difference, but does not even
render a greater number of observations or experiments necessary: two
instances, the one positive and the other negative, are still sufficient
for the most complete and rigorous induction. Not so, however, with the
Method of Agreement. The conclusions which that yields, when the number of
instances compared is small, are of no real value, except as, in the
character of suggestions, they may lead either to experiments bringing
them to the test of the Method of Difference, or to reasonings which may
explain and verify them deductively.

It is only when the instances, being indefinitely multiplied and varied,
continue to suggest the same result, that this result acquires any high
degree of independent value. If there are but two instances, A B C and A D
E, though these instances have no antecedent in common except A, yet as
the effect may possibly have been produced in the two cases by different
causes, the result is at most only a slight probability in favor of A;
there may be causation, but it is almost equally probable that there was
only a coincidence. But the oftener we repeat the observation, varying the
circumstances, the more we advance toward a solution of this doubt. For if
we try A F G, A H K, etc., all unlike one another except in containing the
circumstance A, and if we find the effect _a_ entering into the result in
all these cases, we must suppose one of two things, either that it is
caused by A, or that it has as many different causes as there are
instances. With each addition, therefore, to the number of instances, the
presumption is strengthened in favor of A. The inquirer, of course, will
not neglect, if an opportunity present itself, to exclude A from some one
of these combinations, from A H K for instance, and by trying H K
separately, appeal to the Method of Difference in aid of the Method of
Agreement. By the Method of Difference alone can it be ascertained that A
is the cause of _a_; but that it is either the cause, or another effect of
the same cause, may be placed beyond any reasonable doubt by the Method of
Agreement, provided the instances are very numerous as well as
sufficiently various.

After how great a multiplication, then, of varied instances, all agreeing
in no other antecedent except A, is the supposition of a plurality of
causes sufficiently rebutted, and the conclusion that _a_ is connected
with A divested of the characteristic imperfection, and reduced to a
virtual certainty? This is a question which we can not be exempted from
answering: but the consideration of it belongs to what is called the
Theory of Probability, which will form the subject of a chapter hereafter.
It is seen, however, at once, that the conclusion does amount to a
practical certainty after a sufficient number of instances, and that the
method, therefore, is not radically vitiated by the characteristic
imperfection. The result of these considerations is only, in the first
place, to point out a new source of inferiority in the Method of Agreement
as compared with other modes of investigation, and new reasons for never
resting contented with the results obtained by it, without attempting to
confirm them either by the Method of Difference, or by connecting them
deductively with some law or laws already ascertained by that superior
method. And, in the second place, we learn from this the true theory of
the value of mere _number_ of instances in inductive inquiry. The
Plurality of Causes is the only reason why mere number is of any
importance. The tendency of unscientific inquirers is to rely too much on
number, without analyzing the instances; without looking closely enough
into their nature to ascertain what circumstances are or are not
eliminated by means of them. Most people hold their conclusions with a
degree of assurance proportioned to the mere _mass_ of the experience on
which they appear to rest; not considering that by the addition of
instances to instances, all of the same kind, that is, differing from one
another only in points already recognized as immaterial, nothing whatever
is added to the evidence of the conclusion. A single instance eliminating
some antecedent which existed in all the other cases, is of more value
than the greatest multitude of instances which are reckoned by their
number alone. It is necessary, no doubt, to assure ourselves, by
repetition of the observation or experiment, that no error has been
committed concerning the individual facts observed; and until we have
assured ourselves of this, instead of varying the circumstances, we can
not too scrupulously repeat the same experiment or observation without any
change. But when once this assurance has been obtained, the multiplication
of instances which do not exclude any more circumstances is entirely
useless, provided there have been already enough to exclude the
supposition of Plurality of Causes.

It is of importance to remark, that the peculiar modification of the
Method of Agreement, which, as partaking in some degree of the nature of
the Method of Difference, I have called the Joint Method of Agreement and
Difference, is not affected by the characteristic imperfection now pointed
out. For, in the joint method, it is supposed not only that the instances
in which _a_ is, agree only in containing A, but also that the instances
in which _a_ is not, agree only in not containing A. Now, if this be so, A
must be not only the cause of _a_, but the only possible cause: for if
there were another, as for example B, then in the instances in which _a_
is not, B must have been absent as well as A, and it would not be true
that these instances agree _only_ in not containing A. This, therefore,
constitutes an immense advantage of the joint method over the simple
Method of Agreement. It may seem, indeed, that the advantage does not
belong so much to the joint method, as to one of its two premises (if they
may be so called), the negative premise. The Method of Agreement, when
applied to negative instances, or those in which a phenomenon does _not_
take place, is certainly free from the characteristic imperfection which
affects it in the affirmative case. The negative premise, it might
therefore be supposed, could be worked as a simple case of the Method of
Agreement, without requiring an affirmative premise to be joined with it.
But though this is true in principle, it is generally altogether
impossible to work the Method of Agreement by negative instances without
positive ones; it is so much more difficult to exhaust the field of
negation than that of affirmation. For instance, let the question be what
is the cause of the transparency of bodies; with what prospect of success
could we set ourselves to inquire directly in what the multifarious
substances which are _not_ transparent agree? But we might hope much
sooner to seize some point of resemblance among the comparatively few and
definite species of objects which _are_ transparent; and this being
attained, we should quite naturally be put upon examining whether the
_absence_ of this one circumstance be not precisely the point in which all
opaque substances will be found to resemble.

The Joint Method of Agreement and Difference, therefore, or as I have
otherwise called it, the Indirect Method of Difference (because, like the
Method of Difference properly so-called, it proceeds by ascertaining how
and in what the cases where the phenomenon is present differ from those in
which it is absent) is, after the Direct Method of Difference, the most
powerful of the remaining instruments of inductive investigation; and in
the sciences which depend on pure observation, with little or no aid from
experiment, this method, so well exemplified in the speculation on the
cause of dew, is the primary resource, so far as direct appeals to
experience are concerned.

§ 3. We have thus far treated Plurality of Causes only as a possible
supposition, which, until removed, renders our inductions uncertain; and
have only considered by what means, where the plurality does not really
exist, we may be enabled to disprove it. But we must also consider it as a
case actually occurring in nature, and which, as often as it does occur,
our methods of induction ought to be capable of ascertaining and
establishing. For this, however, there is required no peculiar method.
When an effect is really producible by two or more causes, the process for
detecting them is in no way different from that by which we discover
single causes. They may (first) be discovered as separate sequences, by
separate sets of instances. One set of observations or experiments shows
that the sun is a cause of heat, another that friction is a source of it,
another that percussion, another that electricity, another that chemical
action is such a source. Or (secondly) the plurality may come to light in
the course of collating a number of instances, when we attempt to find
some circumstance in which they all agree, and fail in doing so. We find
it impossible to trace, in all the cases in which the effect is met with,
any common circumstance. We find that we can eliminate _all_ the
antecedents; that no one of them is present in all the instances, no one
of them indispensable to the effect. On closer scrutiny, however, it
appears that though no one is always present, one or other of several
always is. If, on further analysis, we can detect in these any common
element, we may be able to ascend from them to some one cause which is the
really operative circumstance in them all. Thus it is now thought that in
the production of heat by friction, percussion, chemical action, etc., the
ultimate source is one and the same. But if (as continually happens) we
can not take this ulterior step, the different antecedents must be set
down provisionally as distinct causes, each sufficient of itself to
produce the effect.

We here close our remarks on the Plurality of Causes, and proceed to the
still more peculiar and more complex case of the Intermixture of Effects,
and the interference of causes with one another: a case constituting the
principal part of the complication and difficulty of the study of nature;
and with which the four only possible methods of directly inductive
investigation by observation and experiment, are, for the most part, as
will appear presently, quite unequal to cope. The instrument of Deduction
alone is adequate to unravel the complexities proceeding from this source;
and the four methods have little more in their power than to supply
premises for, and a verification of, our deductions.

§ 4. A concurrence of two or more causes, not separately producing each
its own effect, but interfering with or modifying the effects of one
another, takes place, as has already been explained in two different ways.
In the one, which is exemplified by the joint operation of different
forces in mechanics, the separate effects of all the causes continue to be
produced, but are compounded with one another, and disappear in one total.
In the other, illustrated by the case of chemical action, the separate
effects cease entirely, and are succeeded by phenomena altogether
different, and governed by different laws.

Of these cases the former is by far the more frequent, and this case it is
which, for the most part, eludes the grasp of our experimental methods.
The other and exceptional case is essentially amenable to them. When the
laws of the original agents cease entirely, and a phenomenon makes its
appearance, which, with reference to those laws, is quite heterogeneous;
when, for example, two gaseous substances, hydrogen and oxygen, on being
brought together, throw off their peculiar properties, and produce the
substance called water; in such cases the new fact may be subjected to
experimental inquiry, like any other phenomenon; and the elements which
are said to compose it may be considered as the mere agents of its
production—the conditions on which it depends, the facts which make up its
cause.

The _effects_ of the new phenomenon, the _properties_ of water, for
instance, are as easily found by experiment as the effects of any other
cause. But to discover the _cause_ of it, that is, the particular
conjunction of agents from which it results, is often difficult enough. In
the first place, the origin and actual production of the phenomenon are
most frequently inaccessible to our observation. If we could not have
learned the composition of water until we found instances in which it was
actually produced from oxygen and hydrogen, we should have been forced to
wait until the casual thought struck some one of passing an electric spark
through a mixture of the two gases, or inserting a lighted taper into it,
merely to try what would happen. Besides, many substances, though they can
be analyzed, can not by any known artificial means be recompounded.
Further, even if we could have ascertained, by the Method of Agreement,
that oxygen and hydrogen were both present when water is produced, no
experimentation on oxygen and hydrogen separately, no knowledge of their
laws, could have enabled us deductively to infer that they would produce
water. We require a specific experiment on the two combined.

Under these difficulties, we should generally have been indebted for our
knowledge of the causes of this class of effects, not to any inquiry
directed specifically toward that end, but either to accident, or to the
gradual progress of experimentation on the different combinations of which
the producing agents are susceptible; if it were not for a peculiarity
belonging to effects of this description, that they often, under some
particular combination of circumstances, reproduce their causes. If water
results from the juxtaposition of hydrogen and oxygen whenever this can be
made sufficiently close and intimate, so, on the other hand, if water
itself be placed in certain situations, hydrogen and oxygen are reproduced
from it: an abrupt termination is put to the new laws, and the agents
re-appear separately with their own properties as at first. What is called
chemical analysis is the process of searching for the causes of a
phenomenon among its effects, or rather among the effects produced by the
action of some other causes upon it.

Lavoisier, by heating mercury to a high temperature in a close vessel
containing air, found that the mercury increased in weight, and became
what was then called red precipitate, while the air, on being examined
after the experiment, proved to have lost weight, and to have become
incapable of supporting life or combustion. When red precipitate was
exposed to a still greater heat, it became mercury again, and gave off a
gas which did support life and flame. Thus the agents which by their
combination produced red precipitate, namely, the mercury and the gas,
reappear as effects resulting from that precipitate when acted upon by
heat. So, if we decompose water by means of iron filings, we produce two
effects, rust and hydrogen. Now rust is already known, by experiments upon
the component substances, to be an effect of the union of iron and oxygen:
the iron we ourselves supplied, but the oxygen must have been produced
from the water. The result, therefore, is that water has disappeared, and
hydrogen and oxygen have appeared in its stead; or, in other words, the
original laws of these gaseous agents, which had been suspended by the
superinduction of the new laws called the properties of water, have again
started into existence, and the causes of water are found among its
effects.

Where two phenomena, between the laws or properties of which, considered
in themselves, no connection can be traced, are thus reciprocally cause
and effect, each capable in its turn of being produced from the other, and
each, when it produces the other, ceasing itself to exist (as water is
produced from oxygen and hydrogen, and oxygen and hydrogen are reproduced
from water); this causation of the two phenomena by one another, each
being generated by the other’s destruction, is properly transformation.
The idea of chemical composition is an idea of transformation, but of a
transformation which is incomplete; since we consider the oxygen and
hydrogen to be present in the water _as_ oxygen and hydrogen, and capable
of being discovered in it if our senses were sufficiently keen: a
supposition (for it is no more) grounded solely on the fact that the
weight of the water is the sum of the separate weights of the two
ingredients. If there had not been this exception to the entire
disappearance, in the compound, of the laws of the separate ingredients;
if the combined agents had not, in this one particular of weight,
preserved their own laws, and produced a joint result equal to the sum of
their separate results; we should never, probably, have had the notion now
implied by the words chemical composition; and, in the facts of water
produced from hydrogen and oxygen, and hydrogen and oxygen produced from
water, as the transformation would have been complete, we should have seen
only a transformation.

In these cases, where the heteropathic effect (as we called it in a former
chapter)(147) is but a transformation of its cause, or in other words,
where the effect and its cause are reciprocally such, and mutually
convertible into each other; the problem of finding the cause resolves
itself into the far easier one of finding an effect, which is the kind of
inquiry that admits of being prosecuted by direct experiment. But there
are other cases of heteropathic effects to which this mode of
investigation is not applicable. Take, for instance, the heteropathic laws
of mind; that portion of the phenomena of our mental nature which are
analogous to chemical rather than to dynamical phenomena; as when a
complex passion is formed by the coalition of several elementary impulses,
or a complex emotion by several simple pleasures or pains, of which it is
the result without being the aggregate, or in any respect homogeneous with
them. The product, in these cases, is generated by its various factors;
but the factors can not be reproduced from the product; just as a youth
can grow into an old man, but an old man can not grow into a youth. We can
not ascertain from what simple feelings any of our complex states of mind
are generated, as we ascertain the ingredients of a chemical compound, by
making it, in its turn, generate them. We can only, therefore, discover
these laws by the slow process of studying the simple feelings themselves,
and ascertaining synthetically, by experimenting on the various
combinations of which they are susceptible, what they, by their mutual
action upon one another, are capable of generating.

§ 5. It might have been supposed that the other, and apparently simpler
variety of the mutual interference of causes, where each cause continues
to produce its own proper effect according to the same laws to which it
conforms in its separate state, would have presented fewer difficulties to
the inductive inquirer than that of which we have just finished the
consideration. It presents, however, so far as direct induction apart from
deduction is concerned, infinitely greater difficulties. When a
concurrence of causes gives rise to a new effect, bearing no relation to
the separate effects of those causes, the resulting phenomenon stands
forth undisguised, inviting attention to its peculiarity, and presenting
no obstacle to our recognizing its presence or absence among any number of
surrounding phenomena. It admits, therefore, of being easily brought under
the canons of Induction, provided instances can be obtained such as those
canons require; and the non-occurrence of such instances, or the want of
means to produce them artificially, is the real and only difficulty in
such investigations; a difficulty not logical but in some sort physical.
It is otherwise with cases of what, in a preceding chapter, has been
denominated the Composition of Causes. There, the effects of the separate
causes do not terminate and give place to others, thereby ceasing to form
any part of the phenomenon to be investigated; on the contrary, they still
take place, but are intermingled with, and disguised by, the homogeneous
and closely allied effects of other causes. They are no longer _a_, _b_,
_c_, _d_, _e_, existing side by side, and continuing to be separately
discernible; they are +_a_, -_a_, ½_b_, _-b_, 2_b_, etc.; some of which
cancel one another, while many others do not appear distinguishably, but
merge in one sum; forming altogether a result, between which and the
causes whereby it was produced there is often an insurmountable difficulty
in tracing by observation any fixed relation whatever.

The general idea of the Composition of Causes has been seen to be, that
though two or more laws interfere with one another, and apparently
frustrate or modify one another’s operation, yet in reality all are
fulfilled, the collective effect being the exact sum of the effects of the
causes taken separately. A familiar instance is that of a body kept in
equilibrium by two equal and contrary forces. One of the forces if acting
alone would carry the body in a given time a certain distance to the west,
the other if acting alone would carry it exactly as far toward the east;
and the result is the same as if it had been first carried to the west as
far as the one force would carry it, and then back toward the east as far
as the other would carry it—that is, precisely the same distance; being
ultimately left where it was found at first.

All laws of causation are liable to be in this manner counteracted, and
seemingly frustrated, by coming into conflict with other laws, the
separate result of which is opposite to theirs, or more or less
inconsistent with it. And hence, with almost every law, many instances in
which it really is entirely fulfilled, do not, at first sight, appear to
be cases of its operation at all. It is so in the example just adduced: a
force in mechanics means neither more nor less than a cause of motion, yet
the sum of the effects of two causes of motion may be rest. Again, a body
solicited by two forces in directions making an angle with one another,
moves in the diagonal; and it seems a paradox to say that motion in the
diagonal is the sum of two motions in two other lines. Motion, however, is
but change of place, and at every instant the body is in the exact place
it would have been in if the forces had acted during alternate instants
instead of acting in the same instant (saving that if we suppose two
forces to act successively which are in truth simultaneous we must of
course allow them double the time). It is evident, therefore, that each
force has had, during each instant, all the effect which belonged to it;
and that the modifying influence which one of two concurrent causes is
said to exercise with respect to the other may be considered as exerted
not over the action of the cause itself, but over the effect after it is
completed. For all purposes of predicting, calculating, or explaining
their joint result, causes which compound their effects may be treated as
if they produced simultaneously each of them its own effect, and all these
effects co-existed visibly.

Since the laws of causes are as really fulfilled when the causes are said
to be counteracted by opposing causes, as when they are left to their own
undisturbed action, we must be cautious not to express the laws in such
terms as would render the assertion of their being fulfilled in those
cases a contradiction. If, for instance, it were stated as a law of nature
that a body to which a force is applied moves in the direction of the
force, with a velocity proportioned to the force directly, and to its own
mass inversely; when in point of fact some bodies to which a force is
applied do not move at all, and those which do move (at least in the
region of our earth) are, from the very first, retarded by the action of
gravity and other resisting forces, and at last stopped altogether; it is
clear that the general proposition, though it would be true under a
certain hypothesis, would not express the facts as they actually occur. To
accommodate the expression of the law to the real phenomena, we must say,
not that the object moves, but that it _tends_ to move, in the direction
and with the velocity specified. We might, indeed, guard our expression in
a different mode, by saying that the body moves in that manner unless
prevented, or except in so far as prevented, by some counteracting cause.
But the body does not only move in that manner unless counteracted; it
_tends_ to move in that manner even when counteracted; it still exerts, in
the original direction, the same energy of movement as if its first
impulse had been undisturbed, and produces, by that energy, an exactly
equivalent quantity of effect. This is true even when the force leaves the
body as it found it, in a state of absolute rest; as when we attempt to
raise a body of three tons’ weight with a force equal to one ton. For if,
while we are applying this force, wind or water or any other agent
supplies an additional force just exceeding two tons, the body will be
raised; thus proving that the force we applied exerted its full effect, by
neutralizing an equivalent portion of the weight which it was insufficient
altogether to overcome. And if, while we are exerting this force of one
ton upon the object in a direction contrary to that of gravity, it be put
into a scale and weighed, it will be found to have lost a ton of its
weight, or, in other words, to press downward with a force only equal to
the difference of the two forces.

These facts are correctly indicated by the expression _tendency_. All laws
of causation, in consequence of their liability to be counteracted,
require to be stated in words affirmative of tendencies only, and not of
actual results. In those sciences of causation which have an accurate
nomenclature, there are special words which signify a tendency to the
particular effect with which the science is conversant; thus _pressure_,
in mechanics, is synonymous with tendency to motion, and forces are not
reasoned on as causing actual motion, but as exerting pressure. A similar
improvement in terminology would be very salutary in many other branches
of science.

The habit of neglecting this necessary element in the precise expression
of the laws of nature, has given birth to the popular prejudice that all
general truths have exceptions; and much unmerited distrust has thence
accrued to the conclusions of science, when they have been submitted to
the judgment of minds insufficiently disciplined and cultivated. The rough
generalizations suggested by common observation usually have exceptions;
but principles of science, or, in other words, laws of causation, have
not. “What is thought to be an exception to a principle” (to quote words
used on a different occasion), “is always some other and distinct
principle cutting into the former; some other force which impinges(148)
against the first force, and deflects it from its direction. There are not
a law and an exception to that law, the law acting in ninety-nine cases,
and the exception in one. There are two laws, each possibly acting in the
whole hundred cases, and bringing about a common effect by their conjunct
operation. If the force which, being the less conspicuous of the two, is
called the _disturbing_ force, prevails sufficiently over the other force
in some one case, to constitute that case what is commonly called an
exception, the same disturbing force probably acts as a modifying cause in
many other cases which no one will call exceptions.

“Thus if it were stated to be a law of nature that all heavy bodies fall
to the ground, it would probably be said that the resistance of the
atmosphere, which prevents a balloon from falling, constitutes the balloon
an exception to that pretended law of nature. But the real law is, that
all heavy bodies _tend_ to fall; and to this there is no exception, not
even the sun and moon; for even they, as every astronomer knows, tend
toward the earth, with a force exactly equal to that with which the earth
tends toward them. The resistance of the atmosphere might, in the
particular case of the balloon, from a misapprehension of what the law of
gravitation is, be said to _prevail over_ the law; but its disturbing
effect is quite as real in every other case, since though it does not
prevent, it retards the fall of all bodies whatever. The rule, and the
so-called exception, do not divide the cases between them; each of them is
a comprehensive rule extending to all cases. To call one of these
concurrent principles an exception to the other, is superficial, and
contrary to the correct principles of nomenclature and arrangement. An
effect of precisely the same kind, and arising from the same cause, ought
not to be placed in two different categories, merely as there does or does
not exist another cause preponderating over it.”(149)

§ 6. We have now to consider according to what method these complex
effects, compounded of the effects of many causes, are to be studied; how
we are enabled to trace each effect to the concurrence of causes in which
it originated, and ascertain the conditions of its recurrence—the
circumstances in which it may be expected again to occur. The conditions
of a phenomenon which arises from a composition of causes, may be
investigated either deductively or experimentally.

The case, it is evident, is naturally susceptible of the deductive mode of
investigation. The law of an effect of this description is a result of the
laws of the separate causes on the combination of which it depends, and
is, therefore, in itself capable of being deduced from these laws. This is
called the method _a priori_. The other, or _a posteriori_ method,
professes to proceed according to the canons of experimental inquiry.
Considering the whole assemblage of concurrent causes which produced the
phenomenon, as one single cause, it attempts to ascertain the cause in the
ordinary manner, by a comparison of instances. This second method
subdivides itself into two different varieties. If it merely collates
instances of the effect, it is a method of pure observation. If it
operates upon the causes, and tries different combinations of them, in
hopes of ultimately hitting the precise combination which will produce the
given total effect, it is a method of experiment.

In order more completely to clear up the nature of each of these three
methods, and determine which of them deserves the preference, it will be
expedient (conformably to a favorite maxim of Lord Chancellor Eldon, to
which, though it has often incurred philosophical ridicule, a deeper
philosophy will not refuse its sanction) to “clothe them in
circumstances.” We shall select for this purpose a case which as yet
furnishes no very brilliant example of the success of any of the three
methods, but which is all the more suited to illustrate the difficulties
inherent in them. Let the subject of inquiry be, the conditions of health
and disease in the human body; or (for greater simplicity) the conditions
of recovery from a given disease; and in order to narrow the question
still more, let it be limited, in the first instance, to this one inquiry:
Is, or is not, some particular medicament (mercury, for instance) a remedy
for the given disease.

Now, the deductive method would set out from known properties of mercury,
and known laws of the human body, and by reasoning from these, would
attempt to discover whether mercury will act upon the body when in the
morbid condition supposed, in such a manner as would tend to restore
health. The experimental method would simply administer mercury in as many
cases as possible, noting the age, sex, temperament, and other
peculiarities of bodily constitution, the particular form or variety of
the disease, the particular stage of its progress, etc., remarking in
which of these cases it was attended with a salutary effect, and with what
circumstances it was on those occasions combined. The method of simple
observation would compare instances of recovery, to find whether they
agreed in having been preceded by the administration of mercury; or would
compare instances of recovery with instances of failure, to find cases
which, agreeing in all other respects, differed only in the fact that
mercury had been administered, or that it had not.

§ 7. That the last of these three modes of investigation is applicable to
the case, no one has ever seriously contended. No conclusions of value on
a subject of such intricacy ever were obtained in that way. The utmost
that could result would be a vague general impression for or against the
efficacy of mercury, of no avail for guidance unless confirmed by one of
the other two methods. Not that the results, which this method strives to
obtain, would not be of the utmost possible value if they could be
obtained. If all the cases of recovery which presented themselves, in an
examination extending to a great number of instances, were cases in which
mercury had been administered, we might generalize with confidence from
this experience, and should have obtained a conclusion of real value. But
no such basis for generalization can we, in a case of this description,
hope to obtain. The reason is that which we have spoken of as constituting
the characteristic imperfection of the Method of Agreement, Plurality of
Causes. Supposing even that mercury does tend to cure the disease, so many
other causes, both natural and artificial, also tend to cure it, that
there are sure to be abundant instances of recovery in which mercury has
not been administered, unless, indeed, the practice be to administer it in
all cases; on which supposition it will equally be found in the cases of
failure.

When an effect results from the union of many causes, the share which each
has in the determination of the effect can not in general be great, and
the effect is not likely, even in its presence or absence, still less in
its variations, to follow, even approximately, any one of the causes.
Recovery from a disease is an event to which, in every case, many
influences must concur. Mercury may be one such influence; but from the
very fact that there are many other such, it will necessarily happen that
although mercury is administered, the patient, for want of other
concurring influences, will often not recover, and that he often will
recover when it is not administered, the other favorable influences being
sufficiently powerful without it. Neither, therefore, will the instances
of recovery agree in the administration of mercury, nor will the instances
of failure agree in its non-administration. It is much if, by multiplied
and accurate returns from hospitals and the like, we can collect that
there are rather more recoveries and rather fewer failures when mercury is
administered than when it is not; a result of very secondary value even as
a guide to practice, and almost worthless as a contribution to the theory
of the subject.(150)

§ 8. The inapplicability of the method of simple observation to ascertain
the conditions of effects dependent on many concurring causes, being thus
recognized, we shall next inquire whether any greater benefit can be
expected from the other branch of the _a posteriori_ method, that which
proceeds by directly trying different combinations of causes, either
artificially produced or found in nature, and taking notice what is their
effect; as, for example, by actually trying the effect of mercury in as
many different circumstances as possible. This method differs from the one
which we have just examined in turning our attention directly to the
causes or agents, instead of turning it to the effect, recovery from the
disease. And since, as a general rule, the effects of causes are far more
accessible to our study than the causes of effects, it is natural to think
that this method has a much better chance of proving successful than the
former.

The method now under consideration is called the Empirical Method; and in
order to estimate it fairly, we must suppose it to be completely, not
incompletely, empirical. We must exclude from it every thing which
partakes of the nature not of an experimental but of a deductive
operation. If, for instance, we try experiments with mercury upon a person
in health, in order to ascertain the general laws of its action upon the
human body, and then reason from these laws to determine how it will act
upon persons affected with a particular disease, this may be a really
effectual method; but this is deduction. The experimental method does not
derive the law of a complex case from the simpler laws which conspire to
produce it, but makes its experiments directly upon the complex case. We
must make entire abstraction of all knowledge of the simpler tendencies,
the _modi operandi_ of mercury in detail. Our experimentation must aim at
obtaining a direct answer to the specific question, Does or does not
mercury tend to cure the particular disease?

Let us see, therefore, how far the case admits of the observance of those
rules of experimentation which it is found necessary to observe in other
cases. When we devise an experiment to ascertain the effect of a given
agent, there are certain precautions which we never, if we can help it,
omit. In the first place, we introduce the agent into the midst of a set
of circumstances which we have exactly ascertained. It needs hardly be
remarked how far this condition is from being realized in any case
connected with the phenomena of life; how far we are from knowing what are
all the circumstances which pre-exist in any instance in which mercury is
administered to a living being. This difficulty, however, though
insuperable in most cases, may not be so in all; there are sometimes
concurrences of many causes, in which we yet know accurately what the
causes are. Moreover, the difficulty may be attenuated by sufficient
multiplication of experiments, in circumstances rendering it improbable
that any of the unknown causes should exist in them all. But when we have
got clear of this obstacle, we encounter another still more serious. In
other cases, when we intend to try an experiment, we do not reckon it
enough that there be no circumstance in the case the presence of which is
unknown to us. We require, also, that none of the circumstances which we
do know shall have effects susceptible of being confounded with those of
the agents whose properties we wish to study. We take the utmost pains to
exclude all causes capable of composition with the given cause; or, if
forced to let in any such causes, we take care to make them such that we
can compute and allow for their influence, so that the effect of the given
cause may, after the subduction of those other effects, be apparent as a
residual phenomenon.

These precautions are inapplicable to such cases as we are now
considering. The mercury of our experiment being tried with an unknown
multitude (or even let it be a known multitude) of other influencing
circumstances, the mere fact of their being influencing circumstances
implies that they disguise the effect of the mercury, and preclude us from
knowing whether it has any effect or not. Unless we already knew what and
how much is owing to every other circumstance (that is, unless we suppose
the very problem solved which we are considering the means of solving), we
can not tell that those other circumstances may not have produced the
whole of the effect, independently or even in spite of the mercury. The
Method of Difference, in the ordinary mode of its use, namely, by
comparing the state of things following the experiment with the state
which preceded it, is thus, in the case of intermixture of effects,
entirely unavailing; because other causes than that whose effect we are
seeking to determine have been operating during the transition. As for the
other mode of employing the Method of Difference, namely, by comparing,
not the same case at two different periods, but different cases, this in
the present instance is quite chimerical. In phenomena so complicated it
is questionable if two cases, similar in all respects but one, ever
occurred; and were they to occur, we could not possibly know that they
were so exactly similar.

Any thing like a scientific use of the method of experiment, in these
complicated cases, is therefore out of the question. We can generally,
even in the most favorable cases, only discover by a succession of trials,
that a certain cause is _very often_ followed by a certain effect. For, in
one of these conjunct effects, the portion which is determined by any one
of the influencing agents, is usually, as we before remarked, but small;
and it must be a more potent cause than most, if even the tendency which
it really exerts is not thwarted by other tendencies in nearly as many
cases as it is fulfilled. Some causes indeed there are which are more
potent than any counteracting causes to which they are commonly exposed;
and accordingly there are some truths in medicine which are sufficiently
proved by direct experiment. Of these the most familiar are those that
relate to the efficacy of the substances known as Specifics for particular
diseases, “quinine, colchicum, lime-juice, cod-liver oil,”(151) and a few
others. Even these are not invariably followed by success; but they
succeed in so large a proportion of cases, and against such powerful
obstacles, that their _tendency_ to restore health in the disorders for
which they are prescribed may be regarded as an experimental truth.(152)

If so little can be done by the experimental method to determine the
conditions of an effect of many combined causes, in the case of medical
science; still less is this method applicable to a class of phenomena more
complicated than even those of physiology, the phenomena of politics and
history. There, Plurality of Causes exists in almost boundless excess, and
effects are, for the most part, inextricably interwoven with one another.
To add to the embarrassment, most of the inquiries in political science
relate to the production of effects of a most comprehensive description,
such as the public wealth, public security, public morality, and the like:
results liable to be affected directly or indirectly either in _plus_ or
in _minus_ by nearly every fact which exists, or event which occurs, in
human society. The vulgar notion, that the safe methods on political
subjects are those of Baconian induction—that the true guide is not
general reasoning, but specific experience—will one day be quoted as among
the most unequivocal marks of a low state of the speculative faculties in
any age in which it is accredited. Nothing can be more ludicrous than the
sort of parodies on experimental reasoning which one is accustomed to meet
with, not in popular discussion only, but in grave treatises, when the
affairs of nations are the theme. “How,” it is asked, “can an institution
be bad, when the country has prospered under it?” “How can such or such
causes have contributed to the prosperity of one country, when another has
prospered without them?” Whoever makes use of an argument of this kind,
not intending to deceive, should be sent back to learn the elements of
some one of the more easy physical sciences. Such reasoners ignore the
fact of Plurality of Causes in the very case which affords the most signal
example of it. So little could be concluded, in such a case, from any
possible collation of individual instances, that even the impossibility,
in social phenomena, of making artificial experiments, a circumstance
otherwise so prejudicial to directly inductive inquiry, hardly affords, in
this case, additional reason of regret. For even if we could try
experiments upon a nation or upon the human race, with as little scruple
as M. Magendie tried them on dogs and rabbits, we should never succeed in
making two instances identical in every respect except the presence or
absence of some one definite circumstance. The nearest approach to an
experiment in the philosophical sense, which takes place in politics, is
the introduction of a new operative element into national affairs by some
special and assignable measure of government, such as the enactment or
repeal of a particular law. But where there are so many influences at
work, it requires some time for the influence of any new cause upon
national phenomena to become apparent; and as the causes operating in so
extensive a sphere are not only infinitely numerous, but in a state of
perpetual alteration, it is always certain that before the effect of the
new cause becomes conspicuous enough to be a subject of induction, so many
of the other influencing circumstances will have changed as to vitiate the
experiment.(153)

Two, therefore, of the three possible methods for the study of phenomena
resulting from the composition of many causes, being, from the very nature
of the case, inefficient and illusory, there remains only the third—that
which considers the causes separately, and infers the effect from the
balance of the different tendencies which produce it: in short, the
deductive, or _a priori_ method. The more particular consideration of this
intellectual process requires a chapter to itself.



                               Chapter XI.


Of The Deductive Method.


§ 1. The mode of investigation which, from the proved inapplicability of
direct methods of observation and experiment, remains to us as the main
source of the knowledge we possess or can acquire respecting the
conditions and laws of recurrence, of the more complex phenomena, is
called, in its most general expression, the Deductive Method; and consists
of three operations: the first, one of direct induction; the second, of
ratiocination; the third, of verification.

I call the first step in the process an inductive operation, because there
must be a direct induction as the basis of the whole; though in many
particular investigations the place of the induction may be supplied by a
prior deduction; but the premises of this prior deduction must have been
derived from induction.

The problem of the Deductive Method is, to find the law of an effect, from
the laws of the different tendencies of which it is the joint result. The
first requisite, therefore, is to know the laws of those tendencies; the
law of each of the concurrent causes: and this supposes a previous process
of observation or experiment upon each cause separately; or else a
previous deduction, which also must depend for its ultimate premises on
observation or experiment. Thus, if the subject be social or historical
phenomena, the premises of the Deductive Method must be the laws of the
causes which determine that class of phenomena; and those causes are human
actions, together with the general outward circumstances under the
influence of which mankind are placed, and which constitute man’s position
on the earth. The Deductive Method, applied to social phenomena, must
begin, therefore, by investigating, or must suppose to have been already
investigated, the laws of human action, and those properties of outward
things by which the actions of human beings in society are determined.
Some of these general truths will naturally be obtained by observation and
experiment, others by deduction: the more complex laws of human action,
for example, may be deduced from the simpler ones; but the simple or
elementary laws will always, and necessarily, have been obtained by a
directly inductive process.

To ascertain, then, the laws of each separate cause which takes a share in
producing the effect, is the first desideratum of the Deductive Method. To
know what the causes are which must be subjected to this process of study,
may or may not be difficult. In the case last mentioned, this first
condition is of easy fulfillment. That social phenomena depend on the acts
and mental impressions of human beings, never could have been a matter of
any doubt, however imperfectly it may have been known either by what laws
those impressions and actions are governed, or to what social consequences
their laws naturally lead. Neither, again, after physical science had
attained a certain development, could there be any real doubt where to
look for the laws on which the phenomena of life depend, since they must
be the mechanical and chemical laws of the solid and fluid substances
composing the organized body and the medium in which it subsists, together
with the peculiar vital laws of the different tissues constituting the
organic structure. In other cases, really far more simple than these, it
was much less obvious in what quarter the causes were to be looked for: as
in the case of the celestial phenomena. Until, by combining the laws of
certain causes, it was found that those laws explained all the facts which
experience had proved concerning the heavenly motions, and led to
predictions which it always verified, mankind never knew that those _were_
the causes. But whether we are able to put the question before, or not
until after, we have become capable of answering it, in either case it
must be answered; the laws of the different causes must be ascertained,
before we can proceed to deduce from them the conditions of the effect.

The mode of ascertaining those laws neither is, nor can be any other than
the fourfold method of experimental inquiry, already discussed. A few
remarks on the application of that method to cases of the Composition of
Causes are all that is requisite.

It is obvious that we can not expect to find the law of a tendency by an
induction from cases in which the tendency is counteracted. The laws of
motion could never have been brought to light from the observation of
bodies kept at rest by the equilibrium of opposing forces. Even where the
tendency is not, in the ordinary sense of the word, counteracted, but only
modified, by having its effects compounded with the effects arising from
some other tendency or tendencies, we are still in an unfavorable position
for tracing, by means of such cases, the law of the tendency itself. It
would have been scarcely possible to discover the law that every body in
motion tends to continue moving in a straight line, by an induction from
instances in which the motion is deflected into a curve, by being
compounded with the effect of an accelerating force. Notwithstanding the
resources afforded in this description of cases by the Method of
Concomitant Variations, the principles of a judicious experimentation
prescribe that the law of each of the tendencies should be studied, if
possible, in cases in which that tendency operates alone, or in
combination with no agencies but those of which the effect can, from
previous knowledge, be calculated and allowed for.

Accordingly, in the cases, unfortunately very numerous and important, in
which the causes do not suffer themselves to be separated and observed
apart, there is much difficulty in laying down with due certainty the
inductive foundation necessary to support the deductive method. This
difficulty is most of all conspicuous in the case of physiological
phenomena; it being seldom possible to separate the different agencies
which collectively compose an organized body, without destroying the very
phenomena which it is our object to investigate:


    ——following life, in creatures we dissect,
    We lose it, in the moment we detect.


And for this reason I am inclined to the opinion that physiology (greatly
and rapidly progressive as it now is) is embarrassed by greater natural
difficulties, and is probably susceptible of a less degree of ultimate
perfection, than even the social science; inasmuch as it is possible to
study the laws and operations of one human mind apart from other minds,
much less imperfectly than we can study the laws of one organ or tissue of
the human body apart from the other organs or tissues.

It has been judiciously remarked that pathological facts, or, to speak in
common language, diseases in their different forms and degrees afford in
the case of physiological investigation the most valuable equivalent to
experimentation properly so called; inasmuch as they often exhibit to us a
definite disturbance in some one organ or organic function, the remaining
organs and functions being, in the first instance at least, unaffected. It
is true that from the perpetual actions and reactions which are going on
among all parts of the organic economy, there can be no prolonged
disturbance in any one function without ultimately involving many of the
others; and when once it has done so, the experiment for the most part
loses its scientific value. All depends on observing the early stages of
the derangement; which, unfortunately, are of necessity the least marked.
If, however, the organs and functions not disturbed in the first instance
become affected in a fixed order of succession, some light is thereby
thrown upon the action which one organ exercises over another: and we
occasionally obtain a series of effects which we can refer with some
confidence to the original local derangement; but for this it is necessary
that we should know that the original derangement _was_ local. If it was
what is termed constitutional; that is, if we do not know in what part of
the animal economy it took its rise, or the precise nature of the
disturbance which took place in that part, we are unable to determine
which of the various derangements was cause and which effect; which of
them were produced by one another, and which by the direct, though perhaps
tardy, action of the original cause.

Besides natural pathological facts, we can produce pathological facts
artificially: we can try experiments, even in the popular sense of the
term, by subjecting the living being to some external agent, such as the
mercury of our former example, or the section of a nerve to ascertain the
functions of different parts of the nervous system. As this
experimentation is not intended to obtain a direct solution of any
practical question, but to discover general laws, from which afterward the
conditions of any particular effect may be obtained by deduction, the best
cases to select are those of which the circumstances can be best
ascertained: and such are generally not those in which there is any
practical object in view. The experiments are best tried, not in a state
of disease, which is essentially a changeable state, but in the condition
of health, comparatively a fixed state. In the one, unusual agencies are
at work, the results of which we have no means of predicting: in the
other, the course of the accustomed physiological phenomena would, it may
generally be presumed, remain undisturbed, were it not for the disturbing
cause which we introduce.

Such, with the occasional aid of the Method of Concomitant Variations (the
latter not less encumbered than the more elementary methods by the
peculiar difficulties of the subject), are our inductive resources for
ascertaining the laws of the causes considered separately, when we have it
not in our power to make trial of them in a state of actual separation.
The insufficiency of these resources is so glaring, that no one can be
surprised at the backward state of the science of physiology; in which
indeed our knowledge of causes is so imperfect, that we can neither
explain, nor could without specific experience have predicted, many of the
facts which are certified to us by the most ordinary observation.
Fortunately, we are much better informed as to the empirical laws of the
phenomena, that is, the uniformities respecting which we can not yet
decide whether they are cases of causation, or mere results of it. Not
only has the order in which the facts of organization and life
successively manifest themselves, from the first germ of existence to
death, been found to be uniform, and very accurately ascertainable; but,
by a great application of the Method of Concomitant Variations to the
entire facts of comparative anatomy and physiology, the characteristic
organic structure corresponding to each class of functions has been
determined with considerable precision. Whether these organic conditions
are the whole of the conditions, and in many cases whether they are
conditions at all, or mere collateral effects of some common cause, we are
quite ignorant; nor are we ever likely to know, unless we could construct
an organized body and try whether it would live.

Under such disadvantages do we, in cases of this description, attempt the
initial, or inductive step, in the application of the Deductive Method to
complex phenomena. But such, fortunately, is not the common case. In
general, the laws of the causes on which the effect depends may be
obtained by an induction from comparatively simple instances, or, at the
worst, by deduction from the laws of simpler causes, so obtained. By
simple instances are meant, of course, those in which the action of each
cause was not intermixed or interfered with, or not to any great extent,
by other causes whose laws were unknown. And only when the induction which
furnished the premises to the Deductive method rested on such instances
has the application of such a method to the ascertainment of the laws of a
complex effect, been attended with brilliant results.

§ 2. When the laws of the causes have been ascertained, and the first
stage of the great logical operation now under discussion satisfactorily
accomplished, the second part follows; that of determining from the laws
of the causes what effect any given combination of those causes will
produce. This is a process of calculation, in the wider sense of the term;
and very often involves processes of calculation in the narrowest sense.
It is a ratiocination; and when our knowledge of the causes is so perfect
as to extend to the exact numerical laws which they observe in producing
their effects, the ratiocination may reckon among its premises the
theorems of the science of number, in the whole immense extent of that
science. Not only are the most advanced truths of mathematics often
required to enable us to compute an effect, the numerical law of which we
already know; but, even by the aid of those most advanced truths, we can
go but a little way. In so simple a case as the common problem of three
bodies gravitating toward one another, with a force directly as their mass
and inversely as the square of the distance, all the resources of the
calculus have not hitherto sufficed to obtain any general solution, but an
approximate one. In a case a little more complex, but still one of the
simplest which arise in practice, that of the motion of a projectile, the
causes which affect the velocity and range (for example) of a cannon-ball
may be all known and estimated: the force of the gunpowder, the angle of
elevation, the density of the air, the strength and direction of the wind;
but it is one of the most difficult of mathematical problems to combine
all these, so as to determine the effect resulting from their collective
action.

Besides the theorems of number, those of geometry also come in as
premises, where the effects take place in space, and involve motion and
extension, as in mechanics, optics, acoustics, astronomy. But when the
complication increases, and the effects are under the influence of so many
and such shifting causes as to give no room either for fixed numbers, or
for straight lines and regular curves (as in the case of physiological, to
say nothing of mental and social phenomena), the laws of number and
extension are applicable, if at all, only on that large scale on which
precision of details becomes unimportant. Although these laws play a
conspicuous part in the most striking examples of the investigation of
nature by the Deductive Method, as for example in the Newtonian theory of
the celestial motions, they are by no means an indispensable part of every
such process. All that is essential in it is reasoning from a general law
to a particular case, that is, determining by means of the particular
circumstances of that case, what result is required in that instance to
fulfill the law. Thus in the Torricellian experiment, if the fact that air
has weight had been previously known, it would have been easy, without any
numerical data, to deduce from the general law of equilibrium, that the
mercury would stand in the tube at such a height that the column of
mercury would exactly balance a column of the atmosphere of equal
diameter; because, otherwise, equilibrium would not exist.

By such ratiocinations from the separate laws of the causes, we may, to a
certain extent, succeed in answering either of the following questions:
Given a certain combination of causes, what effect will follow? and, What
combination of causes, if it existed, would produce a given effect? In the
one case, we determine the effect to be expected in any complex
circumstances of which the different elements are known: in the other case
we learn, according to what law—under what antecedent conditions—a given
complex effect will occur.

§ 3. But (it may here be asked) are not the same arguments by which the
methods of direct observation and experiment were set aside as illusory
when applied to the laws of complex phenomena, applicable with equal force
against the Method of Deduction? When in every single instance a
multitude, often an unknown multitude, of agencies, are clashing and
combining, what security have we that in our computation _a priori_ we
have taken all these into our reckoning? How many must we not generally be
ignorant of? Among those which we know, how probable that some have been
overlooked; and, even were all included, how vain the pretense of summing
up the effects of many causes, unless we know accurately the numerical law
of each—a condition in most cases not to be fulfilled; and even when it is
fulfilled, to make the calculation transcends, in any but very simple
cases, the utmost power of mathematical science with all its most modern
improvements.

These objections have real weight, and would be altogether unanswerable,
if there were no test by which, when we employ the Deductive Method, we
might judge whether an error of any of the above descriptions had been
committed or not. Such a test, however, there is: and its application
forms, under the name of Verification, the third essential component part
of the Deductive Method; without which all the results it can give have
little other value than that of conjecture. To warrant reliance on the
general conclusions arrived at by deduction, these conclusions must be
found, on careful comparison, to accord with the results of direct
observation wherever it can be had. If, when we have experience to compare
with them, this experience confirms them, we may safely trust to them in
other cases of which our specific experience is yet to come. But if our
deductions have led to the conclusion that from a particular combination
of causes a given effect would result, then in all known cases where that
combination can be shown to have existed, and where the effect has not
followed, we must be able to show (or at least to make a probable surmise)
what frustrated it: if we can not, the theory is imperfect, and not yet to
be relied upon. Nor is the verification complete, unless some of the cases
in which the theory is borne out by the observed result are of at least
equal complexity with any other cases in which its application could be
called for.

If direct observation and collation of instances have furnished us with
any empirical laws of the effect (whether true in all observed cases, or
only true for the most part), the most effectual verification of which the
theory could be susceptible, would be, that it led deductively to those
empirical laws; that the uniformities, whether complete or incomplete,
which were observed to exist among the phenomena, were accounted for by
the laws of the causes—were such as could not but exist if those be really
the causes by which the phenomena are produced. Thus it was very
reasonably deemed an essential requisite of any true theory of the causes
of the celestial motions, that it should lead by deduction to Kepler’s
laws; which, accordingly, the Newtonian theory did.

In order, therefore, to facilitate the verification of theories obtained
by deduction, it is important that as many as possible of the empirical
laws of the phenomena should be ascertained, by a comparison of instances,
conformably to the Method of Agreement: as well as (it must be added) that
the phenomena themselves should be described, in the most comprehensive as
well as accurate manner possible; by collecting from the observation of
parts, the simplest possible correct expressions for the corresponding
wholes: as when the series of the observed places of a planet was first
expressed by a circle, then by a system of epicycles, and subsequently by
an ellipse.

It is worth remarking, that complex instances which would have been of no
use for the discovery of the simple laws into which we ultimately analyze
their phenomena, nevertheless, when they have served to verify the
analysis, become additional evidence of the laws themselves. Although we
could not have got at the law from complex cases, still when the law, got
at otherwise, is found to be in accordance with the result of a complex
case, that case becomes a new experiment on the law, and helps to confirm
what it did not assist to discover. It is a new trial of the principle in
a different set of circumstances; and occasionally serves to eliminate
some circumstance not previously excluded, and the exclusion of which
might require an experiment impossible to be executed. This was strikingly
conspicuous in the example formerly quoted, in which the difference
between the observed and the calculated velocity of sound was ascertained
to result from the heat extricated by the condensation which takes place
in each sonorous vibration. This was a trial, in new circumstances, of the
law of the development of heat by compression; and it added materially to
the proof of the universality of that law. Accordingly, any law of nature
is deemed to have gained in point of certainty, by being found to explain
some complex case which had not previously been thought of in connection
with it; and this indeed is a consideration to which it is the habit of
scientific inquirers to attach rather too much value than too little.

To the Deductive Method, thus characterized in its three constituent
parts, Induction, Ratiocination, and Verification, the human mind is
indebted for its most conspicuous triumphs in the investigation of nature.
To it we owe all the theories by which vast and complicated phenomena are
embraced under a few simple laws, which, considered as the laws of those
great phenomena, could never have been detected by their direct study. We
may form some conception of what the method has done for us from the case
of the celestial motions: one of the simplest among the greater instances
of the Composition of Causes, since (except in a few cases not of primary
importance) each of the heavenly bodies may be considered, without
material inaccuracy, to be never at one time influenced by the attraction
of more than two bodies, the sun and one other planet or satellite;
making, with the reaction of the body itself, and the force generated by
the body’s own motion and acting in the direction of the tangent, only
four different agents on the concurrence of which the motions of that body
depend; a much smaller number, no doubt, than that by which any other of
the great phenomena of nature is determined or modified. Yet how could we
ever have ascertained the combination of forces on which the motions of
the earth and planets are dependent, by merely comparing the orbits or
velocities of different planets, or the different velocities or positions
of the same planet? Notwithstanding the regularity which manifests itself
in those motions, in a degree so rare among the effects of concurrence of
causes; and although the periodical recurrence of exactly the same effect,
affords positive proof that all the combinations of causes which occur at
all, recur periodically; we should not have known what the causes were, if
the existence of agencies precisely similar on our own earth had not,
fortunately, brought the causes themselves within the reach of
experimentation under simple circumstances. As we shall have occasion to
analyze, further on, this great example of the Method of Deduction, we
shall not occupy any time with it here, but shall proceed to that
secondary application of the Deductive Method, the result of which is not
to prove laws of phenomena, but to explain them.



                               Chapter XII.


Of The Explanation Of Laws Of Nature.


§ 1. The deductive operation by which we derive the law of an effect from
the laws of the causes, the concurrence of which gives rise to it, may be
undertaken either for the purpose of discovering the law, or of explaining
a law already discovered. The word _explanation_ occurs so continually,
and holds so important a place in philosophy, that a little time spent in
fixing the meaning of it will be profitably employed.

An individual fact is said to be explained, by pointing out its cause,
that is, by stating the law or laws of causation, of which its production
is an instance. Thus, a conflagration is explained, when it is proved to
have arisen from a spark falling into the midst of a heap of combustibles.
And in a similar manner, a law or uniformity in nature is said to be
explained, when another law or laws are pointed out, of which that law
itself is but a case, and from which it could be deduced.

§ 2. There are three distinguishable sets of circumstances in which a law
of causation may be explained from, or, as it also is often expressed,
resolved into, other laws.

The first is the case already so fully considered; an intermixture of
laws, producing a joint effect equal to the sum of the effects of the
causes taken separately. The law of the complex effect is explained, by
being resolved into the separate laws of the causes which contribute to
it. Thus, the law of the motion of a planet is resolved into the law of
the acquired force, which tends to produce a uniform motion in the
tangent, and the law of the centripetal force, which tends to produce an
accelerating motion toward the sun; the real motion being a compound of
the two.

It is necessary here to remark, that in this resolution of the law of a
complex effect, the laws of which it is compounded are not the only
elements. It is resolved into the laws of the separate causes, together
with the fact of their co-existence. The one is as essential an ingredient
as the other; whether the object be to discover the law of the effect, or
only to explain it. To deduce the laws of the heavenly motions, we require
not only to know the law of a rectilineal and that of a gravitative force,
but the existence of both these forces in the celestial regions, and even
their relative amount. The complex laws of causation are thus resolved
into two distinct kinds of elements: the one, simpler laws of causation,
the other (in the aptly selected expression of Dr. Chalmers) collocations;
the collocations consisting in the existence of certain agents or powers,
in certain circumstances of place and time. We shall hereafter have
occasion to return to this distinction, and to dwell on it at such length
as dispenses with the necessity of further insisting on it here. The first
mode, then, of the explanation of Laws of Causation, is when the law of an
effect is resolved into the various tendencies of which it is the result,
together with the laws of those tendencies.

§ 3. A second case is when, between what seemed the cause and what was
supposed to be its effect, further observation detects an intermediate
link; a fact caused by the antecedent, and in its turn causing the
consequent; so that the cause at first assigned is but the remote cause,
operating through the intermediate phenomenon. A seemed the cause of C,
but it subsequently appeared that A was only the cause of B, and that it
is B which was the cause of C. For example: mankind were aware that the
act of touching an outward object caused a sensation. It was subsequently
discovered that after we have touched the object, and before we experience
the sensation, some change takes place in a kind of thread called a nerve,
which extends from our outward organs to the brain. Touching the object,
therefore, is only the remote cause of our sensation; that is, not the
cause, properly speaking, but the cause of the cause; the real cause of
the sensation is the change in the state of the nerve. Future experience
may not only give us more knowledge than we now have of the particular
nature of this change, but may also interpolate another link: between the
contact (for example) of the object with our outward organs, and the
production of the change of state in the nerve, there may take place some
electric phenomenon, or some phenomenon of a nature not resembling the
effects of any known agency. Hitherto, however, no such intermediate link
has been discovered; and the touch of the object must be considered,
provisionally, as the proximate cause of the affection of the nerve. The
sequence, therefore, of a sensation of touch on contact with an object is
ascertained not to be an ultimate law; it is resolved, as the phrase is,
into two other laws—the law that contact with an object produces an
affection of the nerve, and the law that an affection of the nerve
produces sensation.

To take another example: the more powerful acids corrode or blacken
organic compounds. This is a case of causation, but of remote causation;
and is said to be explained when it is shown that there is an intermediate
link, namely, the separation of some of the chemical elements of the
organic structure from the rest, and their entering into combination with
the acid. The acid causes this separation of the elements, and the
separation of the elements causes the disorganization, and often the
charring of the structure. So, again, chlorine extracts coloring matters
(whence its efficacy in bleaching) and purifies the air from infection.
This law is resolved into the two following laws: Chlorine has a powerful
affinity for bases of all kinds, particularly metallic bases and hydrogen:
such bases are essential elements of coloring matters and contagious
compounds, which substances, therefore, are decomposed and destroyed by
chlorine.

§ 4. It is of importance to remark, that when a sequence of phenomena is
thus resolved into other laws, they are always laws more general than
itself. The law that A is followed by C, is less general than either of
the laws which connect B with C and A with B. This will appear from very
simple considerations.

All laws of causation are liable to be counteracted or frustrated, by the
non-fulfillment of some negative condition; the tendency, therefore, of B
to produce C may be defeated. Now the law that A produces B, is equally
fulfilled whether B is followed by C or not; but the law that A produces C
by means of B, is of course only fulfilled when B is really followed by C,
and is, therefore, less general than the law that A produces B. It is also
less general than the law that B produces C. For B may have other causes
besides A; and as A produces C only by means of B, while B produces C,
whether it has itself been produced by A or by any thing else, the second
law embraces a greater number of instances, covers as it were a greater
space of ground, than the first.

Thus, in our former example, the law that the contact of an object causes
a change in the state of the nerve, is more general than the law that
contact with an object causes sensation, since, for aught we know, the
change in the nerve may equally take place when, from a counteracting
cause, as, for instance, strong mental excitement, the sensation does not
follow; as in a battle, where wounds are sometimes received without any
consciousness of receiving them. And again, the law that change in the
state of a nerve produces sensation, is more general than the law that
contact with an object produces sensation; since the sensation equally
follows the change in the nerve when not produced by contact with an
object, but by some other cause; as in the well-known case, when a person
who has lost a limb feels the same sensation which he has been accustomed
to call a pain in the limb.

Not only are the laws of more immediate sequence into which the law of a
remote sequence is resolved, laws of greater generality than that law is,
but (as a consequence of, or rather as implied in, their greater
generality) they are more to be relied on; there are fewer chances of
their being ultimately found not to be universally true. From the moment
when the sequence of A and C is shown not to be immediate, but to depend
on an intervening phenomenon, then, however constant and invariable the
sequence of A and C has hitherto been found, possibilities arise of its
failure, exceeding those which can effect either of the more immediate
sequences, A, B, and B, C. The tendency of A to produce C may be defeated
by whatever is capable of defeating either the tendency of A to produce B,
or the tendency of B to produce C; it is, therefore, twice as liable to
failure as either of those more elementary tendencies; and the
generalization that A is always followed by C, is twice as likely to be
found erroneous. And so of the converse generalization, that C is always
preceded and caused by A; which will be erroneous not only if there should
happen to be a second immediate mode of production of C itself, but
moreover if there be a second mode of production of B, the immediate
antecedent of C in the sequence.

The resolution of the one generalization into the other two, not only
shows that there are possible limitations of the former, from which its
two elements are exempt, but shows also where these are to be looked for.
As soon as we know that B intervenes between A and C, we also know that if
there be cases in which the sequence of A and C does not hold, these are
most likely to be found by studying the effects or the conditions of the
phenomenon B.

It appears, then, that in the second of the three modes in which a law may
be resolved into other laws, the latter are more general, that is, extend
to more cases, and are also less likely to require limitation from
subsequent experience, than the law which they serve to explain. They are
more nearly unconditional; they are defeated by fewer contingencies; they
are a nearer approach to the universal truth of nature. The same
observations are still more evidently true with regard to the first of the
three modes of resolution. When the law of an effect of combined forces is
resolved into the separate laws of the causes, the nature of the case
implies that the law of the effect is less general than the law of any of
the causes, since it only holds when they are combined; while the law of
any one of the causes holds good both then, and also when that cause acts
apart from the rest.

It is also manifest that the complex law is liable to be oftener
unfulfilled than any one of the simpler laws of which it is the result,
since every contingency which defeats any of the laws prevents so much of
the effect as depends on it, and thereby defeats the complex law. The mere
rusting, for example, of some small part of a great machine, often
suffices entirely to prevent the effect which ought to result from the
joint action of all the parts. The law of the effect of a combination of
causes is always subject to the whole of the negative conditions which
attach to the action of all the causes severally.

There is another and an equally strong reason why the law of a complex
effect must be less general than the laws of the causes which conspire to
produce it. The same causes, acting according to the same laws, and
differing only in the proportions in which they are combined, often
produce effects which differ not merely in quantity, but in kind. The
combination of a centripetal with a projectile force, in the proportions
which obtain in all the planets and satellites of our solar system, gives
rise to an elliptical motion; but if the ratio of the two forces to each
other were slightly altered, it is demonstrated that the motion produced
would be in a circle, or a parabola, or an hyperbola; and it is thought
that in the case of some comets one of these is probably the fact. Yet the
law of the parabolic motion would be resolvable into the very same simple
laws into which that of the elliptical motion is resolved, namely, the law
of the permanence of rectilineal motion, and the law of gravitation. If,
therefore, in the course of ages, some circumstance were to manifest
itself which, without defeating the law of either of those forces, should
merely alter their proportion to one another (such as the shock of some
solid body, or even the accumulating effect of the resistance of the
medium in which astronomers have been led to surmise that the motions of
the heavenly bodies take place), the elliptical motion might be changed
into a motion in some other conic section; and the complex law, that the
planetary motions take place in ellipses, would be deprived of its
universality, though the discovery would not at all detract from the
universality of the simpler laws into which that complex law is resolved.
The law, in short, of each of the concurrent causes remains the same,
however their collocations may vary; but the law of their joint effect
varies with every difference in the collocations. There needs no more to
show how much more general the elementary laws must be than any of the
complex laws which are derived from them.

§ 5. Besides the two modes which have been treated of, there is a third
mode in which laws are resolved into one another; and in this it is
self-evident that they are resolved into laws more general than
themselves. This third mode is the _subsumption_ (as it has been called)
of one law under another; or (what comes to the same thing) the gathering
up of several laws into one more general law which includes them all. The
most splendid example of this operation was when terrestrial gravity and
the central force of the solar system were brought together under the
general law of gravitation. It had been proved antecedently that the earth
and the other planets tend to the sun; and it had been known from the
earliest times that terrestrial bodies tend toward the earth. These were
similar phenomena; and to enable them both to be subsumed under one law,
it was only necessary to prove that, as the effects were similar in
quality so also they, as to quantity, conform to the same rules. This was
first shown to be true of the moon, which agreed with terrestrial objects
not only in tending to a centre, but in the fact that this centre was the
earth. The tendency of the moon toward the earth being ascertained to vary
as the inverse square of the distance, it was deduced from this, by direct
calculation, that if the moon were as near to the earth as terrestrial
objects are, and the acquired force in the direction of the tangent were
suspended, the moon would fall toward the earth through exactly as many
feet in a second as those objects do by virtue of their weight. Hence the
inference was irresistible, that the moon also tends to the earth by
virtue of its weight: and that the two phenomena, the tendency of the moon
to the earth and the tendency of terrestrial objects to the earth, being
not only similar in quality, but, when in the same circumstances,
identical in quantity, are cases of one and the same law of causation. But
the tendency of the moon to the earth, and the tendency of the earth and
planets to the sun, were already known to be cases of the same law of
causation; and thus the law of all these tendencies, and the law of
terrestrial gravity, were recognized as identical, and were subsumed under
one general law, that of gravitation.

In a similar manner, the laws of magnetic phenomena have more recently
been subsumed under known laws of electricity. It is thus that the most
general laws of nature are usually arrived at: we mount to them by
successive steps. For, to arrive by correct induction at laws which hold
under such an immense variety of circumstances, laws so general as to be
independent of any varieties of space or time which we are able to
observe, requires for the most part many distinct sets of experiments or
observations, conducted at different times and by different people. One
part of the law is first ascertained, afterward another part: one set of
observations teaches us that the law holds good under some conditions,
another that it holds good under other conditions, by combining which
observations we find that it holds good under conditions much more
general, or even universally. The general law, in this case, is literally
the sum of all the partial ones; it is a recognition of the same sequence
in different sets of instances; and may, in fact, be regarded as merely
one step in the process of elimination. The tendency of bodies toward one
another, which we now call gravity, had at first been observed only on the
earth’s surface, where it manifested itself only as a tendency of all
bodies toward the earth, and might, therefore, be ascribed to a peculiar
property of the earth itself: one of the circumstances, namely, the
proximity of the earth, had not been eliminated. To eliminate this
circumstance required a fresh set of instances in other parts of the
universe: these we could not ourselves create; and though nature had
created them for us, we were placed in very unfavorable circumstances for
observing them. To make these observations, fell naturally to the lot of a
different set of persons from those who studied terrestrial phenomena; and
had, indeed, been a matter of great interest at a time when the idea of
explaining celestial facts by terrestrial laws was looked upon as the
confounding of an indefeasible distinction. When, however, the celestial
motions were accurately ascertained, and the deductive processes
performed, from which it appeared that their laws and those of terrestrial
gravity corresponded, those celestial observations became a set of
instances which exactly eliminated the circumstance of proximity to the
earth; and proved that in the original case, that of terrestrial objects,
it was not the earth, as such, that caused the motion or the pressure, but
the circumstance common to that case with the celestial instances, namely,
the presence of some great body within certain limits of distance.

§ 6. There are, then, three modes of explaining laws of causation, or,
which is the same thing, resolving them into other laws. First, when the
law of an effect of combined causes is resolved into the separate laws of
the causes, together with the fact of their combination. Secondly, when
the law which connects any two links, not proximate, in a chain of
causation, is resolved into the laws which connect each with the
intermediate links. Both of these are cases of resolving one law into two
or more; in the third, two or more are resolved into one: when, after the
law has been shown to hold good in several different classes of cases, we
decide that what is true in each of these classes of cases, is true under
some more general supposition, consisting of what all those classes of
cases have in common. We may here remark that this last operation involves
none of the uncertainties attendant on induction by the Method of
Agreement, since we need not suppose the result to be extended by way of
inference to any new class of cases different from those by the comparison
of which it was engendered.

In all these three processes, laws are, as we have seen, resolved into
laws more general than themselves; laws extending to all the cases which
the former extended to, and others besides. In the first two modes they
are also resolved into laws more certain, in other words, more universally
true than themselves; they are, in fact, proved not to be themselves laws
of nature, the character of which is to be universally true, but _results_
of laws of nature, which may be only true conditionally, and for the most
part. No difference of this sort exists in the third case; since here the
partial laws are, in fact, the very same law as the general one, and any
exception to them would be an exception to it too.

By all the three processes, the range of deductive science is extended;
since the laws, thus resolved, may be thenceforth deduced demonstratively
from the laws into which they are resolved. As already remarked, the same
deductive process which proves a law or fact of causation if unknown,
serves to explain it when known.

The word explanation is here used in its philosophical sense. What is
called explaining one law of nature by another, is but substituting one
mystery for another; and does nothing to render the general course of
nature other than mysterious: we can no more assign a _why_ for the more
extensive laws than for the partial ones. The explanation may substitute a
mystery which has become familiar, and has grown to _seem_ not mysterious,
for one which is still strange. And this is the meaning of explanation, in
common parlance. But the process with which we are here concerned often
does the very contrary: it resolves a phenomenon with which we are
familiar into one of which we previously knew little or nothing; as when
the common fact of the fall of heavy bodies was resolved into the tendency
of all particles of matter toward one another. It must be kept constantly
in view, therefore, that in science, those who speak of explaining any
phenomenon mean (or should mean) pointing out not some more familiar, but
merely some more general, phenomenon, of which it is a partial
exemplification; or some laws of causation which produce it by their joint
or successive action, and from which, therefore, its conditions may be
determined deductively. Every such operation brings us a step nearer
toward answering the question which was stated in a previous chapter as
comprehending the whole problem of the investigation of nature, viz.: what
are the fewest assumptions, which being granted, the order of nature as it
exists would be the result? What are the fewest, general propositions from
which all the uniformities existing in nature could be deduced?

The laws, thus explained or resolved, are sometimes said to be _accounted
for_; but the expression is incorrect, if taken to mean any thing more
than what has been already stated. In minds not habituated to accurate
thinking, there is often a confused notion that the general laws are the
_causes_ of the partial ones; that the law of general gravitation, for
example, causes the phenomenon of the fall of bodies to the earth. But to
assert this would be a misuse of the word cause: terrestrial gravity is
not an effect of general gravitation, but a _case_ of it; that is, one
kind of the particular instances in which that general law obtains. To
account for a law of nature means, and can mean, nothing more than to
assign other laws more general, together with collocations, which laws and
collocations being supposed, the partial law follows without any
additional supposition.



                              Chapter XIII.


Miscellaneous Examples Of The Explanation Of Laws Of Nature.


§ 1. The most striking example which the history of science presents, of
the explanation of laws of causation and other uniformities of sequence
among special phenomena, by resolving them into laws of greater simplicity
and generality, is the great Newtonian generalization; respecting which
typical instance, so much having already been said, it is sufficient to
call attention to the great number and variety of the special observed
uniformities, which are in this case accounted for, either as particular
cases, or as consequences, of one very simple law of universal nature. The
simple fact of a tendency of every particle of matter toward every other
particle, varying inversely as the square of the distance, explains the
fall of bodies to the earth, the revolutions of the planets and
satellites, the motions (so far as known) of comets, and all the various
regularities which have been observed in these special phenomena; such as
the elliptical orbits, and the variations from exact ellipses; the
relation between the solar distances of the planets and the duration of
their revolutions; the precession of the equinoxes; the tides, and a vast
number of minor astronomical truths.

Mention has also been made in the preceding chapter of the explanation of
the phenomena of magnetism from laws of electricity; the special laws of
magnetic agency having been affiliated by deduction to observed laws of
electric action, in which they have ever since been considered to be
included as special cases. An example not so complete in itself, but even
more fertile in consequences, having been the starting-point of the really
scientific study of physiology, is the affiliation, commenced by Bichat,
and carried on by subsequent biologists, of the properties of the bodily
organs, to the elementary properties of the tissues into which they are
anatomically decomposed.

Another striking instance is afforded by Dalton’s generalization, commonly
known as the atomic theory. It had been known from the very commencement
of accurate chemical observation, that any two bodies combine chemically
with one another in only a certain number of proportions; but those
proportions were in each case expressed by a percentage—so many parts (by
weight) of each ingredient, in 100 of the compound (say 35 and a fraction
of one element, 64 and a fraction of the other); in which mode of
statement no relation was perceived between the proportion in which a
given element combines with one substance, and that in which it combines
with others. The great step made by Dalton consisted in perceiving that a
unit of weight might be established for each substance, such that by
supposing the substance to enter into all its combinations in the ratio
either of that unit, or of some low multiple of that unit, all the
different proportions, previously expressed by percentages, were found to
result. Thus 1 being assumed as the unit of hydrogen, if 8 were then taken
as that of oxygen, the combination of one unit of hydrogen with one unit
of oxygen would produce the exact proportion of weight between the two
substances which is known to exist in water; the combination of one unit
of hydrogen with two units of oxygen would produce the proportion which
exists in the other compound of the same two elements, called peroxide of
hydrogen; and the combinations of hydrogen and of oxygen with all other
substances, would correspond with the supposition that those elements
enter into combination by single units, or twos, or threes, of the numbers
assigned to them, 1 and 8, and the other substances by ones or twos or
threes of other determinate numbers proper to each. The result is that a
table of the equivalent numbers, or, as they are called, atomic weights,
of all the elementary substances, comprises in itself, and scientifically
explains, all the proportions in which any substance, elementary or
compound, is found capable of entering into chemical combination with any
other substance whatever.

§ 2. Some interesting cases of the explanation of old uniformities by
newly ascertained laws are afforded by the researches of Professor Graham.
That eminent chemist was the first who drew attention to the distinction
which may be made of all substances into two classes, termed by him
crystalloids and colloids; or rather, of all states of matter into the
crystalloid and the colloidal states, for many substances are capable of
existing in either. When in the colloidal state, their sensible properties
are very different from those of the same substance when crystallized, or
when in a state easily susceptible of crystallization. Colloid substances
pass with extreme difficulty and slowness into the crystalline state, and
are extremely inert in all the ordinary chemical relations. Substances in
the colloid state are almost always, when combined with water, more or
less viscous or gelatinous. The most prominent examples of the state are
certain animal and vegetable substances, particularly gelatine, albumen,
starch, the gums, caramel, tannin, and some others. Among substances not
of organic origin, the most notable instances are hydrated silicic acid,
and hydrated alumina, with other metallic peroxides of the aluminous
class.

Now it is found, that while colloidal substances are easily penetrated by
water, and by the solutions of crystalloid substances, they are very
little penetrable by one another: which enabled Professor Graham to
introduce a highly effective process (termed dialysis) for separating the
crystalloid substances contained in any liquid mixture, by passing them
through a thin septum of colloidal matter, which does not suffer any thing
colloidal to pass, or suffers it only in very minute quantity. This
property of colloids enabled Mr. Graham to account for a number of special
results of observation, not previously explained.

For instance, “while soluble crystalloids are always highly sapid, soluble
colloids are singularly insipid,” as might be expected; for, as the
sentient extremities of the nerves of the palate “are probably protected
by a colloidal membrane,” impermeable to other colloids, a colloid, when
tasted, probably never reaches those nerves. Again, “it has been observed
that vegetable gum is not digested in the stomach; the coats of that organ
dialyse the soluble food, absorbing crystalloids, and rejecting all
colloids.” One of the mysterious processes accompanying digestion, the
secretion of free muriatic acid by the coats of the stomach, obtains a
probable hypothetical explanation through the same law. Finally, much
light is thrown upon the observed phenomena of osmose (the passage of
fluids outward and inward through animal membranes) by the fact that the
membranes are colloidal. In consequence, the water and saline solutions
contained in the animal body pass easily and rapidly through the
membranes, while the substances directly applicable to nutrition, which
are mostly colloidal, are detained by them.(154)

The property which salt possesses of preserving animal substances from
putrefaction is resolved by Liebig into two more general laws, the strong
attraction of salt for water, and the necessity of the presence of water
as a condition of putrefaction. The intermediate phenomenon which is
interpolated between the remote cause and the effect, can here be not
merely inferred but seen; for it is a familiar fact, that flesh upon which
salt has been thrown is speedily found swimming in brine.

The second of the two factors (as they may be termed) into which the
preceding law has been resolved, the necessity of water to putrefaction,
itself affords an additional example of the Resolution of Laws. The law
itself is proved by the Method of Difference, since flesh completely dried
and kept in a dry atmosphere does not putrefy; as we see in the case of
dried provisions and human bodies in very dry climates. A deductive
explanation of this same law results from Liebig’s speculations. The
putrefaction of animal and other azotized bodies is a chemical process, by
which they are gradually dissipated in a gaseous form, chiefly in that of
carbonic acid and ammonia; now to convert the carbon of the animal
substance into carbonic acid requires oxygen, and to convert the azote
into ammonia requires hydrogen, which are the elements of water. The
extreme rapidity of the putrefaction of azotized substances, compared with
the gradual decay of non-azotized bodies (such as wood and the like) by
the action of oxygen alone, he explains from the general law that
substances are much more easily decomposed by the action of two different
affinities upon two of their elements than by the action of only one.

§ 3. Among the many important properties of the nervous system which have
either been first discovered or strikingly illustrated by Dr.
Brown-Séquard, I select the reflex influence of the nervous system on
nutrition and secretion. By reflex nervous action is meant, action which
one part of the nervous system exerts over another part, without any
intermediate action on the brain, and consequently without consciousness;
or which, if it does pass through the brain, at least produces its effects
independently of the will. There are many experiments which prove that
irritation of a nerve in one part of the body may in this manner excite
powerful action in another part; for example, food injected into the
stomach through a divided œsophagus, nevertheless produces secretion of
saliva; warm water injected into the bowels, and various other irritations
of the lower intestines, have been found to excite secretion of the
gastric juice, and so forth. The reality of the power being thus proved,
its agency explains a great variety of apparently anomalous phenomena; of
which I select the following from Dr. Brown-Séquard’s _Lectures on the
Nervous System_:

The production of tears by irritation of the eye, or of the mucous
membrane of the nose;

The secretions of the eye and nose increased by exposure of other parts of
the body to cold;

Inflammation of the eye, especially when of traumatic origin, very
frequently excites a similar affection in the other eye, which may be
cured by section of the intervening nerve;

Loss of sight sometimes produced by neuralgia, and has been known to be at
once cured by the extirpation (for instance) of a carious tooth;

Even cataract has been produced in a healthy eye by cataract in the other
eye, or by neuralgia, or by a wound of the frontal nerve;

The well-known phenomenon of a sudden stoppage of the heart’s action, and
consequent death, produced by irritation of some of the nervous
extremities; _e.g._, by drinking very cold water, or by a blow on the
abdomen, or other sudden excitation of the abdominal sympathetic nerve,
though this nerve may be irritated to any extent without stopping the
heart’s action, if a section be made of the communicating nerves;

The extraordinary effects produced on the internal organs by an extensive
burn on the surface of the body, consisting in violent inflammation of the
tissues of the abdomen, chest, or head, which, when death ensues from this
kind of injury, is one of the most frequent causes of it;

Paralysis and anæsthesia of one part of the body from neuralgia in another
part; and muscular atrophy from neuralgia, even when there is no
paralysis;

Tetanus produced by the lesion of a nerve. Dr. Brown-Séquard thinks it
highly probable that hydrophobia is a phenomenon of a similar nature;

Morbid changes in the nutrition of the brain and spinal cord, manifesting
themselves by epilepsy, chorea, hysteria, and other diseases, occasioned
by lesion of some of the nervous extremities in remote places, as by
worms, calculi, tumors, carious bones, and in some cases even by very
slight irritations of the skin.

§ 4. From the foregoing and similar instances, we may see the importance,
when a law of nature previously unknown has been brought to light, or when
new light has been thrown upon a known law by experiment, of examining all
cases which present the conditions necessary for bringing that law into
action; a process fertile in demonstrations of special laws previously
unsuspected, and explanations of others already empirically known.

For instance, Faraday discovered by experiment, that voltaic electricity
could be evolved from a natural magnet, provided a conducting body were
set in motion at right angles to the direction of the magnet; and this he
found to hold not only of small magnets, but of that great magnet, the
earth. The law being thus established experimentally, that electricity is
evolved, by a magnet, and a conductor moving at right angles to the
direction of its poles, we may now look out for fresh instances in which
these conditions meet. Wherever a conductor moves or revolves at right
angles to the direction of the earth’s magnetic poles, there we may expect
an evolution of electricity. In the northern regions, where the polar
direction is nearly perpendicular to the horizon, all horizontal motions
of conductors will produce electricity; horizontal wheels, for example,
made of metal; likewise all running streams will evolve a current of
electricity, which will circulate round them; and the air thus charged
with electricity may be one of the causes of the Aurora Borealis. In the
equatorial regions, on the contrary, upright wheels placed parallel to the
equator will originate a voltaic circuit, and water-falls will naturally
become electric.

For a second example, it has been proved, chiefly by the researches of
Professor Graham, that gases have a strong tendency to permeate animal
membranes, and diffuse themselves through the spaces which such membranes
inclose, notwithstanding the presence of other gases in those spaces.
Proceeding from this general law, and reviewing a variety of cases in
which gases lie contiguous to membranes, we are enabled to demonstrate or
to explain the following more special laws: 1st. The human or animal body,
when surrounded with any gas not already contained within the body,
absorbs it rapidly; such, for instance, as the gases of putrefying
matters: which helps to explain malaria. 2d. The carbonic acid gas of
effervescing drinks, evolved in the stomach, permeates its membranes, and
rapidly spreads through the system. 3d. Alcohol taken into the stomach
passes into vapor, and spreads through the system with great rapidity
(which, combined with the high combustibility of alcohol, or in other
words its ready combination with oxygen, may perhaps help to explain the
bodily warmth immediately consequent on drinking spirituous liquors). 4th.
In any state of the body in which peculiar gases are formed within it,
these will rapidly exhale through all parts of the body; and hence the
rapidity with which, in certain states of disease, the surrounding
atmosphere becomes tainted. 5th. The putrefaction of the interior parts of
a carcass will proceed as rapidly as that of the exterior, from the ready
passage outward of the gaseous products. 6th. The exchange of oxygen and
carbonic acid in the lungs is not prevented, but rather promoted, by the
intervention of the membrane of the lungs and the coats of the
blood-vessels between the blood and the air. It is necessary, however,
that there should be a substance in the blood with which the oxygen of the
air may immediately combine; otherwise, instead of passing into the blood,
it would permeate the whole organism: and it is necessary that the
carbonic acid, as it is formed in the capillaries, should also find a
substance in the blood with which it can combine; otherwise it would leave
the body at all points, instead of being discharged through the lungs.

§ 5. The following is a deduction which confirms, by explaining, the
empirical generalization, that soda powders weaken the human system. These
powders, consisting of a mixture of tartaric acid with bicarbonate of
soda, from which the carbonic acid is set free, must pass into the stomach
as tartrate of soda. Now, neutral tartrates, citrates, and acetates of the
alkalis are found, in their passage through the system, to be changed into
carbonates; and to convert a tartrate into a carbonate requires an
additional quantity of oxygen, the abstraction of which must lessen the
oxygen destined for assimilation with the blood, on the quantity of which
the vigorous action of the human system partly depends.

The instances of new theories agreeing with and explaining old
empiricisms, are innumerable. All the just remarks made by experienced
persons on human character and conduct, are so many special laws, which
the general laws of the human mind explain and resolve. The empirical
generalizations on which the operations of the arts have usually been
founded, are continually justified and confirmed on the one hand, or
corrected and improved on the other, by the discovery of the simpler
scientific laws on which the efficacy of those operations depends. The
effects of the rotation of crops, of the various manures, and other
processes of improved agriculture, have been for the first time resolved
in our own day into known laws of chemical and organic action, by Davy,
Liebig, and others. The processes of the medical art are even now mostly
empirical: their efficacy is concluded, in each instance, from a special
and most precarious experimental generalization: but as science advances
in discovering the simple laws of chemistry and physiology, progress is
made in ascertaining the intermediate links in the series of phenomena,
and the more general laws on which they depend; and thus, while the old
processes are either exploded, or their efficacy, in so far as real,
explained, better processes, founded on the knowledge of proximate causes,
are continually suggested and brought into use.(155) Many even of the
truths of geometry were generalizations from experience before they were
deduced from first principles. The quadrature of the cycloid is said to
have been first effected by measurement, or rather by weighing a cycloidal
card, and comparing its weight with that of a piece of similar card of
known dimensions.

§ 6. To the foregoing examples from physical science, let us add another
from mental. The following is one of the simple laws of mind: Ideas of a
pleasurable or painful character form associations more easily and
strongly than other ideas, that is, they become associated after fewer
repetitions, and the association is more durable. This is an experimental
law, grounded on the Method of Difference. By deduction from this law,
many of the more special laws which experience shows to exist among
particular mental phenomena may be demonstrated and explained: the ease
and rapidity, for instance, with which thoughts connected with our
passions or our more cherished interests are excited, and the firm hold
which the facts relating to them have on our memory; the vivid
recollection we retain of minute circumstances which accompanied any
object or event that deeply interested us, and of the times and places in
which we have been very happy or very miserable; the horror with which we
view the accidental instrument of any occurrence which shocked us, or the
locality where it took place and the pleasure we derive from any memorial
of past enjoyment; all these effects being proportional to the sensibility
of the individual mind, and to the consequent intensity of the pain or
pleasure from which the association originated. It has been suggested by
the able writer of a biographical sketch of Dr. Priestley in a monthly
periodical,(156) that the same elementary law of our mental constitution,
suitably followed out, would explain a variety of mental phenomena
previously inexplicable, and in particular some of the fundamental
diversities of human character and genius. Associations being of two
sorts, either between synchronous, or between successive impressions; and
the influence of the law which renders associations stronger in proportion
to the pleasurable or painful character of the impressions, being felt
with peculiar force in the synchronous class of associations; it is
remarked by the writer referred to, that in minds of strong organic
sensibility synchronous associations will be likely to predominate,
producing a tendency to conceive things in pictures and in the concrete,
richly clothed in attributes and circumstances, a mental habit which is
commonly called Imagination, and is one of the peculiarities of the
painter and the poet; while persons of more moderate susceptibility to
pleasure and pain will have a tendency to associate facts chiefly in the
order of their succession, and such persons, if they possess mental
superiority, will addict themselves to history or science rather than to
creative art. This interesting speculation the author of the present work
has endeavored, on another occasion, to pursue further, and to examine how
far it will avail toward explaining the peculiarities of the poetical
temperament.(157) It is at least an example which may serve, instead of
many others, to show the extensive scope which exists for deductive
investigation in the important and hitherto so imperfect Science of Mind.

§ 7. The copiousness with which the discovery and explanation of special
laws of phenomena by deduction from simpler and more general ones has here
been exemplified, was prompted by a desire to characterize clearly, and
place in its due position of importance, the Deductive Method; which, in
the present state of knowledge, is destined henceforth irrevocably to
predominate in the course of scientific investigation. A revolution is
peaceably and progressively effecting itself in philosophy, the reverse of
that to which Bacon has attached his name. That great man changed the
method of the sciences from deductive to experimental, and it is now
rapidly reverting from experimental to deductive. But the deductions which
Bacon abolished were from premises hastily snatched up, or arbitrarily
assumed. The principles were neither established by legitimate canons of
experimental inquiry, nor the results tested by that indispensable element
of a rational Deductive Method, verification by specific experience.
Between the primitive method of Deduction and that which I have attempted
to characterize, there is all the difference which exists between the
Aristotelian physics and the Newtonian theory of the heavens.

It would, however, be a mistake to expect that those great
generalizations, from which the subordinate truths of the more backward
sciences will probably at some future period be deduced by reasoning (as
the truths of astronomy are deduced from the generalities of the Newtonian
theory), will be found in all, or even in most cases, among truths now
known and admitted. We may rest assured, that many of the most general
laws of nature are as yet entirely unthought of; and that many others,
destined hereafter to assume the same character, are known, if at all,
only as laws or properties of some limited class of phenomena; just as
electricity, now recognized as one of the most universal of natural
agencies, was once known only as a curious property which certain
substances acquired by friction, of first attracting and then repelling
light bodies. If the theories of heat, cohesion, crystallization, and
chemical action are destined, as there can be little doubt that they are,
to become deductive, the truths which will then be regarded as the
_principia_ of those sciences would probably, if now announced, appear
quite as novel(158) as the law of gravitation appeared to the
contemporaries of Newton; possibly even more so, since Newton’s law, after
all, was but an extension of the law of weight—that is, of a
generalization familiar from of old, and which already comprehended a not
inconsiderable body of natural phenomena. The general laws of a similarly
commanding character, which we still look forward to the discovery of, may
not always find so much of their foundations already laid.

These general truths will doubtless make their first appearance in the
character of hypotheses; not proved, nor even admitting of proof, in the
first instance, but assumed as premises for the purpose of deducing from
them the known laws of concrete phenomena. But this, though their initial,
can not be their final state. To entitle an hypothesis to be received as
one of the truths of nature, and not as a mere technical help to the human
faculties, it must be capable of being tested by the canons of legitimate
induction, and must actually have been submitted to that test. When this
shall have been done, and done successfully, premises will have been
obtained from which all the other propositions of the science will
thenceforth be presented as conclusions, and the science will, by means of
a new and unexpected Induction, be rendered Deductive.



                               Chapter XIV.


Of The Limits To The Explanation Of Laws Of Nature; And Of Hypotheses.


§ 1. The preceding considerations have led us to recognize a distinction
between two kinds of laws, or observed uniformities in nature: ultimate
laws, and what may be termed derivative laws. Derivative laws are such as
are deducible from, and may, in any of the modes which we have pointed
out, be resolved into, other and more general ones. Ultimate laws are
those which can not. We are not sure that any of the uniformities with
which we are yet acquainted are ultimate laws; but we know that there must
be ultimate laws; and that every resolution of a derivative law into more
general laws brings us nearer to them.

Since we are continually discovering that uniformities, not previously
known to be other than ultimate, are derivative, and resolvable into more
general laws; since (in other words) we are continually discovering the
explanation of some sequence which was previously known only as a fact; it
becomes an interesting question whether there are any necessary limits to
this philosophical operation, or whether it may proceed until all the
uniform sequences in nature are resolved into some one universal law. For
this seems, at first sight, to be the ultimatum toward which the progress
of induction by the Deductive Method, resting on a basis of observation
and experiment, is tending. Projects of this kind were universal in the
infancy of philosophy; any speculations which held out a less brilliant
prospect being in these early times deemed not worth pursuing. And the
idea receives so much apparent countenance from the nature of the most
remarkable achievements of modern science, that speculators are even now
frequently appearing, who profess either to have solved the problem, or to
suggest modes in which it may one day be solved. Even where pretensions of
this magnitude are not made, the character of the solutions which are
given or sought of particular classes of phenomena, often involves such
conceptions of what constitutes explanation, as would render the notion of
explaining all phenomena whatever by means of some one cause or law,
perfectly admissible.

§ 2. It is, therefore, useful to remark that the ultimate Laws of Nature
can not possibly be less numerous than the distinguishable sensations or
other feelings of our nature; those, I mean, which are distinguishable
from one another in quality, and not merely in quantity or degree. For
example: since there is a phenomenon _sui generis_, called color, which
our consciousness testifies to be not a particular degree of some other
phenomenon, as heat or odor or motion, but intrinsically unlike all
others, it follows that there are ultimate laws of color; that though the
facts of color may admit of explanation, they never can be explained from
laws of heat or odor alone, or of motion alone, but that, however far the
explanation may be carried, there will always remain in it a law of color.
I do not mean that it might not possibly be shown that some other
phenomenon, some chemical or mechanical action, for example, invariably
precedes, and is the cause of, every phenomenon of color. But though this,
if proved, would be an important extension of our knowledge of nature, it
would not explain how or why a motion, or a chemical action, can produce a
sensation of color; and, however diligent might be our scrutiny of the
phenomena, whatever number of hidden links we might detect in the chain of
causation terminating in the color, the last link would still be a law of
color, not a law of motion, nor of any other phenomenon whatever. Nor does
this observation apply only to color, as compared with any other of the
great classes of sensations; it applies to every particular color, as
compared with others. White color can in no manner be explained
exclusively by the laws of the production of red color. In any attempt to
explain it, we can not but introduce, as one element of the explanation,
the proposition that some antecedent or other produces the sensation of
white.

The ideal limit, therefore, of the explanation of natural phenomena
(toward which as toward other ideal limits we are constantly tending,
without the prospect of ever completely attaining it) would be to show
that each distinguishable variety of our sensations, or other states of
consciousness, has only one sort of cause; that, for example, whenever we
perceive a white color, there is some one condition or set of conditions
which is always present, and the presence of which always produces in us
that sensation. As long as there are several known modes of production of
a phenomenon (several different substances, for instance, which have the
property of whiteness, and between which we can not trace any other
resemblance) so long it is not impossible that one of these modes of
production may be resolved into another, or that all of them may be
resolved into some more general mode of production not hitherto
recognized. But when the modes of production are reduced to one, we can
not, in point of simplification, go any further. This one may not, after
all, be the ultimate mode; there may be other links to be discovered
between the supposed cause and the effect; but we can only further resolve
the known law, by introducing some other law hitherto unknown, which will
not diminish the number of ultimate laws.

In what cases, accordingly, has science been most successful in explaining
phenomena, by resolving their complex laws into laws of greater simplicity
and generality? Hitherto chiefly in cases of the propagation of various
phenomena through space; and, first and principally, the most extensive
and important of all facts of that description, mechanical motion. Now
this is exactly what might be expected from the principles here laid down.
Not only is motion one of the most universal of all phenomena, it is also
(as might be expected from that circumstance) one of those which,
apparently at least, are produced in the greatest number of ways; but the
phenomenon itself is always, to our sensations, the same in every respect
but degree. Differences of duration or of velocity, are evidently
differences in degree only; and differences of direction in space, which
alone has any semblance of being a distinction in kind, entirely disappear
(so far as our sensations are concerned) by a change in our own position;
indeed, the very same motion appears to us, according to our position, to
take place in every variety of direction, and motions in every different
direction to take place in the same. And again, motion in a straight line
and in a curve are no otherwise distinct than that the one is motion
continuing in the same direction, the other is motion which at each
instant changes its direction. There is, therefore, according to the
principles I have stated, no absurdity in supposing that all motion may be
produced in one and the same way, by the same kind of cause. Accordingly,
the greatest achievements in physical science have consisted in resolving
one observed law of the production of motion into the laws of other known
modes of production, or the laws of several such modes into one more
general mode; as when the fall of bodies to the earth, and the motions of
the planets, were brought under the one law of the mutual attraction of
all particles of matter; when the motions said to be produced by magnetism
were shown to be produced by electricity; when the motions of fluids in a
lateral direction, or even contrary to the direction of gravity, were
shown to be produced by gravity; and the like. There is an abundance of
distinct causes of motion still unresolved into one another: gravitation,
heat, electricity, chemical action, nervous action, and so forth; but
whether the efforts of the present generation of savants to resolve all
these different modes of production into one are ultimately successful or
not, the attempt so to resolve them is perfectly legitimate. For, though
these various causes produce, in other respects, sensations intrinsically
different, and are not, therefore, capable of being resolved into one
another, yet, in so far as they all produce motion, it is quite possible
that the immediate antecedent of the motion may in all these different
cases be the same; nor is it impossible that these various agencies
themselves may, as the new doctrines assert, all of them have for their
own immediate antecedent modes of molecular motion.

We need not extend our illustration to other cases, as, for instance, to
the propagation of light, sound, heat, electricity, etc., through space,
or any of the other phenomena which have been found susceptible of
explanation by the resolution of their observed laws into more general
laws. Enough has been said to display the difference between the kind of
explanation and resolution of laws which is chimerical, and that of which
the accomplishment is the great aim of science; and to show into what sort
of elements the resolution must be effected, if at all.(159)

§ 3. As, however, there is scarcely any one of the principles of a true
method of philosophizing which does not require to be guarded against
errors on both sides, I must enter a caveat against another
misapprehension, of a kind directly contrary to the preceding. M. Comte,
among other occasions on which he has condemned, with some asperity, any
attempt to explain phenomena which are “evidently primordial” (meaning,
apparently, no more than that every peculiar phenomenon must have at least
one peculiar and therefore inexplicable law), has spoken of the attempt to
furnish any explanation of the color belonging to each substance, “la
couleur élémentaire propre à chaque substance,” as essentially illusory.
“No one,” says he, “in our time attempts to explain the particular
specific gravity of each substance or of each structure. Why should it be
otherwise as to the specific color, the notion of which is undoubtedly no
less primordial?”(160)

Now although, as he elsewhere observes, a color must always remain a
different thing from a weight or a sound, varieties of color might
nevertheless follow, or correspond to, given varieties of weight, or
sound, or some other phenomenon as different as these are from color
itself. It is one question what a thing is, and another what it depends
on; and though to ascertain the conditions of an elementary phenomenon is
not to obtain any new insight into the nature of the phenomenon itself,
that is no reason against attempting to discover the conditions. The
interdict against endeavoring to reduce distinctions of color to any
common principle, would have held equally good against a like attempt on
the subject of distinctions of sound; which nevertheless have been found
to be immediately preceded and caused by distinguishable varieties in the
vibrations of elastic bodies; though a sound, no doubt, is quite as
different as a color is from any motion of particles, vibratory or
otherwise. We might add, that, in the case of colors, there are strong
positive indications that they are not ultimate properties of the
different kinds of substances, but depend on conditions capable of being
superinduced upon all substances; since there is no substance which can
not, according to the kind of light thrown upon it, be made to assume
almost any color; and since almost every change in the mode of aggregation
of the particles of the same substance is attended with alterations in its
color, and in its optical properties generally.

The really weak point in the attempts which have been made to account for
colors by the vibrations of a fluid, is not that the attempt itself is
unphilosophical, but that the existence of the fluid, and the fact of its
vibratory motion, are not proved, but are assumed, on no other ground than
the facility they are supposed to afford of explaining the phenomena. And
this consideration leads to the important question of the proper use of
scientific hypotheses, the connection of which with the subject of the
explanation of the phenomena of nature, and of the necessary limits to
that explanation, need not be pointed out.

§ 4. An hypothesis is any supposition which we make (either without actual
evidence, or on evidence avowedly insufficient) in order to endeavor to
deduce from it conclusions in accordance with facts which are known to be
real; under the idea that if the conclusions to which the hypothesis leads
are known truths, the hypothesis itself either must be, or at least is
likely to be, true. If the hypothesis relates to the cause or mode of
production of a phenomenon, it will serve, if admitted, to explain such
facts as are found capable of being deduced from it. And this explanation
is the purpose of many, if not most hypotheses. Since explaining, in the
scientific sense, means resolving a uniformity which is not a law of
causation, into the laws of causation from which it results, or a complex
law of causation into simpler and more general ones from which it is
capable of being deductively inferred, if there do not exist any known
laws which fulfill this requirement, we may feign or imagine some which
would fulfill it; and this is making an hypothesis.

An hypothesis being a mere supposition, there are no other limits to
hypotheses than those of the human imagination; we may, if we please,
imagine, by way of accounting for an effect, some cause of a kind utterly
unknown, and acting according to a law altogether fictitious. But as
hypotheses of this sort would not have any of the plausibility belonging
to those which ally themselves by analogy with known laws of nature, and
besides would not supply the want which arbitrary hypotheses are generally
invented to satisfy, by enabling the imagination to represent to itself an
obscure phenomenon in a familiar light, there is probably no hypothesis in
the history of science in which both the agent itself and the law of its
operation were fictitious. Either the phenomenon assigned as the cause is
real, but the law according to which it acts merely supposed; or the cause
is fictitious, but is supposed to produce its effects according to laws
similar to those of some known class of phenomena. An instance of the
first kind is afforded by the different suppositions made respecting the
law of the planetary central force, anterior to the discovery of the true
law, that the force varies as the inverse square of the distance; which
also suggested itself to Newton, in the first instance, as an hypothesis,
and was verified by proving that it led deductively to Kepler’s laws.
Hypotheses of the second kind are such as the vortices of Descartes, which
were fictitious, but were supposed to obey the known laws of rotatory
motion; or the two rival hypotheses respecting the nature of light, the
one ascribing the phenomena to a fluid emitted from all luminous bodies,
the other (now generally received) attributing them to vibratory motions
among the particles of an ether pervading all space. Of the existence of
either fluid there is no evidence, save the explanation they are
calculated to afford of some of the phenomena; but they are supposed to
produce their effects according to known laws: the ordinary laws of
continued locomotion in the one case, and in the other those of the
propagation of undulatory movements among the particles of an elastic
fluid.

According to the foregoing remarks, hypotheses are invented to enable the
Deductive Method to be earlier applied to phenomena. But(161) in order to
discover the cause of any phenomenon by the Deductive Method, the process
must consist of three parts: induction, ratiocination, and verification.
Induction (the place of which, however, may be supplied by a prior
deduction), to ascertain the laws of the causes; ratiocination, to compute
from those laws how the causes will operate in the particular combination
known to exist in the case in hand; verification, by comparing this
calculated effect with the actual phenomenon. No one of these three parts
of the process can be dispensed with. In the deduction which proves the
identity of gravity with the central force of the solar system, all the
three are found. First, it is proved from the moon’s motions, that the
earth attracts her with a force varying as the inverse square of the
distance. This (though partly dependent on prior deductions) corresponds
to the first, or purely inductive, step: the ascertainment of the law of
the cause. Secondly, from this law, and from the knowledge previously
obtained of the moon’s mean distance from the earth, and of the actual
amount of her deflection from the tangent, it is ascertained with what
rapidity the earth’s attraction would cause the moon to fall, if she were
no further off, and no more acted upon by extraneous forces, than
terrestrial bodies are: that is the second step, the ratiocination.
Finally, this calculated velocity being compared with the observed
velocity with which all heavy bodies fall, by mere gravity, toward the
surface of the earth (sixteen feet in the first second, forty-eight in the
second, and so forth, in the ratio of the odd numbers, 1, 3, 5, etc.), the
two quantities are found to agree. The order in which the steps are here
presented was not that of their discovery; but it is their correct logical
order, as portions of the proof that the same attraction of the earth
which causes the moon’s motion causes also the fall of heavy bodies to the
earth: a proof which is thus complete in all its parts.

Now, the Hypothetical Method suppresses the first of the three steps, the
induction to ascertain the law; and contents itself with the other two
operations, ratiocination and verification; the law which is reasoned from
being assumed instead of proved.

This process may evidently be legitimate on one supposition, namely, if
the nature of the case be such that the final step, the verification,
shall amount to, and fulfill the conditions of, a complete induction. We
want to be assured that the law we have hypothetically assumed is a true
one; and its leading deductively to true results will afford this
assurance, provided the case be such that a false law can not lead to a
true result; provided no law, except the very one which we have assumed,
can lead deductively to the same conclusions which that leads to. And this
proviso is often realized. For example, in the very complete specimen of
deduction which we just cited, the original major premise of the
ratiocination, the law of the attractive force, was ascertained in this
mode; by this legitimate employment of the Hypothetical Method. Newton
began by an assumption that the force which at each instant deflects a
planet from its rectilineal course, and makes it describe a curve round
the sun, is a force tending directly toward the sun. He then proved that
if this be so, the planet will describe, as we know by Kepler’s first law
that it does describe, equal areas in equal times; and, lastly, he proved
that if the force acted in any other direction whatever, the planet would
not describe equal areas in equal times. It being thus shown that no other
hypothesis would accord with the facts, the assumption was proved; the
hypothesis became an inductive truth. Not only did Newton ascertain by
this hypothetical process the direction of the deflecting force; he
proceeded in exactly the same manner to ascertain the law of variation of
the quantity of that force. He assumed that the force varied inversely as
the square of the distance; showed that from this assumption the remaining
two of Kepler’s laws might be deduced; and, finally, that any other law of
variation would give results inconsistent with those laws, and
inconsistent, therefore, with the real motions of the planets, of which
Kepler’s laws were known to be a correct expression.

I have said that in this case the verification fulfills the conditions of
an induction; but an induction of what sort? On examination we find that
it conforms to the canon of the Method of Difference. It affords the two
instances, A B C, _a b c_, and B C, _b c_. A represents central force; A B
C, the planets _plus_ a central force; B C, the planets apart from a
central force. The planets with a central force give _a_, areas
proportional to the times; the planets without a central force give _b c_
(a set of motions) without _a_, or with something else instead of _a_.
This is the Method of Difference in all its strictness. It is true, the
two instances which the method requires are obtained in this case, not by
experiment, but by a prior deduction. But that is of no consequence. It is
immaterial what is the nature of the evidence from which we derive the
assurance that A B C will produce _a b c_, and B C only _b c_; it is
enough that we have that assurance. In the present case, a process of
reasoning furnished Newton with the very instances which, if the nature of
the case had admitted of it, he would have sought by experiment.

It is thus perfectly possible, and indeed is a very common occurrence,
that what was an hypothesis at the beginning of the inquiry becomes a
proved law of nature before its close. But in order that this should
happen, we must be able, either by deduction or experiment, to obtain
_both_ the instances which the Method of Difference requires. That we are
able from the hypothesis to deduce the known facts, gives only the
affirmative instance, A B C, _a b c_. It is equally necessary that we
should be able to obtain, as Newton did, the negative instance B C, _b c_;
by showing that no antecedent, except the one assumed in the hypothesis,
would in conjunction with B C produce _a_.

Now it appears to me that this assurance can not be obtained, when the
cause assumed in the hypothesis is an unknown cause imagined solely to
account for _a_. When we are only seeking to determine the precise law of
a cause already ascertained, or to distinguish the particular agent which
is in fact the cause, among several agents of the same kind, one or other
of which it is already known to be, we may then obtain the negative
instance. An inquiry which of the bodies of the solar system causes by its
attraction some particular irregularity in the orbit or periodic time of
some satellite or comet, would be a case of the second description.
Newton’s was a case of the first. If it had not been previously known that
the planets were hindered from moving in straight lines by some force
tending toward the interior of their orbit, though the exact direction was
doubtful; or if it had not been known that the force increased in some
proportion or other as the distance diminished, and diminished as it
increased, Newton’s argument would not have proved his conclusion. These
facts, however, being already certain, the range of admissible
suppositions was limited to the various possible directions of a line, and
the various possible numerical relations between the variations of the
distance, and the variations of the attractive force. Now among these it
was easily shown that different suppositions could not lead to identical
consequences.

Accordingly, Newton could not have performed his second great scientific
operation: that of identifying terrestrial gravity with the central force
of the solar system by the same hypothetical method. When the law of the
moon’s attraction had been proved from the data of the moon itself, then,
on finding the same law to accord with the phenomena of terrestrial
gravity, he was warranted in adopting it as the law of those phenomena
likewise; but it would not have been allowable for him, without any lunar
data, to assume that the moon was attracted toward the earth with a force
as the inverse square of the distance, merely because that ratio would
enable him to account for terrestrial gravity; for it would have been
impossible for him to prove that the observed law of the fall of heavy
bodies to the earth could not result from any force, save one extending to
the moon, and proportional to the inverse square.

It appears, then, to be a condition of the most genuinely scientific
hypothesis, that it be not destined always to remain an hypothesis, but be
of such a nature as to be either proved or disproved by comparison with
observed facts. This condition is fulfilled when the effect is already
known to depend on the very cause supposed, and the hypothesis relates
only to the precise mode of dependence; the law of the variation of the
effect according to the variations in the quantity or in the relations of
the cause. With these may be classed the hypotheses which do not make any
supposition with regard to causation, but only with regard to the law of
correspondence between facts which accompany each other in their
variations, though there may be no relation of cause and effect between
them. Such were the different false hypotheses which Kepler made
respecting the law of the refraction of light. It was known that the
direction of the line of refraction varied with every variation in the
direction of the line of incidence, but it was not known how; that is,
what changes of the one corresponded to the different changes of the
other. In this case any law different from the true one must have led to
false results. And, lastly, we must add to these all hypothetical modes of
merely representing or _describing_ phenomena; such as the hypothesis of
the ancient astronomers that the heavenly bodies moved in circles; the
various hypotheses of eccentrics, deferents, and epicycles, which were
added to that original hypothesis; the nineteen false hypotheses which
Kepler made and abandoned respecting the form of the planetary orbits; and
even the doctrine in which he finally rested, that those orbits are
ellipses, which was but an hypothesis like the rest until verified by
facts.

In all these cases, verification is proof; if the supposition accords with
the phenomena there needs no other evidence of it. But in order that this
may be the case, I conceive it to be necessary, when the hypothesis
relates to causation, that the supposed cause should not only be a real
phenomenon, something actually existing in nature, but should be already
known to exercise, or at least to be capable of exercising, an influence
of some sort over the effect. In any other case, it is no sufficient
evidence of the truth of the hypothesis that we are able to deduce the
real phenomena from it.

Is it, then, never allowable, in a scientific hypothesis, to assume a
cause, but only to ascribe an assumed law to a known cause? I do not
assert this. I only say, that in the latter case alone can the hypothesis
be received as true merely because it explains the phenomena. In the
former case it may be very useful by suggesting a line of investigation
which may possibly terminate in obtaining real proof. But for this
purpose, as is justly remarked by M. Comte, it is indispensable that the
cause suggested by the hypothesis should be in its own nature susceptible
of being proved by other evidence. This seems to be the philosophical
import of Newton’s maxim, (so often cited with approbation by subsequent
writers), that the cause assigned for any phenomenon must not only be such
as if admitted would explain the phenomenon, but must also be a _vera
causa_. What he meant by a _vera causa_ Newton did not indeed very
explicitly define; and Dr. Whewell, who dissents from the propriety of any
such restriction upon the latitude of framing hypotheses, has had little
difficulty in showing(162) that his conception of it was neither precise
nor consistent with itself; accordingly his optical theory was a signal
instance of the violation of his own rule. It is certainly not necessary
that the cause assigned should be a cause already known; otherwise we
should sacrifice our best opportunities of becoming acquainted with new
causes. But what is true in the maxim is, that the cause, though not known
previously, should be capable of being known thereafter; that its
existence should be capable of being detected, and its connection with the
effect ascribed to it should be susceptible of being proved, by
independent evidence. The hypothesis, by suggesting observations and
experiments, puts us on the road to that independent evidence, if it be
really attainable; and till it be attained, the hypothesis ought only to
count for a more or less plausible conjecture.

§ 5. This function, however, of hypotheses, is one which must be reckoned
absolutely indispensable in science. When Newton said, “Hypotheses non
fingo,” he did not mean that he deprived himself of the facilities of
investigation afforded by assuming in the first instance what he hoped
ultimately to be able to prove. Without such assumptions, science could
never have attained its present state; they are necessary steps in the
progress to something more certain; and nearly every thing which is now
theory was once hypothesis. Even in purely experimental science, some
inducement is necessary for trying one experiment rather than another; and
though it is abstractedly possible that all the experiments which have
been tried, might have been produced by the mere desire to ascertain what
would happen in certain circumstances, without any previous conjecture as
to the result; yet, in point of fact, those unobvious, delicate, and often
cumbrous and tedious processes of experiment, which have thrown most light
upon the general constitution of nature, would hardly ever have been
undertaken by the persons or at the time they were, unless it had seemed
to depend on them whether some general doctrine or theory which had been
suggested, but not yet proved, should be admitted or not. If this be true
even of merely experimental inquiry, the conversion of experimental into
deductive truths could still less have been effected without large
temporary assistance from hypotheses. The process of tracing regularity in
any complicated, and at first sight confused, set of appearances, is
necessarily tentative; we begin by making any supposition, even a false
one, to see what consequences will follow from it; and by observing how
these differ from the real phenomena, we learn what corrections to make in
our assumption. The simplest supposition which accords with the more
obvious facts is the best to begin with; because its consequences are the
most easily traced. This rude hypothesis is then rudely corrected, and the
operation repeated; and the comparison of the consequences deducible from
the corrected hypothesis, with the observed facts, suggests still further
correction, until the deductive results are at last made to tally with the
phenomena. “Some fact is as yet little understood, or some law is unknown;
we frame on the subject an hypothesis as accordant as possible with the
whole of the data already possessed; and the science, being thus enabled
to move forward freely, always ends by leading to new consequences capable
of observation, which either confirm or refute, unequivocally, the first
supposition.” Neither induction nor deduction would enable us to
understand even the simplest phenomena, “if we did not often commence by
anticipating on the results; by making a provisional supposition, at first
essentially conjectural, as to some of the very notions which constitute
the final object of the inquiry.”(163) Let any one watch the manner in
which he himself unravels a complicated mass of evidence; let him observe
how, for instance, he elicits the true history of any occurrence from the
involved statements of one or of many witnesses; he will find that he does
not take all the items of evidence into his mind at once, and attempt to
weave them together; he extemporizes, from a few of the particulars, a
first rude theory of the mode in which the facts took place, and then
looks at the other statements one by one, to try whether they can be
reconciled with that provisional theory, or what alterations or additions
it requires to make it square with them. In this way, which has been
justly compared to the Methods of Approximation of mathematicians, we
arrive, by means of hypotheses, at conclusions not hypothetical.(164)

§ 6. It is perfectly consistent with the spirit of the method, to assume
in this provisional manner not only an hypothesis respecting the law of
what we already know to be the cause, but an hypothesis respecting the
cause itself. It is allowable, useful, and often even necessary, to begin
by asking ourselves what cause _may_ have produced the effect, in order
that we may know in what direction to look out for evidence to determine
whether it actually _did_. The vortices of Descartes would have been a
perfectly legitimate hypothesis, if it had been possible, by any mode of
exploration which we could entertain the hope of ever possessing, to bring
the reality of the vortices, as a fact in nature, conclusively to the test
of observation. The vice of the hypothesis was that it could not lead to
any course of investigation capable of converting it from an hypothesis
into a proved fact. It might chance to be _dis_proved, either by some want
of correspondence with the phenomena it purported to explain, or (as
actually happened) by some extraneous fact. “The free passage of comets
through the spaces in which these vortices should have been, convinced men
that these vortices did not exist.”(165) But the hypothesis would have
been false, though no such direct evidence of its falsity had been
procurable. Direct evidence of its truth there could not be.

The prevailing hypothesis of a luminiferous ether, in other respects not
without analogy to that of Descartes, is not in its own nature entirely
cut off from the possibility of direct evidence in its favor. It is well
known that the difference between the calculated and the observed times of
the periodical return of Encke’s comet, has led to a conjecture that a
medium capable of opposing resistance to motion is diffused through space.
If this surmise should be confirmed, in the course of ages, by the gradual
accumulation of a similar variance in the case of the other bodies of the
solar system, the luminiferous ether would have made a considerable
advance toward the character of a _vera causa_, since the existence would
have been ascertained of a great cosmical agent, possessing some of the
attributes which the hypothesis assumes; though there would still remain
many difficulties, and the identification of the ether with the resisting
medium would even, I imagine, give rise to new ones. At present, however,
this supposition can not be looked upon as more than a conjecture; the
existence of the ether still rests on the possibility of deducing from its
assumed laws a considerable number of actual phenomena; and this evidence
I can not regard as conclusive, because we can not have, in the case of
such an hypothesis, the assurance that if the hypothesis be false it must
lead to results at variance with the true facts.

Accordingly, most thinkers of any degree of sobriety allow that an
hypothesis of this kind is not to be received as probably true because it
accounts for all the known phenomena; since this is a condition sometimes
fulfilled tolerably well by two conflicting hypotheses; while there are
probably many others which are equally possible, but which, for want of
any thing analogous in our experience, our minds are unfitted to conceive.
But it seems to be thought that an hypothesis of the sort in question is
entitled to a more favorable reception, if, besides accounting for all the
facts previously known, it has led to the anticipation and prediction of
others which experience afterward verified; as the undulatory theory of
light led to the prediction, subsequently realized by experiment, that two
luminous rays might meet each other in such a manner as to produce
darkness. Such predictions and their fulfillment are, indeed, well
calculated to impress the uninformed, whose faith in science rests solely
on similar coincidences between its prophecies and what comes to pass. But
it is strange that any considerable stress should be laid upon such a
coincidence by persons of scientific attainments. If the laws of the
propagation of light accord with those of the vibrations of an elastic
fluid in as many respects as is necessary to make the hypothesis afford a
correct expression of all or most of the phenomena known at the time, it
is nothing strange that they should accord with each other in one respect
more. Though twenty such coincidences should occur, they would not prove
the reality of the undulatory ether; it would not follow that the
phenomena of light were results of the laws of elastic fluids, but at most
that they are governed by laws partially identical with these; which, we
may observe, is already certain, from the fact that the hypothesis in
question could be for a moment tenable.(166) Cases may be cited, even in
our imperfect acquaintance with nature, where agencies that we have good
reason to consider as radically distinct produce their effects, or some of
their effects, according to laws which are identical. The law, for
example, of the inverse square of the distance, is the measure of the
intensity not only of gravitation, but (it is believed) of illumination,
and of heat diffused from a centre. Yet no one looks upon this identity as
proving similarity in the mechanism by which the three kinds of phenomena
are produced.

According to Dr. Whewell, the coincidence of results predicted from an
hypothesis with facts afterward observed, amounts to a conclusive proof of
the truth of the theory. “If I copy a long series of letters, of which the
last half-dozen are concealed, and if I guess these aright, as is found to
be the case when they are afterward uncovered, this must be because I have
made out the import of the inscription. To say that because I have copied
all that I could see, it is nothing strange that I should guess those
which I can not see, would be absurd, without supposing such a ground for
guessing.”(167) If any one, from examining the greater part of a long
inscription, can interpret the characters so that the inscription gives a
rational meaning in a known language, there is a strong presumption that
his interpretation is correct; but I do not think the presumption much
increased by his being able to guess the few remaining letters without
seeing them; for we should naturally expect (when the nature of the case
excludes chance) that even an erroneous interpretation which accorded with
all the visible parts of the inscription would accord also with the small
remainder; as would be the case, for example, if the inscription had been
designedly so contrived as to admit of a double sense. I assume that the
uncovered characters afford an amount of coincidence too great to be
merely casual; otherwise the illustration is not a fair one. No one
supposes the agreement of the phenomena of light with the theory of
undulations to be merely fortuitous. It must arise from the actual
identity of some of the laws of undulations with some of those of light;
and if there be that identity, it is reasonable to suppose that its
consequences would not end with the phenomena which first suggested the
identification, nor be even confined to such phenomena as were known at
the time. But it does not follow, because some of the laws agree with
those of undulations, that there are any actual undulations; no more than
it followed because some (though not so many) of the same laws agreed with
those of the projection of particles, that there was actual emission of
particles. Even the undulatory hypothesis does not account for all the
phenomena of light. The natural colors of objects, the compound nature of
the solar ray, the absorption of light, and its chemical and vital action,
the hypothesis leaves as mysterious as it found them; and some of these
facts are, at least apparently, more reconcilable with the emission theory
than with that of Young and Fresnel. Who knows but that some third
hypothesis, including all these phenomena, may in time leave the
undulatory theory as far behind as that has left the theory of Newton and
his successors?

To the statement, that the condition of accounting for all the known
phenomena is often fulfilled equally well by two conflicting hypotheses,
Dr. Whewell makes answer that he knows “of no such case in the history of
science, where the phenomena are at all numerous and complicated.”(168)
Such an affirmation, by a writer of Dr. Whewell’s minute acquaintance with
the history of science, would carry great authority, if he had not, a few
pages before, taken pains to refute it,(169) by maintaining that even the
exploded scientific hypotheses might always, or almost always, have been
so modified as to make them correct representations of the phenomena. The
hypothesis of vortices, he tells us, was, by successive modifications,
brought to coincide in its results with the Newtonian theory and with the
facts. The vortices did not, indeed, explain all the phenomena which the
Newtonian theory was ultimately found to account for, such as the
precession of the equinoxes; but this phenomenon was not, at the time, in
the contemplation of either party, as one of the facts to be accounted
for. All the facts which they did contemplate, we may believe on Dr.
Whewell’s authority to have accorded as accurately with the Cartesian
hypothesis, in its finally improved state, as with Newton’s.

But it is not, I conceive, a valid reason for accepting any given
hypothesis, that we are unable to imagine any other which will account for
the facts. There is no necessity for supposing that the true explanation
must be one which, with only our present experience, we could imagine.
Among the natural agents with which we are acquainted, the vibrations of
an elastic fluid may be the only one whose laws bear a close resemblance
to those of light; but we can not tell that there does not exist an
unknown cause, other than an elastic ether diffused through space, yet
producing effects identical in some respects with those which would result
from the undulations of such an ether. To assume that no such cause can
exist, appears to me an extreme case of assumption without evidence. And
at the risk of being charged with want of modesty, I can not help
expressing astonishment that a philosopher of Dr. Whewell’s abilities and
attainments should have written an elaborate treatise on the philosophy of
induction, in which he recognizes absolutely no mode of induction except
that of trying hypothesis after hypothesis until one is found which fits
the phenomena; which one, when found, is to be assumed as true, with no
other reservation than that if, on re-examination, it should appear to
assume more than is needful for explaining the phenomena, the superfluous
part of the assumption should be cut off. And this without the slightest
distinction between the cases in which it may be known beforehand that two
different hypotheses can not lead to the same result, and those in which,
for aught we can ever know, the range of suppositions, all equally
consistent with the phenomena, may be infinite.(170)

Nevertheless, I do not agree with M. Comte in condemning those who employ
themselves in working out into detail the application of these hypotheses
to the explanation of ascertained facts, provided they bear in mind that
the utmost they can prove is, not that the hypothesis is, but that it
_may_ be true. The ether hypothesis has a very strong claim to be so
followed out, a claim greatly strengthened since it has been shown to
afford a mechanism which would explain the mode of production, not of
light only, but also of heat. Indeed, the speculation has a smaller
element of hypothesis in its application to heat, than in the case for
which it was originally framed. We have proof by our senses of the
existence of molecular movement among the particles of all heated bodies;
while we have no similar experience in the case of light. When, therefore,
heat is communicated from the sun to the earth across apparently empty
space, the chain of causation has molecular motion both at the beginning
and end. The hypothesis only makes the motion continuous by extending it
to the middle. Now, motion in a body is known to be capable of being
imparted to another body contiguous to it; and the intervention of a
hypothetical elastic fluid occupying the space between the sun and the
earth, supplies the contiguity which is the only condition wanting, and
which can be supplied by no supposition but that of an intervening medium.
The supposition, notwithstanding, is at best a probable conjecture, not a
proved truth. For there is no proof that contiguity is absolutely required
for the communication of motion from one body to another. Contiguity does
not always exist, to our senses at least, in the cases in which motion
produces motion. The forces which go under the name of attraction,
especially the greatest of all, gravitation, are examples of motion
producing motion without apparent contiguity. When a planet moves, its
distant satellites accompany its motion. The sun carries the whole solar
system along with it in the progress which it is ascertained to be
executing through space. And even if we were to accept as conclusive the
geometrical reasonings (strikingly similar to those by which the
Cartesians defended their vortices) by which it has been attempted to show
that the motions of the ether may account for gravitation itself, even
then it would only have been proved that the supposed mode of production
may be, but not that no other mode can be, the true one.

§ 7. It is necessary, before quitting the subject of hypotheses, to guard
against the appearance of reflecting upon the scientific value of several
branches of physical inquiry, which, though only in their infancy, I hold
to be strictly inductive. There is a great difference between inventing
agencies to account for classes of phenomena, and endeavoring, in
conformity with known laws, to conjecture what former collocations of
known agents may have given birth to individual facts still in existence.
The latter is the legitimate operation of inferring from an observed
effect the existence, in time past, of a cause similar to that by which we
know it to be produced in all cases in which we have actual experience of
its origin. This, for example, is the scope of the inquiries of geology;
and they are no more illogical or visionary than judicial inquiries, which
also aim at discovering a past event by inference from those of its
effects which still subsist. As we can ascertain whether a man was
murdered or died a natural death, from the indications exhibited by the
corpse, the presence or absence of signs of struggling on the ground or on
the adjacent objects, the marks of blood, the footsteps of the supposed
murderers, and so on, proceeding throughout on uniformities ascertained by
a perfect induction without any mixture of hypothesis; so if we find, on
and beneath the surface of our planet, masses exactly similar to deposits
from water, or to results of the cooling of matter melted by fire, we may
justly conclude that such has been their origin; and if the effects,
though similar in kind, are on a far larger scale than any which are now
produced, we may rationally, and without hypothesis, conclude either that
the causes existed formerly with greater intensity, or that they have
operated during an enormous length of time. Further than this no geologist
of authority has, since the rise of the present enlightened school of
geological speculation, attempted to go.

In many geological inquiries it doubtless happens that though the laws to
which the phenomena are ascribed are known laws, and the agents known
agents, those agents are not known to have been present in the particular
case. In the speculation respecting the igneous origin of trap or granite,
the fact does not admit of direct proof that those substances have been
actually subjected to intense heat. But the same thing might be said of
all judicial inquiries which proceed on circumstantial evidence. We can
conclude that a man was murdered, though it is not proved by the testimony
of eye-witnesses that some person who had the intention of murdering him
was present on the spot. It is enough for most purposes, if no other known
cause could have generated the effects shown to have been produced.

                  -------------------------------------

The celebrated speculation of Laplace concerning the origin of the earth
and planets, participates essentially in the inductive character of modern
geological theory. The speculation is, that the atmosphere of the sun
originally extended to the present limits of the solar system; from which,
by the process of cooling, it has contracted to its present dimensions;
and since, by the general principles of mechanics the rotation of the sun
and of its accompanying atmosphere must increase in rapidity as its volume
diminishes, the increased centrifugal force generated by the more rapid
rotation, overbalancing the action of gravitation, has caused the sun to
abandon successive rings of vaporous matter, which are supposed to have
condensed by cooling, and to have become the planets. There is in this
theory no unknown substance introduced on supposition, nor any unknown
property or law ascribed to a known substance. The known laws of matter
authorize us to suppose that a body which is constantly giving out so
large an amount of heat as the sun is, must be progressively cooling, and
that, by the process of cooling it must contract; if, therefore, we
endeavor, from the present state of that luminary, to infer its state in a
time long past, we must necessarily suppose that its atmosphere extended
much farther than at present, and we are entitled to suppose that it
extended as far as we can trace effects such as it might naturally leave
behind it on retiring; and such the planets are. These suppositions being
made, it follows from known laws that successive zones of the solar
atmosphere might be abandoned; that these would continue to revolve round
the sun with the same velocity as when they formed part of its substance;
and that they would cool down, long before the sun itself, to any given
temperature, and consequently to that at which the greater part of the
vaporous matter of which they consisted would become liquid or solid. The
known law of gravitation would then cause them to agglomerate in masses,
which would assume the shape our planets actually exhibit; would acquire,
each about its own axis, a rotatory movement; and would in that state
revolve, as the planets actually do, about the sun, in the same direction
with the sun’s rotation, but with less velocity, because in the same
periodic time which the sun’s rotation occupied when his atmosphere
extended to that point. There is thus, in Laplace’s theory, nothing,
strictly speaking, hypothetical; it is an example of legitimate reasoning
from a present effect to a possible past cause, according to the known
laws of that cause. The theory, therefore, is, as I have said, of a
similar character to the theories of geologists; but considerably inferior
to them in point of evidence. Even if it were proved (which it is not)
that the conditions necessary for determining the breaking off of
successive rings would certainly occur, there would still be a much
greater chance of error in assuming that the existing laws of nature are
the same which existed at the origin of the solar system, than in merely
presuming (with geologists) that those laws have lasted through a few
revolutions and transformations of a single one among the bodies of which
that system is composed.



                               Chapter XV.


Of Progressive Effects; And Of The Continued Action Of Causes.


§ 1. In the last four chapters we have traced the general outlines of the
theory of the generation of derivative laws from ultimate ones. In the
present chapter our attention will be directed to a particular case of the
derivation of laws from other laws, but a case so general, and so
important as not only to repay, but to require, a separate examination.
This is the case of a complex phenomenon resulting from one simple law, by
the continual addition of an effect to itself.

There are some phenomena, some bodily sensations, for example, which are
essentially instantaneous, and whose existence can only be prolonged by
the prolongation of the existence of the cause by which they are produced.
But most phenomena are in their own nature permanent; having begun to
exist, they would exist forever unless some cause intervened having a
tendency to alter or destroy them. Such, for example, are all the facts of
phenomena which we call bodies. Water, once produced, will not of itself
relapse into a state of hydrogen and oxygen; such a change requires some
agent having the power of decomposing the compound. Such, again, are the
positions in space and the movements of bodies. No object at rest alters
its position without the intervention of some conditions extraneous to
itself; and when once in motion, no object returns to a state of rest, or
alters either its direction or its velocity, unless some new external
conditions are superinduced. It, therefore, perpetually happens that a
temporary cause gives rise to a permanent effect. The contact of iron with
moist air for a few hours, produces a rust which may endure for centuries;
or a projectile force which launches a cannon-ball into space, produces a
motion which would continue forever unless some other force counteracted
it.

Between the two examples which we have here given, there is a difference
worth pointing out. In the former (in which the phenomenon produced is a
substance, and not a motion of a substance), since the rust remains
forever and unaltered unless some new cause supervenes, we may speak of
the contact of air a hundred years ago as even the proximate cause of the
rust which has existed from that time until now. But when the effect is
motion, which is itself a change, we must use a different language. The
permanency of the effect is now only the permanency of a series of
changes. The second foot, or inch, or mile of motion is not the mere
prolonged duration of the first foot, or inch, or mile, but another fact
which succeeds, and which may in some respects be very unlike the former,
since it carries the body through a different region of space. Now, the
original projectile force which set the body moving is the remote cause of
all its motion, however long continued, but the proximate cause of no
motion except that which took place at the first instant. The motion at
any subsequent instant is proximately caused by the motion which took
place at the instant preceding. It is on that, and not on the original
moving cause, that the motion at any given moment depends. For, suppose
that the body passes through some resisting medium, which partially
counteracts the effect of the original impulse, and retards the motion;
this counteraction (it need scarcely here be repeated) is as strict an
example of obedience to the law of the impulse, as if the body had gone on
moving with its original velocity; but the motion which results is
different, being now a compound of the effects of two causes acting in
contrary directions, instead of the single effect of one cause. Now, what
cause does the body obey in its subsequent motion? The original cause of
motion, or the actual motion at the preceding instant? The latter; for
when the object issues from the resisting medium, it continues moving, not
with its original, but with its retarded velocity. The motion having once
been diminished, all that which follows is diminished. The effect changes,
because the cause which it really obeys, the proximate cause, the real
cause in fact, has changed. This principle is recognized by mathematicians
when they enumerate among the causes by which the motion of a body is at
any instant determined the _force generated_ by the previous motion; an
expression which would be absurd if taken to imply that this “force” was
an intermediate link between the cause and the effect, but which really
means only the previous motion itself, considered as a cause of further
motion. We must, therefore, if we would speak with perfect precision,
consider each link in the succession of motions as the effect of the link
preceding it. But if, for the convenience of discourse, we speak of the
whole series as one effect, it must be as an effect produced by the
original impelling force; a permanent effect produced by an instantaneous
cause, and possessing the property of self-perpetuation.

Let us now suppose that the original agent or cause, instead of being
instantaneous, is permanent. Whatever effect has been produced up to a
given time, would (unless prevented by the intervention of some new cause)
subsist permanently, even if the cause were to perish. Since, however, the
cause does not perish, but continues to exist and to operate, it must go
on producing more and more of the effect; and instead of a uniform effect,
we have a progressive series of effects, arising from the accumulated
influence of a permanent cause. Thus, the contact of iron with the
atmosphere causes a portion of it to rust; and if the cause ceased, the
effect already produced would be permanent, but no further effect would be
added. If, however, the cause, namely, exposure to moist air, continues,
more and more of the iron becomes rusted, until all which is exposed is
converted into a red powder, when one of the conditions of the production
of rust, namely, the presence of unoxidized iron, has ceased, and the
effect can not any longer be produced. Again, the earth causes bodies to
fall toward it; that is, the existence of the earth at a given instant
causes an unsupported body to move toward it at the succeeding instant;
and if the earth were annihilated, as much of the effect as is already
produced would continue; the object would go on moving in the same
direction, with its acquired velocity, until intercepted by some body or
deflected by some other force. The earth, however, not being annihilated,
goes on producing in the second instant an effect similar and of equal
amount with the first, which two effects being added together, there
results an accelerated velocity; and this operation being repeated at each
successive instant, the mere permanence of the cause, though without
increase, gives rise to a constant progressive increase of the effect, so
long as all the conditions, negative and positive, of the production of
that effect continue to be realized.

It is obvious that this state of things is merely a case of the
Composition of Causes. A cause which continues in action must on a strict
analysis be considered as a number of causes exactly similar, successively
introduced, and producing by their combination the sum of the effects
which they would severally produce if they acted singly. The progressive
rusting of the iron is in strictness the sum of the effects of many
particles of air acting in succession upon corresponding particles of
iron. The continued action of the earth upon a falling body is equivalent
to a series of forces, applied in successive instants, each tending to
produce a certain constant quantity of motion; and the motion at each
instant is the sum of the effects of the new force applied at the
preceding instant, and the motion already acquired. In each instant a
fresh effect, of which gravity is the proximate cause, is added to the
effect of which it was the remote cause; or (to express the same thing in
another manner), the effect produced by the earth’s influence at the
instant last elapsed is added to the sum of the effects of which the
remote causes were the influences exerted by the earth at all the previous
instants since the motion began. The case, therefore, comes under the
principle of a concurrence of causes producing an effect equal to the sum
of their separate effects. But as the causes come into play not all at
once, but successively, and as the effect at each instant is the sum of
the effects of those causes only which have come into action up to that
instant, the result assumes the form of an ascending series; a succession
of sums, each greater than that which preceded it; and we have thus a
progressive effect from the continued action of a cause.

Since the continuance of the cause influences the effect only by adding to
its quantity, and since the addition takes place according to a fixed law
(equal quantities in equal times), the result is capable of being computed
on mathematical principles. In fact, this case, being that of
infinitesimal increments, is precisely the case which the differential
calculus was invented to meet. The questions, what effect will result from
the continual addition of a given cause to itself, and what amount of the
cause, being continually added to itself, will produce a given amount of
the effect, are evidently mathematical questions, and to be treated,
therefore, deductively. If, as we have seen, cases of the Composition of
Causes are seldom adapted for any other than deductive investigation, this
is especially true in the case now examined, the continual composition of
a cause with its own previous effects; since such a case is peculiarly
amenable to the deductive method, while the undistinguishable manner in
which the effects are blended with one another and with the causes, must
make the treatment of such an instance experimentally still more
chimerical than in any other case.

§ 2. We shall next advert to a rather more intricate operation of the same
principle, namely, when the cause does not merely continue in action, but
undergoes, during the same time, a progressive change in those of its
circumstances which contribute to determine the effect. In this case, as
in the former, the total effect goes on accumulating by the continual
addition of a fresh effect to that already produced, but it is no longer
by the addition of equal quantities in equal times; the quantities added
are unequal, and even the quality may now be different. If the change in
the state of the permanent cause be progressive, the effect will go
through a double series of changes, arising partly from the accumulated
action of the cause, and partly from the changes in its action. The effect
is still a progressive effect, produced, however, not by the mere
continuance of a cause, but by its continuance and its progressiveness
combined.

A familiar example is afforded by the increase of the temperature as
summer advances, that is, as the sun draws nearer to a vertical position,
and remains a greater number of hours above the horizon. This instance
exemplifies in a very interesting manner the twofold operation on the
effect, arising from the continuance of the cause, and from its
progressive change. When once the sun has come near enough to the zenith,
and remains above the horizon long enough, to give more warmth during one
diurnal rotation than the counteracting cause, the earth’s radiation, can
carry off, the mere continuance of the cause would progressively increase
the effect, even if the sun came no nearer and the days grew no longer;
but in addition to this, a change takes place in the accidents of the
cause (its series of diurnal positions), tending to increase the quantity
of the effect. When the summer solstice has passed, the progressive change
in the cause begins to take place the reverse way, but, for some time, the
accumulating effect of the mere continuance of the cause exceeds the
effect of the changes in it, and the temperature continues to increase.

Again, the motion of a planet is a progressive effect, produced by causes
at once permanent and progressive. The orbit of a planet is determined
(omitting perturbations) by two causes: first, the action of the central
body, a permanent cause, which alternately increases and diminishes as the
planet draws nearer to or goes farther from its perihelion, and which acts
at every point in a different direction; and, secondly, the tendency of
the planet to continue moving in the direction and with the velocity which
it has already acquired. This force also grows greater as the planet draws
nearer to its perihelion, because as it does so its velocity increases,
and less, as it recedes from its perihelion; and this force as well as the
other acts at each point in a different direction, because at every point
the action of the central force, by deflecting the planet from its
previous direction, alters the line in which it tends to continue moving.
The motion at each instant is determined by the amount and direction of
the motion, and the amount and direction of the sun’s action, at the
previous instant; and if we speak of the entire revolution of the planet
as one phenomenon (which, as it is periodical and similar to itself, we
often find it convenient to do), that phenomenon is the progressive effect
of two permanent and progressive causes, the central force and the
acquired motion. Those causes happening to be progressive in the
particular way which is called periodical, the effect necessarily is so
too; because the quantities to be added together returning in a regular
order, the same sums must also regularly return.

This example is worthy of consideration also in another respect. Though
the causes themselves are permanent, and independent of all conditions
known to us, the changes which take place in the quantities and relations
of the causes are actually caused by the periodical changes in the
effects. The causes, as they exist at any moment, having produced a
certain motion, that motion, becoming itself a cause, reacts upon the
causes, and produces a change in them. By altering the distance and
direction of the central body relatively to the planet, and the direction
and quantity of the force in the direction of the tangent, it alters the
elements which determine the motion at the next succeeding instant. This
change renders the next motion somewhat different; and this difference, by
a fresh reaction upon the causes, renders the next motion again different,
and so on. The original state of the causes might have been such that this
series of actions modified by reactions would not have been periodical.
The sun’s action, and the original impelling force, might have been in
such a ratio to one another, that the reaction of the effect would have
been such as to alter the causes more and more, without ever bringing them
back to what they were at any former time. The planet would then have
moved in a parabola, or an hyperbola, curves not returning into
themselves. The quantities of the two forces were, however, originally
such, that the successive reactions of the effect bring back the causes,
after a certain time, to what they were before; and from that time all the
variations continued to recur again and again in the same periodical
order, and must so continue while the causes subsist and are not
counteracted.

§ 3. In all cases of progressive effects, whether arising from the
accumulation of unchanging or of changing elements, there is a uniformity
of succession not merely between the cause and the effect, but between the
first stages of the effect and its subsequent stages. That a body _in
vacuo_ falls sixteen feet in the first second, forty-eight in the second,
and so on in the ratio of the odd numbers, is as much a uniform sequence
as that when the supports are removed the body falls. The sequence of
spring and summer is as regular and invariable as that of the approach of
the sun and spring; but we do not consider spring to be the cause of
summer; it is evident that both are successive effects of the heat
received from the sun, and that, considered merely in itself, spring might
continue forever without having the slightest tendency to produce summer.
As we have so often remarked, not the conditional, but the unconditional
invariable antecedent is termed the cause. That which would not be
followed by the effect unless something else had preceded, and which if
that something else had preceded, would not have been required, is not the
cause, however invaluable the sequence may in fact be.

It is in this way that most of those uniformities of succession are
generated, which are not cases of causation. When a phenomenon goes on
increasing, or periodically increases and diminishes, or goes through any
continued and unceasing process of variation reducible to a uniform rule
or law of succession, we do not on this account presume that any two
successive terms of the series are cause and effect. We presume the
contrary; we expect to find that the whole series originates either from
the continued action of fixed causes or from causes which go through a
corresponding process of continuous change. A tree grows from half an inch
high to a hundred feet; and some trees will generally grow to that height
unless prevented by some counteracting cause. But we do not call the
seedling the cause of the full-grown tree; the invariable antecedent it
certainly is, and we know very imperfectly on what other antecedents the
sequence is contingent, but we are convinced that it is contingent on
something; because the homogeneousness of the antecedent with the
consequent, the close resemblance of the seedling to the tree in all
respects except magnitude, and the graduality of the growth, so exactly
resembling the progressively accumulating effect produced by the long
action of some one cause, leave no possibility of doubting that the
seedling and the tree are two terms in a series of that description, the
first term of which is yet to seek. The conclusion is further confirmed by
this, that we are able to prove by strict induction the dependence of the
growth of the tree, and even of the continuance of its existence, upon the
continued repetition of certain processes of nutrition, the rise of the
sap, the absorptions and exhalations by the leaves, etc.; and the same
experiments would probably prove to us that the growth of the tree is the
accumulated sum of the effects of these continued processes, were we not,
for want of sufficiently microscopic eyes, unable to observe correctly and
in detail what those effects are.

This supposition by no means requires that the effect should not, during
its progress, undergo many modifications besides those of quantity, or
that it should not sometimes appear to undergo a very marked change of
character. This may be either because the unknown cause consists of
several component elements or agents, whose effects, accumulating
according to different laws, are compounded in different proportions at
different periods in the existence of the organized being; or because, at
certain points in its progress, fresh causes or agencies come in, or are
evolved, which intermix their laws with those of the prime agent.



                               Chapter XVI.


Of Empirical Laws.


§ 1. Scientific inquirers give the name of Empirical Laws to those
uniformities which observation or experiment has shown to exist, but on
which they hesitate to rely in cases varying much from those which have
been actually observed, for want of seeing any reason _why_ such a law
should exist. It is implied, therefore, in the notion of an empirical law,
that it is not an ultimate law; that if true at all, its truth is capable
of being, and requires to be, accounted for. It is a derivative law, the
derivation of which is not yet known. To state the explanation, the _why_,
of the empirical law, would be to state the laws from which it is
derived—the ultimate causes on which it is contingent. And if we knew
these, we should also know what are its limits; under what conditions it
would cease to be fulfilled.

The periodical return of eclipses, as originally ascertained by the
persevering observation of the early Eastern astronomers, was an empirical
law, until the general laws of the celestial motions had accounted for it.
The following are empirical laws still waiting to be resolved into the
simpler laws from which they are derived: the local laws of the flux and
reflux of the tides in different places; the succession of certain kinds
of weather to certain appearances of sky; the apparent exceptions to the
almost universal truth that bodies expand by increase of temperature; the
law that breeds, both animal and vegetable, are improved by crossing; that
gases have a strong tendency to permeate animal membranes; that substances
containing a very high proportion of nitrogen (such as hydrocyanic acid
and morphia) are powerful poisons; that when different metals are fused
together the alloy is harder than the various elements; that the number of
atoms of acid required to neutralize one atom of any base is equal to the
number of atoms of oxygen in the base; that the solubility of substances
in one another depends,(171) at least in some degree, on the similarity of
their elements.

An empirical law, then, is an observed uniformity, presumed to be
resolvable into simpler laws, but not yet resolved into them. The
ascertainment of the empirical laws of phenomena often precedes by a long
interval the explanation of those laws by the Deductive Method; and the
verification of a deduction usually consists in the comparison of its
results with empirical laws previously ascertained.

§ 2. From a limited number of ultimate laws of causation, there are
necessarily generated a vast number of derivative uniformities, both of
succession and co-existence. Some are laws of succession or of
co-existence between different effects of the same cause; of these we had
examples in the last chapter. Some are laws of succession between effects
and their remote causes, resolvable into the laws which connect each with
the intermediate link. Thirdly, when causes act together and compound
their effects, the laws of those causes generate the fundamental law of
the effect, namely, that it depends on the co-existence of those causes.
And, finally, the order of succession or of co-existence which obtains
among effects necessarily depends on their causes. If they are effects of
the same cause, it depends on the laws of that cause; if on different
causes, it depends on the laws of those causes severally, and on the
circumstances which determine their co-existence. If we inquire further
when and how the causes will co-exist, that, again, depends on _their_
causes; and we may thus trace back the phenomena higher and higher, until
the different series of effects meet in a point, and the whole is shown to
have depended ultimately on some common cause; or until, instead of
converging to one point, they terminate in different points, and the order
of the effects is proved to have arisen from the collocation of some of
the primeval causes, or natural agents. For example, the order of
succession and of co-existence among the heavenly motions, which is
expressed by Kepler’s laws, is derived from the co-existence of two
primeval causes, the sun, and the original impulse or projectile force
belonging to each planet.(172) Kepler’s laws are resolved into the laws of
these causes and the fact of their co-existence.

Derivative laws, therefore, do not depend solely on the ultimate laws into
which they are resolvable; they mostly depend on those ultimate laws, and
an ultimate fact; namely, the mode of co-existence of some of the
component elements of the universe. The ultimate laws of causation might
be the same as at present, and yet the derivative laws completely
different, if the causes co-existed in different proportions, or with any
difference in those of their relations by which the effects are
influenced. If, for example, the sun’s attraction, and the original
projectile force, had existed in some other ratio to one another than they
did (and we know of no reason why this should not have been the case), the
derivative laws of the heavenly motions might have been quite different
from what they are. The proportions which exist happen to be such as to
produce regular elliptical motions; any other proportions would have
produced different ellipses, or circular, or parabolic, or hyperbolic
motions, but still regular ones; because the effects of each of the agents
accumulate according to a uniform law; and two regular series of
quantities, when their corresponding terms are added, must produce a
regular series of some sort, whatever the quantities themselves are.

§ 3. Now this last-mentioned element in the resolution of a derivative
law, the element which is not a law of causation, but a collocation of
causes, can not itself be reduced to any law. There is, as formerly
remarked,(173) no uniformity, no _norma_, principle, or rule, perceivable
in the distribution of the primeval natural agents through the universe.
The different substances composing the earth, the powers that pervade the
universe, stand in no constant relation to one another. One substance is
more abundant than others, one power acts through a larger extent of space
than others, without any pervading analogy that we can discover. We not
only do not know of any reason why the sun’s attraction and the force in
the direction of the tangent co-exist in the exact proportion they do, but
we can trace no coincidence between it and the proportions in which any
other elementary powers in the universe are intermingled. The utmost
disorder is apparent in the combination of the causes, which is consistent
with the most regular order in their effects; for when each agent carries
on its own operations according to a uniform law, even the most capricious
combination of agencies will generate a regularity of some sort; as we see
in the kaleidoscope, where any casual arrangement of colored bits of glass
produces by the laws of reflection a beautiful regularity in the effect.

§ 4. In the above considerations lies the justification of the limited
degree of reliance which scientific inquirers are accustomed to place in
empirical laws.

A derivative law which results wholly from the operation of some one
cause, will be as universally true as the laws of the cause itself; that
is, it will always be true except where some one of those effects of the
cause, on which the derivative law depends, is defeated by a counteracting
cause. But when the derivative law results not from different effects of
one cause, but from effects of several causes, we can not be certain that
it will be true under any variation in the mode of co-existence of those
causes, or of the primitive natural agents on which the causes ultimately
depend. The proposition that coal-beds rest on certain descriptions of
strata exclusively, though true on the earth, so far as our observation
has reached, can not be extended to the moon or the other planets,
supposing coal to exist there; because we can not be assured that the
original constitution of any other planet was such as to produce the
different depositions in the same order as in our globe. The derivative
law in this case depends not solely on laws, but on a collocation; and
collocations can not be reduced to any law.

Now it is the very nature of a derivative law which has not yet been
resolved into its elements, in other words, an empirical law, that we do
not know whether it results from the different effects of one cause, or
from effects of different causes. We can not tell whether it depends
wholly on laws, or partly on laws and partly on a collocation. If it
depends on a collocation, it will be true in all the cases in which that
particular collocation exists. But, since we are entirely ignorant, in
case of its depending on a collocation, what the collocation is, we are
not safe in extending the law beyond the limits of time and place in which
we have actual experience of its truth. Since within those limits the law
has always been found true, we have evidence that the collocations,
whatever they are, on which it depends, do really exist within those
limits. But, knowing of no rule or principle to which the collocations
themselves conform, we can not conclude that because a collocation is
proved to exist within certain limits of place or time, it will exist
beyond those limits. Empirical laws, therefore, can only be received as
true within the limits of time and place in which they have been found
true by observation; and not merely the limits of time and place, but of
time, place, and circumstance; for, since it is the very meaning of an
empirical law that we do not know the ultimate laws of causation on which
it is dependent, we can not foresee, without actual trial, in what manner
or to what extent the introduction of any new circumstance may affect it.

§ 5. But how are we to know that a uniformity ascertained by experience is
only an empirical law? Since, by the supposition, we have not been able to
resolve it into any other laws, how do we know that it is not an ultimate
law of causation?

I answer that no generalization amounts to more than an empirical law when
the only proof on which it rests is that of the Method of Agreement. For
it has been seen that by that method alone we never can arrive at causes.
The utmost that the Method of Agreement can do is, to ascertain the whole
of the circumstances common to all cases in which a phenomenon is
produced; and this aggregate includes not only the cause of the
phenomenon, but all phenomena with which it is connected by any derivative
uniformity, whether as being collateral effects of the same cause, or
effects of any other cause which, in all the instances we have been able
to observe, co-existed with it. The method affords no means of determining
which of these uniformities are laws of causation, and which are merely
derivative laws, resulting from those laws of causation and from the
collocation of the causes. None of them, therefore, can be received in any
other character than that of derivative laws, the derivation of which has
not been traced; in other words, empirical laws: in which light all
results obtained by the Method of Agreement (and therefore almost all
truths obtained by simple observation without experiment) must be
considered, until either confirmed by the Method of Difference, or
explained deductively; in other words, accounted for _a priori_.

These empirical laws may be of greater or less authority, according as
there is reason to presume that they are resolvable into laws only, or
into laws and collocations together. The sequences which we observe in the
production and subsequent life of an animal or a vegetable, resting on the
Method of Agreement only, are mere empirical laws; but though the
antecedents in those sequences may not be the causes of the consequents,
both the one and the other are doubtless, in the main, successive stages
of a progressive effect originating in a common cause, and therefore
independent of collocations. The uniformities, on the other hand, in the
order of superposition of strata on the earth, are empirical laws of a
much weaker kind, since they not only are not laws of causation, but there
is no reason to believe that they depend on any common cause; all
appearances are in favor of their depending on the particular collocation
of natural agents which at some time or other existed on our globe, and
from which no inference can be drawn as to the collocation which exists or
has existed in any other portion of the universe.

§ 6. Our definition of an empirical law, including not only those
uniformities which are not known to be laws of causation, but also those
which are, provided there be reason to presume that they are not ultimate
laws; this is the proper place to consider by what signs we may judge that
even if an observed uniformity be a law of causation, it is not an
ultimate, but a derivative law.

The first sign is, if between the antecedent _a_ and the consequent _b_
there be evidence of some intermediate link; some phenomenon of which we
can surmise the existence, though from the imperfection of our senses or
of our instruments we are unable to ascertain its precise nature and laws.
If there be such a phenomenon (which may be denoted by the letter _x_), it
follows that even if _a_ be the cause of _b_, it is but the remote cause,
and that the law, _a_ causes _b_, is resolvable into at least two laws,
_a_ causes _x_, and _x_ causes _b_. This is a very frequent case, since
the operations of nature mostly take place on so minute a scale, that many
of the successive steps are either imperceptible, or very indistinctly
perceived.

Take, for example, the laws of the chemical composition of substances; as
that hydrogen and oxygen being combined, water is produced. All we see of
the process is, that the two gases being mixed in certain proportions, and
heat or electricity being applied, an explosion takes place, the gases
disappear, and water remains. There is no doubt about the law, or about
its being a law of causation. But between the antecedent (the gases in a
state of mechanical mixture, heated or electrified), and the consequent
(the production of water), there must be an intermediate process which we
do not see. For if we take any portion whatever of the water, and subject
it to analysis, we find that it always contains hydrogen and oxygen; nay,
the very same proportions of them, namely, two-thirds, in volume, of
hydrogen, and one-third oxygen. This is true of a single drop; it is true
of the minutest portion which our instruments are capable of appreciating.
Since, then, the smallest perceptible portion of the water contains both
those substances, portions of hydrogen and oxygen smaller than the
smallest perceptible must have come together in every such minute portion
of space; must have come closer together than when the gases were in a
state of mechanical mixture, since (to mention no other reasons) the water
occupies far less space than the gases. Now, as we can not see this
contact or close approach of the minute particles, we can not observe with
what circumstances it is attended, or according to what laws it produces
its effects. The production of water, that is, of the sensible phenomena
which characterize the compound, may be a very remote effect of those
laws. There may be innumerable intervening links; and we are sure that
there must be some. Having full proof that corpuscular action of some kind
takes place previous to any of the great transformations in the sensible
properties of substances, we can have no doubt that the laws of chemical
action, as at present known, are not ultimate, but derivative laws;
however ignorant we may be, and even though we should forever remain
ignorant, of the nature of the laws of corpuscular action from which they
are derived.

In like manner, all the processes of vegetative life, whether in the
vegetable properly so called or in the animal body, are corpuscular
processes. Nutrition is the addition of particles to one another,
sometimes merely replacing other particles separated and excreted,
sometimes occasioning an increase of bulk or weight so gradual that only
after a long continuance does it become perceptible. Various organs, by
means of peculiar vessels, secrete from the blood fluids, the component
particles of which must have been in the blood, but which differ from it
most widely both in mechanical properties and in chemical composition.
Here, then, are abundance of unknown links to be filled up; and there can
be no doubt that the laws of the phenomena of vegetative or organic life
are derivative laws, dependent on properties of the corpuscles, and of
those elementary tissues which are comparatively simple combinations of
corpuscles.

The first sign, then, from which a law of causation, though hitherto
unresolved, may be inferred to be a derivative law, is any indication of
the existence of an intermediate link or links between the antecedent and
the consequent. The second is, when the antecedent is an extremely complex
phenomenon, and its effects, therefore, probably in part at least,
compounded of the effects of its different elements; since we know that
the case in which the effect of the whole is not made up of the effects of
its parts is exceptional, the Composition of Causes being by far the more
ordinary case.

We will illustrate this by two examples, in one of which the antecedent is
the sum of many homogeneous, in the other of heterogeneous, parts. The
weight of a body is made up of the weights of its minute particles; a
truth which astronomers express in its most general terms when they say
that bodies, at equal distances, gravitate to one another in proportion to
their quantity of matter. All true propositions, therefore, which can be
made concerning gravity, are derivative laws; the ultimate law into which
they are all resolvable being, that every particle of matter attracts
every other. As our second example, we may take any of the sequences
observed in meteorology; for instance, a diminution of the pressure of the
atmosphere (indicated by a fall of the barometer) is followed by rain. The
antecedent is here a complex phenomenon, made up of heterogeneous
elements; the column of the atmosphere over any particular place
consisting of two parts, a column of air, and a column of aqueous vapor
mixed with it; and the change in the two together manifested by a fall of
the barometer, and followed by rain, must be either a change in one of
these, or in the other, or in both. We might, then, even in the absence of
any other evidence, form a reasonable presumption, from the invariable
presence of both these elements in the antecedent, that the sequence is
probably not an ultimate law, but a result of the laws of the two
different agents; a presumption only to be destroyed when we had made
ourselves so well acquainted with the laws of both, as to be able to
affirm that those laws could not by themselves produce the observed
result.

There are but few known cases of succession from very complex antecedents
which have not either been actually accounted for from simpler laws, or
inferred with great probability (from the ascertained existence of
intermediate links of causation not yet understood) to be capable of being
so accounted for. It is, therefore, highly probable that all sequences
from complex antecedents are thus resolvable, and that ultimate laws are
in all cases comparatively simple. If there were not the other reasons
already mentioned for believing that the laws of organized nature are
resolvable into simpler laws, it would be almost a sufficient reason that
the antecedents in most of the sequences are so very complex.

§ 7. In the preceding discussion we have recognized two kinds of empirical
laws: those known to be laws of causation, but presumed to be resolvable
into simpler laws; and those not known to be laws of causation at all.
Both these kinds of laws agree in the demand which they make for being
explained by deduction, and agree in being the appropriate means of
verifying such deduction, since they represent the experience with which
the result of the deduction must be compared. They agree, further, in
this, that until explained, and connected with the ultimate laws from
which they result, they have not attained the highest degree of certainty
of which laws are susceptible. It has been shown on a former occasion that
laws of causation which are derivative, and compounded of simpler laws,
are not only, as the nature of the case implies, less general, but even
less certain, than the simpler laws from which they result; not in the
same degree to be relied on as universally true. The inferiority of
evidence, however, which attaches to this class of laws, is trifling,
compared with that which is inherent in uniformities not known to be laws
of causation at all. So long as these are unresolved, we can not tell on
how many collocations, as well as laws, their truth may be dependent; we
can never, therefore, extend them with any confidence to cases in which we
have not assured ourselves, by trial, that the necessary collocation of
causes, whatever it may be, exists. It is to this class of laws alone that
the property, which philosophers usually consider as characteristic of
empirical laws, belongs in all its strictness—the property of being unfit
to be relied on beyond the limits of time, place, and circumstance in
which the observations have been made. These are empirical laws in a more
emphatic sense; and when I employ that term (except where the context
manifestly indicates the reverse) I shall generally mean to designate
those uniformities only, whether of succession or of co-existence, which
are not known to be laws of causation.



                              Chapter XVII.


Of Chance And Its Elimination.


§ 1. Considering, then, as empirical laws only those observed uniformities
respecting which the question whether they are laws of causation must
remain undecided until they can be explained deductively, or until some
means are found of applying the Method of Difference to the case, it has
been shown in the preceding chapter that until a uniformity can, in one or
the other of these modes, be taken out of the class of empirical laws, and
brought either into that of laws of causation or of the demonstrated
results of laws of causation, it can not with any assurance be pronounced
true beyond the local and other limits within which it has been found so
by actual observation. It remains to consider how we are to assure
ourselves of its truth even within those limits; after what quantity of
experience a generalization which rests solely on the Method of Agreement
can be considered sufficiently established, even as an empirical law. In a
former chapter, when treating of the Methods of Direct Induction, we
expressly reserved this question,(174) and the time is now come for
endeavoring to solve it.

We found that the Method of Agreement has the defect of not proving
causation, and can, therefore, only be employed for the ascertainment of
empirical laws. But we also found that besides this deficiency, it labors
under a characteristic imperfection, tending to render uncertain even such
conclusions as it is in itself adapted to prove. This imperfection arises
from Plurality of Causes. Although two or more cases in which the
phenomenon _a_ has been met with may have no common antecedent except A,
this does not prove that there is any connection between _a_ and A, since
_a_ may have many causes, and may have been produced, in these different
instances, not by any thing which the instances had in common, but by some
of those elements in them which were different. We nevertheless observed,
that in proportion to the multiplication of instances pointing to A as the
antecedent, the characteristic uncertainty of the method diminishes, and
the existence of a law of connection between A and _a_ more nearly
approaches to certainty. It is now to be determined after what amount of
experience this certainty may be deemed to be practically attained, and
the connection between A and _a_ may be received as an empirical law.

This question may be otherwise stated in more familiar terms: After how
many and what sort of instances may it be concluded that an observed
coincidence between two phenomena is not the effect of chance?

It is of the utmost importance for understanding the logic of induction,
that we should form a distinct conception of what is meant by chance, and
how the phenomena which common language ascribes to that abstraction are
really produced.

§ 2. Chance is usually spoken of in direct antithesis to law; whatever, it
is supposed, can not be ascribed to any law is attributed to chance. It
is, however, certain that whatever happens is the result of some law; is
an effect of causes, and could have been predicted from a knowledge of the
existence of those causes, and from their laws. If I turn up a particular
card, that is a consequence of its place in the pack. Its place in the
pack was a consequence of the manner in which the cards were shuffled, or
of the order in which they were played in the last game; which, again,
were effects of prior causes. At every stage, if we had possessed an
accurate knowledge of the causes in existence, it would have been
abstractedly possible to foretell the effect.

An event occurring by chance may be better described as a coincidence from
which we have no ground to infer a uniformity—the occurrence of a
phenomenon in certain circumstances, without our having reason on that
account to infer that it will happen again in those circumstances. This,
however, when looked closely into, implies that the enumeration of the
circumstances is not complete. Whatever the fact be, since it has occurred
once, we may be sure that if _all_ the same circumstances were repeated it
would occur again; and not only if all, but there is some particular
portion of those circumstances on which the phenomenon is invariably
consequent. With most of them, however, it is not connected in any
permanent manner; its conjunction with those is said to be the effect of
chance, to be merely casual. Facts casually conjoined are separately the
effects of causes, and therefore of laws; but of different causes, and
causes not connected by any law.

It is incorrect, then, to say that any phenomenon is produced by chance;
but we may say that two or more phenomena are conjoined by chance, that
they co-exist or succeed one another only by chance; meaning that they are
in no way related through causation; that they are neither cause and
effect, nor effects of the same cause, nor effects of causes between which
there subsists any law of co-existence, nor even effects of the same
collocation of primeval causes.

If the same casual coincidence never occurred a second time, we should
have an easy test for distinguishing such from the coincidences which are
the results of a law. As long as the phenomena had been found together
only once, so long, unless we knew some more general laws from which the
coincidence might have resulted, we could not distinguish it from a casual
one; but if it occurred twice, we should know that the phenomena so
conjoined must be in some way connected through their causes.

There is, however, no such test. A coincidence may occur again and again,
and yet be only casual. Nay, it would be inconsistent with what we know of
the order of nature to doubt that every casual coincidence will sooner or
later be repeated, as long as the phenomena between which it occurred do
not cease to exist, or to be reproduced. The recurrence, therefore, of the
same coincidence more than once, or even its frequent recurrence, does not
prove that it is an instance of any law; does not prove that it is not
casual, or, in common language, the effect of chance.

And yet, when a coincidence can not be deduced from known laws, nor proved
by experiment to be itself a case of causation, the frequency of its
occurrence is the only evidence from which we can infer that it is the
result of a law. Not, however, its absolute frequency. The question is not
whether the coincidence occurs often or seldom, in the ordinary sense of
those terms; but whether it occurs more often than chance will account
for; more often than might rationally be expected if the coincidence were
casual. We have to decide, therefore, what degree of frequency in a
coincidence chance will account for; and to this there can be no general
answer. We can only state the principle by which the answer must be
determined; the answer itself will be different in every different case.

Suppose that one of the phenomena, A, exists always, and the other
phenomenon, B, only occasionally; it follows that every instance of B will
be an instance of its coincidence with A, and yet the coincidence will be
merely casual, not the result of any connection between them. The fixed
stars have been constantly in existence since the beginning of human
experience, and all phenomena that have come under human observation have,
in every single instance, co-existed with them; yet this coincidence,
though equally invariable with that which exists between any of those
phenomena and its own cause, does not prove that the stars are its cause,
nor that they are in anywise connected with it. As strong a case of
coincidence, therefore, as can possibly exist, and a much stronger one in
point of mere frequency than most of those which prove laws, does not here
prove a law; why? because, since the stars exist always, they _must_
co-exist with every other phenomenon, whether connected with them by
causation or not. The uniformity, great though it be, is no greater than
would occur on the supposition that no such connection exists.

On the other hand, suppose that we were inquiring whether there be any
connection between rain and any particular wind. Rain, we know,
occasionally occurs with every wind; therefore, the connection, if it
exists, can not be an actual law; but still rain may be connected with
some particular wind through causation; that is, though they can not be
always effects of the same cause (for if so they would regularly
co-exist), there may be some causes common to the two, so that in so far
as either is produced by those common causes, they will, from the laws of
the causes, be found to co-exist. How, then, shall we ascertain this? The
obvious answer is, by observing whether rain occurs with one wind more
frequently than with any other. That, however, is not enough; for perhaps
that one wind blows more frequently than any other; so that its blowing
more frequently in rainy weather is no more than would happen, although it
had no connection with the causes of rain, provided it were not connected
with causes adverse to rain. In England, westerly winds blow during about
twice as great a portion of the year as easterly. If, therefore, it rains
only twice as often with a westerly as with an easterly wind, we have no
reason to infer that any law of nature is concerned in the coincidence. If
it rains more than twice as often, we may be sure that some law is
concerned; either there is some cause in nature which, in this climate,
tends to produce both rain and a westerly wind, or a westerly wind has
itself some tendency to produce rain. But if it rains less than twice as
often, we may draw a directly opposite inference: the one, instead of
being a cause, or connected with causes of the other, must be connected
with causes adverse to it, or with the absence of some cause which
produces it; and though it may still rain much oftener with a westerly
wind than with an easterly, so far would this be from proving any
connection between the phenomena, that the connection proved would be
between rain and an easterly wind, to which, in mere frequency of
coincidence, it is less allied.

Here, then, are two examples: in one, the greatest possible frequency of
coincidence, with no instance whatever to the contrary, does not prove
that there is any law; in the other, a much less frequency of coincidence,
even when non-coincidence is still more frequent, does prove that there is
a law. In both cases the principle is the same. In both we consider the
positive frequency of the phenomena themselves, and how great frequency of
coincidence that must of itself bring about, without supposing any
connection between them, provided there be no repugnance; provided neither
be connected with any cause tending to frustrate the other. If we find a
greater frequency of coincidence than this, we conclude that there is some
connection; if a less frequency, that there is some repugnance. In the
former case, we conclude that one of the phenomena can under some
circumstances cause the other, or that there exists something capable of
causing them both; in the latter, that one of them, or some cause which
produces one of them, is capable of counteracting the production of the
other. We have thus to deduct from the observed frequency of coincidence
as much as may be the effect of chance, that is, of the mere frequency of
the phenomena themselves; and if any thing remains, what does remain is
the residual fact which proves the existence of a law.

The frequency of the phenomena can only be ascertained within definite
limits of space and time; depending as it does on the quantity and
distribution of the primeval natural agents, of which we can know nothing
beyond the boundaries of human observation, since no law, no regularity,
can be traced in it, enabling us to infer the unknown from the known. But
for the present purpose this is no disadvantage, the question being
confined within the same limits as the data. The coincidences occurred in
certain places and times, and within those we can estimate the frequency
with which such coincidences would be produced by chance. If, then, we
find from observation that A exists in one case out of every two, and B in
one case out of every three; then, if there be neither connection nor
repugnance between them, or between any of their causes, the instances in
which A and B will both exist, that is to say will co-exist, will be one
case in every six. For A exists in three cases out of six; and B, existing
in one case out of every three without regard to the presence or absence
of A, will exist in one case out of those three. There will therefore be,
of the whole number of cases, two in which A exists without B; one case of
B without A; two in which neither B nor A exists, and one case out of six
in which they both exist. If, then, in point of fact, they are found to
co-exist oftener than in one case out of six; and, consequently, A does
not exist without B so often as twice in three times, nor B without A so
often as once in every twice, there is some cause in existence which tends
to produce a conjunction between A and B.

Generalizing the result, we may say that if A occurs in a larger
proportion of the cases where B is than of the cases where B is not, then
will B also occur in a larger proportion of the cases where A is than of
the cases where A is not; and there is some connection, through causation,
between A and B. If we could ascend to the causes of the two phenomena, we
should find, at some stage, either proximate or remote, some cause or
causes common to both; and if we could ascertain what these are, we could
frame a generalization which would be true without restriction of place or
time; but until we can do so, the fact of a connection between the two
phenomena remains an empirical law.

§ 3. Having considered in what manner it may be determined whether any
given conjunction of phenomena is casual, or the result of some law, to
complete the theory of chance it is necessary that we should now consider
those effects which are partly the result of chance and partly of law, or,
in other words, in which the effects of casual conjunctions of causes are
habitually blended in one result with the effects of a constant cause.

This is a case of Composition of Causes; and the peculiarity of it is,
that instead of two or more causes intermixing their effects in a regular
manner with those of one another, we have now one constant cause,
producing an effect which is successively modified by a series of variable
causes. Thus, as summer advances, the approach of the sun to a vertical
position tends to produce a constant increase of temperature; but with
this effect of a constant cause, there are blended the effects of many
variable causes, winds, clouds, evaporation, electric agencies and the
like, so that the temperature of any given day depends in part on these
fleeting causes, and only in part on the constant cause. If the effect of
the constant cause is always accompanied and disguised by effects of
variable causes, it is impossible to ascertain the law of the constant
cause in the ordinary manner by separating it from all other causes and
observing it apart. Hence arises the necessity of an additional rule of
experimental inquiry.

When the action of a cause A is liable to be interfered with, not steadily
by the same cause or causes, but by different causes at different times,
and when these are so frequent, or so indeterminate, that we can not
possibly exclude all of them from any experiment, though we may vary them;
our resource is, to endeavor to ascertain what is the effect of all the
variable causes taken together. In order to do this, we make as many
trials as possible, preserving A invariable. The results of these
different trials will naturally be different, since the indeterminate
modifying causes are different in each; if, then, we do not find these
results to be progressive, but, on the contrary, to oscillate about a
certain point, one experiment giving a result a little greater, another a
little less, one a result tending a little more in one direction, another
a little more in the contrary direction; while the average or middle point
does not vary, but different sets of experiments (taken in as great a
variety of circumstances as possible) yield the same mean, provided only
they be sufficiently numerous; then that mean, or average result, is the
part, in each experiment, which is due to the cause A, and is the effect
which would have been obtained if A could have acted alone; the variable
remainder is the effect of chance, that is, of causes the co-existence of
which with the cause A was merely casual. The test of the sufficiency of
the induction in this case is, when any increase of the number of trials
from which the average is struck does not materially alter the average.

This kind of elimination, in which we do not eliminate any one assignable
cause, but the multitude of floating unassignable ones, may be termed the
Elimination of Chance. We afford an example of it when we repeat an
experiment, in order, by taking the mean of different results, to get rid
of the effects of the unavoidable errors of each individual experiment.
When there is no permanent cause, such as would produce a tendency to
error peculiarly in one direction, we are warranted by experience in
assuming that the errors on one side will, in a certain number of
experiments, about balance the errors on the contrary side. We therefore
repeat the experiment, until any change which is produced in the average
of the whole by further repetition, falls within limits of error
consistent with the degree of accuracy required by the purpose we have in
view.(175)

§ 4. In the supposition hitherto made, the effect of the constant cause A
has been assumed to form so great and conspicuous a part of the general
result, that its existence never could be a matter of uncertainty, and the
object of the eliminating process was only to ascertain _how much_ is
attributable to that cause; what is its exact law. Cases, however, occur
in which the effect of a constant cause is so small, compared with that of
some of the changeable causes with which it is liable to be casually
conjoined, that of itself it escapes notice, and the very existence of any
effect arising from a constant cause is first learned by the process which
in general serves only for ascertaining the quantity of that effect. This
case of induction may be characterized as follows: A given effect is known
to be chiefly, and not known not to be wholly, determined by changeable
causes. If it be wholly so produced, then if the aggregate be taken of a
sufficient number of instances, the effects of these different causes will
cancel one another. If, therefore, we do not find this to be the case,
but, on the contrary, after such a number of trials has been made that no
further increase alters the average result, we find that average to be,
not zero, but some other quantity, about which, though small in comparison
with the total effect, the effect nevertheless oscillates, and which is
the middle point in its oscillation; we may conclude this to be the effect
of some constant cause; which cause, by some of the methods already
treated of, we may hope to detect. This may be called _the discovery of a
residual phenomenon by eliminating the effects of chance_.

It is in this manner, for example, that loaded dice may be discovered. Of
course no dice are so clumsily loaded that they must always throw certain
numbers; otherwise the fraud would be instantly detected. The loading, a
constant cause, mingles with the changeable causes which determine what
cast will be thrown in each individual instance. If the dice were not
loaded, and the throw were left to depend entirely on the changeable
causes, these in a sufficient number of instances would balance one
another, and there would be no preponderant number of throws of any one
kind. If, therefore, after such a number of trials that no further
increase of their number has any material effect upon the average, we find
a preponderance in favor of a particular throw; we may conclude with
assurance that there is some constant cause acting in favor of that throw,
or, in other words, that the dice are not fair; and the exact amount of
the unfairness. In a similar manner, what is called the diurnal variation
of the barometer, which is very small compared with the variations arising
from the irregular changes in the state of the atmosphere, was discovered
by comparing the average height of the barometer at different hours of the
day. When this comparison was made, it was found that there was a small
difference, which on the average was constant, however the absolute
quantities might vary, and which difference, therefore, must be the effect
of a constant cause. This cause was afterward ascertained, deductively, to
be the rarefaction of the air, occasioned by the increase of temperature
as the day advances.

§ 5. After these general remarks on the nature of chance, we are prepared
to consider in what manner assurance may be obtained that a conjunction
between two phenomena, which has been observed a certain number of times,
is not casual, but a result of causation, and to be received, therefore,
as one of the uniformities of nature, though (until accounted for _a
priori_) only as an empirical law.

We will suppose the strongest case, namely, that the phenomenon B has
never been observed except in conjunction with A. Even then, the
probability that they are connected is not measured by the total number of
instances in which they have been found together, but by the excess of
that number above the number due to the absolutely frequency of A. If, for
example, A exists always, and therefore co-exists with every thing, no
number of instances of its co-existence with B would prove a connection;
as in our example of the fixed stars. If A be a fact of such common
occurrence that it may be presumed to be present in half of all the cases
that occur, and therefore in half the cases in which B occurs, it is only
the proportional excess above half that is to be reckoned as evidence
toward proving a connection between A and B.

In addition to the question, What is the number of coincidences which, on
an average of a great multitude of trials, may be expected to arise from
chance alone? there is also another question, namely, Of what extent of
deviation from that average is the occurrence credible, from chance alone,
in some number of instances smaller than that required for striking a fair
average? It is not only to be considered what is the general result of the
chances in the long run, but also what are the extreme limits of variation
from the general result, which may occasionally be expected as the result
of some smaller number of instances.

The consideration of the latter question, and any consideration of the
former beyond that already given to it, belong to what mathematicians term
the doctrine of chances, or, in a phrase of greater pretension, the Theory
of Probabilities.



                              Chapter XVIII.


Of The Calculation Of Chances.


§ 1. “Probability,” says Laplace,(176) “has reference partly to our
ignorance, partly to our knowledge. We know that among three or more
events, one, and only one, must happen; but there is nothing leading us to
believe that any one of them will happen rather than the others. In this
state of indecision, it is impossible for us to pronounce with certainty
on their occurrence. It is, however, probable that any one of these
events, selected at pleasure, will not take place; because we perceive
several cases, all equally possible, which exclude its occurrence, and
only one which favors it.

“The theory of chances consists in reducing all events of the same kind to
a certain number of cases equally possible, that is, such that we are
_equally undecided_ as to their existence; and in determining the number
of these cases which are favorable to the event of which the probability
is sought. The ratio of that number to the number of all the possible
cases is the measure of the probability; which is thus a fraction, having
for its numerator the number of cases favorable to the event, and for its
denominator the number of all the cases which are possible.”

To a calculation of chances, then, according to Laplace, two things are
necessary; we must know that of several events some one will certainly
happen, and no more than one; and we must not know, nor have any reason to
expect, that it will be one of these events rather than another. It has
been contended that these are not the only requisites, and that Laplace
has overlooked, in the general theoretical statement, a necessary part of
the foundation of the doctrine of chances. To be able (it has been said)
to pronounce two events equally probable, it is not enough that we should
know that one or the other must happen, and should have no grounds for
conjecturing which. Experience must have shown that the two events are of
equally frequent occurrence. Why, in tossing up a half-penny, do we reckon
it equally probable that we shall throw cross or pile? Because we know
that in any great number of throws, cross and pile are thrown about
equally often; and that the more throws we make, the more nearly the
equality is perfect. We may know this if we please by actual experiment,
or by the daily experience which life affords of events of the same
general character, or, deductively, from the effect of mechanical laws on
a symmetrical body acted upon by forces varying indefinitely in quantity
and direction. We may know it, in short, either by specific experience, or
on the evidence of our general knowledge of nature. But, in one way or the
other, we must know it, to justify us in calling the two events equally
probable; and if we knew it not, we should proceed as much at hap-hazard
in staking equal sums on the result, as in laying odds.

This view of the subject was taken in the first edition of the present
work; but I have since become convinced that the theory of chances, as
conceived by Laplace and by mathematicians generally, has not the
fundamental fallacy which I had ascribed to it.

We must remember that the probability of an event is not a quality of the
event itself, but a mere name for the degree of ground which we, or some
one else, have for expecting it. The probability of an event to one person
is a different thing from the probability of the same event to another, or
to the same person after he has acquired additional evidence. The
probability to me, that an individual of whom I know nothing but his name
will die within the year, is totally altered by my being told the next
minute that he is in the last stage of a consumption. Yet this makes no
difference in the event itself, nor in any of the causes on which it
depends. Every event is in itself certain, not probable; if we knew all,
we should either know positively that it will happen, or positively that
it will not. But its probability to us means the degree of expectation of
its occurrence, which we are warranted in entertaining by our present
evidence.

Bearing this in mind, I think it must be admitted, that even when we have
no knowledge whatever to guide our expectations, except the knowledge that
what happens must be some one of a certain number of possibilities, we may
still reasonably judge, that one supposition is more probable _to us_ than
another supposition; and if we have any interest at stake, we shall best
provide for it by acting conformably to that judgment.

§ 2. Suppose that we are required to take a ball from a box, of which we
only know that it contains balls both black and white, and none of any
other color. We know that the ball we select will be either a black or a
white ball; but we have no ground for expecting black rather than white,
or white rather than black. In that case, if we are obliged to make a
choice, and to stake something on one or the other supposition, it will,
as a question of prudence, be perfectly indifferent which; and we shall
act precisely as we should have acted if we had known beforehand that the
box contained an equal number of black and white balls. But though our
conduct would be the same, it would not be founded on any surmise that the
balls were in fact thus equally divided; for we might, on the contrary,
know by authentic information that the box contained ninety-nine balls of
one color, and only one of the other; still, if we are not told which
color has only one, and which has ninety-nine, the drawing of a white and
of a black ball will be equally probable to us. We shall have no reason
for staking any thing on the one event rather than on the other; the
option between the two will be a matter of indifference; in other words,
it will be an even chance.

But let it now be supposed that instead of two there are three
colors—white, black, and red; and that we are entirely ignorant of the
proportion in which they are mingled. We should then have no reason for
expecting one more than another, and if obliged to bet, should venture our
stake on red, white, or black with equal indifference. But should we be
indifferent whether we betted for or against some one color, as, for
instance, white? Surely not. From the very fact that black and red are
each of them separately equally probable to us with white, the two
together must be twice as probable. We should in this case expect not
white rather than white, and so much rather that we would lay two to one
upon it. It is true, there might, for aught we knew, be more white balls
than black and red together; and if so, our bet would, if we knew more, be
seen to be a disadvantageous one. But so also, for aught we knew, might
there be more red balls than black and white, or more black balls than
white and red, and in such case the effect of additional knowledge would
be to prove to us that our bet was more advantageous than we had supposed
it to be. There is in the existing state of our knowledge a rational
probability of two to one against white; a probability fit to be made a
basis of conduct. No reasonable person would lay an even wager in favor of
white against black and red; though against black alone or red alone he
might do so without imprudence.

The common theory, therefore, of the calculation of chances, appears to be
tenable. Even when we know nothing except the number of the possible and
mutually excluding contingencies, and are entirely ignorant of their
comparative frequency, we may have grounds, and grounds numerically
appreciable, for acting on one supposition rather than on another; and
this is the meaning of Probability.

§ 3. The principle, however, on which the reasoning proceeds, is
sufficiently evident. It is the obvious one that when the cases which
exist are shared among several kinds, it is impossible that _each_ of
those kinds should be a majority of the whole: on the contrary, there must
be a majority against each kind, except one at most; and if any kind has
more than its share in proportion to the total number, the others
collectively must have less. Granting this axiom, and assuming that we
have no ground for selecting any one kind as more likely than the rest to
surpass the average proportion, it follows that we can not rationally
presume this of any, which we should do if we were to bet in favor of it,
receiving less odds than in the ratio of the number of the other kinds.
Even, therefore, in this extreme case of the calculation of probabilities,
which does not rest on special experience at all, the logical ground of
the process is our knowledge—such knowledge as we then have—of the laws
governing the frequency of occurrence of the different cases; but in this
case the knowledge is limited to that which, being universal and
axiomatic, does not require reference to specific experience, or to any
considerations arising out of the special nature of the problem under
discussion.

Except, however, in such cases as games of chance, where the very purpose
in view requires ignorance instead of knowledge, I can conceive no case in
which we ought to be satisfied with such an estimate of chances as this—an
estimate founded on the absolute minimum of knowledge respecting the
subject. It is plain that, in the case of the colored balls, a very slight
ground of surmise that the white balls were really more numerous than
either of the other colors, would suffice to vitiate the whole of the
calculations made in our previous state of indifference. It would place us
in that position of more advanced knowledge, in which the probabilities,
to us, would be different from what they were before; and in estimating
these new probabilities we should have to proceed on a totally different
set of data, furnished no longer by mere counting of possible
suppositions, but by specific knowledge of facts. Such data it should
always be our endeavor to obtain; and in all inquiries, unless on subjects
equally beyond the range of our means of knowledge and our practical uses,
they may be obtained, if not good, at least better than none at all.(177)

It is obvious, too, that even when the probabilities are derived from
observation and experiment, a very slight improvement in the data, by
better observations, or by taking into fuller consideration the special
circumstances of the case, is of more use than the most elaborate
application of the calculus to probabilities founded on the data in their
previous state of inferiority. The neglect of this obvious reflection has
given rise to misapplications of the calculus of probabilities which have
made it the real opprobrium of mathematics. It is sufficient to refer to
the applications made of it to the credibility of witnesses, and to the
correctness of the verdicts of juries. In regard to the first, common
sense would dictate that it is impossible to strike a general average of
the veracity and other qualifications for true testimony of mankind, or of
any class of them; and even if it were possible, the employment of it for
such a purpose implies a misapprehension of the use of averages, which
serve, indeed, to protect those whose interest is at stake, against
mistaking the general result of large masses of instances, but are of
extremely small value as grounds of expectation in any one individual
instance, unless the case be one of those in which the great majority of
individual instances do not differ much from the average. In the case of a
witness, persons of common sense would draw their conclusions from the
degree of consistency of his statements, his conduct under
cross-examination, and the relation of the case itself to his interests,
his partialities, and his mental capacity, instead of applying so rude a
standard (even if it were capable of being verified) as the ratio between
the number of true and the number of erroneous statements which he may be
supposed to make in the course of his life.

Again, on the subject of juries or other tribunals, some mathematicians
have set out from the proposition that the judgment of any one judge or
juryman is, at least in some small degree, more likely to be right than
wrong, and have concluded that the chance of a number of persons
concurring in a wrong verdict is diminished the more the number is
increased; so that if the judges are only made sufficiently numerous, the
correctness of the judgment may be reduced almost to certainty. I say
nothing of the disregard shown to the effect produced on the moral
position of the judges by multiplying their numbers, the virtual
destruction of their individual responsibility, and weakening of the
application of their minds to the subject. I remark only the fallacy of
reasoning from a wide average to cases necessarily differing greatly from
any average. It may be true that, taking all causes one with another, the
opinion of any one of the judges would be oftener right than wrong; but
the argument forgets that in all but the more simple cases, in all cases
in which it is really of much consequence what the tribunal is, the
proposition might probably be reversed; besides which, the cause of error,
whether arising from the intricacy of the case or from some common
prejudice or mental infirmity, if it acted upon one judge, would be
extremely likely to affect all the others in the same manner, or at least
a majority, and thus render a wrong instead of a right decision more
probable the more the number was increased.

These are but samples of the errors frequently committed by men who,
having made themselves familiar with the difficult formulæ which algebra
affords for the estimation of chances under suppositions of a complex
character, like better to employ those formulæ in computing what are the
probabilities to a person half informed about a case than to look out for
means of being better informed. Before applying the doctrine of chances to
any scientific purpose, the foundation must be laid for an evaluation of
the chances, by possessing ourselves of the utmost attainable amount of
positive knowledge. The knowledge required is that of the comparative
frequency with which the different events in fact occur. For the purposes,
therefore, of the present work, it is allowable to suppose that
conclusions respecting the probability of a fact of a particular kind rest
on our knowledge of the proportion between the cases in which facts of
that kind occur, and those in which they do not occur; this knowledge
being either derived from specific experiment, or deduced from our
knowledge of the causes in operation which tend to produce, compared with
those which tend to prevent, the fact in question.

Such calculation of chances is grounded on an induction; and to render the
calculation legitimate, the induction must be a valid one. It is not less
an induction, though it does not prove that the event occurs in all cases
of a given description, but only that out of a given number of such cases
it occurs in about so many. The fraction which mathematicians use to
designate the probability of an event is the ratio of these two numbers;
the ascertained proportion between the number of cases in which the event
occurs and the sum of all the cases, those in which it occurs and in which
it does not occur, taken together. In playing at cross and pile, the
description of cases concerned are throws, and the probability of cross is
one-half, because if we throw often enough cross is thrown about once in
every two throws. In the cast of a die, the probability of ace is
one-sixth; not simply because there are six possible throws, of which ace
is one, and because we do not know any reason why one should turn up
rather than another—though I have admitted the validity of this ground in
default of a better—but because we do actually know, either by reasoning
or by experience, that in a hundred or a million of throws ace is thrown
in about one-sixth of that number, or once in six times.

§ 4. I say, “either by reasoning or by experience,” meaning specific
experience. But in estimating probabilities, it is not a matter of
indifference from which of these two sources we derive our assurance. The
probability of events, as calculated from their mere frequency in past
experience, affords a less secure basis for practical guidance than their
probability as deduced from an equally accurate knowledge of the frequency
of occurrence of their causes.

The generalization that an event occurs in ten out of every hundred cases
of a given description, is as real an induction as if the generalization
were that it occurs in all cases. But when we arrive at the conclusion by
merely counting instances in actual experience, and comparing the number
of cases in which A has been present with the number in which it has been
absent, the evidence is only that of the Method of Agreement, and the
conclusion amounts only to an empirical law. We can make a step beyond
this when we can ascend to the causes on which the occurrence of A or its
non-occurrence will depend, and form an estimate of the comparative
frequency of the causes favorable and of those unfavorable to the
occurrence. These are data of a higher order, by which the empirical law
derived from a mere numerical comparison of affirmative and negative
instances will be either corrected or confirmed, and in either case we
shall obtain a more correct measure of probability than is given by that
numerical comparison. It has been well remarked that in the kind of
examples by which the doctrine of chances is usually illustrated, that of
balls in a box, the estimate of probabilities is supported by reasons of
causation, stronger than specific experience. “What is the reason that in
a box where there are nine black balls and one white, we expect to draw a
black ball nine times as much (in other words, nine times as often,
frequency being the gauge of intensity in expectation) as a white?
Obviously because the local conditions are nine times as favorable;
because the hand may alight in nine places and get a black ball, while it
can only alight in one place and find a white ball; just for the same
reason that we do not expect to succeed in finding a friend in a crowd,
the conditions in order that we and he should come together being many and
difficult. This of course would not hold to the same extent were the white
balls of smaller size than the black, neither would the probability remain
the same; the larger ball would be much more likely to meet the
hand.”(178)

It is, in fact, evident that when once causation is admitted as a
universal law, our expectation of events can only be rationally grounded
on that law. To a person who recognizes that every event depends on
causes, a thing’s having happened once is a reason for expecting it to
happen again, only because proving that there exists, or is liable to
exist, a cause adequate to produce it.(179) The frequency of the
particular event, apart from all surmise respecting its cause, can give
rise to no other induction than that _per enumerationem simplicem_; and
the precarious inferences derived from this are superseded, and disappear
from the field as soon as the principle of causation makes its appearance
there.

Notwithstanding, however, the abstract superiority of an estimate of
probability grounded on causes, it is a fact that in almost all cases in
which chances admit of estimation sufficiently precise to render their
numerical appreciation of any practical value, the numerical data are not
drawn from knowledge of the causes, but from experience of the events
themselves. The probabilities of life at different ages or in different
climates; the probabilities of recovery from a particular disease; the
chances of the birth of male or female offspring; the chances of the
destruction of houses or other property by fire; the chances of the loss
of a ship in a particular voyage, are deduced from bills of mortality,
returns from hospitals, registers of births, of shipwrecks, etc., that is,
from the observed frequency not of the causes, but of the effects. The
reason is, that in all these classes of facts the causes are either not
amenable to direct observation at all, or not with the requisite
precision, and we have no means of judging of their frequency except from
the empirical law afforded by the frequency of the effects. The inference
does not the less depend on causation alone. We reason from an effect to a
similar effect by passing through the cause. If the actuary of an
insurance office infers from his tables that among a hundred persons now
living of a particular age, five on the average will attain the age of
seventy, his inference is legitimate, not for the simple reason that this
is the proportion who have lived till seventy in times past, but because
the fact of their having so lived shows that this is the proportion
existing, at that place and time, between the causes which prolong life to
the age of seventy and those tending to bring it to an earlier close.(180)

§ 5. From the preceding principles it is easy to deduce the demonstration
of that theorem of the doctrine of probabilities which is the foundation
of its application to inquiries for ascertaining the occurrence of a given
event, or the reality of an individual fact. The signs or evidences by
which a fact is usually proved are some of its consequences; and the
inquiry hinges upon determining what cause is most likely to have produced
a given effect. The theorem applicable to such investigations is the Sixth
Principle in Laplace’s “_Essai Philosophique sur les Probabilités_,” which
is described by him as the “fundamental principle of that branch of the
Analysis of Chances which consists in ascending from events to their
causes.”(181)

Given an effect to be accounted for, and there being several causes which
might have produced it, but of the presence of which in the particular
case nothing is known; the probability that the effect was produced by any
one of these causes _is as the antecedent probability of the cause,
multiplied by the probability that the cause, if it existed, would have
produced the given effect_.

Let M be the effect, and A, B, two causes, by either of which it might
have been produced. To find the probability that it was produced by the
one and not by the other, ascertain which of the two is most likely to
have existed, and which of them, if it did exist, was most likely to
produce the effect M: the probability sought is a compound of these two
probabilities.

CASE I. Let the causes be both alike in the second respect: either A or B,
when it exists, being supposed equally likely (or equally certain) to
produce M; but let A be in itself twice as likely as B to exist, that is,
twice as frequent a phenomenon. Then it is twice as likely to have existed
in this case, and to have been the cause which produced M.

For, since A exists in nature twice as often as B, in any 300 cases in
which one or other existed, A has existed 200 times and B 100. But either
A or B must have existed wherever M is produced; therefore, in 300 times
that M is produced, A was the producing cause 200 times, B only 100, that
is, in the ratio of 2 to 1. Thus, then, if the causes are alike in their
capacity of producing the effect, the probability as to which actually
produced it is in the ratio of their antecedent probabilities.

CASE II. Reversing the last hypothesis, let us suppose that the causes are
equally frequent, equally likely to have existed, but not equally likely,
if they did exist, to produce M; that in three times in which A occurs, it
produces that effect twice, while B, in three times, produces it only
once. Since the two causes are equally frequent in their occurrence; in
every six times that either one or the other exists, A exists three times
and B three times. A, of its three times, produces M in two; B, of its
three times, produces M in one. Thus, in the whole six times, M is only
produced thrice; but of that thrice it is produced twice by A, once only
by B. Consequently, when the antecedent probabilities of the causes are
equal, the chances that the effect was produced by them are in the ratio
of the probabilities that if they did exist they would produce the effect.

CASE III. The third case, that in which the causes are unlike in both
respects, is solved by what has preceded. For, when a quantity depends on
two other quantities, in such a manner that while either of them remains
constant it is proportional to the other, it must necessarily be
proportional to the product of the two quantities, the product being the
only function of the two which obeys that law of variation. Therefore, the
probability that M was produced by either cause, is as the antecedent
probability of the cause, multiplied by the probability that if it existed
it would produce M. Which was to be demonstrated.

Or we may prove the third case as we proved the first and second. Let A be
twice as frequent as B, and let them also be unequally likely, when they
exist, to produce M; let A produce it twice in four times, B thrice in
four times. The antecedent probability of A is to that of B as 2 to 1; the
probabilities of their producing M are as 2 to 3; the product of these
ratios is the ratio of 4 to 3; and this will be the ratio of the
probabilities that A or B was the producing cause in the given instance.
For, since A is twice as frequent as B, out of twelve cases in which one
or other exists, A exists in 8 and B in 4. But of its eight cases, A, by
the supposition, produces M in only 4, while B of its four cases produces
M in 3. M, therefore, is only produced at all in seven of the twelve
cases; but in four of these it is produced by A, in three by B; hence the
probabilities of its being produced by A and by B are as 4 to 3, and are
expressed by the fractions 4/7 and 3/7. Which was to be demonstrated.

§ 6. It remains to examine the bearing of the doctrine of chances on the
peculiar problem which occupied us in the preceding chapter, namely, how
to distinguish coincidences which are casual from those which are the
result of law; from those in which the facts which accompany or follow one
another are somehow connected through causation.

The doctrine of chances affords means by which, if we knew the _average_
number of coincidences to be looked for between two phenomena connected
only casually, we could determine how often any given deviation from that
average will occur by chance. If the probability of any casual
coincidence, considered in itself, be 1/_m_, the probability that the same
coincidence will be repeated _n_ times in succession is 1/_m_n. For
example, in one throw of a die the probability of ace being 1/6; the
probability of throwing ace twice in succession will be 1 divided by the
square of 6, or 1/36. For ace is thrown at the first throw once in six, or
six in thirty-six times, and of those six, the die being cast again, ace
will be thrown but once; being altogether once in thirty-six times. The
chance of the same cast three times successively is, by a similar
reasoning, 1/63 or 1/216; that is, the event will happen, on a large
average, only once in two hundred and sixteen throws.

We have thus a rule by which to estimate the probability that any given
series of coincidences arises from chance, provided we can measure
correctly the probability of a single coincidence. If we can obtain an
equally precise expression for the probability that the same series of
coincidences arises from causation, we should only have to compare the
numbers. This, however, can rarely be done. Let us see what degree of
approximation can practically be made to the necessary precision.

The question falls within Laplace’s sixth principle, just demonstrated.
The given fact, that is to say, the series of coincidences, may have
originated either in a casual conjunction of causes or in a law of nature.
The probabilities, therefore, that the fact originated in these two modes,
are as their antecedent probabilities, multiplied by the probabilities
that if they existed they would produce the effect. But the particular
combination of chances, if it occurred, or the law of nature if real,
would certainly produce the series of coincidences. The probabilities,
therefore, that the coincidences are produced by the two causes in
question are as the antecedent probabilities of the causes. One of these,
the antecedent probability of the combination of mere chances which would
produce the given result, is an appreciable quantity. The antecedent
probability of the other supposition may be susceptible of a more or less
exact estimation, according to the nature of the case.

In some cases, the coincidence, supposing it to be the result of causation
at all, must be the result of a known cause; as the succession of aces, if
not accidental, must arise from the loading of the die. In such cases we
may be able to form a conjecture as to the antecedent probability of such
a circumstance from the characters of the parties concerned, or other such
evidence; but it would be impossible to estimate that probability with any
thing like numerical precision. The counter-probability, however, that of
the accidental origin of the coincidence, dwindling so rapidly as it does
at each new trial, the stage is soon reached at which the chance of
unfairness in the die, however small in itself, must be greater than that
of a casual coincidence; and on this ground, a practical decision can
generally be come to without much hesitation, if there be the power of
repeating the experiment.

When, however, the coincidence is one which can not be accounted for by
any known cause, and the connection between the two phenomena, if produced
by causation, must be the result of some law of nature hitherto unknown;
which is the case we had in view in the last chapter; then, though the
probability of a casual coincidence may be capable of appreciation, that
of the counter-supposition, the existence of an undiscovered law of
nature, is clearly unsusceptible of even an approximate valuation. In
order to have the data which such a case would require, it would be
necessary to know what proportion of all the individual sequences or
co-existences occurring in nature are the result of law, and what
proportion are mere casual coincidences. It being evident that we can not
form any plausible conjecture as to this proportion, much less appreciate
it numerically, we can not attempt any precise estimation of the
comparitive probabilities. But of this we are sure, that the detection of
an unknown law of nature—of some previously unrecognized constancy of
conjunction among phenomena—is no uncommon event. If, therefore, the
number of instances in which a coincidence is observed, over and above
that which would arise on the average from the mere concurrence of
chances, be such that so great an amount of coincidences from accident
alone would be an extremely uncommon event; we have reason to conclude
that the coincidence is the effect of causation, and may be received
(subject to correction from further experience) as an empirical law.
Further than this, in point of precision, we can not go; nor, in most
cases, is greater precision required, for the solution of any practical
doubt.(182)



                               Chapter XIX.


Of The Extension Of Derivative Laws To Adjacent Cases.


§ 1. We have had frequent occasion to notice the inferior generality of
derivative laws, compared with the ultimate laws from which they are
derived. This inferiority, which affects not only the extent of the
propositions themselves, but their degree of certainty within that extent,
is most conspicuous in the uniformities of co-existence and sequence
obtaining between effects which depend ultimately on different primeval
causes. Such uniformities will only obtain where there exists the same
collocation of those primeval causes. If the collocation varies, though
the laws themselves remain the same, a totally different set of derivative
uniformities may, and generally will, be the result.

Even where the derivative uniformity is between different effects of the
same cause, it will by no means obtain as universally as the law of the
cause itself. If _a_ and _b_ accompany or succeed one another as effects
of the cause A, it by no means follows that A is the only cause which can
produce them, or that if there be another cause, as B, capable of
producing _a_, it must produce _b_ likewise. The conjunction, therefore,
of _a_ and _b_ perhaps does not hold universally, but only in the
instances in which _a_ arises from A. When it is produced by _a_ cause
other than A, _a_ and _b_ may be dissevered. Day (for example) is always
in our experience followed by night; but day is not the cause of night;
both are successive effects of _a_ common cause, the periodical passage of
the spectator into and out of the earth’s shadow, consequent on the
earth’s rotation, and on the illuminating property of the sun. If,
therefore, day is ever produced by a different cause or set of causes from
this, day will not, or at least may not, be followed by night. On the
sun’s own surface, for instance, this may be the case.

Finally, even when the derivative uniformity is itself a law of causation
(resulting from the combination of several causes), it is not altogether
independent of collocations. If a cause supervenes, capable of wholly or
partially counteracting the effect of any one of the conjoined causes, the
effect will no longer conform to the derivative law. While, therefore,
each ultimate law is only liable to frustration from one set of
counteracting causes, the derivative law is liable to it from several.
Now, the possibility of the occurrence of counteracting causes which do
not arise from any of the conditions involved in the law itself depends on
the original collocations.

It is true that, as we formerly remarked, laws of causation, whether
ultimate or derivative, are, in most cases, fulfilled even when
counteracted; the cause produces its effect, though that effect is
destroyed by something else. That the effect may be frustrated, is,
therefore, no objection to the universality of laws of causation. But it
is fatal to the universality of the sequences or co-existences of effects,
which compose the greater part of the derivative laws flowing from laws of
causation. When, from the law of a certain combination of causes, there
results a certain order in the effects; as from the combination of a
single sun with the rotation of an opaque body round its axis, there
results, on the whole surface of that opaque body, an alternation of day
and night; then, if we suppose one of the combined causes counteracted,
the rotation stopped, the sun extinguished, or a second sun superadded,
the truth of that particular law of causation is in no way affected; it is
still true that one sun shining on an opaque revolving body will
alternately produce day and night; but since the sun no longer does shine
on such a body, the derivative uniformity, the succession of day and night
on the given planet, is no longer true. Those derivative uniformities,
therefore, which are not laws of causation, are (except in the rare case
of their depending on one cause alone, not on a combination of causes)
always more or less contingent on collocations; and are hence subject to
the characteristic infirmity of empirical laws—that of being admissible
only where the collocations are known by experience to be such as are
requisite for the truth of the law; that is, only within the conditions of
time and place confirmed by actual observation.

§ 2. This principle, when stated in general terms, seems clear and
indisputable; yet many of the ordinary judgments of mankind, the propriety
of which is not questioned, have at least the semblance of being
inconsistent with it. On what grounds, it may be asked, do we expect that
the sun will rise to-morrow? To-morrow is beyond the limits of time
comprehended in our observations. They have extended over some thousands
of years past, but they do not include the future. Yet we infer with
confidence that the sun will rise to-morrow; and nobody doubts that we are
entitled to do so. Let us consider what is the warrant for this
confidence.

In the example in question, we know the causes on which the derivative
uniformity depends. They are: the sun giving out light, the earth in a
state of rotation and intercepting light. The induction which shows these
to be the real causes, and not merely prior effects of a common cause,
being complete, the only circumstances which could defeat the derivative
law are such as would destroy or counteract one or other of the combined
causes. While the causes exist and are not counteracted, the effect will
continue. If they exist and are not counteracted to-morrow, the sun will
rise to-morrow.

Since the causes, namely, the sun and the earth, the one in the state of
giving out light, the other in a state of rotation, will exist until
something destroys them, all depends on the probabilities of their
destruction, or of their counteraction. We know by observation (omitting
the inferential proofs of an existence for thousands of ages anterior)
that these phenomena have continued for (say) five thousand years. Within
that time there has existed no cause sufficient to diminish them
appreciably, nor which has counteracted their effect in any appreciable
degree. The chance, therefore, that the sun may not rise to-morrow amounts
to the chance that some cause, which has not manifested itself in the
smallest degree during five thousand years, will exist to-morrow in such
intensity as to destroy the sun or the earth, the sun’s light or the
earth’s rotation, or to produce an immense disturbance in the effect
resulting from those causes.

Now, if such a cause will exist to-morrow, or at any future time, some
cause, proximate or remote, of that cause must exist now, and must have
existed during the whole of the five thousand years. If, therefore, the
sun do not rise to-morrow, it will be because some cause has existed, the
effects of which, though during five thousand years they have not amounted
to a perceptible quantity, will in one day become overwhelming. Since this
cause has not been recognized during such an interval of time by observers
stationed on our earth, it must, if it be a single agent, be either one
whose effects develop themselves gradually and very slowly, or one which
existed in regions beyond our observation, and is now on the point of
arriving in our part of the universe. Now all causes which we have
experience of act according to laws incompatible with the supposition that
their effects, after accumulating so slowly as to be imperceptible for
five thousand years, should start into immensity in a single day. No
mathematical law of proportion between an effect and the quantity or
relations of its cause could produce such contradictory results. The
sudden development of an effect of which there was no previous trace
always arises from the coming together of several distinct causes, not
previously conjoined; but if such sudden conjunction is destined to take
place, the causes, or _their_ causes, must have existed during the entire
five thousand years; and their not having once come together during that
period shows how rare that particular combination is. We have, therefore,
the warrant of a rigid induction for considering it probable, in a degree
undistinguishable from certainty, that the known conditions requisite for
the sun’s rising will exist to-morrow.

§ 3. But this extension of derivative laws, not causative, beyond the
limits of observation can only be to _adjacent_ cases. If, instead of
to-morrow, we had said this day twenty thousand years, the inductions
would have been any thing but conclusive. That a cause which, in
opposition to very powerful causes, produced no perceptible effect during
five thousand years, should produce a very considerable one by the end of
twenty thousand, has nothing in it which is not in conformity with our
experience of causes. We know many agents, the effect of which in a short
period does not amount to a perceptible quantity, but by accumulating for
a much longer period becomes considerable. Besides, looking at the immense
multitude of the heavenly bodies, their vast distances, and the rapidity
of the motion of such of them as are known to move, it is a supposition
not at all contradictory to experience that some body may be in motion
toward us, or we toward it, within the limits of whose influence we have
not come during five thousand years, but which in twenty thousand more may
be producing effects upon us of the most extraordinary kind. Or the fact
which is capable of preventing sunrise may be, not the cumulative effect
of one cause, but some new combination of causes; and the chances
favorable to that combination, though they have not produced it once in
five thousand years, may produce it once in twenty thousand. So that the
inductions which authorize us to expect future events, grow weaker and
weaker the further we look into the future, and at length become
inappreciable.

We have considered the probabilities of the sun’s rising to-morrow, as
derived from the real laws; that is, from the laws of the causes on which
that uniformity is dependent. Let us now consider how the matter would
have stood if the uniformity had been known only as an empirical law; if
we had not been aware that the sun’s light and the earth’s rotation (or
the sun’s motion) were the causes on which the periodical occurrence of
daylight depends. We could have extended this empirical law to cases
adjacent in time, though not to so great a distance of time as we can now.
Having evidence that the effects had remained unaltered and been
punctually conjoined for five thousand years, we could infer that the
unknown causes on which the conjunction is dependent had existed
undiminished and uncounteracted during the same period. The same
conclusions, therefore, would follow as in the preceding case, except that
we should only know that during five thousand years nothing had occurred
to defeat perceptibly this particular effect; while, when we know the
causes, we have the additional assurance that during that interval no such
change has been noticeable in the causes themselves as by any degree of
multiplication or length of continuance could defeat the effect.

To this must be added, that when we know the causes, we may be able to
judge whether there exists any known cause capable of counteracting them,
while as long as they are unknown, we can not be sure but that if we did
know them, we could predict their destruction from causes actually in
existence. A bed-ridden savage, who had never seen the cataract of
Niagara, but who lived within hearing of it, might imagine that the sound
he heard would endure forever; but if he knew it to be the effect of a
rush of waters over a barrier of rock which is progressively wearing away,
he would know that within a number of ages which may be calculated it will
be heard no more. In proportion, therefore, to our ignorance of the causes
on which the empirical law depends, we can be less assured that it will
continue to hold good; and the further we look into futurity, the less
improbable is it that some one of the causes, whose co-existence gives
rise to the derivative uniformity, may be destroyed or counteracted. With
every prolongation of time the chances multiply of such an event; that is
to say, its non-occurrence hitherto becomes a less guarantee of its not
occurring within the given time. If, then, it is only to cases which in
point of time are adjacent (or nearly adjacent) to those which we have
actually observed, that _any_ derivative law, not of causation, can be
extended with an assurance equivalent to certainty, much more is this true
of a merely empirical law. Happily, for the purposes of life it is to such
cases alone that we can almost ever have occasion to extend them.

In respect of place, it might seem that a merely empirical law could not
be extended even to adjacent cases; that we could have no assurance of its
being true in any place where it has not been specially observed. The past
duration of a cause is a guarantee for its future existence, unless
something occurs to destroy it; but the existence of a cause in one or any
number of places is no guarantee for its existence in any other place,
since there is no uniformity in the collocations of primeval causes. When,
therefore, an empirical law is extended beyond the local limits within
which it has been found true by observation, the cases to which it is thus
extended must be such as are presumably within the influence of the same
individual agents. If we discover a new planet within the known bounds of
the solar system (or even beyond those bounds, but indicating its
connection with the system by revolving round the sun), we may conclude,
with great probability, that it revolves on its axis. For all the known
planets do so; and this uniformity points to some common cause, antecedent
to the first records of astronomical observation; and though the nature of
this cause can only be matter of conjecture, yet if it be, as is not
unlikely, and as Laplace’s theory supposes, not merely the same kind of
cause, but the same individual cause (such as an impulse given to all the
bodies at once), that cause, acting at the extreme points of the space
occupied by the sun and planets, is likely, unless defeated by some
counteracting cause, to have acted at every intermediate point, and
probably somewhat beyond; and therefore acted, in all probability, upon
the supposed newly-discovered planet.

When, therefore, effects which are always found conjoined can be traced
with any probability to an identical (and not merely a similar) origin, we
may with the same probability extend the empirical law of their
conjunction to all places within the extreme local boundaries within which
the fact has been observed, subject to the possibility of counteracting
causes in some portion of the field. Still more confidently may we do so
when the law is not merely empirical; when the phenomena which we find
conjoined are effects of ascertained causes, from the laws of which the
conjunction of their effects is deducible. In that case, we may both
extend the derivative uniformity over a larger space, and with less
abatement for the chance of counteracting causes. The first, because
instead of the local boundaries of our observation of the fact itself, we
may include the extreme boundaries of the ascertained influence of its
causes. Thus the succession of day and night, we know, holds true of all
the bodies of the solar system except the sun itself; but we know this
only because we are acquainted with the causes. If we were not, we could
not extend the proposition beyond the orbits of the earth and moon, at
both extremities of which we have the evidence of observation for its
truth. With respect to the probability of counteracting causes, it has
been seen that this calls for a greater abatement of confidence, in
proportion to our ignorance of the causes on which the phenomena depend.
On both accounts, therefore, a derivative law which we know how to
resolve, is susceptible of a greater extension to cases adjacent in place,
than a merely empirical law.



                               Chapter XX.


Of Analogy.


§ 1. The word Analogy, as the name of a mode of reasoning, is generally
taken for some kind of argument supposed to be of an inductive nature, but
not amounting to a complete induction. There is no word, however, which is
used more loosely, or in a greater variety of senses, than Analogy. It
sometimes stands for arguments which may be examples of the most rigorous
induction. Archbishop Whately, for instance, following Ferguson and other
writers, defines Analogy conformably to its primitive acceptation, that
which was given to it by mathematicians: Resemblance of Relations. In this
sense, when a country which has sent out colonies is termed the mother
country, the expression is analogical, signifying that the colonies of a
country stand in the same _relation_ to her in which children stand to
their parents. And if any inference be drawn from this resemblance of
relations, as, for instance, that obedience or affection is due from
colonies to the mother country, this is called reasoning by analogy. Or,
if it be argued that a nation is most beneficially governed by an assembly
elected by the people, from the admitted fact that other associations for
a common purpose, such as joint-stock companies, are best managed by a
committee chosen by the parties interested; this, too, is an argument from
analogy in the preceding sense, because its foundation is, not that a
nation is like a joint-stock company, or Parliament like a board of
directors, but that Parliament stands in the same _relation_ to the nation
in which a board of directors stands to a joint-stock company. Now, in an
argument of this nature, there is no inherent inferiority of
conclusiveness. Like other arguments from resemblance, it may amount to
nothing, or it may be a perfect and conclusive induction. The circumstance
in which the two cases resemble, may be capable of being shown to be the
_material_ circumstance; to be that on which all the consequences,
necessary to be taken into account in the particular discussion, depend.
In the example last given, the resemblance is one of relation; the
_fundamentum relationis_ being the management, by a few persons, of
affairs in which a much greater number are interested along with them.
Now, some may contend that this circumstance which is common to the two
cases, and the various consequences which follow from it, have the chief
share in determining all the effects which make up what we term good or
bad administration. If they can establish this, their argument has the
force of a rigorous induction; if they can not, they are said to have
failed in proving the analogy between the two cases; a mode of speech
which implies that when the analogy can be proved, the argument founded on
it can not be resisted.

§ 2. It is on the whole more usual, however, to extend the name of
analogical evidence to arguments from any sort of resemblance, provided
they do not amount to a complete induction; without peculiarly
distinguishing resemblance of relations. Analogical reasoning, in this
sense, may be reduced to the following formula: Two things resemble each
other in one or more respects; a certain proposition is true of the one;
therefore it is true of the other. But we have nothing here by which to
discriminate analogy from induction, since this type will serve for all
reasoning from experience. In the strictest induction, equally with the
faintest analogy, we conclude because A resembles B in one or more
properties, that it does so in a certain other property. The difference
is, that in the case of a complete induction it has been previously shown,
by due comparison of instances, that there is an invariable conjunction
between the former property or properties and the latter property; but in
what is called analogical reasoning, no such conjunction has been made
out. There have been no opportunities of putting in practice the Method of
Difference, or even the Method of Agreement; but we conclude (and that is
all which the argument of analogy amounts to) that a fact _m_, known to be
true of A, is more likely to be true of B if B agrees with A in some of
its properties (even though no connection is known to exist between _m_
and those properties), than if no resemblance at all could be traced
between B and any other thing known to possess the attribute _m_.

To this argument it is of course requisite that the properties common to A
with B shall be merely not known to be connected with _m_; they must not
be properties known to be unconnected with it. If, either by processes of
elimination, or by deduction from previous knowledge of the laws of the
properties in question, it can be concluded that they have nothing to do
with _m_, the argument of analogy is put out of court. The supposition
must be that _m_ is an effect really dependent on some property of A, but
we know not on which. We can not point out any of the properties of A,
which is the cause of _m_, or united with it by any law. After rejecting
all which we know to have nothing to do with it, there remain several
between which we are unable to decide; of which remaining properties, B
possesses one or more. This, accordingly, we consider as affording
grounds, of more or less strength, for concluding by analogy that B
possesses the attribute _m_.

There can be no doubt that every such resemblance which can be pointed out
between B and A, affords some degree of probability, beyond what would
otherwise exist, in favor of the conclusion drawn from it. If B resembled
A in all its ultimate properties, its possessing the attribute _m_ would
be a certainty, not a probability; and every resemblance which can be
shown to exist between them, places it by so much the nearer to that
point. If the resemblance be in an ultimate property, there will be
resemblance in all the derivative properties dependent on that ultimate
property, and of these _m_ may be one. If the resemblance be in a
derivative property, there is reason to expect resemblance in the ultimate
property on which it depends, and in the other derivative properties
dependent on the same ultimate property. Every resemblance which can be
shown to exist, affords ground for expecting an indefinite number of other
resemblances; the particular resemblance sought will, therefore, be
oftener found among things thus known to resemble, than among things
between which we know of no resemblance.

For example, I might infer that there are probably inhabitants in the
moon, because there are inhabitants on the earth, in the sea, and in the
air: and this is the evidence of analogy. The circumstance of having
inhabitants is here assumed not to be an ultimate property, but (as is
reasonable to suppose) a consequence of other properties; and depending,
therefore, in the case of the earth, on some of its properties as a
portion of the universe, but on which of those properties we know not. Now
the moon resembles the earth in being a solid, opaque, nearly spherical
substance, appearing to contain, or to have contained, active volcanoes;
receiving heat and light from the sun, in about the same quantity as our
earth; revolving on its axis; composed of materials which gravitate, and
obeying all the various laws resulting from that property. And I think no
one will deny that if this were all that was known of the moon, the
existence of inhabitants in that luminary would derive from these various
resemblances to the earth, a greater degree of probability than it would
otherwise have; though the amount of the augmentation it would be useless
to attempt to estimate.

If, however, every resemblance proved between B and A, in any point not
known to be immaterial with respect to _m_, forms some additional reason
for presuming that B has the attribute _m_; it is clear, _è contra_, that
every dissimilarity which can be proved between them furnishes a
counter-probability of the same nature on the other side. It is not,
indeed, unusual that different ultimate properties should, in some
particular instances, produce the same derivative property; but on the
whole it is certain that things which differ in their ultimate properties,
will differ at least as much in the aggregate of their derivative
properties, and that the differences which are unknown will, on the
average of cases, bear some proportion to those which are known. There
will, therefore, be a competition between the known points of agreement
and the known points of difference in A and B; and according as the one or
the other may be deemed to preponderate, the probability derived from
analogy will be for or against B’s having the property _m_. The moon, for
instance, agrees with the earth in the circumstances already mentioned;
but differs in being smaller, in having its surface more unequal, and
apparently volcanic throughout, in having, at least on the side next the
earth, no atmosphere sufficient to refract light, no clouds, and (it is
therefore concluded) no water. These differences, considered merely as
such, might perhaps balance the resemblances, so that analogy would afford
no presumption either way. But considering that some of the circumstances
which are wanting on the moon are among those which, on the earth, are
found to be indispensable conditions of animal life, we may conclude that
if that phenomenon does exist in the moon (or at all events on the nearer
side), it must be as an effect of causes totally different from those on
which it depends here; as a consequence, therefore, of the moon’s
differences from the earth, not of the points of agreement. Viewed in this
light, all the resemblances which exist become presumptions against, not
in favor of, the moon’s being inhabited. Since life can not exist there in
the manner in which it exists here, the greater the resemblance of the
lunar world to the terrestrial in other respects, the less reason we have
to believe that it can contain life.

There are, however, other bodies in our system, between which and the
earth there is a much closer resemblance; which possess an atmosphere,
clouds, consequently water (or some fluid analogous to it), and even give
strong indications of snow in their polar regions; while the cold, or
heat, though differing greatly on the average from ours, is, in some parts
at least of those planets, possibly not more extreme than in some regions
of our own which are habitable. To balance these agreements, the
ascertained differences are chiefly in the average light and heat,
velocity of rotation, density of material, intensity of gravity, and
similar circumstances of a secondary kind. With regard to these planets,
therefore, the argument of analogy gives a decided preponderance in favor
of their resembling the earth in any of its derivative properties, such as
that of having inhabitants; though when we consider how immeasurably
multitudinous are those of their properties which we are entirely ignorant
of, compared with the few which we know, we can attach but trifling weight
to any considerations of resemblance in which the known elements bear so
inconsiderable a proportion to the unknown.

Besides the competition between analogy and diversity, there may be a
competition of conflicting analogies. The new case may be similar in some
of its circumstances to cases in which the fact _m_ exists, but in others
to cases in which it is known not to exist. Amber has some properties in
common with vegetable, others with mineral products. A painting of unknown
origin may resemble, in certain of its characters, known works of a
particular master, but in others it may as strikingly resemble those of
some other painter. A vase may bear some analogy to works of Grecian, and
some to those of Etruscan, or Egyptian art. We are of course supposing
that it does not possess any quality which has been ascertained, by a
sufficient induction, to be a conclusive mark either of the one or of the
other.

§ 3. Since the value of an analogical argument inferring one resemblance
from other resemblances without any antecedent evidence of a connection
between them, depends on the extent of ascertained resemblance, compared
first with the amount of ascertained difference, and next with the extent
of the unexplored region of unascertained properties; it follows that
where the resemblance is very great, the ascertained difference very
small, and our knowledge of the subject-matter tolerably extensive, the
argument from analogy may approach in strength very near to a valid
induction. If, after much observation of B, we find that it agrees with A
in nine out of ten of its known properties, we may conclude with a
probability of nine to one, that it will possess any given derivative
property of A. If we discover, for example, an unknown animal or plant,
resembling closely some known one in the greater number of the properties
we observe in it, but differing in some few, we may reasonably expect to
find in the unobserved remainder of its properties, a general agreement
with those of the former; but also a difference corresponding
proportionately to the amount of observed diversity.

It thus appears that the conclusions derived from analogy are only of any
considerable value, when the case to which we reason is an adjacent case;
adjacent, not as before, in place or time, but in circumstances. In the
case of effects of which the causes are imperfectly or not at all known,
when consequently the observed order of their occurrence amounts only to
an empirical law, it often happens that the conditions which have
co-existed whenever the effect was observed, have been very numerous. Now
if a new case presents itself, in which all these conditions do not exist,
but the far greater part of them do, some one or a few only being wanting,
the inference that the effect will occur, notwithstanding this deficiency
of complete resemblance to the cases in which it has been observed, may,
though of the nature of analogy, possess a high degree of probability. It
is hardly necessary to add that, however considerable this probability may
be, no competent inquirer into nature will rest satisfied with it when a
complete induction is attainable; but will consider the analogy as a mere
guide-post, pointing out the direction in which more rigorous
investigations should be prosecuted.

It is in this last respect that considerations of analogy have the highest
scientific value. The cases in which analogical evidence affords in itself
any very high degree of probability, are, as we have observed, only those
in which the resemblance is very close and extensive; but there is no
analogy, however faint, which may not be of the utmost value in suggesting
experiments or observations that may lead to more positive conclusions.
When the agents and their effects are out of the reach of further
observation and experiment, as in the speculations already alluded to
respecting the moon and planets, such slight probabilities are no more
than an interesting theme for the pleasant exercise of imagination; but
any suspicion, however slight, that sets an ingenious person at work to
contrive an experiment, or affords a reason for trying one experiment
rather than another, may be of the greatest benefit to science.

On this ground, though I can not accept as positive truths any of those
scientific hypotheses which are unsusceptible of being ultimately brought
to the test of actual induction, such, for instance, as the two theories
of light, the emission theory of the last century, and the undulatory
theory which predominates in the present, I am yet unable to agree with
those who consider such hypotheses to be worthy of entire disregard. As is
well said by Hartley (and concurred in by a thinker in general so
diametrically opposed to Hartley’s opinions as Dugald Stewart), “any
hypothesis which has so much plausibility as to explain a considerable
number of facts, helps us to digest these facts in proper order, to bring
new ones to light, and make _experimenta crucis_ for the sake of future
inquirers.”(183) If an hypothesis both explains known facts, and has led
to the prediction of others previously unknown, and since verified by
experience, the laws of the phenomenon which is the subject of inquiry
must bear at least a great similarity to those of the class of phenomena
to which the hypothesis assimilates it; and since the analogy which
extends so far may probably extend further, nothing is more likely to
suggest experiments tending to throw light upon the real properties of the
phenomenon, than the following out such an hypothesis. But to this end it
is by no means necessary that the hypothesis be mistaken for a scientific
truth. On the contrary, that illusion is in this respect, as in every
other, an impediment to the progress of real knowledge, by leading
inquirers to restrict themselves arbitrarily to the particular hypothesis
which is most accredited at the time, instead of looking out for every
class of phenomena between the laws of which and those of the given
phenomenon any analogy exists, and trying all such experiments as may tend
to the discovery of ulterior analogies pointing in the same direction.



                               Chapter XXI.


Of The Evidence Of The Law Of Universal Causation.


§ 1. We have now completed our review of the logical processes by which
the laws, or uniformities, of the sequence of phenomena, and those
uniformities in their co-existence which depend on the laws of their
sequence, are ascertained or tested. As we recognized in the commencement,
and have been enabled to see more clearly in the progress of the
investigation, the basis of all these logical operations is the law of
causation.

The validity of all the Inductive Methods depends on the assumption that
every event, or the beginning of every phenomenon, must have some cause;
some antecedent, on the existence of which it is invariably and
unconditionally consequent. In the Method of Agreement this is obvious;
that method avowedly proceeding on the supposition that we have found the
true cause as soon as we have negatived every other. The assertion is
equally true of the Method of Difference. That method authorizes us to
infer a general law from two instances; one, in which A exists together
with a multitude of other circumstances, and B follows; another, in which,
A being removed, and all other circumstances remaining the same, B is
prevented. What, however, does this prove? It proves that B, in the
particular instance, can not have had any other cause than A; but to
conclude from this that A was the cause, or that A will on other occasions
be followed by B, is only allowable on the assumption that B must have
some cause; that among its antecedents in any single instance in which it
occurs, there must be one which has the capacity of producing it at other
times. This being admitted, it is seen that in the case in question that
antecedent can be no other than A; but that if it be no other than A it
must be A, is not proved, by these instances at least, but taken for
granted. There is no need to spend time in proving that the same thing is
true of the other Inductive Methods. The universality of the law of
causation is assumed in them all.

But is this assumption warranted? Doubtless (it may be said) _most_
phenomena are connected as effects with some antecedent or cause, that is,
are never produced unless some assignable fact has preceded them; but the
very circumstance that complicated processes of induction are sometimes
necessary, shows that cases exist in which this regular order of
succession is not apparent to our unaided apprehension. If, then, the
processes which bring these cases within the same category with the rest,
require that we should assume the universality of the very law which they
do not at first sight appear to exemplify, is not this a _petitio
principii_? Can we prove a proposition, by an argument which takes it for
granted? And if not so proved, on what evidence does it rest?

For this difficulty, which I have purposely stated in the strongest terms
it will admit of, the school of metaphysicians who have long predominated
in this country find a ready salvo. They affirm, that the universality of
causation is a truth which we can not help believing; that the belief in
it is an instinct, one of the laws of our believing faculty. As the proof
of this, they say, and they have nothing else to say, that every body does
believe it; and they number it among the propositions, rather numerous in
their catalogue, which may be logically argued against, and perhaps can
not be logically proved, but which are of higher authority than logic, and
so essentially inherent in the human mind, that even he who denies them in
speculation, shows by his habitual practice that his arguments make no
impression upon himself.

Into the merits of this question, considered as one of psychology, it
would be foreign to my purpose to enter here; but I must protest against
adducing, as evidence of the truth of a fact in external nature, the
disposition, however strong or however general, of the human mind to
believe it. Belief is not proof, and does not dispense with the necessity
of proof. I am aware, that to ask for evidence of a proposition which we
are supposed to believe instinctively, is to expose one’s self to the
charge of rejecting the authority of the human faculties; which of course
no one can consistently do, since the human faculties are all which any
one has to judge by; and inasmuch as the meaning of the word evidence is
supposed to be, something which when laid before the mind, induces it to
believe; to demand evidence when the belief is insured by the mind’s own
laws, is supposed to be appealing to the intellect against the intellect.
But this, I apprehend, is a misunderstanding of the nature of evidence. By
evidence is not meant any thing and every thing which produces belief.
There are many things which generate belief besides evidence. A mere
strong association of ideas often causes a belief so intense as to be
unshakable by experience or argument. Evidence is not that which the mind
does or must yield to, but that which it ought to yield to, namely, that,
by yielding to which its belief is kept conformable to fact. There is no
appeal from the human faculties generally, but there is an appeal from one
human faculty to another; from the judging faculty, to those which take
cognizance of fact, the faculties of sense and consciousness. The
legitimacy of this appeal is admitted whenever it is allowed that our
judgments ought to be conformable to fact. To say that belief suffices for
its own justification is making opinion the test of opinion; it is denying
the existence of any outward standard, the conformity of an opinion to
which constitutes its truth. We call one mode of forming opinions right
and another wrong, because the one does, and the other does not, tend to
make the opinion agree with the fact—to make people believe what really
is, and expect what really will be. Now a mere disposition to believe,
even if supposed instinctive, is no guarantee for the truth of the thing
believed. If, indeed, the belief ever amounted to an irresistible
necessity, there would then be no _use_ in appealing from it, because
there would be no possibility of altering it. But even then the truth of
the belief would not follow; it would only follow that mankind were under
a permanent necessity of believing what might possibly not be true; in
other words, that a case might occur in which our senses or consciousness,
if they could be appealed to, might testify one thing, and our reason
believe another. But in fact there is no such permanent necessity. There
is no proposition of which it can be asserted that every human mind must
eternally and irrevocably believe it. Many of the propositions of which
this is most confidently stated, great numbers of human beings have
disbelieved. The things which it has been supposed that nobody could
possibly help believing, are innumerable; but no two generations would
make out the same catalogue of them. One age or nation believes implicitly
what to another seems incredible and inconceivable; one individual has not
a vestige of a belief which another deems to be absolutely inherent in
humanity. There is not one of these supposed instinctive beliefs which is
really inevitable. It is in the power of every one to cultivate habits of
thought which make him independent of them. The habit of philosophical
analysis (of which it is the surest effect to enable the mind to command,
instead of being commanded by, the laws of the merely passive part of its
own nature), by showing to us that things are not necessarily connected in
fact because their ideas are connected in our minds, is able to loosen
innumerable associations which reign despotically over the undisciplined
or early-prejudiced mind. And this habit is not without power even over
those associations which the school of which I have been speaking regard
as connate and instinctive. I am convinced that any one accustomed to
abstraction and analysis, who will fairly exert his faculties for the
purpose, will, when his imagination has once learned to entertain the
notion, find no difficulty in conceiving that in some one, for instance,
of the many firmaments into which sidereal astronomy now divides the
universe, events may succeed one another at random, without any fixed law;
nor can any thing in our experience, or in our mental nature, constitute a
sufficient, or indeed any, reason for believing that this is nowhere the
case.

Were we to suppose (what it is perfectly possible to imagine) that the
present order of the universe were brought to an end, and that a chaos
succeeded in which there was no fixed succession of events, and the past
gave no assurance of the future; if a human being were miraculously kept
alive to witness this change, he surely would soon cease to believe in any
uniformity, the uniformity itself no longer existing. If this be admitted,
the belief in uniformity either is not an instinct, or it is an instinct
conquerable, like all other instincts, by acquired knowledge.

But there is no need to speculate on what might be, when we have positive
and certain knowledge of what has been. It is not true, as a matter of
fact, that mankind have always believed that all the successions of events
were uniform and according to fixed laws. The Greek philosophers, not even
excepting Aristotle, recognized Chance and Spontaneity (τύχη and τὸ
αὐτομάτον) as among the agents in nature; in other words, they believed
that to that extent there was no guarantee that the past had been similar
to itself, or that the future would resemble the past. Even now a full
half of the philosophical world, including the very same metaphysicians
who contend most for the instinctive character of the belief in
uniformity, consider one important class of phenomena, volitions, to be an
exception to the uniformity, and not governed by a fixed law.(184)

§ 2. As was observed in a former place,(185) the belief we entertain in
the universality, throughout nature, of the law of cause and effect, is
itself an instance of induction; and by no means one of the earliest which
any of us, or which mankind in general, can have made. We arrive at this
universal law, by generalization from many laws of inferior generality. We
should never have had the notion of causation (in the philosophical
meaning of the term) as a condition of all phenomena, unless many cases of
causation, or in other words, many partial uniformities of sequence, had
previously become familiar. The more obvious of the particular
uniformities suggest, and give evidence of, the general uniformity, and
the general uniformity, once established, enables us to prove the
remainder of the particular uniformities of which it is made up. As,
however, all rigorous processes of induction presuppose the general
uniformity, our knowledge of the particular uniformities from which it was
first inferred was not, of course, derived from rigorous induction, but
from the loose and uncertain mode of induction _per enumerationem
simplicem_; and the law of universal causation, being collected from
results so obtained, can not itself rest on any better foundation.

It would seem, therefore, that induction _per enumerationem simplicem_ not
only is not necessarily an illicit logical process, but is in reality the
only kind of induction possible; since the more elaborate process depends
for its validity on a law, itself obtained in that inartificial mode. Is
there not then an inconsistency in contrasting the looseness of one method
with the rigidity of another, when that other is indebted to the looser
method for its own foundation?

The inconsistency, however, is only apparent. Assuredly, if induction by
simple enumeration were an invalid process, no process grounded on it
could be valid; just as no reliance could be placed on telescopes, if we
could not trust our eyes. But though a valid process, it is a fallible
one, and fallible in very different degrees: if, therefore, we can
substitute for the more fallible forms of the process, an operation
grounded on the same process in a less fallible form, we shall have
effected a very material improvement. And this is what scientific
induction does.

A mode of concluding from experience must be pronounced untrustworthy when
subsequent experience refuses to confirm it. According to this criterion,
induction by simple enumeration—in other words, generalization of an
observed fact from the mere absence of any known instance to the
contrary—affords in general a precarious and unsafe ground of assurance;
for such generalizations are incessantly discovered, on further
experience, to be false. Still, however, it affords some assurance,
sufficient, in many cases, for the ordinary guidance of conduct. It would
be absurd to say, that the generalizations arrived at by mankind in the
outset of their experience, such as these—food nourishes, fire burns,
water drowns—were unworthy of reliance.(186) There is a scale of
trustworthiness in the results of the original unscientific induction; and
on this diversity (as observed in the fourth chapter of the present book)
depend the rules for the improvement of the process. The improvement
consists in correcting one of these inartificial generalizations by means
of another. As has been already pointed out, this is all that art can do.
To test a generalization, by showing that it either follows from, or
conflicts with, some stronger induction, some generalization resting on a
broader foundation of experience, is the beginning and end of the logic of
induction.

§ 3. Now the precariousness of the method of simple enumeration is in an
inverse ratio to the largeness of the generalization. The process is
delusive and insufficient, exactly in proportion as the subject-matter of
the observation is special and limited in extent. As the sphere widens,
this unscientific method becomes less and less liable to mislead; and the
most universal class of truths, the law of causation, for instance, and
the principles of number and of geometry, are duly and satisfactorily
proved by that method alone, nor are they susceptible of any other proof.

With respect to the whole class of generalizations of which we have
recently treated, the uniformities which depend on causation, the truth of
the remark just made follows by obvious inference from the principles laid
down in the preceding chapters. When a fact has been observed a certain
number of times to be true, and is not in any instance known to be false,
if we at once affirm that fact as a universal truth or law of nature,
without either testing it by any of the four methods of induction, or
deducing it from other known laws, we shall in general err grossly; but we
are perfectly justified in affirming it as an empirical law, true within
certain limits of time, place, and circumstance, provided the number of
coincidences be greater than can with any probability be ascribed to
chance. The reason for not extending it beyond those limits is, that the
fact of its holding true within them may be a consequence of collocations,
which can not be concluded to exist in one place because they exist in
another; or may be dependent on the accidental absence of counteracting
agencies, which any variation of time, or the smallest change of
circumstances, may possibly bring into play. If we suppose, then, the
subject-matter of any generalization to be so widely diffused that there
is no time, no place, and no combination of circumstances, but must afford
an example either of its truth or of its falsity, and if it be never found
otherwise than true, its truth can not be contingent on any collocations,
unless such as exist at all times and places; nor can it be frustrated by
any counteracting agencies, unless by such as never actually occur. It is,
therefore, an empirical law co-extensive with all human experience; at
which point the distinction between empirical laws and laws of nature
vanishes, and the proposition takes its place among the most firmly
established as well as largest truths accessible to science.

Now, the most extensive in its subject-matter of all generalizations which
experience warrants, respecting the sequences and co-existences of
phenomena, is the law of causation. It stands at the head of all observed
uniformities, in point of universality, and therefore (if the preceding
observations are correct) in point of certainty. And if we consider, not
what mankind would have been justified in believing in the infancy of
their knowledge, but what may rationally be believed in its present more
advanced state, we shall find ourselves warranted in considering this
fundamental law, though itself obtained by induction from particular laws
of causation, as not less certain, but on the contrary, more so, than any
of those from which it was drawn. It adds to them as much proof as it
receives from them. For there is probably no one even of the best
established laws of causation which is not sometimes counteracted, and to
which, therefore, apparent exceptions do not present themselves, which
would have necessarily and justly shaken the confidence of mankind in the
universality of those laws, if inductive processes founded on the
universal law had not enabled us to refer those exceptions to the agency
of counteracting causes, and thereby reconcile them with the law with
which they apparently conflict. Errors, moreover, may have slipped into
the statement of any one of the special laws, through inattention to some
material circumstance: and instead of the true proposition, another may
have been enunciated, false as a universal law, though leading, in all
cases hitherto observed, to the same result. To the law of causation, on
the contrary, we not only do not know of any exception, but the exceptions
which limit or apparently invalidate the special laws, are so far from
contradicting the universal one, that they confirm it; since in all cases
which are sufficiently open to our observation, we are able to trace the
difference of result, either to the absence of a cause which had been
present in ordinary cases, or to the presence of one which had been
absent.

The law of cause and effect, being thus certain, is capable of imparting
its certainty to all other inductive propositions which can be deduced
from it; and the narrower inductions may be regarded as receiving their
ultimate sanction from that law, since there is no one of them which is
not rendered more certain than it was before, when we are able to connect
it with that larger induction, and to show that it can not be denied,
consistently with the law that every thing which begins to exist has a
cause. And hence we are justified in the seeming inconsistency, of holding
induction by simple enumeration to be good for proving this general truth,
the foundation of scientific induction, and yet refusing to rely on it for
any of the narrower inductions. I fully admit that if the law of causation
were unknown, generalization in the more obvious cases of uniformity in
phenomena would nevertheless be possible, and though in all cases more or
less precarious, and in some extremely so, would suffice to constitute a
certain measure of probability; but what the amount of this probability
might be, we are dispensed from estimating, since it never could amount to
the degree of assurance which the proposition acquires, when, by the
application to it of the Four Methods, the supposition of its falsity is
shown to be inconsistent with the Law of Causation. We are therefore
logically entitled, and, by the necessities of scientific induction,
required, to disregard the probabilities derived from the early rude
method of generalizing, and to consider no minor generalization as proved
except so far as the law of causation confirms it, nor probable except so
far as it may reasonably be expected to be so confirmed.

§ 4. The assertion, that our inductive processes assume the law of
causation, while the law of causation is itself a case of induction, is a
paradox, only on the old theory of reasoning, which supposes the universal
truth, or major premise, in a ratiocination, to be the real proof of the
particular truths which are ostensibly inferred from it. According to the
doctrine maintained in the present treatise,(187) the major premise is not
the proof of the conclusion, but is itself proved, along with the
conclusion from the same evidence. “All men are mortal” is not the proof
that Lord Palmerston is mortal; but our past experience of mortality
authorizes us to infer _both_ the general truth and the particular fact,
and the one with exactly the same degree of assurance as the other. The
mortality of Lord Palmerston is not an inference from the mortality of all
men, but from the experience which proves the mortality of all men; and is
a correct inference from experience, if that general truth is so too. This
relation between our general beliefs and their particular applications
holds equally true in the more comprehensive case which we are now
discussing. Any new fact of causation inferred by induction, is rightly
inferred, if no other objection can be made to the inference than can be
made to the general truth that every event has a cause. The utmost
certainty which can be given to a conclusion arrived at in the way of
inference, stops at this point. When we have ascertained that the
particular conclusion must stand or fall with the general uniformity of
the laws of nature—that it is liable to no doubt except the doubt whether
every event has a cause—we have done all that can be done for it. The
strongest assurance we can obtain of any theory respecting the cause of a
given phenomenon, is that the phenomenon has either that cause or none.

The latter supposition might have been an admissible one in a very early
period of our study of nature. But we have been able to perceive that in
the stage which mankind have now reached, the generalization which gives
the Law of Universal Causation has grown into a stronger and better
induction, one deserving of greater reliance, than any of the subordinate
generalizations. We may even, I think, go a step further than this, and
regard the certainty of that great induction as not merely comparative,
but, for all practical purposes, complete.

The considerations, which, as I apprehend, give, at the present day, to
the proof of the law of uniformity of succession as true of all phenomena
without exception, this character of completeness and conclusiveness, are
the following: First, that we now know it directly to be true of far the
greatest number of phenomena; that there are none of which we know it not
to be true, the utmost that can be said being, that of some we can not
positively from direct evidence affirm its truth; while phenomenon after
phenomenon, as they become better known to us, are constantly passing from
the latter class into the former; and in all cases in which that
transition has not yet taken place, the absence of direct proof is
accounted for by the rarity or the obscurity of the phenomena, our
deficient means of observing them, or the logical difficulties arising
from the complication of the circumstances in which they occur; insomuch
that, notwithstanding as rigid a dependence on given conditions as exists
in the case of any other phenomenon, it was not likely that we should be
better acquainted with those conditions than we are. Besides this first
class of considerations, there is a second, which still further
corroborates the conclusion. Although there are phenomena the production
and changes of which elude all our attempts to reduce them universally to
any ascertained law; yet in every such case, the phenomenon, or the
objects concerned in it, are found in some instances to obey the known
laws of nature. The wind, for example, is the type of uncertainty and
caprice, yet we find it in some cases obeying with as much constancy as
any phenomenon in nature the law of the tendency of fluids to distribute
themselves so as to equalize the pressure on every side of each of their
particles; as in the case of the trade-winds and the monsoons.

Lightning might once have been supposed to obey no laws; but since it has
been ascertained to be identical with electricity, we know that the very
same phenomenon in some of its manifestations is implicitly obedient to
the action of fixed causes. I do not believe that there is now one object
or event in all our experience of nature, within the bounds of the solar
system at least, which has not either been ascertained by direct
observation to follow laws of its own, or been proved to be closely
similar to objects and events which, in more familiar manifestations, or
on a more limited scale, follow strict laws; our inability to trace the
same laws on a larger scale and in the more recondite instances, being
accounted for by the number and complication of the modifying causes, or
by their inaccessibility to observation.

The progress of experience, therefore, has dissipated the doubt which must
have rested on the universality of the law of causation while there were
phenomena which seemed to be _sui generis_, not subject to the same laws
with any other class of phenomena, and not as yet ascertained to have
peculiar laws of their own. This great generalization, however, might
reasonably have been, as it in fact was, acted on as a probability of the
highest order, before there were sufficient grounds for receiving it as a
certainty. In matters of evidence, as in all other human things, we
neither require, nor can attain, the absolute. We must hold even our
strongest convictions with an opening left in our minds for the reception
of facts which contradict them; and only when we have taken this
precaution, have we earned the right to act upon our convictions with
complete confidence when no such contradiction appears. Whatever has been
found true in innumerable instances, and never found to be false after due
examination in any, we are safe in acting on as universal provisionally,
until an undoubted exception appears; provided the nature of the case be
such that a real exception could scarcely have escaped notice. When every
phenomenon that we ever knew sufficiently well to be able to answer the
question, had a cause on which it was invariably consequent, it was more
rational to suppose that our inability to assign the causes of other
phenomena arose from our ignorance, than that there were phenomena which
were uncaused, and which happened to be exactly those which we had
hitherto had no sufficient opportunity of studying.

It must, at the same time, be remarked, that the reasons for this reliance
do not hold in circumstances unknown to us, and beyond the possible range
of our experience. In distant parts of the stellar regions, where the
phenomena may be entirely unlike those with which we are acquainted, it
would be folly to affirm confidently that this general law prevails, any
more than those special ones which we have found to hold universally on
our own planet. The uniformity in the succession of events, otherwise
called the law of causation, must be received not as a law of the
universe, but of that portion of it only which is within the range of our
means of sure observation, with a reasonable degree of extension to
adjacent cases. To extend it further is to make a supposition without
evidence, and to which, in the absence of any ground from experience for
estimating its degree of probability, it would be idle to attempt to
assign any.(188)



                              Chapter XXII.


Of Uniformities Of Co-Existence Not Dependent On Causation.


§ 1. The order of the occurrence of phenomena in time, is either
successive or simultaneous; the uniformities, therefore, which obtain in
their occurrence, are either uniformities of succession or of
co-existence. Uniformities of succession are all comprehended under the
law of causation and its consequences. Every phenomenon has a cause, which
it invariably follows; and from this are derived other invariable
sequences among the successive stages of the same effect, as well as
between the effects resulting from causes which invariably succeed one
another.

In the same manner with these derivative uniformities of succession, a
great variety of uniformities of co-existence also take their rise.
Co-ordinate effects of the same cause naturally co-exist with one another.
High water at any point on the earth’s surface, and high water at the
point diametrically opposite to it, are effects uniformly simultaneous,
resulting from the direction in which the combined attractions of the sun
and moon act upon the waters of the ocean. An eclipse of the sun to us,
and an eclipse of the earth to a spectator situated in the moon, are in
like manner phenomena invariably co-existent; and their co-existence can
equally be deduced from the laws of their production.

It is an obvious question, therefore, whether all the uniformities of
co-existence among phenomena may not be accounted for in this manner. And
it can not be doubted that between phenomena which are themselves effects,
the co-existences must necessarily depend on the causes of those
phenomena. If they are effects immediately or remotely of the same cause,
they can not co-exist except by virtue of some laws or properties of that
cause; if they are effects of different causes, they can not co-exist
unless it be because their causes co-exist; and the uniformity of
co-existence, if such there be, between the effects, proves that those
particular causes, within the limits of our observation, have uniformly
been co-existent.

§ 2. But these same considerations compel us to recognize that there must
be one class of co-existences which can not depend on causation: the
co-existences between the ultimate properties of things—those properties
which are the causes of all phenomena, but are not themselves caused by
any phenomenon, and a cause for which could only be sought by ascending to
the origin of all things. Yet among these ultimate properties there are
not only co-existences, but uniformities of co-existence. General
propositions may be, and are, formed, which assert that whenever certain
properties are found, certain others are found along with them. We
perceive an object; say, for instance, water. We recognize it to be water,
of course by certain of its properties. Having recognized it, we are able
to affirm of it innumerable other properties; which we could not do unless
it were a general truth, a law or uniformity in nature, that the set of
properties by which we identify the substance as water always have those
other properties conjoined with them.

In a former place(189) it has been explained, in some detail, what is
meant by the Kinds of objects; those classes which differ from one another
not by a limited and definite, but by an indefinite and unknown, number of
distinctions. To this we have now to add, that every proposition by which
any thing is asserted of a Kind, affirms a uniformity of co-existence.
Since we know nothing of Kinds but their properties, the Kind, to us, _is_
the set of properties by which it is identified, and which must of course
be sufficient to distinguish it from every other kind.(190) In affirming
any thing, therefore, of a Kind, we are affirming something to be
uniformly co-existent with the properties by which the kind is recognized;
and that is the sole meaning of the assertion.

Among the uniformities of co-existence which exist in nature, may hence be
numbered all the properties of Kinds. The whole of these, however, are not
independent of causation, but only a portion of them. Some are ultimate
properties, others derivative: of some, no cause can be assigned, but
others are manifestly dependent on causes. Thus, pure oxygen gas is a
Kind, and one of its most unequivocal properties is its gaseous form; this
property, however, has for its cause the presence of a certain quantity of
latent heat; and if that heat could be taken away (as has been done from
so many gases in Faraday’s experiments), the gaseous form would doubtless
disappear, together with numerous other properties which depend on, or are
caused by, that property.

In regard to all substances which are chemical compounds, and which
therefore may be regarded as products of the juxtaposition of substances
different in Kind from themselves, there is considerable reason to presume
that the specific properties of the compound are consequent, as effects,
on some of the properties of the elements, though little progress has yet
been made in tracing any invariable relation between the latter and the
former. Still more strongly will a similar presumption exist, when the
object itself, as in the case of organized beings, is no primeval agent,
but an effect, which depends on a cause or causes for its very existence.
The Kinds, therefore, which are called in chemistry simple substances, or
elementary natural agents, are the only ones, any of whose properties can
with certainty be considered ultimate; and of these the ultimate
properties are probably much more numerous than we at present recognize,
since every successful instance of the resolution of the properties of
their compounds into simpler laws, generally leads to the recognition of
properties in the elements distinct from any previously known. The
resolution of the laws of the heavenly motions established the previously
unknown ultimate property of a mutual attraction between all bodies; the
resolution, so far as it has yet proceeded, of the laws of
crystallization, of chemical composition, electricity, magnetism, etc.,
points to various polarities, ultimately inherent in the particles of
which bodies are composed; the comparative atomic weights of different
kinds of bodies were ascertained by resolving into more general laws the
uniformities observed in the proportions in which substances combine with
one another, and so forth. Thus, although every resolution of a complex
uniformity into simpler and more elementary laws has an apparent tendency
to diminish the number of the ultimate properties, and really does remove
many properties from the list; yet (since the result of this simplifying
process is to trace up an ever greater variety of different effects to the
same agents) the further we advance in this direction, the greater number
of distinct properties we are forced to recognize in one and the same
object; the co-existences of which properties must accordingly be ranked
among the ultimate generalities of nature.

§ 3. There are, therefore, only two kinds of propositions which assert
uniformity of co-existence between properties. Either the properties
depend on causes or they do not. If they do, the proposition which affirms
them to be co-existent is a derivative law of co-existence between
effects, and, until resolved into the laws of causation on which it
depends, is an empirical law, and to be tried by the principles of
induction to which such laws are amenable. If, on the other hand, the
properties do not depend on causes, but are ultimate properties, then, if
it be true that they invariably co-exist, they must all be ultimate
properties of one and the same Kind; and it is of these only that the
co-existences can be classed as a peculiar sort of laws of nature.

When we affirm that all crows are black, or that all negroes have woolly
hair, we assert a uniformity of co-existence. We assert that the property
of blackness or of having woolly hair invariably co-exists with the
properties which, in common language, or in the scientific classification
that we adopt, are taken to constitute the class crow, or the class negro.
Now, supposing blackness to be an ultimate property of black objects, or
woolly hair an ultimate property of the animals which possess it;
supposing that these properties are not results of causation, are not
connected with antecedent phenomena by any law; then if all crows are
black, and all negroes have woolly hair, these must be ultimate properties
of the kind _crow_, or _negro_, or of some kind which includes them. If,
on the contrary, blackness or woolly hair be an effect depending on
causes, these general propositions are manifestly empirical laws; and all
that has already been said respecting that class of generalizations may be
applied without modification to these.

Now, we have seen that in the case of all compounds—of all things, in
short, except the elementary substances and primary powers of nature—the
presumption is, that the properties do really depend upon causes; and it
is impossible in any case whatever to be certain that they do not. We
therefore should not be safe in claiming for any generalization respecting
the co-existence of properties, a degree of certainty to which, if the
properties should happen to be the result of causes, it would have no
claim. A generalization respecting co-existence, or, in other words,
respecting the properties of kinds, may be an ultimate truth, but it may
also be merely a derivative one; and since, if so, it is one of those
derivative laws which are neither laws of causation nor have been resolved
into the laws of causation on which they depend, it can possess no higher
degree of evidence than belongs to an empirical law.

§ 4. This conclusion will be confirmed by the consideration of one great
deficiency, which precludes the application to the ultimate uniformities
of co-existence, of a system of rigorous scientific induction, such as the
uniformities in the succession of phenomena have been found to admit of.
The basis of such a system is wanting; there is no general axiom standing
in the same relation to the uniformities of co-existence as the law of
causation does to those of succession. The Methods of Induction applicable
to the ascertainment of causes and effects are grounded on the principle
that every thing which has a beginning must have some cause or other; that
among the circumstances which actually existed at the time of its
commencement, there is certainly some one combination, on which the effect
in question is unconditionally consequent, and on the repetition of which
it would certainly again recur. But in an inquiry whether some kind (as
crow) universally possesses a certain property (as blackness), there is no
room for any assumption analogous to this. We have no previous certainty
that the property must have something which constantly co-exists with it;
must have an invariable co-existent, in the same manner as an event must
have an invariable antecedent. When we feel pain, we must be in some
circumstances under which, if exactly repeated, we should always feel
pain. But when we are conscious of blackness, it does not follow that
there is something else present of which blackness is a constant
accompaniment. There is, therefore, no room for elimination; no method of
Agreement or Difference, or of Concomitant Variations (which is but a
modification either of the Method of Agreement or of the Method of
Difference). We can not conclude that the blackness we see in crows must
be an invariable property of crows merely because there is nothing else
present of which it can be an invariable property. We therefore inquire
into the truth of a proposition like “All crows are black,” under the same
disadvantage as if, in our inquiries into causation, we were compelled to
let in, as one of the possibilities, that the effect may in that
particular instance have arisen without any cause at all.

To overlook this grand distinction was, as it seems to me, the capital
error in Bacon’s view of inductive philosophy. The principle of
elimination, that great logical instrument which he had the immense merit
of first bringing into general use, he deemed applicable in the same
sense, and in as unqualified a manner, to the investigation of the
co-existences, as to that of the successions of phenomena. He seems to
have thought that as every event has a cause, or invariable antecedent, so
every property of an object has an invariable co-existent, which he called
its form; and the examples he chiefly selected for the application and
illustration of his method, were inquiries into such forms; attempts to
determine in what else all those objects resembled, which agreed in some
one general property, as hardness or softness, dryness or moistness, heat
or coldness. Such inquiries could lead to no result. The objects seldom
have any such circumstances in common. They usually agree in the one point
inquired into, and in nothing else. A great proportion of the properties
which, so far as we can conjecture, are the likeliest to be really
ultimate, would seem to be inherently properties of many different kinds
of things not allied in any other respect. And as for the properties
which, being effects of causes, we are able to give some account of, they
have generally nothing to do with the ultimate resemblances or diversities
in the objects themselves, but depend on some outward circumstances, under
the influence of which any objects whatever are capable of manifesting
those properties; as is emphatically the case with those favorite subjects
of Bacon’s scientific inquiries, hotness and coldness, as well as with
hardness and softness, solidity and fluidity, and many other conspicuous
qualities.

In the absence, then, of any universal law of co-existence similar to the
universal law of causation which regulates sequence, we are thrown back
upon the unscientific induction of the ancients, _per enumerationem
simplicem, ubi non reperitur instantia contradictoria_. The reason we have
for believing that all crows are black, is simply that we have seen and
heard of many black crows, and never one of any other color. It remains to
be considered how far this evidence can reach, and how we are to measure
its strength in any given case.

§ 5. It sometimes happens that a mere change in the mode of verbally
enunciating a question, though nothing is really added to the meaning
expressed, is of itself a considerable step toward its solution. This, I
think, happens in the present instance. The degree of certainty of any
generalization which rests on no other evidence than the agreement, so far
as it goes, of all past observation, is but another phrase for the degree
of improbability that an exception, if any existed, could have hitherto
remained unobserved. The reason for believing that all crows are black, is
measured by the improbability that crows of any other color should have
existed to the present time without our being aware of it. Let us state
the question in this last mode, and consider what is implied in the
supposition that there may be crows which are not black, and under what
conditions we can be justified in regarding this as incredible.

If there really exist crows which are not black, one of two things must be
the fact. Either the circumstance of blackness, in all crows hitherto
observed, must be, as it were, an accident, not connected with any
distinction of Kind; or if it be a property of Kind, the crows which are
not black must be a new Kind, a Kind hitherto overlooked, though coming
under the same general description by which crows have hitherto been
characterized. The first supposition would be proved true if we were to
discover casually a white crow among black ones, or if it were found that
black crows sometimes turn white. The second would be shown to be the fact
if in Australia or Central Africa a species or a race of white or gray
crows were found to exist.

§ 6. The former of these suppositions necessarily implies that the color
is an effect of causation. If blackness, in the crows in which it has been
observed, be not a property of Kind, but can be present or absent without
any difference generally in the properties of the object, then it is not
an ultimate fact in the individuals themselves, but is certainly dependent
on a cause. There are, no doubt, many properties which vary from
individual to individual of the same Kind, even the same _infima species_,
or lowest Kind. Some flowers may be either white or red, without differing
in any other respect. But these properties are not ultimate; they depend
on causes. So far as the properties of a thing belong to its own nature,
and do not arise from some cause extrinsic to it, they are always the same
in the same Kind. Take, for instance, all simple substances and elementary
powers; the only things of which we are certain that some at least of
their properties are really ultimate. Color is generally esteemed the most
variable of all properties: yet we do not find that sulphur is sometimes
yellow and sometimes white, or that it varies in color at all, except so
far as color is the effect of some extrinsic cause, as of the sort of
light thrown upon it, the mechanical arrangement of the particles (as
after fusion), etc. We do not find that iron is sometimes fluid and
sometimes solid at the same temperature; gold sometimes malleable and
sometimes brittle; that hydrogen will sometimes combine with oxygen and
sometimes not; or the like. If from simple substances we pass to any of
their definite compounds, as water, lime, or sulphuric acid, there is the
same constancy in their properties. When properties vary from individual
to individual, it is either in the case of miscellaneous aggregations,
such as atmospheric air or rock, composed of heterogeneous substances, and
not constituting or belonging to any real Kind,(191) or it is in the case
of organic beings. In them, indeed, there is variability in a high degree.
Animals of the same species and race, human beings of the same age, sex,
and country, will be most different, for example, in face and figure. But
organized beings (from the extreme complication of the laws by which they
are regulated) being more eminently modifiable, that is, liable to be
influenced by a greater number and variety of causes, than any other
phenomena whatever; having also themselves had a beginning, and therefore
a cause; there is reason to believe that none of their properties are
ultimate, but all of them derivative, and produced by causation. And the
presumption is confirmed, by the fact that the properties which vary from
one individual to another, also generally vary more or less at different
times in the same individual; which variation, like any other event,
supposes a cause, and implies, consequently, that the properties are not
independent of causation.

If, therefore, blackness be merely accidental in crows, and capable of
varying while the Kind remains the same, its presence or absence is
doubtless no ultimate fact, but the effect of some unknown cause: and in
that case the universality of the experience that all crows are black is
sufficient proof of a common cause, and establishes the generalization as
an empirical law. Since there are innumerable instances in the
affirmative, and hitherto none at all in the negative, the causes on which
the property depends must exist everywhere in the limits of the
observations which have been made; and the proposition may be received as
universal within those limits, and with the allowable degree of extension
to adjacent cases.

§ 7. If, in the second place, the property, in the instances in which it
has been observed, is not an effect of causation, it is a property of
Kind; and in that case the generalization can only be set aside by the
discovery of a new Kind of crow. That, however, a peculiar Kind not
hitherto discovered should exist in nature, is a supposition so often
realized that it can not be considered at all improbable. We have nothing
to authorize us in attempting to limit the Kinds of things which exist in
nature. The only unlikelihood would be that a new Kind should be
discovered in localities which there was previously reason to believe had
been thoroughly explored; and even this improbability depends on the
degree of conspicuousness of the difference between the newly-discovered
Kind and all others, since new kinds of minerals, plants, and even
animals, previously overlooked or confounded with known species, are still
continually detected in the most frequented situations. On this second
ground, therefore, as well as on the first, the observed uniformity of
co-existence can only hold good as an empirical law, within the limits not
only of actual observation, but of an observation as accurate as the
nature of the case required. And hence it is that (as remarked in an early
chapter of the present book) we so often give up generalizations of this
class at the first summons. If any credible witness stated that he had
seen a white crow, under circumstances which made it not incredible that
it should have escaped notice previously, we should give full credence to
the statement.

It appears, then, that the uniformities which obtain in the co-existence
of phenomena—those which we have reason to consider as ultimate, no less
than those which arise from the laws of causes yet undetected—are entitled
to reception only as empirical laws; are not to be presumed true except
within the limits of time, place, and circumstance, in which the
observations were made, or except in cases strictly adjacent.

§ 8. We have seen in the last chapter that there is a point of generality
at which empirical laws become as certain as laws of nature, or, rather,
at which there is no longer any distinction between empirical laws and
laws of nature. As empirical laws approach this point, in other words, as
they rise in their degree of generality, they become more certain; their
universality may be more strongly relied on. For, in the first place, if
they are results of causation (which, even in the class of uniformities
treated of in the present chapter, we never can be certain that they are
not) the more general they are, the greater is proved to be the space over
which the necessary collocations prevail, and within which no causes exist
capable of counteracting the unknown causes on which the empirical law
depends. To say that any thing is an invariable property of some very
limited class of objects, is to say that it invariably accompanies some
very numerous and complex group of distinguishing properties; which, if
causation be at all concerned in the matter, argues a combination of many
causes, and therefore a great liability to counteraction; while the
comparatively narrow range of the observations renders it impossible to
predict to what extent unknown counteracting causes may be distributed
throughout nature. But when a generalization has been found to hold good
of a very large proportion of all things whatever, it is already proved
that nearly all the causes which exist in nature have no power over it;
that very few changes in the combination of causes can affect it; since
the greater number of possible combinations must have already existed in
some one or other of the instances in which it has been found true. If,
therefore, any empirical law is a result of causation, the more general it
is, the more it may be depended on. And even if it be no result of
causation, but an ultimate co-existence, the more general it is, the
greater amount of experience it is derived from, and the greater therefore
is the probability that if exceptions had existed, some would already have
presented themselves.

For these reasons, it requires much more evidence to establish an
exception to one of the more general empirical laws than to the more
special ones. We should not have any difficulty in believing that there
might be a new Kind of crow; or a new kind of bird resembling a crow in
the properties hitherto considered distinctive of that Kind. But it would
require stronger proof to convince us of the existence of a Kind of crow
having properties at variance with any generally recognized universal
property of birds; and a still higher degree if the properties conflict
with any recognized universal property of animals. And this is conformable
to the mode of judgment recommended by the common sense and general
practice of mankind, who are more incredulous as to any novelties in
nature, according to the degree of generality of the experience which
these novelties seem to contradict.

§ 9. It is conceivable that the alleged properties might conflict with
some recognized universal property of all matter. In that case their
improbability would be at the highest, but would not even then amount to
incredibility. There are only two known properties common to all matter;
in other words, there is but one known uniformity of co-existence of
properties co-extensive with all physical nature, namely, that whatever
opposes resistance to movement gravitates, or, as Professor Bain expresses
it, Inertia and Gravity are co-existent through all matter, and
proportionate in their amount. These properties, as he truly says, are not
mutually implicated; from neither of them could we, on grounds of
causation, presume the other. But, for this very reason, we are never
certain that a Kind may not be discovered possessing one of the properties
without the other. The hypothetical ether, if it exists, may be such a
Kind. Our senses can not recognize in it either resistance or gravity; but
if the reality of a resisting medium should eventually be proved (by
alteration, for example, in the times of revolution of periodic comets,
combined with the evidences afforded by the phenomena of light and heat),
it would be rash to conclude from this alone, without other proofs, that
it must gravitate.

For even the greater generalizations, which embrace comprehensive Kinds
containing under them a great number and variety of _infimæ species_, are
only empirical laws, resting on induction by simple enumeration merely,
and not on any process of elimination—a process wholly inapplicable to
this sort of case. Such generalizations, therefore, ought to be grounded
on an examination of all the _infimæ species_ comprehended in them, and
not of a portion only. We can not conclude (where causation is not
concerned), because a proposition is true of a number of things resembling
one another only in being animals, that it is therefore true of all
animals. If, indeed, any thing be true of species which differ more from
one another than either differs from a third, especially if that third
species occupies in most of its known properties a position between the
two former, there is some probability that the same thing will also be
true of that intermediate species; for it is often, though by no means
universally, found, that there is a sort of parallelism in the properties
of different Kinds, and that their degree of unlikeness in one respect
bears some proportion to their unlikeness in others. We see this
parallelism in the properties of the different metals; in those of
sulphur, phosphorus, and carbon; of chlorine, iodine, and bromine; in the
natural orders of plants and animals, etc. But there are innumerable
anomalies and exceptions to this sort of conformity; if indeed the
conformity itself be any thing but an anomaly and an exception in nature.

Universal propositions, therefore, respecting the properties of superior
Kinds, unless grounded on proved or presumed connection by causation,
ought not to be hazarded except after separately examining every known
sub-kind included in the larger Kind. And even then such generalizations
must be held in readiness to be given up on the occurrence of some new
anomaly, which, when the uniformity is not derived from causation, can
never, even in the case of the most general of these empirical laws, be
considered very improbable. Thus, all the universal propositions which it
has been attempted to lay down respecting simple substances, or concerning
any of the classes which have been formed among simple substances (and the
attempt has been often made), have, with the progress of experience,
either faded into inanity, or been proved to be erroneous; and each Kind
of simple substance remains, with its own collection of properties apart
from the rest, saving a certain parallelism with a few other Kinds, the
most similar to itself. In organized beings, indeed, there are abundance
of propositions ascertained to be universally true of superior genera, to
many of which the discovery hereafter of any exceptions must be regarded
as extremely improbable. But these, as already observed, are, we have
every reason to believe, properties dependent on causation.(192)

Uniformities of co-existence, then, not only when they are consequences of
laws of succession, but also when they are ultimate truths, must be
ranked, for the purpose of logic, among empirical laws; and are amenable
in every respect to the same rules with those unresolved uniformities
which are known to be dependent on causation.(193)



                              Chapter XXIII.


Of Approximate Generalizations, And Probable Evidence.


§ 1. In our inquiries into the nature of the inductive process, we must
not confine our notice to such generalizations from experience as profess
to be universally true. There is a class of inductive truths avowedly not
universal; in which it is not pretended that the predicate is always true
of the subject; but the value of which, as generalizations, is
nevertheless extremely great. An important portion of the field of
inductive knowledge does not consist of universal truths, but of
approximations to such truths; and when a conclusion is said to rest on
probable evidence, the premises it is drawn from are usually
generalizations of this sort.

As every certain inference respecting a particular case implies that there
is ground for a general proposition of the form, every A is B; so does
every probable inference suppose that there is ground for a proposition of
the form, Most A are B; and the degree of probability of the inference in
an average case will depend on the proportion between the number of
instances existing in nature which accord with the generalization, and the
number of those which conflict with it.

§ 2. Propositions in the form, Most A are B, are of a very different
degree of importance in science, and in the practice of life. To the
scientific inquirer they are valuable chiefly as materials for, and steps
toward universal truths. The discovery of these is the proper end of
science; its work is not done if it stops at the proposition that a
majority of A are B, without circumscribing that majority by some common
character, fitted to distinguish them from the minority. Independently of
the inferior precision of such imperfect generalizations, and the inferior
assurance with which they can be applied to individual cases, it is plain
that, compared with exact generalizations, they are almost useless as
means of discovering ulterior truths by way of deduction. We may, it is
true, by combining the proposition Most A are B, with a universal
proposition, Every B is C, arrive at the conclusion that Most A are C. But
when a second proposition of the approximate kind is introduced—or even
when there is but one, if that one be the major premise—nothing can, in
general, be positively concluded. When the major is Most B are D, then,
even if the minor be Every A is B, we can not infer that most A are D, or
with any certainty that even some A are D. Though the majority of the
class B have the attribute signified by D, the whole of the sub-class A
may belong to the minority.(194)

Though so little use can be made, in science, of approximate
generalizations, except as a stage on the road to something better, for
practical guidance they are often all we have to rely on. Even when
science has really determined the universal laws of any phenomenon, not
only are those laws generally too much encumbered with conditions to be
adapted for everyday use, but the cases which present themselves in life
are too complicated, and our decisions require to be taken too rapidly, to
admit of waiting till the existence of a phenomenon can be proved by what
have been scientifically ascertained to be universal marks of it. To be
indecisive and reluctant to act, because we have not evidence of a
perfectly conclusive character to act on, is a defect sometimes incident
to scientific minds, but which, wherever it exists, renders them unfit for
practical emergencies. If we would succeed in action, we must judge by
indications which, though they do not generally mislead us, sometimes do,
and must make up, as far as possible, for the incomplete conclusiveness of
any one indication, by obtaining others to corroborate it. The principles
of induction applicable to approximate generalization are therefore a not
less important subject of inquiry than the rules for the investigation of
universal truths; and might reasonably be expected to detain us almost as
long, were it not that these principles are mere corollaries from those
which have been already treated of.

§ 3. There are two sorts of cases in which we are forced to guide
ourselves by generalizations of the imperfect form, Most A are B. The
first is, when we have no others; when we have not been able to carry our
investigation of the laws of the phenomena any further; as in the
following propositions—Most dark-eyed persons have dark hair; Most springs
contain mineral substances; Most stratified formations contain fossils.
The importance of this class of generalizations is not very great; for,
though it frequently happens that we see no reason why that which is true
of most individuals of a class is not true of the remainder, nor are able
to bring the former under any general description which can distinguish
them from the latter, yet if we are willing to be satisfied with
propositions of a less degree of generality, and to break down the class A
into sub-classes, we may generally obtain a collection of propositions
exactly true. We do not know why most wood is lighter than water, nor can
we point out any general property which discriminates wood that is lighter
than water from that which is heavier. But we know exactly what species
are the one and what the other. And if we meet with a specimen not
conformable to any known species (the only case in which our previous
knowledge affords no other guidance than the approximate generalization),
we can generally make a specific experiment, which is a surer resource.

It often happens, however, that the proposition, Most A are B, is not the
ultimatum of our scientific attainments, though the knowledge we possess
beyond it can not conveniently be brought to bear upon the particular
instance. We may know well enough what circumstances distinguish the
portion of A which has the attribute B from the portion which has it not,
but may have no means, or may not have time, to examine whether those
characteristic circumstances exist or not in the individual case. This is
the situation we are generally in when the inquiry is of the kind called
moral, that is, of the kind which has in view to predict human actions. To
enable us to affirm any thing universally concerning the actions of
classes of human beings, the classification must be grounded on the
circumstances of their mental culture and habits, which in an individual
case are seldom exactly known; and classes grounded on these distinctions
would never precisely accord with those into which mankind are divided for
social purposes. All propositions which can be framed respecting the
actions of human beings as ordinarily classified, or as classified
according to any kind of outward indications, are merely approximate. We
can only say, Most persons of a particular age, profession, country, or
rank in society, have such and such qualities; or, Most persons, when
placed in certain circumstances, act in such and such a way. Not that we
do not often know well enough on what causes the qualities depend, or what
sort of persons they are who act in that particular way; but we have
seldom the means of knowing whether any individual person has been under
the influence of those causes, or is a person of that particular sort. We
could replace the approximate generalizations by propositions universally
true; but these would hardly ever be capable of being applied to practice.
We should be sure of our majors, but we should not be able to get minors
to fit; we are forced, therefore, to draw our conclusions from coarser and
more fallible indications.

§ 4. Proceeding now to consider what is to be regarded as sufficient
evidence of an approximate generalization, we can have no difficulty in at
once recognizing that, when admissible at all, it is admissible only as an
empirical law. Propositions of the form, Every A is B, are not necessarily
laws of causation, or ultimate uniformities of co-existence; propositions
like Most A are B, _can not_ be so. Propositions hitherto found true in
every observed instance may yet be no necessary consequence of laws of
causation, or of ultimate uniformities, and unless they are so, may, for
aught we know, be false beyond the limits of actual observation; still
more evidently must this be the case with propositions which are only true
in a mere majority of the observed instances.

There is some difference, however, in the degree of certainty of the
proposition, Most A are B, according as that approximate generalization
composes the whole of our knowledge of the subject, or not. Suppose,
first, that the former is the case. We know only that most A are B, not
why they are so, nor in what respect those which are differ from those
which are not. How, then, did we learn that most A are B? Precisely in the
manner in which we should have learned, had such happened to be the fact
that all A are B. We collected a number of instances sufficient to
eliminate chance, and, having done so, compared the number of instances in
the affirmative with the number in the negative. The result, like other
unresolved derivative laws, can be relied on solely within the limits not
only of place and time, but also of circumstance, under which its truth
has been actually observed; for, as we are supposed to be ignorant of the
causes which make the proposition true, we can not tell in what manner any
new circumstance might perhaps affect it. The proposition, Most judges are
inaccessible to bribes, would probably be found true of Englishmen,
Frenchmen, Germans, North Americans, and so forth; but if on this evidence
alone we extended the assertion to Orientals, we should step beyond the
limits, not only of place but of circumstance, within which the fact had
been observed, and should let in possibilities of the absence of the
determining causes, or the presence of counteracting ones, which might be
fatal to the approximate generalization.

In the case where the approximate proposition is not the ultimatum of our
scientific knowledge, but only the most available form of it for practical
guidance; where we know, not only that most A have the attribute B, but
also the causes of B, or some properties by which the portion of A which
has that attribute is distinguished from the portion which has it not, we
are rather more favorably situated than in the preceding case. For we have
now a double mode of ascertaining whether it be true that most A are B;
the direct mode, as before, and an indirect one, that of examining whether
the proposition admits of being deduced from the known cause, or from any
known criterion, of B. Let the question, for example, be whether most
Scotchmen can read? We may not have observed, or received the testimony of
others respecting, a sufficient number and variety of Scotchmen to
ascertain this fact; but when we consider that the cause of being able to
read is the having been taught it, another mode of determining the
question presents itself, namely, by inquiring whether most Scotchmen have
been sent to schools where reading is effectually taught. Of these two
modes, sometimes one and sometimes the other is the more available. In
some cases, the frequency of the effect is the more accessible to that
extensive and varied observation which is indispensable to the
establishment of an empirical law; at other times, the frequency of the
causes, or of some collateral indications. It commonly happens that
neither is susceptible of so satisfactory an induction as could be
desired, and that the grounds on which the conclusion is received are
compounded of both. Thus a person may believe that most Scotchmen can
read, because, so far as his information extends, most Scotchmen have been
sent to school, and most Scotch schools teach reading effectually; and
also because most of the Scotchmen whom he has known or heard of could
read; though neither of these two sets of observations may by itself
fulfill the necessary conditions of extent and variety.

Although the approximate generalization may in most cases be indispensable
for our guidance, even when we know the cause, or some certain mark, of
the attribute predicated, it needs hardly be observed that we may always
replace the uncertain indication by a certain one, in any case in which we
can actually recognize the existence of the cause or mark. For example, an
assertion is made by a witness, and the question is whether to believe it.
If we do not look to any of the individual circumstances of the case, we
have nothing to direct us but the approximate generalization, that truth
is more common than falsehood, or, in other words, that most persons, on
most occasions, speak truth. But if we consider in what circumstances the
cases where truth is spoken differ from those in which it is not, we find,
for instance, the following: the witness’s being an honest person or not;
his being an accurate observer or not; his having an interest to serve in
the matter or not. Now, not only may we be able to obtain other
approximate generalizations respecting the degree of frequency of these
various possibilities, but we may know which of them is positively
realized in the individual case. That the witness has or has not an
interest to serve, we perhaps know directly; and the other two points
indirectly, by means of marks; as, for example, from his conduct on some
former occasion; or from his reputation, which, though a very uncertain
mark, affords an approximate generalization (as, for instance, Most
persons who are believed to be honest by those with whom they have had
frequent dealings, are really so), which approaches nearer to a universal
truth than the approximate general proposition with which we set out,
viz., Most persons on most occasions speak truth.

As it seems unnecessary to dwell further on the question of the evidence
of approximate generalizations, we shall proceed to a not less important
topic, that of the cautions to be observed in arguing from these
incompletely universal propositions to particular cases.

§ 5. So far as regards the direct application of an approximate
generalization to an individual instance, this question presents no
difficulty. If the proposition, Most A are B, has been established, by a
sufficient induction, as an empirical law, we may conclude that any
particular A is B with a probability proportioned to the preponderance of
the number of affirmative instances over the number of exceptions. If it
has been found practicable to attain numerical precision in the data, a
corresponding degree of precision may be given to the evaluation of the
chances of error in the conclusion. If it can be established as an
empirical law that nine out of every ten A are B, there will be one chance
in ten of error in assuming that any A, not individually known to us, is a
B: but this of course holds only within the limits of time, place, and
circumstance, embraced in the observations, and therefore can not be
counted on for any sub-class or variety of A (or for A in any set of
external circumstances) which were not included in the average. It must be
added, that we can guide ourselves by the proposition, Nine out of every
ten A are B, only in cases of which we know nothing except that they fall
within the class A. For if we know, of any particular instances _i_, not
only that it falls under A, but to what species or variety of A it
belongs, we shall generally err in applying to _i_ the average struck for
the whole genus, from which the average corresponding to that species
alone would, in all probability, materially differ. And so if _i_, instead
of being a particular sort of instance, is an instance known to be under
the influence of a particular set of circumstances, the presumption drawn
from the numerical proportions in the whole genus would probably, in such
a case, only mislead. A general average should only be applied to cases
which are neither known, nor can be presumed, to be other than average
cases. Such averages, therefore, are commonly of little use for the
practical guidance of any affairs but those which concern large numbers.
Tables of the chances of life are useful to insurance offices, but they go
a very little way toward informing any one of the chances of his own life,
or any other life in which he is interested, since almost every life is
either better or worse than the average. Such averages can only be
considered as supplying the first term in a series of approximations; the
subsequent terms proceeding on an appreciation of the circumstances
belonging to the particular case.

§ 6. From the application of a single approximate generalization to
individual cases, we proceed to the application of two or more of them
together to the same case.

When a judgment applied to an individual instance is grounded on two
approximate generalizations taken in conjunction, the propositions may
cooperate toward the result in two different ways. In the one, each
proposition is separately applicable to the case in hand, and our object
in combining them is to give to the conclusion in that particular case the
double probability arising from the two propositions separately. This may
be called joining two probabilities by way of Addition; and the result is
a probability greater than either. The other mode is, when only one of the
propositions is directly applicable to the case, the second being only
applicable to it by virtue of the application of the first. This is
joining two probabilities by way of Ratiocination or Deduction; the result
of which is a less probability than either. The type of the first argument
is, Most A are B; most C are B; this thing is both an A and a C; therefore
it is probably a B. The type of the second is, Most A are B; most C are A;
this is a C; therefore it is probably an A, therefore it is probably a B.
The first is exemplified when we prove a fact by the testimony of two
unconnected witnesses; the second, when we adduce only the testimony of
one witness that he has heard the thing asserted by another. Or again, in
the first mode it may be argued that the accused committed the crime,
because he concealed himself, and because his clothes were stained with
blood; in the second, that he committed it because he washed or destroyed
his clothes, which is supposed to render it probable that they were
stained with blood. Instead of only two links, as in these instances, we
may suppose chains of any length. A chain of the former kind was termed by
Bentham(195) a self-corroborative chain of evidence; the second, a
self-infirmative chain.

When approximate generalizations are joined by way of addition, we may
deduce from the theory of probabilities laid down in a former chapter, in
what manner each of them adds to the probability of a conclusion which has
the warrant of them all.

If, on an average, two of every three As are Bs, and three of every four
Cs are Bs, the probability that something which is both an A and a C is a
B, will be more than two in three, or than three in four. Of every twelve
things which are As, all except four are Bs by the supposition; and if the
whole twelve, and consequently those four, have the characters of C
likewise, three of these will be Bs on that ground. Therefore, out of
twelve which are both As and Cs, eleven are Bs. To state the argument in
another way; a thing which is both an A and a C, but which is not a B, is
found in only one of three sections of the class A, and in only one of
four sections of the class C; but this fourth of C being spread over the
whole of A indiscriminately, only one-third part of it (or one-twelfth of
the whole number) belongs to the third section of A; therefore a thing
which is not a B occurs only once, among twelve things which are both As
and Cs. The argument would, in the language of the doctrine of chances, be
thus expressed: the chance that an A is not a B is 1/3, the chance that a
C is not a B is 1/4; hence if the thing be both an A and a C, the chance
is 1/3 of 1/4 = 1/12.(196)

In this computation it is of course supposed that the probabilities
arising from A and C are independent of each other. There must not be any
such connection between A and C, that when a thing belongs to the one
class it will therefore belong to the other, or even have a greater chance
of doing so. Otherwise the not-Bs which are Cs may be, most or even all of
them, identical with the not-Bs which are As; in which last case the
probability arising from A and C together will be no greater than that
arising from A alone.

When approximate generalizations are joined together in the other mode,
that of deduction, the degree of probability of the inference, instead of
increasing, diminishes at each step. From two such premises as Most A are
B, Most B are C, we can not with certainty conclude that even a single A
is C; for the whole of the portion of A which in any way falls under B,
may perhaps be comprised in the exceptional part of it. Still, the two
propositions in question afford an appreciable probability that any given
A is C, provided the average on which the second proposition is grounded
was taken fairly with reference to the first; provided the proposition,
Most B are C, was arrived at in a manner leaving no suspicion that the
probability arising from it is otherwise than fairly distributed over the
section of B which belongs to A. For though the instances which are A
_may_ be all in the minority, they may, also, be all in the majority; and
the one possibility is to be set against the other. On the whole, the
probability arising from the two propositions taken together, will be
correctly measured by the probability arising from the one, abated in the
ratio of that arising from the other. If nine out of ten Swedes have light
hair, and eight out of nine inhabitants of Stockholm are Swedes, the
probability arising from these two propositions, that any given inhabitant
of Stockholm is light-haired, will amount to eight in ten; though it is
rigorously possible that the whole Swedish population of Stockholm might
belong to that tenth section of the people of Sweden who are an exception
to the rest.

If the premises are known to be true not of a bare majority, but of nearly
the whole, of their respective subjects, we may go on joining one such
proposition to another for several steps, before we reach a conclusion not
presumably true even of a majority. The error of the conclusion will
amount to the aggregate of the errors of all the premises. Let the
proposition, most A are B, be true of nine in ten; Most B are C, of eight
in nine; then not only will one A in ten not be C, because not B, but even
of the nine-tenths which are B, only eight-ninths will be C; that is, the
cases of A which are C will be only 8/9 of 9/10, or four-fifths. Let us
now add Most C are D, and suppose this to be true of seven cases out of
eight; the proportion of A which is D will be only 7/8 of 8/9 of 9/10, or
7/10. Thus the probability progressively dwindles. The experience,
however, on which our approximate generalizations are grounded, has so
rarely been subjected to, or admits of, accurate numerical estimation,
that we can not in general apply any measurement to the diminution of
probability which takes place at each illation; but must be content with
remembering that it does diminish at every step, and that unless the
premises approach very nearly indeed to being universally true, the
conclusion after a very few steps is worth nothing. A hearsay of a
hearsay, or an argument from presumptive evidence depending not on
immediate marks but on marks of marks, is worthless at a very few removes
from the first stage.

§ 7. There are, however, two cases in which reasonings depending on
approximate generalizations may be carried to any length we please with as
much assurance, and are as strictly scientific, as if they were composed
of universal laws of nature. But these cases are exceptions of the sort
which are currently said to prove the rule. The approximate
generalizations are as suitable, in the cases in question, for purposes of
ratiocination, as if they were complete generalizations, because they are
capable of being transformed into complete generalizations exactly
equivalent.

First: If the approximate generalization is of the class in which our
reason for stopping at the approximation is not the impossibility, but
only the inconvenience, of going further; if we are cognizant of the
character which distinguishes the cases that accord with the
generalization from those which are exceptions to it; we may then
substitute for the approximate proposition, a universal proposition with a
proviso. The proposition, Most persons who have uncontrolled power employ
it ill, is a generalization of this class, and may be transformed into the
following: All persons who have uncontrolled power employ it ill, provided
they are not persons of unusual strength of judgment and rectitude of
purpose. The proposition, carrying the hypothesis or proviso with it, may
then be dealt with no longer as an approximate, but as a universal
proposition; and to whatever number of steps the reasoning may reach, the
hypothesis, being carried forward to the conclusion, will exactly indicate
how far that conclusion is from being applicable universally. If in the
course of the argument other approximate generalizations are introduced,
each of them being in like manner expressed as a universal proposition
with a condition annexed, the sum of all the conditions will appear at the
end as the sum of all the errors which affect the conclusion. Thus, to the
proposition last cited, let us add the following: All absolute monarchs
have uncontrolled power, unless their position is such that they need the
active support of their subjects (as was the case with Queen Elizabeth,
Frederick of Prussia, and others). Combining these two propositions, we
can deduce from them a universal conclusion, which will be subject to both
the hypotheses in the premises; All absolute monarchs employ their power
ill, unless their position makes them need the active support of their
subjects, or unless they are persons of unusual strength of judgment and
rectitude of purpose. It is of no consequence how rapidly the errors in
our premises accumulate, if we are able in this manner to record each
error, and keep an account of the aggregate as it swells up.

Secondly: there is a case in which approximate propositions, even without
our taking note of the conditions under which they are not true of
individual cases, are yet, for the purposes of science, universal ones;
namely, in the inquiries which relate to the properties not of
individuals, but of multitudes. The principal of these is the science of
politics, or of human society. This science is principally concerned with
the actions not of solitary individuals, but of masses; with the fortunes
not of single persons, but of communities. For the statesman, therefore,
it is generally enough to know that _most_ persons act or are acted upon
in a particular way; since his speculations and his practical arrangements
refer almost exclusively to cases in which the whole community, or some
large portion of it, is acted upon at once, and in which, therefore, what
is done or felt by _most_ persons determines the result produced by or
upon the body at large. He can get on well enough with approximate
generalizations on human nature, since what is true approximately of all
individuals is true absolutely of all masses. And even when the operations
of individual men have a part to play in his deductions, as when he is
reasoning of kings, or other single rulers, still, as he is providing for
indefinite duration, involving an indefinite succession of such
individuals, he must in general both reason and act as if what is true of
most persons were true of all.

The two kinds of considerations above adduced are a sufficient refutation
of the popular error, that speculations on society and government, as
resting on merely probable evidence, must be inferior in certainty and
scientific accuracy to the conclusions of what are called the exact
sciences, and less to be relied on in practice. There are reasons enough
why the moral sciences must remain inferior to at least the more perfect
of the physical; why the laws of their more complicated phenomena can not
be so completely deciphered, nor the phenomena predicted with the same
degree of assurance. But though we can not attain to so many truths, there
is no reason that those we can attain should deserve less reliance, or
have less of a scientific character. Of this topic, however, I shall treat
more systematically in the concluding Book, to which place any further
consideration of it must be deferred.



                              Chapter XXIV.


Of The Remaining Laws Of Nature.


§ 1. In the First Book we found that all the assertions which can be
conveyed by language, express some one or more of five different things:
Existence; Order in Place; Order in Time; Causation; and Resemblance.(197)
Of these, Causation, in our view of the subject, not being fundamentally
different from Order in Time, the five species of possible assertions are
reduced to four. The propositions which affirm Order in Time in either of
its two modes, Co-existence and Succession, have formed, thus far, the
subject of the present Book. And we have now concluded the exposition, so
far as it falls within the limits assigned to this work, of the nature of
the evidence on which these propositions rest, and the processes of
investigation by which they are ascertained and proved. There remain three
classes of facts: Existence, Order in Place, and Resemblance; in regard to
which the same questions are now to be resolved.

Regarding the first of these, very little needs be said. Existence in
general, is a subject not for our science, but for metaphysics. To
determine what things can be recognized as really existing, independently
of our own sensible or other impressions, and in what meaning the term is,
in that case, predicated of them, belongs to the consideration of “Things
in themselves,” from which, throughout this work, we have as much as
possible kept aloof. Existence, so far as Logic is concerned about it, has
reference only to phenomena; to actual, or possible, states of external or
internal consciousness, in ourselves or others. Feelings of sensitive
beings, or possibilities of having such feelings, are the only things the
existence of which can be a subject of logical induction, because the only
things of which the existence in individual cases can be a subject of
experience.

It is true that a thing is said by us to exist, even when it is absent,
and therefore is not and can not be perceived. But even then, its
existence is to us only another word for our conviction that we should
perceive it on a certain supposition; namely, if we were in the needful
circumstances of time and place, and endowed with the needful perfection
of organs. My belief that the Emperor of China exists, is simply my belief
that if I were transported to the imperial palace or some other locality
in Pekin, I should see him. My belief that Julius Cæsar existed, is my
belief that I should have seen him if I had been present in the field of
Pharsalia, or in the senate-house at Rome. When I believe that stars exist
beyond the utmost range of my vision, though assisted by the most powerful
telescopes yet invented, my belief, philosophically expressed, is, that
with still better telescopes, if such existed, I could see them, or that
they may be perceived by beings less remote from them in space, or whose
capacities of perception are superior to mine.

The existence, therefore, of a phenomenon, is but another word for its
being perceived, or for the inferred possibility of perceiving it. When
the phenomenon is within the range of present observation, by present
observation we assure ourselves of its existence; when it is beyond that
range, and is therefore said to be absent, we infer its existence from
marks or evidences. But what can these evidences be? Other phenomena;
ascertained by induction to be connected with the given phenomenon, either
in the way of succession or of co-existence. The simple existence,
therefore, of an individual phenomenon, when not directly perceived, is
inferred from some inductive law of succession or co-existence; and is
consequently not amenable to any peculiar inductive principles. We prove
the existence of a thing, by proving that it is connected by succession or
co-existence with some known thing.

With respect to _general_ propositions of this class, that is, which
affirm the bare fact of existence, they have a peculiarity which renders
the logical treatment of them a very easy matter; they are generalizations
which are sufficiently proved by a single instance. That ghosts, or
unicorns, or sea-serpents exist, would be fully established if it could be
ascertained positively that such things had been even once seen. Whatever
has once happened, is capable of happening again; the only question
relates to the conditions under which it happens.

So far, therefore, as relates to simple existence, the Inductive Logic has
no knots to untie. And we may proceed to the remaining two of the great
classes into which facts have been divided; Resemblance, and Order in
Place.

§ 2. Resemblance and its opposite, except in the case in which they assume
the names of Equality and Inequality, are seldom regarded as subjects of
science; they are supposed to be perceived by simple apprehension; by
merely applying our senses or directing our attention to the two objects
at once, or in immediate succession. And this simultaneous, or virtually
simultaneous, application of our faculties to the two things which are to
be compared, does necessarily constitute the ultimate appeal, wherever
such application is practicable. But, in most cases, it is not
practicable: the objects can not be brought so close together that the
feeling of their resemblance (at least a complete feeling of it) directly
arises in the mind. We can only compare each of them with some third
object, capable of being transported from one to the other. And besides,
even when the objects can be brought into immediate juxtaposition, their
resemblance or difference is but imperfectly known to us, unless we have
compared them minutely, part by part. Until this has been done, things in
reality very dissimilar often appear undistinguishably alike. Two lines of
very unequal length will appear about equal when lying in different
directions; but place them parallel with their farther extremities even,
and if we look at the nearer extremities, their inequality becomes a
matter of direct perception.

To ascertain whether, and in what, two phenomena resemble or differ, is
not always, therefore, so easy a thing as it might at first appear. When
the two can not be brought into juxtaposition, or not so that the observer
is able to compare their several parts in detail, he must employ the
indirect means of reasoning and general propositions. When we can not
bring two straight lines together, to determine whether they are equal, we
do it by the physical aid of a foot-rule applied first to one and then to
the other, and the logical aid of the general proposition or formula,
“Things which are equal to the same thing are equal to one another.” The
comparison of two things through the intervention of a third thing, when
their direct comparison is impossible, is the appropriate scientific
process for ascertaining resemblances and dissimilarities, and is the sum
total of what Logic has to teach on the subject.

An undue extension of this remark induced Locke to consider reasoning
itself as nothing but the comparison of two ideas through the medium of a
third, and knowledge as the perception of the agreement or disagreement of
two ideas; doctrines which the Condillac school blindly adopted, without
the qualifications and distinctions with which they were studiously
guarded by their illustrious author. Where, indeed, the agreement or
disagreement (otherwise called resemblance or dissimilarity) of any two
things is the very matter to be determined, as is the case particularly in
the sciences of quantity and extension; there, the process by which a
solution, if not attainable by direct perception, must be indirectly
sought, consists in comparing these two things through the medium of a
third. But this is far from being true of all inquiries. The knowledge
that bodies fall to the ground is not a perception of agreement or
disagreement, but of a series of physical occurrences, a succession of
sensations. Locke’s definitions of knowledge and of reasoning required to
be limited to our knowledge of, and reasoning about, resemblances. Nor,
even when thus restricted, are the propositions strictly correct; since
the comparison is not made, as he represents, between the ideas of the two
phenomena, but between the phenomena themselves. This mistake has been
pointed out in an earlier part of our inquiry,(198) and we traced it to an
imperfect conception of what takes place in mathematics, where very often
the comparison is really made between the ideas, without any appeal to the
outward senses; only, however, because in mathematics a comparison of the
ideas is strictly equivalent to a comparison of the phenomena themselves.
Where, as in the case of numbers, lines, and figures, our idea of an
object is a complete picture of the object, so far as respects the matter
in hand; we can, of course, learn from the picture, whatever could be
learned from the object itself by mere contemplation of it as it exists at
the particular instant when the picture is taken. No mere contemplation of
gunpowder would ever teach us that a spark would make it explode, nor,
consequently, would the contemplation of the idea of gunpowder do so; but
the mere contemplation of a straight line shows that it can not inclose a
space; accordingly the contemplation of the idea of it will show the same.
What takes place in mathematics is thus no argument that the comparison is
between the ideas only. It is always, either indirectly or directly, a
comparison of the phenomena.

In cases in which we can not bring the phenomena to the test of direct
inspection at all, or not in a manner sufficiently precise, but must judge
of their resemblance by inference from other resemblances or
dissimilarities more accessible to observation, we of course require, as
in all cases of ratiocination, generalizations or formulæ applicable to
the subject. We must reason from laws of nature; from the uniformities
which are observable in the fact of likeness or unlikeness.

§ 3. Of these laws or uniformities, the most comprehensive are those
supplied by mathematics; the axioms relating to equality, inequality, and
proportionality, and the various theorems thereon founded. And these are
the only Laws of Resemblance which require to be, or which can be, treated
apart. It is true there are innumerable other theorems which affirm
resemblances among phenomena; as that the angle of the reflection of light
is _equal_ to its angle of incidence (equality being merely exact
resemblance in magnitude). Again, that the heavenly bodies describe
_equal_ areas in equal times; and that their periods of revolution are
_proportional_ (another species of resemblance) to the sesquiplicate
powers of their distances from the centre of force. These and similar
propositions affirm resemblances, of the same nature with those asserted
in the theorems of mathematics; but the distinction is, that the
propositions of mathematics are true of all phenomena whatever, or at
least without distinction of origin; while the truths in question are
affirmed only of special phenomena, which originate in a certain way; and
the equalities, proportionalities, or other resemblances, which exist
between such phenomena, must necessarily be either derived from, or
identical with, the law of their origin—the law of causation on which they
depend. The equality of the areas described in equal times by the planets,
is _derived_ from the laws of the causes; and, until its derivation was
shown, it was an empirical law. The equality of the angles of reflection
and incidence is _identical_ with the law of the cause; for the cause is
the incidence of a ray of light upon a reflecting surface, and the
equality in question is the very law according to which that cause
produces its effects. This class, therefore, of the uniformities of
resemblance between phenomena, are inseparable, in fact and in thought,
from the laws of the production of those phenomena; and the principles of
induction applicable to them are no other than those of which we have
treated in the preceding chapters of this Book.

It is otherwise with the truths of mathematics. The laws of equality and
inequality between spaces, or between numbers, have no connection with
laws of causation. That the angle of reflection is equal to the angle of
incidence, is a statement of the mode of action of a particular cause; but
that when two straight lines intersect each other the opposite angles are
equal, is true of all such lines and angles, by whatever cause produced.
That the squares of the periodic times of the planets are proportional to
the cubes of their distances from the sun, is a uniformity derived from
the laws of the causes (or forces) which produce the planetary motions;
but that the square of any number is four times the square of half the
number, is true independently of any cause. The only laws of resemblance,
therefore, which we are called upon to consider independently of
causation, belong to the province of mathematics.

§ 4. The same thing is evident with respect to the only one remaining of
our five categories, Order in Place. The order in place, of the effects of
a cause, is (like every thing else belonging to the effects) a consequence
of the laws of that cause. The order in place, or, as we have termed it,
the collocation, of the primeval causes, is (as well as their resemblance)
in each instance an ultimate fact, in which no laws or uniformities are
traceable. The only remaining general propositions respecting order in
place, and the only ones which have nothing to do with causation, are some
of the truths of geometry; laws through which we are able, from the order
in place of certain points, lines, or spaces, to infer the order in place
of others which are connected with the former in some known mode; quite
independently of the particular nature of those points, lines, or spaces,
in any other respect than position or magnitude, as well as independently
of the physical cause from which in any particular case they happen to
derive their origin.

It thus appears that mathematics is the only department of science into
the methods of which it still remains to inquire. And there is the less
necessity that this inquiry should occupy us long, as we have already, in
the Second Book, made considerable progress in it. We there remarked, that
the directly inductive truths of mathematics are few in number; consisting
of the axioms, together with certain propositions concerning existence,
tacitly involved in most of the so-called definitions. And we gave what
appeared conclusive reasons for affirming that these original premises,
from which the remaining truths of the science are deduced, are,
notwithstanding all appearances to the contrary, results of observation
and experience; founded, in short, on the evidence of the senses. That
things equal to the same thing are equal to one another, and that two
straight lines which have once intersected one another continue to
diverge, are inductive truths; resting, indeed, like the law of universal
causation, only on induction _per enumerationem simplicem_; on the fact
that they have been perpetually perceived to be true, and never once found
to be false. But, as we have seen in a recent chapter that this evidence,
in the case of a law so completely universal as the law of causation,
amounts to the fullest proof, so is this even more evidently true of the
general propositions to which we are now adverting; because, as a
perception of their truth in any individual case whatever, requires only
the simple act of looking at the objects in a proper position, there never
could have been in their case (what, for a long period, there were in the
case of the law of causation) instances which were apparently, though not
really, exceptions to them. Their infallible truth was recognized from the
very dawn of speculation; and as their extreme familiarity made it
impossible for the mind to conceive the objects under any other law, they
were, and still are, generally considered as truths recognized by their
own evidence, or by instinct.

§ 5. There is something which seems to require explanation, in the fact
that the immense multitude of truths (a multitude still as far from being
exhausted as ever) comprised in the mathematical sciences, can be elicited
from so small a number of elementary laws. One sees not, at first, how it
is that there can be room for such an infinite variety of true
propositions, on subjects apparently so limited.

To begin with the science of number. The elementary or ultimate truths of
this science are the common axioms concerning equality, namely, “Things
which are equal to the same thing are equal to one another,” and “Equals
added to equals make equal sums” (no other axioms are required),(199)
together with the definitions of the various numbers. Like other so-called
definitions, these are composed of two things, the explanation of a name,
and the assertion of a fact; of which the latter alone can form a first
principle or premise of a science. The fact asserted in the definition of
a number is a physical fact. Each of the numbers two, three, four, etc.,
denotes physical phenomena, and connotes a physical property of those
phenomena. Two, for instance, denotes all pairs of things, and twelve all
dozens of things, connoting what makes them pairs, or dozens; and that
which makes them so is something physical; since it can not be denied that
two apples are physically distinguishable from three apples, two horses
from one horse, and so forth; that they are a different visible and
tangible phenomenon. I am not undertaking to say what the difference is;
it is enough that there is a difference of which the senses can take
cognizance. And although a hundred and two horses are not so easily
distinguished from a hundred and three, as two horses are from
three—though in most positions the senses do not perceive any
difference—yet they may be so placed that a difference will be
perceptible, or else we should never have distinguished them, and given
them different names. Weight is confessedly a physical property of things;
yet small differences between great weights are as imperceptible to the
senses in most situations, as small differences between great numbers; and
are only put in evidence by placing the two objects in a peculiar
position—namely, in the opposite scales of a delicate balance.

What, then, is that which is connoted by a name of number? Of course, some
property belonging to the agglomeration of things which we call by the
name; and that property is, the characteristic manner in which the
agglomeration is made up of, and may be separated into, parts. I will
endeavor to make this more intelligible by a few explanations.

When we call a collection of objects _two_, _three_, or _four_, they are
not two, three, or four in the abstract; they are two, three, or four
things of some particular kind; pebbles, horses, inches, pounds’ weight.
What the name of number connotes is, the manner in which single objects of
the given kind must be put together, in order to produce that particular
aggregate. If the aggregate be of pebbles, and we call it _two_, the name
implies that, to compose the aggregate, one pebble must be joined to one
pebble. If we call it _three_, one and one and one pebble must be brought
together to produce it, or else one pebble must be joined to an aggregate
of the kind called _two_, already existing. The aggregate which we call
_four_, has a still greater number of characteristic modes of formation.
One and one and one and one pebble may be brought together; or two
aggregates of the kind called _two_ may be united; or one pebble may be
added to an aggregate of the kind called _three_. Every succeeding number
in the ascending series, may be formed by the junction of smaller numbers
in a progressively greater variety of ways. Even limiting the parts to
two, the number may be formed, and consequently may be divided, in as many
different ways as there are numbers smaller than itself; and, if we admit
of threes, fours, etc., in a still greater variety. Other modes of
arriving at the same aggregate present themselves, not by the union of
smaller, but by the dismemberment of larger aggregates. Thus, _three
pebbles_ may be formed by taking away one pebble from an aggregate of
four; _two pebbles_, by an equal division of a similar aggregate; and so
on.

Every arithmetical proposition; every statement of the result of an
arithmetical operation; is a statement of one of the modes of formation of
a given number. It affirms that a certain aggregate might have been formed
by putting together certain other aggregates, or by withdrawing certain
portions of some aggregate; and that, by consequence, we might reproduce
those aggregates from it, by reversing the process.

Thus, when we say that the cube of 12 is 1728, what we affirm is this:
that if, having a sufficient number of pebbles or of any other objects, we
put them together into the particular sort of parcels or aggregates called
twelves; and put together these twelves again into similar collections;
and, finally, make up twelve of these largest parcels; the aggregate thus
formed will be such a one as we call 1728; namely, that which (to take the
most familiar of its modes of formation) may be made by joining the parcel
called a thousand pebbles, the parcel called seven hundred pebbles, the
parcel called twenty pebbles, and the parcel called eight pebbles.

The converse proposition that the cube root of 1728 is 12, asserts that
this large aggregate may again be decomposed into the twelve twelves of
twelves of pebbles which it consists of.

The modes of formation of any number are innumerable; but when we know one
mode of formation of each, all the rest may be determined deductively. If
we know that _a_ is formed from _b_ and _c_, _b_ from _a_ and _e_, _c_
from _d_ and _f_, and so forth, until we have included all the numbers of
any scale we choose to select (taking care that for each number the mode
of formation be really a distinct one, not bringing us round again to the
former numbers, but introducing a new number), we have a set of
propositions from which we may reason to all the other modes of formation
of those numbers from one another. Having established a chain of inductive
truths connecting together all the numbers of the scale, we can ascertain
the formation of any one of those numbers from any other by merely
traveling from one to the other along the chain. Suppose that we know only
the following modes of formation: 6=4+2, 4=7-3, 7=5+2, 5=9-4. We could
determine how 6 may be formed from 9. For 6=4+2=7-3+2=5+2-3+2=9-4+2-3+2.
It may therefore be formed by taking away 4 and 3, and adding 2 and 2. If
we know besides that 2+2=4, we obtain 6 from 9 in a simpler mode, by
merely taking away 3.

It is sufficient, therefore, to select one of the various modes of
formation of each number, as a means of ascertaining all the rest. And
since things which are uniform, and therefore simple, are most easily
received and retained by the understanding, there is an obvious advantage
in selecting a mode of formation which shall be alike for all; in fixing
the connotation of names of number on one uniform principle. The mode in
which our existing numerical nomenclature is contrived possesses this
advantage, with the additional one, that it happily conveys to the mind
two of the modes of formation of every number. Each number is considered
as formed by the addition of a unit to the number next below it in
magnitude, and this mode of formation is conveyed by the place which it
occupies in the series. And each is also considered as formed by the
addition of a number of units less than ten, and a number of aggregates
each equal to one of the successive powers of ten; and this mode of its
formation is expressed by its spoken name, and by its numerical character.

What renders arithmetic the type of a deductive science, is the fortunate
applicability to it of a law so comprehensive as “The sums of equals are
equals:” or (to express the same principle in less familiar but more
characteristic language), Whatever is made up of parts, is made up of the
parts of those parts. This truth, obvious to the senses in all cases which
can be fairly referred to their decision, and so general as to be
co-extensive with nature itself, being true of all sorts of phenomena (for
all admit of being numbered), must be considered an inductive truth, or
law of nature, of the highest order. And every arithmetical operation is
an application of this law, or of other laws capable of being deduced from
it. This is our warrant for all calculations. We believe that five and two
are equal to seven, on the evidence of this inductive law, combined with
the definitions of those numbers. We arrive at that conclusion (as all
know who remember how they first learned it) by adding a single unit at a
time: 5 + 1=6, therefore 5+1+1=6+1=7; and again 2=1+1, therefore
5+2=5+1+1=7.

§ 6. Innumerable as are the true propositions which can be formed
concerning particular numbers, no adequate conception could be gained,
from these alone, of the extent of the truths composing the science of
number. Such propositions as we have spoken of are the least general of
all numerical truths. It is true that even these are co-extensive with all
nature; the properties of the number four are true of all objects that are
divisible into four equal parts, and all objects are either actually or
ideally so divisible. But the propositions which compose the science of
algebra are true, not of a particular number, but of all numbers; not of
all things under the condition of being divided in a particular way, but
of all things under the condition of being divided in any way—of being
designated by a number at all.

Since it is impossible for different numbers to have any of their modes of
formation completely in common, it is a kind of paradox to say, that all
propositions which can be made concerning numbers relate to their modes of
formation from other numbers, and yet that there are propositions which
are true of all numbers. But this very paradox leads to the real principle
of generalization concerning the properties of numbers. Two different
numbers can not be formed in the same manner from the same numbers; but
they may be formed in the same manner from different numbers; as nine is
formed from three by multiplying it into itself, and sixteen is formed
from four by the same process. Thus there arises a classification of modes
of formation, or in the language commonly used by mathematicians, a
classification of Functions. Any number, considered as formed from any
other number, is called a function of it; and there are as many kinds of
functions as there are modes of formation. The simple functions are by no
means numerous, most functions being formed by the combination of several
of the operations which form simple functions, or by successive
repetitions of some one of those operations. The simple functions of any
number _x_ are all reducible to the following forms: _x_+_a_, _x_-_a_,
_ax_, _x_/_a_, log. _x_ (to the base _a_), and the same expressions varied
by putting _x_ for _a_ and _a_ for _x_, wherever that substitution would
alter the value: to which, perhaps, ought to be added sin _x_, and arc
(sin=_x_). All other functions of _x_ are formed by putting some one or
more of the simple functions in the place of _x_ or _a_, and subjecting
them to the same elementary operations.

In order to carry on general reasonings on the subject of Functions, we
require a nomenclature enabling us to express any two numbers by names
which, without specifying what particular numbers they are, shall show
what function each is of the other; or, in other words, shall put in
evidence their mode of formation from one another. The system of general
language called algebraical notation does this. The expressions _a_ and
a2+3a denote, the one any number, the other the number formed from it in a
particular manner. The expressions _a_, _b_, _n_, and (_a+b_)n, denote any
three numbers, and a fourth which is formed from them in a certain mode.

The following may be stated as the general problem of the algebraical
calculus: F being a certain function of a given number, to find what
function F will be of any function of that number. For example, a binomial
_a + b_ is a function of its two parts _a_ and _b_, and the parts are, in
their turn, functions of _a + b_: now (_a + b_)n is a certain function of
the binomial; what function will this be of _a_ and _b_, the two parts?
The answer to this question is the binomial theorem. The formula _(a +
b)__n__ = a__n__ + n/1 a__n-1__ b + n.n-1/1.2 a__n-2__ b__2_, etc., shows
in what manner the number which is formed by multiplying _a + b_ into
itself _n_ times, might be formed without that process, directly from _a,
b_, and _n_. And of this nature are all the theorems of the science of
number. They assert the identity of the result of different modes of
formation. They affirm that some mode of formation from _x_, and some mode
of formation from a certain function of _x_, produce the same number.

Such, as above described, is the aim and end of the calculus. As for its
processes, every one knows that they are simply deductive. In
demonstrating an algebraical theorem, or in resolving an equation, we
travel from the _datum_ to the _quæsitum_ by pure ratiocination; in which
the only premises introduced, besides the original hypotheses, are the
fundamental axioms already mentioned—that things equal to the same thing
are equal to one another, and that the sums of equal things are equal. At
each step in the demonstration or in the calculation, we apply one or
other of these truths, or truths deducible from them, as, that the
differences, products, etc., of equal numbers are equal.

It would be inconsistent with the scale of this work, and not necessary to
its design, to carry the analysis of the truths and processes of algebra
any further; which is also the less needful, as the task has been, to a
very great extent, performed by other writers. Peacock’s Algebra, and Dr.
Whewell’s _Doctrine of Limits_, are full of instruction on the subject.
The profound treatises of a truly philosophical mathematician, Professor
De Morgan, should be studied by every one who desires to comprehend the
evidence of mathematical truths, and the meaning of the obscurer processes
of the calculus, and the speculations of M. Comte, in his _Cours de
Philosophie Positive_, on the philosophy of the higher branches of
mathematics, are among the many valuable gifts for which philosophy is
indebted to that eminent thinker.

§ 7. If the extreme generality, and remoteness not so much from sense as
from the visual and tactual imagination, of the laws of number, renders it
a somewhat difficult effort of abstraction to conceive those laws as being
in reality physical truths obtained by observation; the same difficulty
does not exist with regard to the laws of extension. The facts of which
those laws are expressions, are of a kind peculiarly accessible to the
senses, and suggesting eminently distinct images to the fancy. That
geometry is a strictly physical science would doubtless have been
recognized in all ages, had it not been for the illusions produced by two
circumstances. One of these is the characteristic property, already
noticed, of the facts of geometry, that they may be collected from our
ideas or mental pictures of objects as effectually as from the objects
themselves. The other is, the demonstrative character of geometrical
truths; which was at one time supposed to constitute a radical distinction
between them and physical truths; the latter, as resting on merely
probable evidence, being deemed essentially uncertain and unprecise. The
advance of knowledge has, however, made it manifest that physical science,
in its better understood branches, is quite as demonstrative as geometry.
The task of deducing its details from a few comparatively simple
principles is found to be any thing but the impossibility it was once
supposed to be; and the notion of the superior certainty of geometry is an
illusion, arising from the ancient prejudice which, in that science,
mistakes the ideal data from which we reason, for a peculiar class of
realities, while the corresponding ideal data of any deductive physical
science are recognized as what they really are, hypotheses.

Every theorem in geometry is a law of external nature, and might have been
ascertained by generalizing from observation and experiment, which in this
case resolve themselves into comparison and measurement. But it was found
practicable, and, being practicable, was desirable, to deduce these truths
by ratiocination from a small number of general laws of nature, the
certainty and universality of which are obvious to the most careless
observer, and which compose the first principles and ultimate premises of
the science. Among these general laws must be included the same two which
we have noticed as ultimate principles of the Science of Number also, and
which are applicable to every description of quantity; viz., The sums of
equals are equal, and Things which are equal to the same thing are equal
to one another; the latter of which may be expressed in a manner more
suggestive of the inexhaustible multitude of its consequences, by the
following terms: Whatever is equal to any one of a number of equal
magnitudes, is equal to any other of them. To these two must be added, in
geometry, a third law of equality, namely, that lines, surfaces, or solid
spaces, which can be so applied to one another as to coincide, are equal.
Some writers have asserted that this law of nature is a mere verbal
definition; that the expression “equal magnitudes” _means_ nothing but
magnitudes which can be so applied to one another as to coincide. But in
this opinion I can not agree. The equality of two geometrical magnitudes
can not differ fundamentally in its nature from the equality of two
weights, two degrees of heat, or two portions of duration, to none of
which would this definition of equality be suitable. None of these things
can be so applied to one another as to coincide, yet we perfectly
understand what we mean when we call them equal. Things are equal in
magnitude, as things are equal in weight, when they are felt to be exactly
similar in respect of the attribute in which we compare them: and the
application of the objects to each other in the one case, like the
balancing them with a pair of scales in the other, is but a mode of
bringing them into a position in which our senses can recognize
deficiencies of exact resemblance that would otherwise escape our notice.

Along with these three general principles or axioms, the remainder of the
premises of geometry consists of the so-called definitions: that is to
say, propositions asserting the real existence of the various objects
therein designated, together with some one property of each. In some cases
more than one property is commonly assumed, but in no case is more than
one necessary. It is assumed that there are such things in nature as
straight lines, and that any two of them setting out from the same point,
diverge more and more without limit. This assumption (which includes and
goes beyond Euclid’s axiom that two straight lines can not inclose a
space) is as indispensable in geometry, and as evident, resting on as
simple, familiar, and universal observation, as any of the other axioms.
It is also assumed that straight lines diverge from one another in
different degrees; in other words, that there are such things as angles,
and that they are capable of being equal or unequal. It is assumed that
there is such a thing as a circle, and that all its radii are equal; such
things as ellipses, and that the sums of the focal distances are equal for
every point in an ellipse; such things as parallel lines, and that those
lines are everywhere equally distant.(200)

§ 8. It is a matter of more than curiosity to consider, to what
peculiarity of the physical truths which are the subject of geometry, it
is owing that they can all be deduced from so small a number of original
premises; why it is that we can set out from only one characteristic
property of each kind of phenomenon, and with that and two or three
general truths relating to equality, can travel from mark to mark until we
obtain a vast body of derivative truths, to all appearance extremely
unlike those elementary ones.

The explanation of this remarkable fact seems to lie in the following
circumstances. In the first place, all questions of position and figure
may be resolved into questions of magnitude. The position and figure of
any object are determined by determining the position of a sufficient
number of points in it; and the position of any point may be determined by
the magnitude of three rectangular co-ordinates, that is, of the
perpendiculars drawn from the point to three planes at right angles to one
another, arbitrarily selected. By this transformation of all questions of
quality into questions only of quantity, geometry is reduced to the single
problem of the measurement of magnitudes, that is, the ascertainment of
the equalities which exist between them. Now when we consider that by one
of the general axioms, any equality, when ascertained, is proof of as many
other equalities as there are other things equal to either of the two
equals; and that by another of those axioms, any ascertained equality is
proof of the equality of as many pairs of magnitudes as can be formed by
the numerous operations which resolve themselves into the addition of the
equals to themselves or to other equals; we cease to wonder that in
proportion as a science is conversant about equality, it should afford a
more copious supply of marks of marks; and that the sciences of number and
extension, which are conversant with little else than equality, should be
the most deductive of all the sciences.

There are also two or three of the principal laws of space or extension
which are unusually fitted for rendering one position or magnitude a mark
of another, and thereby contributing to render the science largely
deductive. First, the magnitudes of inclosed spaces, whether superficial
or solid, are completely determined by the magnitudes of the lines and
angles which bound them. Secondly, the length of any line, whether
straight or curve, is measured (certain other things being given) by the
angle which it subtends, and _vicè versa_. Lastly, the angle which any two
straight lines make with each other at an inaccessible point, is measured
by the angles they severally make with any third line we choose to select.
By means of these general laws, the measurement of all lines, angles, and
spaces whatsoever might be accomplished by measuring a single straight
line and a sufficient number of angles; which is the plan actually pursued
in the trigonometrical survey of a country; and fortunate it is that this
is practicable, the exact measurement of long straight lines being always
difficult, and often impossible, but that of angles very easy. Three such
generalizations as the foregoing afford such facilities for the indirect
measurement of magnitudes (by supplying us with known lines or angles
which are marks of the magnitude of unknown ones, and thereby of the
spaces which they inclose), that it is easily intelligible how from a few
data we can go on to ascertain the magnitude of an indefinite multitude of
lines, angles, and spaces, which we could not easily, or could not at all,
measure by any more direct process.

§ 9. Such are the remarks which it seems necessary to make in this place,
respecting the laws of nature which are the peculiar subject of the
sciences of number and extension. The immense part which those laws take
in giving a deductive character to the other departments of physical
science, is well known; and is not surprising, when we consider that all
causes operate according to mathematical laws. The effect is always
dependent on, or is a function of, the quantity of the agent; and
generally of its position also. We can not, therefore, reason respecting
causation, without introducing considerations of quantity and extension at
every step; and if the nature of the phenomena admits of our obtaining
numerical data of sufficient accuracy, the laws of quantity become the
grand instrument for calculating forward to an effect, or backward to a
cause. That in all other sciences, as well as in geometry, questions of
quality are scarcely ever independent of questions of quantity, may be
seen from the most familiar phenomena. Even when several colors are mixed
on a painter’s palette, the comparative quantity of each entirely
determines the color of the mixture.

With this mere suggestion of the general causes which render mathematical
principles and processes so predominant in those deductive sciences which
afford precise numerical data, I must, on the present occasion, content
myself; referring the reader who desires a more thorough acquaintance with
the subject, to the first two volumes of M. Comte’s systematic work.

In the same work, and more particularly in the third volume, are also
fully discussed the limits of the applicability of mathematical principles
to the improvement of other sciences. Such principles are manifestly
inapplicable, where the causes on which any class of phenomena depend are
so imperfectly accessible to our observation, that we can not ascertain,
by a proper induction, their numerical laws; or where the causes are so
numerous, and intermixed in so complex a manner with one another, that
even supposing their laws known, the computation of the aggregate effect
transcends the powers of the calculus as it is, or is likely to be; or,
lastly, where the causes themselves are in a state of perpetual
fluctuation; as in physiology, and still more, if possible, in the social
science. The mathematical solutions of physical questions become
progressively more difficult and imperfect, in proportion as the questions
divest themselves of their abstract and hypothetical character, and
approach nearer to the degree of complication actually existing in nature;
insomuch that beyond the limits of astronomical phenomena, and of those
most nearly analogous to them, mathematical accuracy is generally obtained
“at the expense of the reality of the inquiry:” while even in astronomical
questions, “notwithstanding the admirable simplicity of their mathematical
elements, our feeble intelligence becomes incapable of following out
effectually the logical combinations of the laws on which the phenomena
are dependent, as soon as we attempt to take into simultaneous
consideration more than two or three essential influences.”(201) Of this,
the problem of the Three Bodies has already been cited, more than once, as
a remarkable instance; the complete solution of so comparatively simple a
question having vainly tried the skill of the most profound
mathematicians. We may conceive, then, how chimerical would be the hope
that mathematical principles could be advantageously applied to phenomena
dependent on the mutual action of the innumerable minute particles of
bodies, as those of chemistry, and still more, of physiology; and for
similar reasons those principles remain inapplicable to the still more
complex inquiries, the subjects of which are phenomena of society and
government.

The value of mathematical instruction as a preparation for those more
difficult investigations, consists in the applicability not of its
doctrines, but of its method. Mathematics will ever remain the most
perfect type of the Deductive Method in general; and the applications of
mathematics to the deductive branches of physics, furnish the only school
in which philosophers can effectually learn the most difficult and
important portion of their art, the employment of the laws of simpler
phenomena for explaining and predicting those of the more complex. These
grounds are quite sufficient for deeming mathematical training an
indispensable basis of real scientific education, and regarding (according
to the _dictum_ which an old but unauthentic tradition ascribes to Plato)
one who is ἀγεωμέτρητος, as wanting in one of the most essential
qualifications for the successful cultivation of the higher branches of
philosophy.



                               Chapter XXV.


Of The Grounds Of Disbelief.


§ 1. The method of arriving at general truths, or general propositions fit
to be believed, and the nature of the evidence on which they are grounded,
have been discussed, as far as space and the writer’s faculties permitted,
in the twenty-four preceding chapters. But the result of the examination
of evidence is not always belief, nor even suspension of judgment; it is
sometimes disbelief. The philosophy, therefore, of induction and
experimental inquiry is incomplete, unless the grounds not only of belief,
but of disbelief, are treated of; and to this topic we shall devote one,
and the final, chapter.

By disbelief is not here to be understood the mere absence of belief. The
ground for abstaining from belief is simply the absence or insufficiency
of proof; and in considering what is sufficient evidence to support any
given conclusion, we have already, by implication, considered what
evidence is not sufficient for the same purpose. By disbelief is here
meant, not the state of mind in which we form no opinion concerning a
subject, but that in which we are fully persuaded that some opinion is not
true; insomuch that if evidence, even of great apparent strength (whether
grounded on the testimony of others or on our own supposed perceptions),
were produced in favor of the opinion, we should believe that the
witnesses spoke falsely, or that they, or we ourselves if we were the
direct percipients, were mistaken.

That there are such cases, no one is likely to dispute. Assertions for
which there is abundant positive evidence are often disbelieved, on
account of what is called their improbability, or impossibility. And the
question for consideration is what, in the present case, these words mean,
and how far and in what circumstances the properties which they express
are sufficient grounds for disbelief.

§ 2. It is to be remarked, in the first place, that the positive evidence
produced in support of an assertion which is nevertheless rejected on the
score of impossibility or improbability, is never such as amounts to full
proof. It is always grounded on some approximate generalization. The fact
may have been asserted by a hundred witnesses; but there are many
exceptions to the universality of the generalization that what a hundred
witnesses affirm is true. We may seem to ourselves to have actually seen
the fact; but that we really see what we think we see, is by no means a
universal truth; our organs may have been in a morbid state; or we may
have inferred something, and imagined that we perceived it. The evidence,
then, in the affirmative being never more than an approximate
generalization, all will depend on what the evidence in the negative is.
If that also rests on an approximate generalization, it is a case for
comparison of probabilities. If the approximate generalizations leading to
the affirmative are, when added together, less strong, or, in other words,
farther from being universal, than the approximate generalizations which
support the negative side of the question, the proposition is said to be
improbable, and is to be disbelieved provisionally. If, however, an
alleged fact be in contradiction, not to any number of approximate
generalizations, but to a completed generalization grounded on a rigorous
induction, it is said to be impossible, and is to be disbelieved totally.

This last principle, simple and evident as it appears, is the doctrine
which, on the occasion of an attempt to apply it to the question of the
credibility of miracles, excited so violent a controversy. Hume’s
celebrated doctrine, that nothing is credible which is contradictory to
experience, or at variance with laws of nature, is merely this very plain
and harmless proposition, that whatever is contradictory to a complete
induction is incredible. That such a maxim as this should either be
accounted a dangerous heresy, or mistaken for a great and recondite truth,
speaks ill for the state of philosophical speculation on such subjects.

But does not (it may be asked) the very statement of the proposition imply
a contradiction? An alleged fact, according to this theory, is not to be
believed if it contradict a complete induction. But it is essential to the
completeness of an induction that it shall not contradict any known fact.
Is it not, then, a _petitio principii_ to say, that the fact ought to be
disbelieved because the induction opposed to it is complete? How can we
have a right to declare the induction complete, while facts, supported by
credible evidence, present themselves in opposition to it?

I answer, we have that right whenever the scientific canons of induction
give it to us; that is, whenever the induction _can_ be complete. We have
it, for example, in a case of causation in which there has been an
_experimentum crucis_. If an antecedent A, superadded to a set of
antecedents in all other respects unaltered, is followed by an effect B
which did not exist before, A is, in that instance at least, the cause of
B, or an indispensable part of its cause; and if A be tried again with
many totally different sets of antecedents and B still follows, then it is
the whole cause. If these observations or experiments have been repeated
so often, and by so many persons, as to exclude all supposition of error
in the observer, a law of nature is established; and so long as this law
is received as such, the assertion that on any particular occasion A took
place, and yet B did not follow, _without any counteracting cause_, must
be disbelieved. Such an assertion is not to be credited on any less
evidence than what would suffice to overturn the law. The general truths,
that whatever has a beginning has a cause, and that when none but the same
causes exist, the same effects follow, rest on the strongest inductive
evidence possible; the proposition that things affirmed by even a crowd of
respectable witnesses are true, is but an approximate generalization;
and—even if we fancy we actually saw or felt the fact which is in
contradiction to the law—what a human being can see is no more than a set
of appearances; from which the real nature of the phenomenon is merely an
inference, and in this inference approximate generalizations usually have
a large share. If, therefore, we make our election to hold by the law, no
quantity of evidence whatever ought to persuade us that there has occurred
any thing in contradiction to it. If, indeed, the evidence produced is
such that it is more likely that the set of observations and experiments
on which the law rests should have been inaccurately performed or
incorrectly interpreted, than that the evidence in question should be
false, we may believe the evidence; but then we must abandon the law. And
since the law was received on what seemed a complete induction, it can
only be rejected on evidence equivalent; namely, as being inconsistent not
with any number of approximate generalizations, but with some other and
better established law of nature. This extreme case, of a conflict between
two supposed laws of nature, has probably never actually occurred where,
in the process of investigating both the laws, the true canons of
scientific induction had been kept in view; but if it did occur, it must
terminate in the total rejection of one of the supposed laws. It would
prove that there must be a flaw in the logical process by which either one
or the other was established; and if there be so, that supposed general
truth is no truth at all. We can not admit a proposition as a law of
nature, and yet believe a fact in real contradiction to it. We must
disbelieve the alleged fact, or believe that we were mistaken in admitting
the supposed law.

But in order that any alleged fact should be contradictory to a law of
causation, the allegation must be, not simply that the cause existed
without being followed by the effect, for that would be no uncommon
occurrence; but that this happened in the absence of any adequate
counteracting cause. Now in the case of an alleged miracle, the assertion
is the exact opposite of this. It is, that the effect was defeated, not in
the absence, but in consequence of a counteracting cause, namely, a direct
interposition of an act of the will of some being who has power over
nature; and in particular of a Being, whose will being assumed to have
endowed all the causes with the powers by which they produce their
effects, may well be supposed able to counteract them. A miracle (as was
justly remarked by Brown)(202) is no contradiction to the law of cause and
effect; it is a new effect, supposed to be produced by the introduction of
a new cause. Of the adequacy of that cause, if present, there can be no
doubt; and the only antecedent improbability which can be ascribed to the
miracle, is the improbability that any such cause existed.

All, therefore, which Hume has made out, and this he must be considered to
have made out, is, that (at least in the imperfect state of our knowledge
of natural agencies, which leaves it always possible that some of the
physical antecedents may have been hidden from us) no evidence can prove a
miracle to any one who did not previously believe the existence of a being
or beings with supernatural power; or who believes himself to have full
proof that the character of the Being whom he recognizes is inconsistent
with his having seen fit to interfere on the occasion in question.

If we do not already believe in supernatural agencies, no miracle can
prove to us their existence. The miracle itself, considered merely as an
extraordinary fact, may be satisfactorily certified by our senses or by
testimony; but nothing can ever prove that it is a miracle; there is still
another possible hypothesis, that of its being the result of some unknown
natural cause; and this possibility can not be so completely shut out, as
to leave no alternative but that of admitting the existence and
intervention of a being superior to nature. Those, however, who already
believe in such a being have two hypotheses to choose from, a supernatural
and an unknown natural agency; and they have to judge which of the two is
the most probable in the particular case. In forming this judgment, an
important element of the question will be the conformity of the result to
the laws of the supposed agent, that is, to the character of the Deity as
they conceive it. But with the knowledge which we now possess of the
general uniformity of the course of nature, religion, following in the
wake of science, has been compelled to acknowledge the government of the
universe as being on the whole carried on by general laws, and not by
special interpositions. To whoever holds this belief, there is a general
presumption against any supposition of divine agency not operating through
general laws, or, in other words, there is an antecedent improbability in
every miracle, which, in order to outweigh it, requires an extraordinary
strength of antecedent probability derived from the special circumstances
of the case.

§ 3. It appears from what has been said, that the assertion that a cause
has been defeated of an effect which is connected with it by a completely
ascertained law of causation, is to be disbelieved or not, according to
the probability or improbability that there existed in the particular
instance an adequate counteracting cause. To form an estimate of this, is
not more difficult than of other probabilities. With regard to all _known_
causes capable of counteracting the given causes, we have generally some
previous knowledge of the frequency or rarity of their occurrence, from
which we may draw an inference as to the antecedent improbability of their
having been present in any particular case. And neither in respect to
known nor unknown causes are we required to pronounce on the probability
of their existing in nature, but only of their having existed at the time
and place at which the transaction is alleged to have happened. We are
seldom, therefore, without the means (when the circumstances of the case
are at all known to us) of judging how far it is likely that such a cause
should have existed at that time and place without manifesting its
presence by some other marks, and (in the case of an unknown cause)
without having hitherto manifested its existence in any other instance.
According as this circumstance, or the falsity of the testimony, appears
more improbable—that is, conflicts with an approximate generalization of a
higher order—we believe the testimony, or disbelieve it; with a stronger
or a weaker degree of conviction, according to the preponderance; at least
until we have sifted the matter further.

So much, then, for the case in which the alleged fact conflicts, or
appears to conflict, with a real law of causation. But a more common case,
perhaps, is that of its conflicting with uniformities of mere
co-existence, not proved to be dependent on causation; in other words,
with the properties of Kinds. It is with these uniformities principally
that the marvelous stories related by travelers are apt to be at variance;
as of men with tails, or with wings, and (until confirmed by experience)
of flying fish; or of ice, in the celebrated anecdote of the Dutch
travelers and the King of Siam. Facts of this description, facts
previously unheard of, but which could not from any known law of causation
be pronounced impossible, are what Hume characterizes as not contrary to
experience, but merely unconformable to it; and Bentham, in his treatise
on Evidence, denominates them facts disconformable _in specie_, as
distinguished from such as are disconformable _in toto_ or in _degree_

In a case of this description, the fact asserted is the existence of a new
Kind; which in itself is not in the slightest degree incredible, and only
to be rejected if the improbability that any variety of object existing at
the particular place and time should not have been discovered sooner, be
greater than that of error or mendacity in the witnesses. Accordingly,
such assertions, when made by credible persons, and of unexplored places,
are not disbelieved, but at most regarded as requiring confirmation from
subsequent observers; unless the alleged properties of the supposed new
Kind are at variance with known properties of some larger kind which
includes it; or, in other words, unless, in the new Kind which is asserted
to exist, some properties are said to have been found disjoined from
others which have always been known to accompany them; as in the case of
Pliny’s men, or any other kind of animal of a structure different from
that which has always been found to co-exist with animal life. On the mode
of dealing with any such case, little needs be added to what has been said
on the same topic in the twenty-second chapter.(203) When the uniformities
of co-existence which the alleged fact would violate, are such as to raise
a strong presumption of their being the result of causation, the fact
which conflicts with them is to be disbelieved; at least provisionally,
and subject to further investigation. When the presumption amounts to a
virtual certainty, as in the case of the general structure of organized
beings, the only question requiring consideration is whether, in phenomena
so little understood, there may not be liabilities to counteraction from
causes hitherto unknown; or whether the phenomena may not be capable of
originating in some other way, which would produce a different set of
derivative uniformities. Where (as in the case of the flying fish, or the
ornithorhynchus) the generalization to which the alleged fact would be an
exception is very special and of limited range, neither of the above
suppositions can be deemed very improbable; and it is generally, in the
case of such alleged anomalies, wise to suspend our judgment, pending the
subsequent inquiries which will not fail to confirm the assertion if it be
true. But when the generalization is very comprehensive, embracing a vast
number and variety of observations, and covering a considerable province
of the domain of nature; then, for reasons which have been fully
explained, such an empirical law comes near to the certainty of an
ascertained law of causation; and any alleged exception to it can not be
admitted, unless on the evidence of some law of causation proved by a
still more complete induction.

Such uniformities in the course of nature as do not bear marks of being
the results of causation are, as we have already seen, admissible as
universal truths with a degree of credence proportioned to their
generality. Those which are true of all things whatever, or at least which
are totally independent of the varieties of Kinds, namely, the laws of
number and extension, to which we may add the law of causation itself, are
probably the only ones, an exception to which is absolutely and
permanently incredible. Accordingly, it is to assertions supposed to be
contradictory to these laws, or to some others coming near to them in
generality, that the word impossibility (at least _total_ impossibility)
seems to be generally confined. Violations of other laws, of special laws
of causation, for instance, are said, by persons studious of accuracy in
expression, to be impossible _in the circumstances of the case_; or
impossible unless some cause had existed which did not exist in the
particular case.(204) Of no assertion, not in contradiction to some of
these very general laws, will more than improbability be asserted by any
cautious person; and improbability not of the highest degree, unless the
time and place in which the fact is said to have occurred, render it
almost certain that the anomaly, if real, could not have been overlooked
by other observers. Suspension of judgment is in all other cases the
resource of the judicious inquirer; provided the testimony in favor of the
anomaly presents, when well sifted, no suspicious circumstances.

But the testimony is scarcely ever found to stand that test, in cases in
which the anomaly is not real. In the instances on record in which a great
number of witnesses, of good reputation and scientific acquirements, have
testified to the truth of something which has turned out untrue, there
have almost always been circumstances which, to a keen observer who had
taken due pains to sift the matter, would have rendered the testimony
untrustworthy. There have generally been means of accounting for the
impression on the senses or minds of the alleged percipients, by
fallacious appearances; or some epidemic delusion, propagated by the
contagious influence of popular feeling, has been concerned in the case;
or some strong interest has been implicated—religious zeal, party feeling,
vanity, or at least the passion for the marvelous, in persons strongly
susceptible of it. When none of these or similar circumstances exist to
account for the apparent strength of the testimony; and where the
assertion is not in contradiction either to those universal laws which
know no counteraction or anomaly, or to the generalizations next in
comprehensiveness to them, but would only amount, if admitted, to the
existence of an unknown cause or an anomalous Kind, in circumstances not
so thoroughly explored but that it is credible that things hitherto
unknown may still come to light; a cautious person will neither admit nor
reject the testimony, but will wait for confirmation at other times and
from other unconnected sources. Such ought to have been the conduct of the
King of Siam when the Dutch travelers affirmed to him the existence of
ice. But an ignorant person is as obstinate in his contemptuous
incredulity as he is unreasonably credulous. Any thing unlike his own
narrow experience he disbelieves, if it flatters no propensity; any
nursery tale is swallowed implicitly by him if it does.

§ 4. I shall now advert to a very serious misapprehension of the
principles of the subject, which has been committed by some of the writers
against Hume’s Essay on Miracles, and by Bishop Butler before them, in
their anxiety to destroy what appeared to them a formidable weapon of
assault against the Christian religion; and the effect of which is
entirely to confound the doctrine of the Grounds of Disbelief. The mistake
consists in overlooking the distinction between (what may be called)
improbability before the fact and improbability after it; or (since, as
Mr. Venn remarks, the distinction of past and future is not the material
circumstance) between the improbability of a mere guess being right, and
the improbability of an alleged fact being true.

Many events are altogether improbable to us, before they have happened, or
before we are informed of their happening, which are not in the least
incredible when we are informed of them, because not contrary to any, even
approximate, induction. In the cast of a perfectly fair die, the chances
are five to one against throwing ace, that is, ace will be thrown on an
average only once in six throws. But this is no reason against believing
that ace was thrown on a given occasion, if any credible witness asserts
it; since though ace is only thrown once in six times, _some_ number which
is only thrown once in six times must have been thrown if the die was
thrown at all. The improbability, then, or, in other words, the
unusualness, of any fact, is no reason for disbelieving it, if the nature
of the case renders it certain that either that or something equally
improbable, that is, equally unusual, did happen. Nor is this all; for
even if the other five sides of the die were all twos, or all threes, yet
as ace would still, on the average, come up once in every six throws, its
coming up in a given throw would be not in any way contradictory to
experience. If we disbelieved all facts which had the chances against them
beforehand, we should believe hardly any thing. We are told that A. B.
died yesterday; the moment before we were so told, the chances against his
having died on that day may have been ten thousand to one; but since he
was certain to die at some time or other, and when he died must
necessarily die on some particular day, while the preponderance of chances
is very great against every day in particular, experience affords no
ground for discrediting any testimony which may be produced to the event’s
having taken place on a given day.

Yet it has been considered by Dr. Campbell and others, as a complete
answer to Hume’s doctrine (that things are incredible which are _contrary_
to the uniform course of experience), that we do not disbelieve, merely
because the chances were against them, things in strict _conformity_ to
the uniform course of experience; that we do not disbelieve an alleged
fact merely because the combination of causes on which it depends occurs
only once in a certain number of times. It is evident that whatever is
shown by observation, or can be proved from laws of nature, to occur in a
certain proportion (however small) of the whole number of possible cases,
is not contrary to experience; though we are right in disbelieving it, if
some other supposition respecting the matter in question involves, on the
whole, a less departure from the ordinary course of events. Yet on such
grounds as this have able writers been led to the extraordinary
conclusion, that nothing supported by credible testimony ought ever to be
disbelieved.

§ 5. We have considered two species of events, commonly said to be
improbable; one kind which are in no way extraordinary, but which, having
an immense preponderance of chances against them, are improbable until
they are affirmed, but no longer; another kind which, being contrary to
some recognized law of nature, are incredible on any amount of testimony
except such as would be sufficient to shake our belief in the law itself.
But between these two classes of events, there is an intermediate class,
consisting of what are commonly termed Coincidences: in other words, those
combinations of chances which present some peculiar and unexpected
regularity, assimilating them, in so far, to the results of law. As if,
for example, in a lottery of a thousand tickets, the numbers should be
drawn in the exact order of what are called the natural numbers, 1, 2, 3,
etc. We have still to consider the principles of evidence applicable to
this case: whether there is any difference between coincidences and
ordinary events, in the amount of testimony or other evidence necessary to
render them credible.

It is certain that on every rational principle of expectation, a
combination of this peculiar sort may be expected quite as often as any
other given series of a thousand numbers; that with perfectly fair dice,
sixes will be thrown twice, thrice, or any number of times in succession,
quite as often in a thousand or a million throws, as any other succession
of numbers fixed upon beforehand; and that no judicious player would give
greater odds against the one series than against the other.
Notwithstanding this, there is a general disposition to regard the one as
much more improbable than the other, and as requiring much stronger
evidence to make it credible. Such is the force of this impression, that
it has led some thinkers to the conclusion, that nature has greater
difficulty in producing regular combinations than irregular ones; or in
other words, that there is some general tendency of things, some law,
which prevents regular combinations from occurring, or at least from
occurring so often as others. Among these thinkers may be numbered
D’Alembert; who, in an Essay on Probabilities to be found in the fifth
volume of his _Mélanges_, contends that regular combinations, though
equally probable according to the mathematical theory with any others, are
physically less probable. He appeals to common sense, or, in other words,
to common impressions; saying, if dice thrown repeatedly in our presence
gave sixes every time, should we not, before the number of throws had
reached ten (not to speak of thousands of millions), be ready to affirm,
with the most positive conviction, that the dice were false?

The common and natural impression is in favor of D’Alembert: the regular
series would be thought much more unlikely than an irregular. But this
common impression is, I apprehend, merely grounded on the fact, that
scarcely any body remembers to have ever seen one of these peculiar
coincidences: the reason of which is simply that no one’s experience
extends to any thing like the number of trials, within which that or any
other given combination of events can be expected to happen. The chance of
sixes on a single throw of two dice being 1/36, the chance of sixes ten
times in succession is 1 divided by the tenth power of 36; in other words,
such a concurrence is only likely to happen once in 3,656,158,440,062,976
trials, a number which no dice-player’s experience comes up to a millionth
part of. But if, instead of sixes ten times, any other given succession of
ten throws had been fixed upon, it would have been exactly as unlikely
that in any individual’s experience that particular succession had ever
occurred; although this does not _seem_ equally improbable, because no one
would be likely to have remembered whether it had occurred or not, and
because the comparison is tacitly made, not between sixes ten times and
any one particular series of throws, but between all regular and all
irregular successions taken together.

That (as D’Alembert says) if the succession of sixes was actually thrown
before our eyes, we should ascribe it not to chance, but to unfairness in
the dice, is unquestionably true. But this arises from a totally different
principle. We should then be considering, not the probability of the fact
in itself, but the comparative probability with which, when it is known to
have happened, it may be referred to one or to another cause. The regular
series is not at all less likely than the irregular one to be brought
about by chance, but it is much more likely than the irregular one to be
produced by design; or by some general cause operating through the
structure of the dice. It is the nature of casual combinations to produce
a repetition of the same event, as often and no oftener than any other
series of events. But it is the nature of general causes to reproduce, in
the same circumstances, always the same event. Common sense and science
alike dictate that, all other things being the same, we should rather
attribute the effect to a cause which if real would be very likely to
produce it, than to a cause which would be very unlikely to produce it.
According to Laplace’s sixth theorem, which we demonstrated in a former
chapter, the difference of probability arising from the superior
_efficacy_ of the constant cause, unfairness in the dice, would after a
very few throws far outweigh any antecedent probability which there could
be against its existence.

D’Alembert should have put the question in another manner. He should have
supposed that we had ourselves previously tried the dice, and knew by
ample experience that they were fair. Another person then tries them in
our absence, and assures us that he threw sixes ten times in succession.
Is the assertion credible or not? Here the effect to be accounted for is
not the occurrence itself, but the fact of the witness’s asserting it.
This may arise either from its having really happened, or from some other
cause. What we have to estimate is the comparative probability of these
two suppositions.

If the witness affirmed that he had thrown any other series of numbers,
supposing him to be a person of veracity, and tolerable accuracy, and to
profess that he took particular notice, we should believe him. But the ten
sixes are exactly as likely to have been really thrown as the other
series. If, therefore, this assertion is less credible than the other, the
reason must be, not that it is less likely than the other to be made
truly, but that it is more likely than the other to be made falsely.

One reason obviously presents itself why what is called a coincidence,
should be oftener asserted falsely than an ordinary combination. It
excites wonder. It gratifies the love of the marvelous. The motives,
therefore, to falsehood, one of the most frequent of which is the desire
to astonish, operate more strongly in favor of this kind of assertion than
of the other kind. Thus far there is evidently more reason for
discrediting an alleged coincidence, than a statement in itself not more
probable, but which if made would not be thought remarkable. There are
cases, however, in which the presumption on this ground would be the other
way. There are some witnesses who, the more extraordinary an occurrence
might appear, would be the more anxious to verify it by the utmost
carefulness of observation before they would venture to believe it, and
still more before they would assert it to others.

§ 6. Independently, however, of any peculiar chances of mendacity arising
from the nature of the assertion, Laplace contends, that merely on the
general ground of the fallibility of testimony, a coincidence is not
credible on the same amount of testimony on which we should be warranted
in believing an ordinary combination of events. In order to do justice to
his argument, it is necessary to illustrate it by the example chosen by
himself.

If, says Laplace, there were one thousand tickets in a box, and one only
has been drawn out, then if an eye-witness affirms that the number drawn
was 79, this, though the chances were 999 in 1000 against it, is not on
that account the less credible; its credibility is equal to the antecedent
probability of the witness’s veracity. But if there were in the box 999
black balls and only one white, and the witness affirms that the white
ball was drawn, the case according to Laplace is very different: the
credibility of his assertion is but a small fraction of what it was in the
former case; the reason of the difference being as follows:

The witnesses of whom we are speaking must, from the nature of the case,
be of a kind whose credibility falls materially short of certainty; let us
suppose, then, the credibility of the witness in the case in question to
be 9/10; that is, let us suppose that in every ten statements which the
witness makes, nine on an average are correct, and one incorrect. Let us
now suppose that there have taken place a sufficient number of drawings to
exhaust all the possible combinations, the witness deposing in every one.
In one case out of every ten in all these drawings he will actually have
made a false announcement. But in the case of the thousand tickets these
false announcements will have been distributed impartially over all the
numbers, and of the 999 cases in which No. 79 was not drawn, there will
have been only one case in which it was announced. On the contrary, in the
case of the thousand balls (the announcement being always either “black”
or “white”), if white was not drawn, and there was a false announcement,
that false announcement _must_ have been white; and since by the
supposition there was a false announcement once in every ten times, white
will have been announced falsely in one-tenth part of all the cases in
which it was not drawn, that is, in one-tenth part of 999 cases out of
every thousand. White, then, is drawn, on an average, exactly as often as
No. 79, but it is announced, without having been really drawn, 999 times
as often as No. 79; the announcement, therefore, requires a much greater
amount of testimony to render it credible.(205)

To make this argument valid it must of course be supposed, that the
announcements made by the witness are average specimens of his general
veracity and accuracy; or, at least, that they are neither more nor less
so in the case of the black and white balls, than in the case of the
thousand tickets. This assumption, however, is not warranted. A person is
far less likely to mistake, who has only one form of error to guard
against, than if he had 999 different errors to avoid. For instance, in
the example chosen, a messenger who might make a mistake once in ten times
in reporting the number drawn in a lottery, might not err once in a
thousand times if sent simply to observe whether a ball was black or
white. Laplace’s argument, therefore, is faulty even as applied to his own
case. Still less can that case be received as completely representing all
cases of coincidence. Laplace has so contrived his example, that though
black answers to 999 distinct possibilities, and white only to one, the
witness has nevertheless no bias which can make him prefer black to white.
The witness did not know that there were 999 black balls in the box and
only one white; or if he did, Laplace has taken care to make all the 999
cases so undistinguishably alike, that there is hardly a possibility of
any cause of falsehood or error operating in favor of any of them, which
would not operate in the same manner if there were only one. Alter this
supposition, and the whole argument falls to the ground. Let the balls,
for instance, be numbered, and let the white ball be No. 79. Considered in
respect of their color, there are but two things which the witness can be
interested in asserting, or can have dreamed or hallucinated, or has to
choose from if he answers at random, viz., black and white; but considered
in respect of the numbers attached to them, there are a thousand; and if
his interest or error happens to be connected with the numbers, though the
only assertion he makes is about the color, the case becomes precisely
assimilated to that of the thousand tickets. Or instead of the balls
suppose a lottery, with 1000 tickets and but one prize, and that I hold
No. 79, and being interested only in that, ask the witness not what was
the number drawn, but whether it was 79 or some other. There are now only
two cases, as in Laplace’s example; yet he surely would not say that if
the witness answered 79, the assertion would be in an enormous proportion
less credible, than if he made the same answer to the same question asked
in the other way. If, for instance (to put a case supposed by Laplace
himself), he has staked a large sum on one of the chances, and thinks that
by announcing its occurrence he shall increase his credit; he is equally
likely to have betted on any one of the 999 numbers which are attached to
black balls, and so far as the chances of mendacity from this cause are
concerned, there will be 999 times as many chances of his announcing black
falsely as white.

Or suppose a regiment of 1000 men, 999 Englishmen and one Frenchman, and
that of these one man has been killed, and it is not known which. I ask
the question, and the witness answers, the Frenchman. This was not only as
improbable _a priori_, but is in itself as singular a circumstance, as
remarkable a coincidence, as the drawing of the white ball; yet we should
believe the statement as readily, as if the answer had been John Thompson.
Because, though the 999 Englishmen were all alike in the point in which
they differed from the Frenchman, they were not, like the 999 black balls,
undistinguishable in every other respect; but being all different, they
admitted as many chances of interest or error, as if each man had been of
a different nation; and if a lie was told or a mistake made, the
misstatement was as likely to fall on any Jones or Thompson of the set, as
on the Frenchman.

The example of a coincidence selected by D’Alembert, that of sixes thrown
on a pair of dice ten times in succession, belongs to this sort of cases
rather than to such as Laplace’s. The coincidence is here far more
remarkable, because of far rarer occurrence, than the drawing of the white
ball. But though the improbability of its really occurring is greater, the
superior probability of its being announced falsely can not be established
with the same evidence. The announcement “black” represented 999 cases,
but the witness may not have known this, and if he did, the 999 cases are
so exactly alike, that there is really only one set of possible causes of
mendacity corresponding to the whole. The announcement “sixes _not_ drawn
ten times,” represents, and is known by the witness to represent, a great
multitude of contingencies, every one of which being unlike every other,
there may be a different and a fresh set of causes of mendacity
corresponding to each.

It appears to me, therefore, that Laplace’s doctrine is not strictly true
of any coincidences, and is wholly inapplicable to most; and that to know
whether a coincidence does or does not require more evidence to render it
credible than an ordinary event, we must refer, in every instance, to
first principles, and estimate afresh what is the probability that the
given testimony would have been delivered in that instance, supposing the
fact which it asserts not to be true.

With these remarks we close the discussion of the Grounds of Disbelief;
and along with it, such exposition as space admits, and as the writer has
it in his power to furnish, of the Logic of Induction.



                                 Book IV.


OF OPERATIONS SUBSIDIARY TO INDUCTION.


    “Clear and distinct ideas are terms which, though familiar and
    frequent in men’s mouths, I have reason to think every one who
    uses does not perfectly understand. And possibly it is but here
    and there one who gives himself the trouble to consider them so
    far as to know what he himself or others precisely mean by them; I
    have, therefore, in most places, chose to put determinate or
    determined, instead of clear and distinct, as more likely to
    direct men’s thoughts to my meaning in this matter.”—LOCKE’S
    _Essay on the Human Understanding_; Epistle to the Reader.

    “Il ne peut y avoir qu’une méthode parfaite, qui est la _méthode
    naturelle_; on nomme ainsi un arrangement dans lequel les êtres du
    même genre seraient plus voisins entre eux que ceux de tous les
    autres genres; les genres du même ordre, plus que ceux de tous les
    autres ordres; et ainsi de suite. Cette méthode est l’idéal auquel
    l’histoire naturelle doit tendre; car il est évident que si l’on y
    parvenait, l’on aurait l’expression exacte et complète de la
    nature entière.”—CUVIER, _Règne Animal_, Introduction.

    “Deux grandes notions philosophiques dominent la théorie
    fondamentale de la méthode naturelle proprement dite, savoir la
    formation des groupes naturels, et ensuite leur succession
    hiérarchique.”—COMTE, _Cours de Philosophie Positive_, 42me leçon.



                                Chapter I.


Of Observation And Description.


§ 1. The inquiry which occupied us in the two preceding Books, has
conducted us to what appears a satisfactory solution of the principal
problem of Logic, according to the conception I have formed of the
science. We have found, that the mental process with which Logic is
conversant, the operation of ascertaining truths by means of evidence, is
always, even when appearances point to a different theory of it, a process
of induction. And we have particularized the various modes of induction,
and obtained a clear view of the principles to which it must conform, in
order to lead to results which can be relied on.

The consideration of Induction, however, does not end with the direct
rules for its performance. Something must be said of those other
operations of the mind, which are either necessarily presupposed in all
induction, or are instrumental to the more difficult and complicated
inductive processes. The present Book will be devoted to the consideration
of these subsidiary operations; among which our attention must first be
given to those, which are indispensable preliminaries to all induction
whatsoever.

Induction being merely the extension to a class of cases, of something
which has been observed to be true in certain individual instances of the
class; the first place among the operations subsidiary to induction, is
claimed by Observation. This is not, however, the place to lay down rules
for making good observers; nor is it within the competence of Logic to do
so, but of the art of intellectual Education. Our business with
observation is only in its connection with the appropriate problem of
logic, the estimation of evidence. We have to consider, not how or what to
observe, but under what conditions observation is to be relied on; what is
needful, in order that the fact, supposed to be observed, may safely be
received as true.

§ 2. The answer to this question is very simple, at least in its first
aspect. The sole condition is, that what is supposed to have been observed
shall really have been observed; that it be an observation, not an
inference. For in almost every act of our perceiving faculties,
observation and inference are intimately blended. What we are said to
observe is usually a compound result, of which one-tenth may be
observation, and the remaining nine-tenths inference.

I affirm, for example, that I hear a man’s voice. This would pass, in
common language, for a direct perception. All, however, which is really
perception, is that I hear a sound. That the sound is a voice, and that
voice the voice of a man, are not perceptions but inferences. I affirm,
again, that I saw my brother at a certain hour this morning. If any
proposition concerning a matter of fact would commonly be said to be known
by the direct testimony of the senses, this surely would be so. The truth,
however, is far otherwise. I only saw a certain colored surface; or rather
I had the kind of visual sensations which are usually produced by a
colored surface; and from these as marks, known to be such by previous
experience, I concluded that I saw my brother. I might have had sensations
precisely similar, when my brother was not there. I might have seen some
other person so nearly resembling him in appearance, as, at the distance,
and, with the degree of attention which I bestowed, to be mistaken for
him. I might have been asleep, and have dreamed that I saw him; or in a
state of nervous disorder, which brought his image before me in a waking
hallucination. In all these modes, many have been led to believe that they
saw persons well known to them, who were dead or far distant. If any of
these suppositions had been true, the affirmation that I saw my brother
would have been erroneous; but whatever was matter of direct perception,
namely the visual sensations, would have been real. The inference only
would have been ill grounded; I should have ascribed those sensations to a
wrong cause.

Innumerable instances might be given, and analyzed in the same manner, of
what are vulgarly called errors of sense. There are none of them properly
errors of sense; they are erroneous inferences from sense. When I look at
a candle through a multiplying glass, I see what seems a dozen candles
instead of one; and if the real circumstances of the case were skillfully
disguised, I might suppose that there were really that number; there would
be what is called an optical deception. In the kaleidoscope there really
is that deception; when I look through the instrument, instead of what is
actually there, namely a casual arrangement of colored fragments, the
appearance presented is that of the same combination several times
repeated in symmetrical arrangement round a point. The delusion is of
course effected by giving me the same sensations which I should have had
if such a symmetrical combination had really been presented to me. If I
cross two of my fingers, and bring any small object, a marble for
instance, into contact with both, at points not usually touched
simultaneously by one object, I can hardly, if my eyes are shut, help
believing that there are two marbles instead of one. But it is not my
touch in this case, nor my sight in the other, which is deceived; the
deception, whether durable or only momentary, is in my judgment. From my
senses I have only the sensations, and those are genuine. Being accustomed
to have those or similar sensations when, and only when, a certain
arrangement of outward objects is present to my organs, I have the habit
of instantly, when I experience the sensations, inferring the existence of
that state of outward things. This habit has become so powerful, that the
inference, performed with the speed and certainty of an instinct, is
confounded with intuitive perceptions. When it is correct, I am
unconscious that it ever needed proof; even when I know it to be
incorrect, I can not without considerable effort abstain from making it.
In order to be aware that it is not made by instinct but by an acquired
habit, I am obliged to reflect on the slow process through which I learned
to judge by the eye of many things which I now appear to perceive directly
by sight; and on the reverse operation performed by persons learning to
draw, who with difficulty and labor divest themselves of their acquired
perceptions, and learn afresh to see things as they appear to the eye.

It would be easy to prolong these illustrations, were there any need to
expatiate on a topic so copiously exemplified in various popular works.
From the examples already given, it is seen sufficiently, that the
individual facts from which we collect our inductive generalizations are
scarcely ever obtained by observation alone. Observation extends only to
the sensations by which we recognize objects; but the propositions which
we make use of, either in science or in common life, relate mostly to the
objects themselves. In every act of what is called observation, there is
at least one inference—from the sensations to the presence of the object;
from the marks or diagnostics, to the entire phenomenon. And hence, among
other consequences, follows the seeming paradox, that a general
proposition collected from particulars is often more certainly true than
any one of the particular propositions from which, by an act of induction,
it was inferred. For, each of those particular (or rather singular)
propositions involved an inference, from the impression on the senses to
the fact which caused that impression; and this inference may have been
erroneous in any one of the instances, but can not well have been
erroneous in all of them, provided their number was sufficient to
eliminate chance. The conclusion, therefore, that is, the general
proposition, may deserve more complete reliance than it would be safe to
repose in any one of the inductive premises.

The logic of observation, then, consists solely in a correct
discrimination between that, in a result of observation, which has really
been perceived, and that which is an inference from the perception.
Whatever portion is inference, is amenable to the rules of induction
already treated of, and requires no further notice here; the question for
us in this place is, when all which is inference is taken away what
remains? There remains, in the first place, the mind’s own feelings or
states of consciousness, namely, its outward feelings or sensations, and
its inward feelings—its thoughts, emotions, and volitions. Whether any
thing else remains, or all else is inference from this; whether the mind
is capable of directly perceiving or apprehending any thing except states
of its own consciousness—is a problem of metaphysics not to be discussed
in this place. But after excluding all questions on which metaphysicians
differ, it remains true, that for most purposes the discrimination we are
called upon practically to exercise is that between sensations or other
feelings, of our own or of other people, and inferences drawn from them.
And on the theory of Observation this is all which seems necessary to be
said for the purposes of the present work.

§ 3. If, in the simplest observation, or in what passes for such, there is
a large part which is not observation but something else; so in the
simplest description of an observation, there is, and must always be, much
more asserted than is contained in the perception itself. We can not
describe a fact, without implying more than the fact. The perception is
only of one individual thing; but to describe it is to affirm a connection
between it and every other thing which is either denoted or connoted by
any of the terms used. To begin with an example, than which none can be
conceived more elementary: I have a sensation of sight, and I endeavor to
describe it by saying that I see something white. In saying this, I do not
solely affirm my sensation; I also class it. I assert a resemblance
between the thing I see, and all things which I and others are accustomed
to call white. I assert that it resembles them in the circumstance in
which they all resemble one another, in that which is the ground of their
being called by the name. This is not merely one way of describing an
observation, but the only way. If I would either register my observation
for my own future use, or make it known for the benefit of others, I must
assert a resemblance between the fact which I have observed and something
else. It is inherent in a description, to be the statement of a
resemblance, or resemblances.

We thus see that it is impossible to express in words any result of
observation, without performing an act possessing what Dr. Whewell
considers to be characteristic of Induction. There is always something
introduced which was not included in the observation itself; some
conception common to the phenomenon with other phenomena to which it is
compared. An observation can not be spoken of in language at all without
declaring more than that one observation; without assimilating it to other
phenomena already observed and classified. But this identification of an
object—this recognition of it as possessing certain known
characteristics—has never been confounded with Induction. It is an
operation which precedes all induction, and supplies it with its
materials. It is a perception of resemblances, obtained by comparison.

These resemblances are not always apprehended directly, by merely
comparing the object observed with some other present object, or with our
recollection of an object which is absent. They are often ascertained
through intermediate marks, that is, deductively. In describing some new
kind of animal, suppose me to say that it measures ten feet in length,
from the forehead to the extremity of the tail. I did not ascertain this
by the unassisted eye. I had a two-foot rule which I applied to the
object, and, as we commonly say, measured it; an operation which was not
wholly manual, but partly also mathematical, involving the two
propositions, Five times two is ten, and Things which are equal to the
same thing are equal to one another. Hence, the fact that the animal is
ten feet long is not an immediate perception, but a conclusion from
reasoning; the minor premises alone being furnished by observation of the
object. Nevertheless, this is called an observation, or a description of
the animal, not an induction respecting it.

To pass at once from a very simple to a very complex example: I affirm
that the earth is globular. The assertion is not grounded on direct
perception; for the figure of the earth can not, by us, be directly
perceived, though the assertion would not be true unless circumstances
could be supposed under which its truth could be so perceived. That the
form of the earth is globular is inferred from certain marks, as for
instance from this, that its shadow thrown upon the moon is circular; or
this, that on the sea, or any extensive plain, our horizon is always a
circle; either of which marks is incompatible with any other than a
globular form. I assert further, that the earth is that particular kind of
a globe which is termed an oblate spheroid; because it is found by
measurement in the direction of the meridian, that the length on the
surface of the earth which subtends a given angle at its centre,
diminishes as we recede from the equator and approach the poles. But these
propositions, that the earth is globular, and that it is an oblate
spheroid, assert, each of them, an individual fact; in its own nature
capable of being perceived by the senses when the requisite organs and the
necessary position are supposed, and only not actually perceived because
those organs and that position are wanting. This identification of the
earth, first as a globe, and next as an oblate spheroid, which, if the
fact could have been seen, would have been called a description of the
figure of the earth, may without impropriety be so called when, instead of
being seen, it is inferred. But we could not without impropriety call
either of these assertions an induction from facts respecting the earth.
They are not general propositions collected from particular facts, but
particular facts deduced from general propositions. They are conclusions
obtained deductively, from premises originating in induction: but of these
premises some were not obtained by observation of the earth, nor had any
peculiar reference to it.

If, then, the truth respecting the figure of the earth is not an
induction, why should the truth respecting the figure of the earth’s orbit
be so? The two cases only differ in this, that the form of the orbit was
not, like the form of the earth itself, deduced by ratiocination from
facts which were marks of ellipticity, but was got at by boldly guessing
that the path was an ellipse, and finding afterward, on examination, that
the observations were in harmony with the hypothesis. According to Dr.
Whewell, however, this process of guessing and verifying our guesses is
not only induction, but the whole of induction: no other exposition can be
given of that logical operation. That he is wrong in the latter assertion,
the whole of the preceding book has, I hope, sufficiently proved; and that
the process by which the ellipticity of the planetary orbits was
ascertained, is not induction at all, was attempted to be shown in the
second chapter of the same Book.(206) We are now, however, prepared to go
more into the heart of the matter than at that earlier period of our
inquiry, and to show, not merely what the operation in question is not,
but what it is.

§ 4. We observed, in the second chapter, that the proposition “the earth
moves in an ellipse,” so far as it only serves for the colligation or
connecting together of actual observations (that is, as it only affirms
that the observed positions of the earth may be correctly represented by
as many points in the circumference of an imaginary ellipse), is not an
induction, but a description: it is an induction, only when it affirms
that the intermediate positions, of which there has been no direct
observation, would be found to correspond to the remaining points of the
same elliptic circumference. Now, though this real induction is one thing,
and the description another, we are in a very different condition for
making the induction before we have obtained the description, and after
it. For inasmuch as the description, like all other descriptions, contains
the assertion of a resemblance between the phenomenon described and
something else; in pointing out something which the series of observed
places of a planet resembles, it points out something in which the several
places themselves agree. If the series of places correspond to as many
points of an ellipse, the places themselves agree in being situated in
that ellipse. We have, therefore, by the same process which gave us the
description, obtained the requisites for an induction by the Method of
Agreement. The successive observed places of the earth being considered as
effects, and its motion as the cause which produces them, we find that
those effects, that is, those places, agree in the circumstance of being
in an ellipse. We conclude that the remaining effects, the places which
have not been observed, agree in the same circumstance, and that the _law_
of the motion of the earth is motion in an ellipse.

The Colligation of Facts, therefore, by means of hypotheses, or, as Dr.
Whewell prefers to say, by means of Conceptions, instead of being, as he
supposes, Induction itself, takes its proper place among operations
subsidiary to Induction. All Induction supposes that we have previously
compared the requisite number of individual instances, and ascertained in
what circumstances they agree. The Colligation of Facts is no other than
this preliminary operation. When Kepler, after vainly endeavoring to
connect the observed places of a planet by various hypotheses of circular
motion, at last tried the hypotheses of an ellipse and found it answer to
the phenomena; what he really attempted, first unsuccessfully and at last
successfully, was to discover the circumstance in which all the observed
positions of the planet agreed. And when he in like manner connected
another set of observed facts, the periodic times of the different
planets, by the proposition that the squares of the times are proportional
to the cubes of the distances, what he did was simply to ascertain the
property in which the periodic times of all the different planets agreed.

Since, therefore, all that is true and to the purpose in Dr. Whewell’s
doctrine of Conceptions might be fully expressed by the more familiar term
Hypothesis; and since his Colligation of Facts by means of appropriate
Conceptions, is but the ordinary process of finding by a comparison of
phenomena, in what consists their agreement or resemblance; I would
willingly have confined myself to those better understood expressions, and
persevered to the end in the same abstinence which I have hitherto
observed from ideological discussions; considering the mechanism of our
thoughts to be a topic distinct from and irrelevant to the principles and
rules by which the trustworthiness of the results of thinking is to be
estimated. Since, however, a work of such high pretensions, and, it must
also be said, of so much real merit, has rested the whole theory of
Induction upon such ideological considerations, it seems necessary for
others who follow to claim for themselves and their doctrines whatever
position may properly belong to them on the same metaphysical ground. And
this is the object of the succeeding chapter.



                               Chapter II.


Of Abstraction, Or The Formation Of Conceptions.


§ 1. The metaphysical inquiry into the nature and composition of what have
been called Abstract Ideas, or, in other words, of the notions which
answer in the mind to classes and to general names, belongs not to Logic,
but to a different science, and our purpose does not require that we
should enter upon it here. We are only concerned with the universally
acknowledged fact, that such notions or conceptions do exist. The mind can
conceive a multitude of individual things as one assemblage or class; and
general names do really suggest to us certain ideas or mental
representations, otherwise we could not use the names with consciousness
of a meaning. Whether the idea called up by a general name is composed of
the various circumstances in which all the individuals denoted by the name
agree, and of no others (which is the doctrine of Locke, Brown, and the
Conceptualists); or whether it be the idea of some one of those
individuals, clothed in its individualizing peculiarities, but with the
accompanying knowledge that those peculiarities are not properties of the
class (which is the doctrine of Berkeley, Mr. Bailey,(207) and the modern
Nominalists); or whether (as held by Mr. James Mill) the idea of the class
is that of a miscellaneous assemblage of individuals belonging to the
class; or whether, finally, it be any one or any other of all these,
according to the accidental circumstances of the case; certain it is, that
_some_ idea or mental conception is suggested by a general name, whenever
we either hear it or employ it with consciousness of a meaning. And this,
which we may call, if we please, a general idea, _represents_ in our minds
the whole class of things to which the name is applied. Whenever we think
or reason concerning the class, we do so by means of this idea. And the
voluntary power which the mind has, of attending to one part of what is
present to it at any moment, and neglecting another part, enables us to
keep our reasonings and conclusions respecting the class unaffected by any
thing in the idea or mental image which is not really, or at least which
we do not really believe to be common, to the whole class.(208)

There are, then, such things as general conceptions, or conceptions by
means of which we can think generally; and when we form a set of phenomena
into a class, that is, when we compare them with one another to ascertain
in what they agree, some general conception is implied in this mental
operation. And inasmuch as such a comparison is a necessary preliminary to
Induction, it is most true that Induction could not go on without general
conceptions.

§ 2. But it does not therefore follow that these general conceptions must
have existed in the mind previously to the comparison. It is not a law of
our intellect, that in comparing things with each other and taking note of
their agreement we merely recognize as realized in the outward world
something that we already had in our minds. The conception originally
found its way to us as the _result_ of such a comparison. It was obtained
(in metaphysical phrase) by _abstraction_ from individual things. These
things may be things which we perceived or thought of on former occasions,
but they may also be the things which we are perceiving or thinking of on
the very occasion. When Kepler compared the observed places of the planet
Mars, and found that they agreed in being points of an elliptic
circumference, he applied a general conception which was already in his
mind, having been derived from his former experience. But this is by no
means universally the case. When we compare several objects and find them
to agree in being white, or when we compare the various species of
ruminating animals and find them to agree in being cloven-footed, we have
just as much a general conception in our minds as Kepler had in his: we
have the conception of “a white thing,” or the conception of “a
cloven-footed animal.” But no one supposes that we necessarily bring these
conceptions with us, and _superinduce_ them (to adopt Dr. Whewell’s
expression) upon the facts: because in these simple cases every body sees
that the very act of comparison which ends in our connecting the facts by
means of the conception, may be the source from which we derive the
conception itself. If we had never seen any white object or had never seen
any cloven-footed animal before, we should at the same time and by the
same mental act acquire the idea, and employ it for the colligation of the
observed phenomena. Kepler, on the contrary, really had to bring the idea
with him, and superinduce it upon the facts; he could not evolve it out of
them: if he had not already had the idea, he would not have been able to
acquire it by a comparison of the planet’s positions. But this inability
was a mere accident; the idea of an ellipse could have been acquired from
the paths of the planets as effectually as from any thing else, if the
paths had not happened to be invisible. If the planet had left a visible
track, and we had been so placed that we could see it at the proper angle,
we might have abstracted our original idea of an ellipse from the
planetary orbit. Indeed, every conception which can be made the instrument
for connecting a set of facts, might have been originally evolved from
those very facts. The conception is a conception _of_ something; and that
which it is a conception of, is really _in_ the facts, and might, under
some supposable circumstances, or by some supposable extension of the
faculties which we actually possess, have been detected in them. And not
only is this always in itself possible, but it actually happens in almost
all cases in which the obtaining of the right conception is a matter of
any considerable difficulty. For if there be no new conception required;
if one of those already familiar to mankind will serve the purpose, the
accident of being the first to whom the right one occurs, may happen to
almost any body; at least in the case of a set of phenomena which the
whole scientific world are engaged in attempting to connect. The honor, in
Kepler’s case, was that of the accurate, patient, and toilsome
calculations by which he compared the results that followed from his
different guesses, with the observations of Tycho Brahe; but the merit was
very small of guessing an ellipse; the only wonder is that men had not
guessed it before, nor could they have failed to do so if there had not
existed an obstinate _a priori_ prejudice that the heavenly bodies must
move, if not in a circle, in some combination of circles.

The really difficult cases are those in which the conception destined to
create light and order out of darkness and confusion has to be sought for
among the very phenomena which it afterward serves to arrange. Why,
according to Dr. Whewell himself, did the ancients fail in discovering the
laws of mechanics, that is, of equilibrium and of the communication of
motion? Because they had not, or at least had not clearly, the ideas or
conceptions of pressure and resistance, momentum, and uniform and
accelerating force. And whence could they have obtained these ideas except
from the very facts of equilibrium and motion? The tardy development of
several of the physical sciences, for example, of optics, electricity,
magnetism, and the higher generalizations of chemistry, he ascribes to the
fact that mankind had not yet possessed themselves of the Idea of
Polarity, that is, the idea of opposite properties in opposite directions.
But what was there to suggest such an idea, until, by a separate
examination of several of these different branches of knowledge, it was
shown that the facts of each of them did present, in some instances at
least, the curious phenomenon of opposite properties in opposite
directions? The thing was superficially manifest only in two cases, those
of the magnet and of electrified bodies; and there the conception was
encumbered with the circumstance of material poles, or fixed points in the
body itself, in which points this opposition of properties seemed to be
inherent. The first comparison and abstraction had led only to this
conception of poles; and if any thing corresponding to that conception had
existed in the phenomena of chemistry or optics, the difficulty now justly
considered so great, would have been extremely small. The obscurity arose
from the fact, that the polarities in chemistry and optics were distinct
species, though of the same genus, with the polarities in electricity and
magnetism; and that in order to assimilate the phenomena to one another,
it was necessary to compare a polarity without poles, such for instance as
is exemplified in the polarization of light, and the polarity with
(apparent) poles, which we see in the magnet; and to recognize that these
polarities, while different in many other respects, agree in the one
character which is expressed by the phrase, opposite properties in
opposite directions. From the result of such a comparison it was that the
minds of scientific men formed this new general conception; between which,
and the first confused feeling of an analogy between some of the phenomena
of light and those of electricity and magnetism, there is a long interval,
filled up by the labors and more or less sagacious suggestions of many
superior minds.

The conceptions, then, which we employ for the colligation and
methodization of facts, do not develop themselves from within, but are
impressed upon the mind from without; they are never obtained otherwise
than by way of comparison and abstraction, and, in the most important and
the most numerous cases, are evolved by abstraction from the very
phenomena which it is their office to colligate. I am far, however, from
wishing to imply that it is not often a very difficult thing to perform
this process of abstraction well, or that the success of an inductive
operation does not, in many cases, principally depend on the skill with
which we perform it. Bacon was quite justified in designating as one of
the principal obstacles to good induction, general conceptions wrongly
formed, “notiones temerè à rebus abstractæ;” to which Dr. Whewell adds,
that not only does bad abstraction make bad induction, but that, in order
to perform induction well, we must have abstracted well; our general
conceptions must be “clear” and “appropriate” to the matter in hand.

§ 3. In attempting to show what the difficulty in this matter really is,
and how it is surmounted, I must beg the reader, once for all, to bear
this in mind; that although, in discussing the opinions of a different
school of philosophy, I am willing to adopt their language, and to speak,
therefore, of connecting facts through the instrumentality of a
conception, this technical phraseology means neither more nor less than
what is commonly called comparing the facts with one another and
determining in what they agree. Nor has the technical expression even the
advantage of being metaphysically correct. The facts are not _connected_,
except in a merely metaphorical acceptation of the term. The _ideas_ of
the facts may become connected, that is, we may be led to think of them
together; but this consequence is no more than what may be produced by any
casual association. What really takes place, is, I conceive, more
philosophically expressed by the common word Comparison, than by the
phrases “to connect” or “to superinduce.” For, as the general conception
is itself obtained by a comparison of particular phenomena, so, when
obtained, the mode in which we apply it to other phenomena is again by
comparison. We compare phenomena with each other to get the conception,
and we then compare those and other phenomena _with_ the conception. We
get the conception of an animal (for instance) by comparing different
animals, and when we afterward see a creature resembling an animal, we
compare it with our general conception of an animal; and if it agrees with
that general conception, we include it in the class. The conception
becomes the type of comparison.

And we need only consider what comparison is, to see that where the
objects are more than two, and still more when they are an indefinite
number, a type of some sort is an indispensable condition of the
comparison. When we have to arrange and classify a great number of objects
according to their agreements and differences, we do not make a confused
attempt to compare all with all. We know that two things are as much as
the mind can easily attend to at a time, and we therefore fix upon one of
the objects, either at hazard or because it offers in a peculiarly
striking manner some important character, and, taking this as our
standard, compare it with one object after another. If we find a second
object which presents a remarkable agreement with the first, inducing us
to class them together, the question instantly arises, in what particular
circumstances do they agree? and to take notice of these circumstances is
already a first stage of abstraction, giving rise to a general conception.
Having advanced thus far, when we now take in hand a third object we
naturally ask ourselves the question, not merely whether this third object
agrees with the first, but whether it agrees with it in the same
circumstances in which the second did? in other words, whether it agrees
with the general conception which has been obtained by abstraction from
the first and second? Thus we see the tendency of general conceptions, as
soon as formed, to substitute themselves as types, for whatever individual
objects previously answered that purpose in our comparisons. We may,
perhaps, find that no considerable number of other objects agree with this
first general conception; and that we must drop the conception, and
beginning again with a different individual case, proceed by fresh
comparisons to a different general conception. Sometimes, again, we find
that the same conception will serve, by merely leaving out some of its
circumstances; and by this higher effort of abstraction, we obtain a still
more general conception; as in the case formerly referred to, the
scientific world rose from the conception of poles to the general
conception of opposite properties in opposite directions; or as those
South-Sea islanders, whose conception of a quadruped had been abstracted
from hogs (the only animals of that description which they had seen), when
they afterward compared that conception with other quadrupeds, dropped
some of the circumstances, and arrived at the more general conception
which Europeans associate with the term.

These brief remarks contain, I believe, all that is well grounded in the
doctrine, that the conception by which the mind arranges and gives unity
to phenomena must be furnished by the mind itself, and that we find the
right conception by a tentative process, trying first one and then another
until we hit the mark. The conception is not furnished _by_ the mind until
it has been furnished _to_ the mind; and the facts which supply it are
sometimes extraneous facts, but more often the very facts which we are
attempting to arrange by it. It is quite true, however, that in
endeavoring to arrange the facts, at whatever point we begin, we never
advance three steps without forming a general conception, more or less
distinct and precise; and that this general conception becomes the clue
which we instantly endeavor to trace through the rest of the facts, or
rather, becomes the standard with which we thenceforth compare them. If we
are not satisfied with the agreements which we discover among the
phenomena by comparing them with this type, or with some still more
general conception which by an additional stage of abstraction we can form
from the type; we change our path, and look out for other agreements; we
recommence the comparison from a different starting-point, and so generate
a different set of general conceptions. This is the tentative process
which Dr. Whewell speaks of; and which has not unnaturally suggested the
theory, that the conception is supplied by the mind itself; since the
different conceptions which the mind successively tries, it either already
possessed from its previous experience, or they were supplied to it in the
first stage of the corresponding act of comparison; so that, in the
subsequent part of the process, the conception manifested itself as
something compared with the phenomena, not evolved from them.

§ 4. If this be a correct account of the instrumentality of general
conceptions in the comparison which necessarily precedes Induction, we are
now able to translate into our own language what Dr. Whewell means by
saying that conceptions, to be subservient to Induction, must be “clear”
and “appropriate.”

If the conception corresponds to a real agreement among the phenomena; if
the comparison which we have made of a set of objects has led us to class
them according to real resemblances and differences; the conception which
does this can not fail to be appropriate, for some purpose or other. The
question of appropriateness is relative to the particular object we have
in view. As soon as, by our comparison, we have ascertained some
agreement, something which can be predicated in common of a number of
objects; we have obtained a basis on which an inductive process is capable
of being founded. But the agreements, or the ulterior consequences to
which those agreements lead, may be of very different degrees of
importance. If, for instance, we only compare animals according to their
color, and class those together which are colored alike, we form the
general conceptions of a white animal, a black animal, etc., which are
conceptions legitimately formed; and if an induction were to be attempted
concerning the causes of the colors of animals, this comparison would be
the proper and necessary preparation for such an induction, but would not
help us toward a knowledge of the laws of any other of the properties of
animals; while if, with Cuvier, we compare and class them according to the
structure of the skeleton, or, with Blainville, according to the nature of
their outward integuments, the agreements and differences which are
observable in these respects are not only of much greater importance in
themselves, but are marks of agreements and differences in many other
important particulars of the structure and mode of life of the animals.
If, therefore, the study of their structure and habits be our object, the
conceptions generated by these last comparisons are far more “appropriate”
than those generated by the former. Nothing, other than this, can be meant
by the appropriateness of a conception.

When Dr. Whewell says that the ancients, or the school-men, or any modern
inquirers, missed discovering the real law of a phenomenon because they
applied to it an inappropriate instead of an appropriate conception; he
can only mean that in comparing various instances of the phenomenon, to
ascertain in what those instances agreed, they missed the important points
of agreement; and fastened upon such as were either imaginary, and not
agreements at all, or, if real agreements, were comparatively trifling,
and had no connection with the phenomenon, the law of which was sought.

Aristotle, philosophizing on the subject of motion, remarked that certain
motions apparently take place spontaneously; bodies fall to the ground,
flame ascends, bubbles of air rise in water, etc.; and these he called
natural motions; while others not only never take place without external
incitement, but even when such incitement is applied, tend spontaneously
to cease; which, to distinguish them from the former, he called violent
motions. Now, in comparing the so-called natural motions with one another,
it appeared to Aristotle that they agreed in one circumstance, namely,
that the body which moved (or seemed to move) spontaneously, was moving
_toward its own place_; meaning thereby the place from whence it
originally came, or the place where a great quantity of matter similar to
itself was assembled. In the other class of motions, as when bodies are
thrown up in the air, they are, on the contrary, moving _from_ their own
place. Now, this conception of a body moving toward its own place may
justly be considered inappropriate; because, though it expresses a
circumstance really found in some of the most familiar instances of motion
apparently spontaneous, yet, first, there are many other cases of such
motion, in which that circumstance is absent; the motion, for instance, of
the earth and planets. Secondly, even when it is present, the motion, on
closer examination, would often be seen not to be spontaneous; as, when
air rises in water, it does not rise by its own nature, but is pushed up
by the superior weight of the water which presses upon it. Finally, there
are many cases in which the spontaneous motion takes place in the contrary
direction to what the theory considers as the body’s own place; for
instance, when a fog rises from a lake, or when water dries up. The
agreement, therefore, which Aristotle selected as his principle of
classification, did not extend to all cases of the phenomenon he wanted to
study, spontaneous motion; while it did include cases of the absence of
the phenomenon, cases of motion not spontaneous. The conception was hence
“inappropriate.” We may add that, in the case in question, no conception
would be appropriate; there is no agreement which runs through all the
cases of spontaneous or apparently spontaneous motion and no others; they
can not be brought under one law; it is a case of Plurality of
Causes.(209)

§ 5. So much for the first of Dr. Whewell’s conditions, that conceptions
must be appropriate. The second is, that they shall be “clear:” and let us
consider what this implies. Unless the conception corresponds to a real
agreement, it has a worse defect than that of not being clear: it is not
applicable to the case at all. Among the phenomena, therefore, which we
are attempting to connect by means of the conception, we must suppose that
there really is an agreement, and that the conception is a conception of
that agreement. In order, then, that it may be clear, the only requisite
is, that we shall know exactly in what the agreement consists; that it
shall have been carefully observed, and accurately remembered. We are said
not to have a clear conception of the resemblance among a set of objects,
when we have only a general feeling that they resemble, without having
analyzed their resemblance, or perceived in what points it consists, and
fixed in our memory an exact recollection of those points. This want of
clearness, or, as it may be otherwise called, this vagueness in the
general conception, may be owing either to our having no accurate
knowledge of the objects themselves, or merely to our not having carefully
compared them. Thus a person may have no clear idea of a ship because he
has never seen one, or because he remembers but little, and that faintly,
of what he has seen. Or he may have a perfect knowledge and remembrance of
many ships of various kinds, frigates among the rest, but he may have no
clear but only a confused idea of a frigate, because he has never been
told, and has not compared them sufficiently to have remarked and
remembered, in what particular points a frigate differs from some other
kind of ship.

It is not, however, necessary, in order to have clear ideas, that we
should know all the common properties of the things which we class
together. That would be to have our conception of the class complete as
well as clear. It is sufficient if we never class things together without
knowing exactly why we do so—without having ascertained exactly what
agreements we are about to include in our conception; and if, after having
thus fixed our conception, we never vary from it, never include in the
class any thing which has not those common properties, nor exclude from it
any thing which has. A clear conception means a determinate conception;
one which does not fluctuate, which is not one thing to-day and another
to-morrow, but remains fixed and invariable, except when, from the
progress of our knowledge, or the correction of some error, we consciously
add to it or alter it. A person of clear ideas is a person who always
knows in virtue of what properties his classes are constituted; what
attributes are connoted by his general names.

The principal requisites, therefore, of clear conceptions, are habits of
attentive observation, an extensive experience, and a memory which
receives and retains an exact image of what is observed. And in proportion
as any one has the habit of observing minutely and comparing carefully a
particular class of phenomena, and an accurate memory for the results of
the observation and comparison, so will his conceptions of that class of
phenomena be clear; provided he has the indispensable habit (naturally,
however, resulting from those other endowments), of never using general
names without a precise connotation.

As the clearness of our conceptions chiefly depends on the _carefulness_
and _accuracy_ of our observing and comparing faculties, so their
appropriateness, or rather the chance we have of hitting upon the
appropriate conception in any case, mainly depends on the _activity_ of
the same faculties. He who by habit, grounded on sufficient natural
aptitude, has acquired a readiness in accurately observing and comparing
phenomena, will perceive so many more agreements, and will perceive them
so much more rapidly than other people, that the chances are much greater
of his perceiving, in any instance, the agreement on which the important
consequences depend.

§ 6. It is of so much importance that the part of the process of
investigating truth, discussed in this chapter, should be rightly
understood, that I think it is desirable to restate the results we have
arrived at, in a somewhat different mode of expression.

We can not ascertain general truths, that is, truths applicable to
classes, unless we have formed the classes in such a manner that general
truths can be affirmed of them. In the formation of any class, there is
involved a conception of it as a class, that is, a conception of certain
circumstances as being those which characterize the class, and distinguish
the objects composing it from all other things. When we know exactly what
these circumstances are, we have a clear idea (or conception) of the
class, and of the meaning of the general name which designates it. The
primary condition implied in having this clear idea, is that the class be
really a class; that it correspond to a real distinction; that the things
it includes really do agree with one another in certain particulars, and
differ, in those same particulars, from all other things. A person without
clear ideas is one who habitually classes together, under the same general
names, things which have no common properties, or none which are not
possessed also by other things; or who, if the usage of other people
prevents him from actually misclassing things, is unable to state to
himself the common properties in virtue of which he classes them rightly.

But is it not the sole requisite of classification that the classes should
be real classes, framed by a legitimate mental process? Some modes of
classing things are more valuable than others for human uses, whether of
speculation or of practice; and our classifications are not well made,
unless the things which they bring together not only agree with each other
in something which distinguishes them from all other things, but agree
with each other and differ from other things in the very circumstances
which are of primary importance for the purpose (theoretical or practical)
which we have in view, and which constitutes the problem before us. In
other words, our conceptions, though they may be clear, are not
_appropriate_ for our purpose, unless the properties we comprise in them
are those which will help us toward what we wish to understand—_i.e._,
either those which go deepest into the nature of the things, if our object
be to understand that, or those which are most closely connected with the
particular property which we are endeavoring to investigate.

We can not, therefore, frame good general conceptions beforehand. That the
conception we have obtained is the one we want, can only be known when we
have done the work for the sake of which we wanted it; when we completely
understand the general character of the phenomena, or the conditions of
the particular property with which we concern ourselves. General
conceptions formed without this thorough knowledge, are Bacon’s “notiones
temerè à rebus abstractæ.” Yet such premature conceptions we must be
continually making up, in our progress to something better. They are an
impediment to the progress of knowledge, only when they are permanently
acquiesced in. When it has become our habit to group things in wrong
classes—in groups which either are not really classes, having no
distinctive points of agreement (absence of _clear_ ideas), or which are
not classes of which any thing important to our purpose can be predicated
(absence of _appropriate_ ideas); and when, in the belief that these badly
made classes are those sanctioned by nature, we refuse to exchange them
for others, and can not or will not make up our general conceptions from
any other elements; in that case all the evils which Bacon ascribes to his
“notiones temerè abstractæ” really occur. This was what the ancients did
in physics, and what the world in general does in morals and politics to
the present day.

It would thus, in my view of the matter, be an inaccurate mode of
expression to say, that obtaining appropriate conceptions is a condition
precedent to generalization. Throughout the whole process of comparing
phenomena with one another for the purpose of generalization, the mind is
trying to make up a conception; but the conception which it is trying to
make up is that of the really important point of agreement in the
phenomena. As we obtain more knowledge of the phenomena themselves, and of
the conditions on which their important properties depend, our views on
this subject naturally alter; and thus we advance from a less to a more
"appropriate" general conception, in the progress of our investigations.

We ought not, at the same time, to forget that the really important
agreement can not always be discovered by mere comparison of the very
phenomena in question, without the aid of a conception acquired elsewhere;
as in the case, so often referred to, of the planetary orbits.

The search for the agreement of a set of phenomena is in truth very
similar to the search for a lost or hidden object. At first we place
ourselves in a sufficiently commanding position, and cast our eyes round
us, and if we can see the object it is well; if not, we ask ourselves
mentally what are the places in which it may be hid, in order that we may
there search for it: and so on, until we imagine the place where it really
is. And here too we require to have had a previous conception, or
knowledge, of those different places. As in this familiar process, so in
the philosophical operation which it illustrates, we first endeavor to
find the lost object or recognize the common attribute, without
conjecturally invoking the aid of any previously acquired conception, or,
in other words, of any hypothesis. Having failed in this, we call upon our
imagination for some hypothesis of a possible place, or a possible point
of resemblance, and then look to see whether the facts agree with the
conjecture.

For such cases something more is required than a mind accustomed to
accurate observation and comparison. It must be a mind stored with general
conceptions, previously acquired, of the sorts which bear affinity to the
subject of the particular inquiry. And much will also depend on the
natural strength and acquired culture of what has been termed the
scientific imagination; on the faculty possessed of mentally arranging
known elements into new combinations, such as have not yet been observed
in nature, though not contradictory to any known laws.

But the variety of intellectual habits, the purposes which they serve, and
the modes in which they may be fostered and cultivated, are considerations
belonging to the Art of Education: a subject far wider than Logic, and
which this treatise does not profess to discuss. Here, therefore, the
present chapter may properly close.



                               Chapter III.


Of Naming, As Subsidiary To Induction.


§ 1. It does not belong to the present undertaking to dwell on the
importance of language as a medium of human intercourse, whether for
purposes of sympathy or of information. Nor does our design admit of more
than a passing allusion to that great property of names, on which their
functions as an intellectual instrument are, in reality, ultimately
dependent; their potency as a means of forming, and of riveting,
associations among our other ideas; a subject on which an able
thinker(210) has thus written:

“Names are impressions of sense, and as such take the strongest hold on
the mind, and of all other impressions can be most easily recalled and
retained in view. They therefore serve to give a point of attachment to
all the more volatile objects of thought and feeling. Impressions that
when passed might be dissipated forever, are, by their connection with
language, always within reach. Thoughts, of themselves, are perpetually
slipping out of the field of immediate mental vision; but the name abides
with us, and the utterance of it restores them in a moment. Words are the
custodiers of every product of mind less impressive than themselves. All
extensions of human knowledge, all new generalizations, are fixed and
spread, even unintentionally, by the use of words. The child growing up
learns, along with the vocables of his mother-tongue, that things which he
would have believed to be different are, in important points, the same.
Without any formal instruction, the language in which we grow up teaches
us all the common philosophy of the age. It directs us to observe and know
things which we should have overlooked; it supplies us with
classifications ready made, by which things are arranged (as far as the
light of by-gone generations admits) with the objects to which they bear
the greatest total resemblance. The number of general names in a language,
and the degree of generality of those names, afford a test of the
knowledge of the era, and of the intellectual insight which is the
birthright of any one born into it.”

It is not, however, of the functions of Names, considered generally, that
we have here to treat, but only of the manner and degree in which they are
directly instrumental to the investigation of truth; in other words, to
the process of induction.

§ 2. Observation and Abstraction, the operations which formed the subject
of the two foregoing chapters, are conditions indispensable to induction;
there can be no induction where they are not. It has been imagined that
Naming is also a condition equally indispensable. There are thinkers who
have held that language is not solely, according to a phrase generally
current, _an_ instrument of thought, but _the_ instrument; that names, or
something equivalent to them, some species of artificial signs, are
necessary to reasoning; that there could be no inference, and consequently
no induction, without them. But if the nature of reasoning was correctly
explained in the earlier part of the present work, this opinion must be
held to be an exaggeration, though of an important truth. If reasoning be
from particulars to particulars, and if it consist in recognizing one fact
as a mark of another, or a mark of a mark of another, nothing is required
to render reasoning possible, except senses and association; senses to
perceive that two facts are conjoined; association, as the law by which
one of those two facts raises up the idea of the other.(211) For these
mental phenomena, as well as for the belief or expectation which follows,
and by which we recognize as having taken place, or as about to take
place, that of which we have perceived a mark, there is evidently no need
of language. And this inference of one particular fact from another is a
case of induction. It is of this sort of induction that brutes are
capable; it is in this shape that uncultivated minds make almost all their
inductions, and that we all do so in the cases in which familiar
experience forces our conclusions upon us without any active process of
inquiry on our part, and in which the belief or expectation follows the
suggestion of the evidence with the promptitude and certainty of an
instinct.(212)

§ 3. But though inference of an inductive character is possible without
the use of signs, it could never, without them, be carried much beyond the
very simple cases which we have just described, and which form, in all
probability, the limit of the reasonings of those animals to whom
conventional language is unknown. Without language, or something
equivalent to it, there could only be as much reasoning from experience as
can take place without the aid of general propositions. Now, though in
strictness we may reason from past experience to a fresh individual case
without the intermediate stage of a general proposition, yet without
general propositions we should seldom remember what past experience we
have had, and scarcely ever what conclusions that experience will warrant.
The division of the inductive process into two parts, the first
ascertaining what is a mark of the given fact, the second whether in the
new case that mark exists, is natural, and scientifically indispensable.
It is, indeed, in a majority of cases, rendered necessary by mere distance
of time. The experience by which we are to guide our judgments may be
other people’s experience, little of which can be communicated to us
otherwise than by language; when it is our own, it is generally experience
long past; unless, therefore, it were recorded by means of artificial
signs, little of it (except in cases involving our intenser sensations or
emotions, or the subjects of our daily and hourly contemplation) would be
retained in the memory. It is hardly necessary to add, that when the
inductive inference is of any but the most direct and obvious nature—when
it requires several observations or experiments, in varying circumstances,
and the comparison of one of these with another—it is impossible to
proceed a step, without the artificial memory which words bestow. Without
words, we should, if we had often seen A and B in immediate and obvious
conjunction, expect B whenever we saw A; but to discover their conjunction
when not obvious, or to determine whether it is really constant or only
casual, and whether there is reason to expect it under any given change of
circumstances, is a process far too complex to be performed without some
contrivance to make our remembrance of our own mental operations accurate.
Now, language is such a contrivance. When that instrument is called to our
aid, the difficulty is reduced to that of making our remembrance of the
meaning of words accurate. This being secured, whatever passes through our
minds may be remembered accurately, by putting it carefully into words,
and committing the words either to writing or to memory.

The function of Naming, and particularly of General Names, in Induction,
may be recapitulated as follows. Every inductive inference which is good
at all, is good for a whole class of cases; and, that the inference may
have any better warrant of its correctness than the mere clinging together
of two ideas, a process of experimentation and comparison is necessary; in
which the whole class of cases must be brought to view, and some
uniformity in the course of nature evolved and ascertained, since the
existence of such a uniformity is required as a justification for drawing
the inference in even a single case. This uniformity, therefore, may be
ascertained once for all; and if, being ascertained, it can be remembered,
it will serve as a formula for making, in particular cases, all such
inferences as the previous experience will warrant. But we can only secure
its being remembered, or give ourselves even a chance of carrying in our
memory any considerable number of such uniformities, by registering them
through the medium of permanent signs; which (being, from the nature of
the case, signs not of an individual fact, but of a uniformity, that is,
of an indefinite number of facts similar to one another) are general
signs; universals; general names, and general propositions.

§ 4. And here I can not omit to notice an oversight committed by some
eminent thinkers; who have said that the cause of our using general names
is the infinite multitude of individual objects, which, making it
impossible to have a name for each, compels us to make one name serve for
many.

This is a very limited view of the function of general names. Even if
there were a name for every individual object, we should require general
names as much as we now do. Without them we could not express the result
of a single comparison, nor record any one of the uniformities existing in
nature; and should be hardly better off in respect to Induction than if we
had no names at all. With none but names of individuals (or, in other
words, proper names), we might, by pronouncing the name, suggest the idea
of the object, but we could not assert any proposition; except the
unmeaning ones formed by predicating two proper names one of another. It
is only by means of general names that we can convey any information,
predicate any attribute, even of an individual, much more of a class.
Rigorously speaking, we could get on without any other general names than
the abstract names of attributes; all our propositions might be of the
form “such an individual object possesses such an attribute,” or “such an
attribute is always (or never) conjoined with such another attribute.” In
fact, however, mankind have always given general names to objects as well
as attributes, and indeed before attributes: but the general names given
to objects imply attributes, derive their whole meaning from attributes;
and are chiefly useful as the language by means of which we predicate the
attributes which they connote.

It remains to be considered what principles are to be adhered to in giving
general names, so that these names, and the general propositions in which
they fill a place, may conduce most to the purposes of Induction.



                               Chapter IV.


Of The Requisites Of A Philosophical Language, And The Principles Of
Definition.


§ 1. In order that we may possess a language perfectly suitable for the
investigation and expression of general truths, there are two principal,
and several minor requisites. The first is, that every general name should
have a meaning, steadily fixed, and precisely determined. When, by the
fulfillment of this condition, such names as we possess are fitted for the
due performance of their functions, the next requisite, and the second in
order of importance, is that we should possess a name wherever one is
needed; wherever there is any thing to be designated by it, which it is of
importance to express.

The former of these requisites is that to which our attention will be
exclusively directed in the present chapter.

§ 2. Every general name, then, must have a certain and knowable meaning.
Now the meaning (as has so often been explained) of a general connotative
name, resides in the connotation; in the attribute on account of which,
and to express which, the name is given. Thus, the name animal being given
to all things which possess the attributes of sensation and voluntary
motion, the word connotes those attributes exclusively, and they
constitute the whole of its meaning. If the name be abstract, its
denotation is the same with the connotation of the corresponding concrete;
it designates directly the attribute, which the concrete term implies. To
give a precise meaning to general names is, then, to fix with steadiness
the attribute or attributes connoted by each concrete general name, and
denoted by the corresponding abstract. Since abstract names, in the order
of their creation, do not precede but follow concrete ones, as is proved
by the etymological fact that they are almost always derived from them; we
may consider their meaning as determined by, and dependent on, the meaning
of their concrete; and thus the problem of giving a distinct meaning to
general language, is all included in that of giving a precise connotation
to all concrete general names.

This is not difficult in the case of new names; of the technical terms
created by scientific inquirers for the purposes of science or art. But
when a name is in common use, the difficulty is greater; the problem in
this case not being that of choosing a convenient connotation for the
name, but of ascertaining and fixing the connotation with which it is
already used. That this can ever be a matter of doubt, is a sort of
paradox. But the vulgar (including in that term all who have not accurate
habits of thought) seldom know exactly what assertion they intend to make,
what common property they mean to express, when they apply the same name
to a number of different things. All which the name expresses with them,
when they predicate it of an object, is a confused feeling of resemblance
between that object and some of the other things which they have been
accustomed to denote by the name. They have applied the name Stone to
various objects previously seen; they see a new object, which appears to
them somewhat like the former, and they call it a stone, without asking
themselves in what respect it is like, or what mode or degree of
resemblance the best authorities, or even they themselves, require as a
warrant for using the name. This rough general impression of resemblance
is, however, made up of particular circumstances of resemblance; and into
these it is the business of the logician to analyze it; to ascertain what
points of resemblance among the different things commonly called by the
name, have produced in the common mind this vague feeling of likeness;
have given to the things the similarity of aspect, which has made them a
class, and has caused the same name to be bestowed upon them.

But though general names are imposed by the vulgar without any more
definite connotation than that of a vague resemblance; general
propositions come in time to be made, in which predicates are applied to
those names, that is, general assertions are made concerning the _whole_
of the things which are denoted by the name. And since by each of these
propositions some attribute, more or less precisely conceived, is of
course predicated, the ideas of these various attributes thus become
associated with the name, and in a sort of uncertain way it comes to
connote them; there is a hesitation to apply the name in any new case in
which any of the attributes familiarly predicated of the class do not
exist. And thus, to common minds, the propositions which they are in the
habit of hearing or uttering concerning a class make up in a loose way a
sort of connotation for the class name. Let us take, for instance, the
word Civilized. How few could be found, even among the most educated
persons, who would undertake to say exactly what the term Civilized
connotes. Yet there is a feeling in the minds of all who use it, that they
are using it with a meaning; and this meaning is made up, in a confused
manner, of every thing which they have heard or read that civilized men or
civilized communities are, or may be expected to be.

It is at this stage, probably, in the progress of a concrete name, that
the corresponding abstract name generally comes into use. Under the notion
that the concrete name must of course convey a meaning, or, in other
words, that there is some property common to all things which it denotes,
people give a name to this common property; from the concrete Civilized,
they form the abstract Civilization. But since most people have never
compared the different things which are called by the concrete name, in
such a manner as to ascertain what properties these things have in common,
or whether they have any; each is thrown back upon the marks by which he
himself has been accustomed to be guided in his application of the term;
and these, being merely vague hearsays and current phrases, are not the
same in any two persons, nor in the same person at different times. Hence
the word (as Civilization, for example) which professes to be the
designation of the unknown common property, conveys scarcely to any two
minds the same idea. No two persons agree in the things they predicate of
it; and when it is itself predicated of any thing, no other person knows,
nor does the speaker himself know with precision, what he means to assert.
Many other words which could be named, as the word _honor_, or the word
_gentleman_, exemplify this uncertainty still more strikingly.

It needs scarcely be observed, that general propositions of which no one
can tell exactly what they assert, can not possibly have been brought to
the test of a correct induction. Whether a name is to be used as an
instrument of thinking, or as a means of communicating the result of
thought, it is imperative to determine exactly the attribute or attributes
which it is to express; to give it, in short, a fixed and ascertained
connotation.

§ 3. It would, however, be a complete misunderstanding of the proper
office of a logician in dealing with terms already in use, if we were to
think that because a name has not at present an ascertained connotation,
it is competent to any one to give it such a connotation at his own
choice. The meaning of a term actually in use is not an arbitrary quantity
to be fixed, but an unknown quantity to be sought.

In the first place, it is obviously desirable to avail ourselves, as far
as possible, of the associations already connected with the name; not
enjoining the employment of it in a manner which conflicts with all
previous habits, and especially not so as to require the rupture of those
strongest of all associations between names, which are created by
familiarity with propositions in which they are predicated of one another.
A philosopher would have little chance of having his example followed, if
he were to give such a meaning to his terms as should require us to call
the North American Indians a civilized people, or the higher classes in
Europe savages; or to say that civilized people live by hunting, and
savages by agriculture. Were there no other reason, the extreme difficulty
of effecting so complete a revolution in speech would be more than a
sufficient one. The endeavor should be, that all generally received
propositions into which the term enters, should be at least as true after
its meaning is fixed, as they were before; and that the concrete name,
therefore, should not receive such a connotation as shall prevent it from
denoting things which, in common language, it is currently affirmed of.
The fixed and precise connotation which it receives should not be in
deviation from, but in agreement (as far as it goes) with, the vague and
fluctuating connotation which the term already had.

To fix the connotation of a concrete name, or the denotation of the
corresponding abstract, is to define the name. When this can be done
without rendering any received assertions inadmissible, the name can be
defined in accordance with its received use, which is vulgarly called
defining not the name but the thing. What is meant by the improper
expression of defining a thing (or rather a class of things—for nobody
talks of defining an individual), is to define the name, subject to the
condition that it shall denote those things. This, of course, supposes a
comparison of the things, feature by feature and property by property, to
ascertain what attributes they agree in; and not unfrequently an operation
strictly inductive, for the purpose of ascertaining some unobvious
agreement, which is the cause of the obvious agreements.

For, in order to give a connotation to a name, consistently with its
denoting certain objects, we have to make our selection from among the
various attributes in which those objects agree. To ascertain in what they
do agree is, therefore, the first logical operation requisite. When this
has been done as far as is necessary or practicable, the question arises,
which of these common attributes shall be selected to be associated with
the name. For if the class which the name denotes be a Kind, the common
properties are innumerable; and even if not, they are often extremely
numerous. Our choice is first limited by the preference to be given to
properties which are well known, and familiarly predicated of the class;
but even these are often too numerous to be all included in the
definition, and, besides, the properties most generally known may not be
those which serve best to mark out the class from all others. We should
therefore select from among the common properties (if among them any such
are to be found) those on which it has been ascertained by experience, or
proved by deduction, that many others depend; or at least which are sure
marks of them, and from whence, therefore, many others will follow by
inference. We thus see that to frame a good definition of a name already
in use, is not a matter of choice but of discussion, and discussion not
merely respecting the usage of language, but respecting the properties of
things, and even the origin of those properties. And hence every
enlargement of our knowledge of the objects to which the name is applied,
is liable to suggest an improvement in the definition. It is impossible to
frame a perfect set of definitions on any subject, until the theory of the
subject is perfect; and as science makes progress, its definitions are
also progressive.

§ 4. The discussion of Definitions, in so far as it does not turn on the
use of words but on the properties of things, Dr. Whewell calls the
Explication of Conceptions. The act of ascertaining, better than before,
in what particulars any phenomena which are classed together agree, he
calls in his technical phraseology, unfolding the general conception in
virtue of which they are so classed. Making allowance for what appears to
me the darkening and misleading tendency of this mode of expression,
several of his remarks are so much to the purpose, that I shall take the
liberty of transcribing them.

He observes,(213) that many of the controversies which have had an
important share in the formation of the existing body of science, have
“assumed the form of a battle of Definitions. For example, the inquiry
concerning the laws of falling bodies led to the question whether the
proper definition of a _uniform force_ is that it generates a velocity
proportional to the _space_ from rest, or to the _time_. The controversy
of the _vis viva_ was what was the proper definition of the _measure of
force_. A principal question in the classification of minerals is, what is
the definition of a _mineral species_. Physiologists have endeavored to
throw light on their subject by defining _organization_, or some similar
term.” Questions of the same nature were long open and are not yet
completely closed, respecting the definitions of Specific Heat, Latent
Heat, Chemical Combination, and Solution.

“It is very important for us to observe, that these controversies have
never been questions of insulated and _arbitrary_ definitions, as men seem
often tempted to imagine them to have been. In all cases there is a tacit
assumption of some proposition which is to be expressed by means of the
definition, and which gives it its importance. The dispute concerning the
definition thus acquires a real value, and becomes a question concerning
true and false. Thus, in the discussion of the question, What is a uniform
force? it was taken for granted that gravity is a uniform force. In the
debate of the _vis viva_, it was assumed that in the mutual action of
bodies the whole effect of the force is unchanged. In the zoological
definition of species (that it consists of individuals which have, or may
have, sprung from the same parents), it is presumed that individuals so
related resemble each other more than those which are excluded by such a
definition; or, perhaps, that species so defined have permanent and
definite differences. A definition of organization, or of some other term
which was not employed to express some principle, would be of no value.

“The establishment, therefore, of a right definition of a term, may be a
useful step in the explication of our conceptions; but this will be the
case then only when we have under our consideration some proposition in
which the term is employed. For then the question really is, how the
conception shall be understood and defined in order that the proposition
may be true.

“To unfold our conceptions by means of definitions has never been
serviceable to science, except when it has been associated with an
immediate use of the definitions. The endeavor to define a Uniform Force
was combined with the assertion that gravity is a uniform force; the
attempt to define Accelerating Force was immediately followed by the
doctrine that accelerating forces may be compounded; the process of
defining Momentum was connected with the principle that momenta gained and
lost are equal; naturalists would have given in vain the definition of
Species which we have quoted, if they had not also given the characters of
species so separated.... Definition may be the best mode of explaining our
conception, but that which alone makes it worth while to explain it in any
mode, is the opportunity of using it in the expression of truth. When a
definition is propounded to us as a useful step in knowledge, we are
always entitled to ask what principle it serves to enunciate.”

In giving, then, an exact connotation to the phrase, “a uniform force,”
the condition was understood, that the phrase should continue to denote
gravity. The discussion, therefore, respecting the definition, resolved
itself into this question, What is there of a uniform nature in the
motions produced by gravity? By observations and comparisons, it was found
that what was uniform in those motions was the ratio of the velocity
acquired to the time elapsed; equal velocities being added in equal times.
A uniform force, therefore, was defined a force which adds equal
velocities in equal times. So, again, in defining momentum. It was already
a received doctrine that, when two objects impinge upon one another, the
momentum lost by the one is equal to that gained by the other. This
proposition it was deemed necessary to preserve, not from the motive
(which operates in many other cases) that it was firmly fixed in popular
belief; for the proposition in question had never been heard of by any but
the scientifically instructed. But it was felt to contain a truth; even a
superficial observation of the phenomena left no doubt that in the
propagation of motion from one body to another, there was something of
which the one body gained precisely what the other lost; and the word
momentum had been invented to express this unknown something. The
settlement, therefore, of the definition of momentum, involved the
determination of the question, What is that of which a body, when it sets
another body in motion, loses exactly as much as it communicates? And when
experiment had shown that this _something_ was the product of the velocity
of the body by its mass, or quantity of matter, this became the definition
of momentum.

The following remarks,(214) therefore, are perfectly just: “The business
of definition is part of the business of discovery.... To define, so that
our definition shall have any scientific value, requires no small portion
of that sagacity by which truth is detected.... When it has been clearly
seen what ought to be our definition, it must be pretty well known what
truth we have to state. The definition, as well as the discovery, supposes
a decided step in our knowledge to have been made. The writers on Logic,
in the Middle Ages, made Definition the last stage in the progress of
knowledge; and in this arrangement at least, the history of science, and
the philosophy derived from the history, confirm their speculative views.”
For in order to judge finally how the name which denotes a class may best
be defined, we must know all the properties common to the class, and all
the relations of causation or dependence among those properties.

If the properties which are fittest to be selected as marks of other
common properties are also obvious and familiar, and especially if they
bear a great part in producing that general air of resemblance which was
the original inducement to the formation of the class, the definition will
then be most felicitous. But it is often necessary to define the class by
some property not familiarly known, provided that property be the best
mark of those which are known. M. De Blainville, for instance, founded his
definition of life on the process of decomposition and recomposition which
incessantly takes place in every living body, so that the particles
composing it are never for two instants the same. This is by no means one
of the most obvious properties of living bodies; it might escape
altogether the notice of an unscientific observer. Yet great authorities
(independently of M. De Blainville, who is himself a first-rate authority)
have thought that no other property so well answers the conditions
required for the definition.

§ 5. Having laid down the principles which ought for the most part to be
observed in attempting to give a precise connotation to a term in use, I
must now add, that it is not always practicable to adhere to those
principles, and that even when practicable, it is occasionally not
desirable.

Cases in which it is impossible to comply with all the conditions of a
precise definition of a name in agreement with usage, occur very
frequently. There is often no one connotation capable of being given to a
word, so that it shall still denote every thing it is accustomed to
denote; or that all the propositions into which it is accustomed to enter,
and which have any foundation in truth, shall remain true. Independently
of accidental ambiguities, in which the different meanings have no
connection with one another; it continually happens that a word is used in
two or more senses derived from each other, but yet radically distinct. So
long as a term is vague, that is, so long as its connotation is not
ascertained and permanently fixed, it is constantly liable to be applied
by _extension_ from one thing to another, until it reaches things which
have little, or even no, resemblance to those which were first designated
by it.

“Suppose,” says Dugald Stewart, in his _Philosophical Essays_,(215) “that
the letters A, B, C, D, E, denote a series of objects; that A possesses
some one quality in common with B; B a quality in common with C; C a
quality in common with D; D a quality in common with E; while at the same
time, no quality can be found which belongs in common to any _three_
objects in the series. Is it not conceivable, that the affinity between A
and B may produce a transference of the name of the first to the second;
and that, in consequence of the other affinities which connect the
remaining objects together, the same name may pass in succession from B to
C; from C to D; and from D to E? In this manner, a common appellation will
arise between A and E, although the two objects may, in their nature and
properties, be so widely distant from each other, that no stretch of
imagination can conceive how the thoughts were led from the former to the
latter. The transitions, nevertheless, may have been all so easy and
gradual, that, were they successfully detected by the fortunate ingenuity
of a theorist, we should instantly recognize, not only the verisimilitude,
but the truth of the conjecture: in the same way as we admit, with the
confidence of intuitive conviction, the certainty of the well-known
etymological process which connects the Latin preposition _e_ or _ex_ with
the English substantive _stranger_, the moment that the intermediate links
of the chain are submitted to our examination.”(216)

The applications which a word acquires by this gradual extension of it
from one set of objects to another, Stewart, adopting an expression from
Mr. Payne Knight, calls its _transitive_ applications; and after briefly
illustrating such of them as are the result of local or casual
associations, he proceeds as follows:(217)

“But although by far the greater part of the transitive or derivative
applications of words depend on casual and unaccountable caprices of the
feelings or the fancy, there are certain cases in which they open a very
interesting field of philosophical speculation. Such are those, in which
an analogous transference of the corresponding term may be remarked
universally, or very generally, in other languages; and in which, of
course, the uniformity of the result must be ascribed to the essential
principles of the human frame. Even in such cases, however, it will by no
means be always found, on examination, that the various applications of
the same term have arisen from any common quality or qualities in the
objects to which they relate. In the greater number of instances, they may
be traced to some natural and universal associations of ideas, founded in
the common faculties, common organs, and common condition of the human
race.... According to the different degrees of intimacy and strength in
the associations on which the _transitions_ of language are founded, very
different effects may be expected to arise. Where the association is
slight and casual, the several meanings will remain distinct from each
other, and will often, in process of time, assume the appearance of
capricious varieties in the use of the same arbitrary sign. _Where the
association is so natural and habitual as to become virtually
indissoluble, the transitive meanings will coalesce in one complex
conception; and every new transition will become a more comprehensive
generalization of the term in question._”

I solicit particular attention to the law of mind expressed in the last
sentence, and which is the source of the perplexity so often experienced
in detecting these transitions of meaning. Ignorance of that law is the
shoal on which some of the most powerful intellects which have adorned the
human race have been stranded. The inquiries of Plato into the definitions
of some of the most general terms of moral speculation are characterized
by Bacon as a far nearer approach to a true inductive method than is
elsewhere to be found among the ancients, and are, indeed, almost perfect
examples of the preparatory process of comparison and abstraction; but,
from being unaware of the law just mentioned, he often wasted the powers
of this great logical instrument on inquiries in which it could realize no
result, since the phenomena, whose common properties he so elaborately
endeavored to detect, had not really any common properties. Bacon himself
fell into the same error in his speculations on the nature of heat, in
which he evidently confounded under the name hot, classes of phenomena
which have no property in common. Stewart certainly overstates the matter
when he speaks of “a prejudice which has descended to modern times from
the scholastic ages, that when a word admits of a variety of
significations, these different significations must all be species of the
same genus, and must consequently include some essential idea common to
every individual to which the generic term can be applied;”(218) for both
Aristotle and his followers were well aware that there are such things as
ambiguities of language, and delighted in distinguishing them. But they
never suspected ambiguity in the cases where (as Stewart remarks) the
association on which the transition of meaning was founded is so natural
and habitual, that the two meanings blend together in the mind, and a real
transition becomes an apparent generalization. Accordingly they wasted
infinite pains in endeavoring to find a definition which would serve for
several distinct meanings at once; as in an instance noticed by Stewart
himself, that of “causation; the ambiguity of the word which, in the Greek
language corresponds to the English word _cause_, having suggested to them
the vain attempt of tracing the common idea which, in the case of any
_effect_, belongs to the _efficient_, to the _matter_, to the _form_, and
to the _end_. The idle generalities” (he adds) “we meet with in other
philosophers, about the ideas of the _good_, the _fit_, and the
_becoming_, have taken their rise from the same undue influence of popular
epithets on the speculations of the learned.”(219)

Among the words which have undergone so many successive transitions of
meaning that every trace of a property common to all the things they are
applied to, or at least common and also peculiar to those things, has been
lost, Stewart considers the word Beautiful to be one. And (without
attempting to decide a question which in no respect belongs to logic) I
can not but feel, with him, considerable doubt whether the word beautiful
connotes the same property when we speak of a beautiful color, a beautiful
face, a beautiful scene, a beautiful character, and a beautiful poem. The
word was doubtless extended from one of these objects to another on
account of a resemblance between them, or, more probably, between the
emotions they excited; and, by this progressive extension, it has at last
reached things very remote from those objects of sight to which there is
no doubt that it was first appropriated; and it is at least questionable
whether there is now any property common to all the things which,
consistently with usage, may be called beautiful, except the property of
agreeableness, which the term certainly does connote, but which can not be
all that people usually intend to express by it, since there are many
agreeable things which are never called beautiful. If such be the case, it
is impossible to give to the word Beautiful any fixed connotation, such
that it shall denote all the objects which in common use it now denotes,
but no others. A fixed connotation, however, it ought to have; for, so
long as it has not, it is unfit to be used as a scientific term, and is a
perpetual source of false analogies and erroneous generalizations.

This, then, constitutes a case in exemplification of our remark, that even
when there is a property common to all the things denoted by a name, to
erect that property into the definition and exclusive connotation of the
name is not always desirable. The various things called beautiful
unquestionably resemble one another in being agreeable; but to make this
the definition of beauty, and so extend the word Beautiful to all
agreeable things, would be to drop altogether a portion of meaning which
the word really, though indistinctly, conveys, and to do what depends on
us toward causing those qualities of the objects which the word
previously, though vaguely, pointed at, to be overlooked and forgotten. It
is better, in such a case, to give a fixed connotation to the term by
restricting, than by extending its use; rather excluding from the epithet
Beautiful some things to which it is commonly considered applicable, than
leaving out of its connotation any of the qualities by which, though
occasionally lost sight of, the general mind may have been habitually
guided in the commonest and most interesting applications of the term. For
there is no question that when people call any thing beautiful, they think
they are asserting more than that it is merely agreeable. They think they
are ascribing a peculiar _sort_ of agreeableness, analogous to that which
they find in some other of the things to which they are accustomed to
apply the same name. If, therefore, there be any peculiar sort of
agreeableness which is common though not to all, yet to the principal
things which are called beautiful, it is better to limit the denotation of
the term to those things, than to leave that kind of quality without a
term to connote it, and thereby divert attention from its peculiarities.

§ 6. The last remark exemplifies a rule of terminology, which is of great
importance, and which has hardly yet been recognized as a rule, but by a
few thinkers of the present century. In attempting to rectify the use of a
vague term by giving it a fixed connotation, we must take care not to
discard (unless advisedly, and on the ground of a deeper knowledge of the
subject) any portion of the connotation which the word, in however
indistinct a manner, previously carried with it. For otherwise language
loses one of its inherent and most valuable properties, that of being the
conservator of ancient experience; the keeper-alive of those thoughts and
observations of former ages, which may be alien to the tendencies of the
passing time. This function of language is so often overlooked or
undervalued, that a few observations on it appear to be extremely
required.

Even when the connotation of a term has been accurately fixed, and still
more if it has been left in the state of a vague unanalyzed feeling of
resemblance; there is a constant tendency in the word, through familiar
use, to part with a portion of its connotation. It is a well-known law of
the mind, that a word originally associated with a very complex cluster of
ideas, is far from calling up all those ideas in the mind, every time the
word is used; it calls up only one or two, from which the mind runs on by
fresh associations to another set of ideas, without waiting for the
suggestion of the remainder of the complex cluster. If this were not the
case, processes of thought could not take place with any thing like the
rapidity which we know they possess. Very often, indeed, when we are
employing a word in our mental operations, we are so far from waiting
until the complex idea which corresponds to the meaning of the word is
consciously brought before us in all its parts, that we run on to new
trains of ideas by the other associations which the mere word excites,
without having realized in our imagination any part whatever of the
meaning; thus using the word, and even using it well and accurately, and
carrying on important processes of reasoning by means of it, in an almost
mechanical manner; so much so, that some metaphysicians, generalizing from
an extreme case, have fancied that all reasoning is but the mechanical use
of a set of terms according to a certain form. We may discuss and settle
the most important interests of towns or nations, by the application of
general theorems or practical maxims previously laid down, without having
had consciously suggested to us, once in the whole process, the houses and
green fields, the thronged market-places and domestic hearths, of which
not only those towns and nations consist, but which the words town and
nation confessedly mean.

Since, then, general names come in this manner to be used (and even to do
a portion of their work well) without suggesting to the mind the whole of
their meaning, and often with the suggestion of a very small, or no part
at all of that meaning; we can not wonder that words so used come in time
to be no longer capable of suggesting any other of the ideas appropriated
to them, than those with which the association is most immediate and
strongest, or most kept up by the incidents of life; the remainder being
lost altogether; unless the mind, by often consciously dwelling on them,
keeps up the association. Words naturally retain much more of their
meaning to persons of active imagination, who habitually represent to
themselves things in the concrete, with the detail which belongs to them
in the actual world. To minds of a different description, the only
antidote to this corruption of language is predication. The habit of
predicating of the name, all the various properties which it originally
connoted, keeps up the association between the name and those properties.

But in order that it may do so, it is necessary that the predicates should
themselves retain their association with the properties which they
severally connote. For the propositions can not keep the meaning of the
words alive, if the meaning of the propositions themselves should die. And
nothing is more common than for propositions to be mechanically repeated,
mechanically retained in the memory, and their truth undoubtingly assented
to and relied on, while yet they carry no meaning distinctly home to the
mind; and while the matter of fact or law of nature which they originally
expressed is as much lost sight of, and practically disregarded, as if it
never had been heard of at all. In those subjects which are at the same
time familiar and complicated, and especially in those which are so in as
great a degree as moral and social subjects are, it is a matter of common
remark how many important propositions are believed and repeated from
habit, while no account could be given, and no sense is practically
manifested, of the truths which they convey. Hence it is, that the
traditional maxims of old experience, though seldom questioned, have often
so little effect on the conduct of life; because their meaning is never,
by most persons, really felt, until personal experience has brought it
home. And thus also it is that so many doctrines of religion, ethics, and
even politics, so full of meaning and reality to first converts, have
manifested (after the association of that meaning with the verbal formulas
has ceased to be kept up by the controversies which accompanied their
first introduction) a tendency to degenerate rapidly into lifeless dogmas;
which tendency, all the efforts of an education expressly and skillfully
directed to keeping the meaning alive, are barely sufficient to
counteract.

Considering, then, that the human mind, in different generations, occupies
itself with different things, and in one age is led by the circumstances
which surround it to fix more of its attention upon one of the properties
of a thing, in another age upon another; it is natural and inevitable that
in every age a certain portion of our recorded and traditional knowledge,
not being continually suggested by the pursuits and inquiries with which
mankind are at that time engrossed, should fall asleep, as it were, and
fade from the memory. It would be in danger of being totally lost, if the
propositions or formulas, the results of the previous experience, did not
remain, as forms of words it may be, but of words that once really
conveyed, and are still supposed to convey, a meaning: which meaning,
though suspended, may be historically traced, and when suggested, may be
recognized by minds of the necessary endowments as being still matter of
fact, or truth. While the formulas remain, the meaning may at any time
revive; and as, on the one hand, the formulas progressively lose the
meaning they were intended to convey, so, on the other, when this
forgetfulness has reached its height and begun to produce obvious
consequences, minds arise which from the contemplation of the formulas
rediscover the truth, when truth it was, which was contained in them, and
announce it again to mankind, not as a discovery, but as the meaning of
that which they have been taught, and still profess to believe.

Thus there is a perpetual oscillation in spiritual truths, and in
spiritual doctrines of any significance, even when not truths. Their
meaning is almost always in a process either of being lost or of being
recovered. Whoever has attended to the history of the more serious
convictions of mankind—of the opinions by which the general conduct of
their lives is, or as they conceive ought to be, more especially
regulated—is aware that even when recognizing verbally the same doctrines,
they attach to them at different periods a greater or a less quantity, and
even a different kind of meaning. The words in their original acceptation
connoted, and the propositions expressed, a complication of outward facts
and inward feelings, to different portions of which the general mind is
more particularly alive in different generations of mankind. To common
minds, only that portion of the meaning is in each generation suggested,
of which that generation possesses the counterpart in its own habitual
experience. But the words and propositions lie ready to suggest to any
mind duly prepared the remainder of the meaning. Such individual minds are
almost always to be found; and the lost meaning, revived by them, again by
degrees works its way into the general mind.

The arrival of this salutary reaction may, however, be materially retarded
by the shallow conceptions and incautious proceedings of mere logicians.
It sometimes happens that toward the close of the downward period, when
the words have lost part of their significance, and have not yet begun to
recover it, persons arise whose leading and favorite idea is the
importance of clear conceptions and precise thought, and the necessity,
therefore, of definite language. These persons, in examining the old
formulas, easily perceive that words are used in them without a meaning;
and if they are not the sort of persons who are capable of rediscovering
the lost signification, they naturally enough dismiss the formula, and
define the name without reference to it. In so doing they fasten down the
name to what it connotes in common use at the time when it conveys the
smallest quantity of meaning; and introduce the practice of employing it,
consistently and uniformly, according to that connotation. The word in
this way acquires an extent of denotation far beyond what it had before;
it becomes extended to many things to which it was previously, in
appearance capriciously, refused. Of the propositions in which it was
formerly used, those which were true in virtue of the forgotten part of
its meaning are now, by the clearer light which the definition diffuses,
seen not to be true according to the definition; which, however, is the
recognized and sufficiently correct expression of all that is perceived to
be in the mind of any one by whom the term is used at the present day. The
ancient formulas are consequently treated as prejudices; and people are no
longer taught as before, though not to understand them, yet to believe
that there is truth in them. They no longer remain in the general mind
surrounded by respect, and ready at any time to suggest their original
meaning. Whatever truths they contain are not only, in these
circumstances, rediscovered far more slowly, but, when rediscovered, the
prejudice with which novelties are regarded is now, in some degree at
least, against them, instead of being on their side.

An example may make these remarks more intelligible. In all ages, except
where moral speculation has been silenced by outward compulsion, or where
the feelings which prompt to it still continue to be satisfied by the
traditional doctrines of an established faith, one of the subjects which
have most occupied the minds of thinking persons is the inquiry, What is
virtue? or, What is a virtuous character? Among the different theories on
the subject which have, at different times, grown up and obtained partial
currency, every one of which reflected as in the clearest mirror the
express image of the age which gave it birth; there was one, according to
which virtue consists in a correct calculation of our own personal
interests, either in this world only, or also in another. To make this
theory plausible, it was of course necessary that the only beneficial
actions which people in general were accustomed to see, or were therefore
accustomed to praise, should be such as were, or at least might without
contradicting obvious facts be supposed to be, the result of a prudential
regard to self-interest; so that the words really connoted no more, in
common acceptation, than was set down in the definition.

Suppose, now, that the partisans of this theory had contrived to introduce
a consistent and undeviating use of the term according to this definition.
Suppose that they had seriously endeavored, and had succeeded in the
endeavor, to banish the word disinterestedness from the language; had
obtained the disuse of all expressions attaching odium to selfishness or
commendation to self-sacrifice, or which implied generosity or kindness to
be any thing but doing a benefit in order to receive a greater personal
advantage in return. Need we say that this abrogation of the old formulas
for the sake of preserving clear ideas and consistency of thought, would
have been a great evil? while the very inconsistency incurred by the
co-existence of the formulas with philosophical opinions which seemed to
condemn them as absurdities, operated as a stimulus to the re-examination
of the subject and thus the very doctrines originating in the oblivion
into which a part of the truth had fallen, were rendered indirectly, but
powerfully, instrumental to its revival.

The doctrine of the Coleridge school, that the language of any people
among whom culture is of old date, is a sacred deposit, the property of
all ages, and which no one age should consider itself empowered to
alter—borders indeed, as thus expressed, on an extravagance; but it is
grounded on a truth, frequently overlooked by that class of logicians who
think more of having a clear than of having a comprehensive meaning; and
who perceive that every age is adding to the truths which it has received
from its predecessors, but fail to see that a counter process of losing
truths already possessed, is also constantly going on, and requiring the
most sedulous attention to counteract it. Language is the depository of
the accumulated body of experience to which all former ages have
contributed their part, and which is the inheritance of all yet to come.
We have no right to prevent ourselves from transmitting to posterity a
larger portion of this inheritance than we may ourselves have profited by.
However much we may be able to improve on the conclusions of our
forefathers, we ought to be careful not inadvertently to let any of their
premises slip through our fingers. It may be good to alter the meaning of
a word, but it is bad to let any part of the meaning drop. Whoever seeks
to introduce a more correct use of a term with which important
associations are connected, should be required to possess an accurate
acquaintance with the history of the particular word, and of the opinions
which in different stages of its progress it served to express. To be
qualified to define the name, we must know all that has ever been known of
the properties of the class of objects which are, or originally were,
denoted by it. For if we give it a meaning according to which any
proposition will be false which has ever been generally held to be true,
it is incumbent on us to be sure that we know and have considered all
which those who believed the proposition understood by it.



                                Chapter V.


On The Natural History Of The Variations In The Meaning Of Terms.


§ 1. It is not only in the mode which has now been pointed out, namely by
gradual inattention to a portion of the ideas conveyed, that words in
common use are liable to shift their connotation. The truth is, that the
connotation of such words is perpetually varying; as might be expected
from the manner in which words in common use acquire their connotation. A
technical term, invented for purposes of art or science, has, from the
first, the connotation given to it by its inventor; but a name which is in
every one’s mouth before any one thinks of defining it, derives its
connotation only from the circumstances which are habitually brought to
mind when it is pronounced. Among these circumstances, the properties
common to the things denoted by the name, have naturally a principal
place; and would have the sole place, if language were regulated by
convention rather than by custom and accident. But besides these common
properties, which if they exist are _certainly_ present whenever the name
is employed, any other circumstance may _casually_ be found along with it,
so frequently as to become associated with it in the same manner, and as
strongly, as the common properties themselves. In proportion as this
association forms itself, people give up using the name in cases in which
those casual circumstances do not exist. They prefer using some other
name, or the same name with some adjunct, rather than employ an expression
which will call up an idea they do not want to excite. The circumstance
originally casual, thus becomes regularly a part of the connotation of the
word.

It is this continual incorporation of circumstances originally accidental,
into the permanent signification of words, which is the cause that there
are so few exact synonyms. It is this also which renders the dictionary
meaning of a word, by universal remark so imperfect an exponent of its
real meaning. The dictionary meaning is marked out in a broad, blunt way,
and probably includes all that was originally necessary for the correct
employment of the term; but in process of time so many collateral
associations adhere to words, that whoever should attempt to use them with
no other guide than the dictionary, would confound a thousand nice
distinctions and subtle shades of meaning which dictionaries take no
account of; as we notice in the use of a language in conversation or
writing by a foreigner not thoroughly master of it. The history of a word,
by showing the causes which determine its use, is in these cases a better
guide to its employment than any definition; for definitions can only show
its meaning at the particular time, or at most the series of its
successive meanings, but its history may show the law by which the
succession was produced. The word _gentleman_, for instance, to the
correct employment of which a dictionary would be no guide, originally
meant simply a man born in a certain rank. From this it came by degrees to
connote all such qualities or adventitious circumstances as were usually
found to belong to persons of that rank. This consideration at once
explains why in one of its vulgar acceptations it means any one who lives
without labor, in another without manual labor, and in its more elevated
signification it has in every age signified the conduct, character,
habits, and outward appearance, in whomsoever found, which, according to
the ideas of that age, belonged or were expected to belong to persons born
and educated in a high social position.

It continually happens that of two words, whose dictionary meanings are
either the same or very slightly different, one will be the proper word to
use in one set of circumstances, another in another, without its being
possible to show how the custom of so employing them originally grew up.
The accident that one of the words was used and not the other on a
particular occasion or in a particular social circle, will be sufficient
to produce so strong an association between the word and some specialty of
circumstances, that mankind abandon the use of it in any other case, and
the specialty becomes part of its signification. The tide of custom first
drifts the word on the shore of a particular meaning, then retires and
leaves it there.

An instance in point is the remarkable change which, in the English
language at least, has taken place in the signification of the word
_loyalty_. That word originally meant in English, as it still means in the
language from whence it came, fair, open dealing, and fidelity to
engagements; in that sense the quality it expressed was part of the ideal
chivalrous or knightly character. By what process, in England, the term
became restricted to the single case of fidelity to the throne, I am not
sufficiently versed in the history of courtly language to be able to
pronounce. The interval between a _loyal chevalier_ and a loyal subject is
certainly great. I can only suppose that the word was, at some period, the
favorite term at court to express fidelity to the oath of allegiance;
until at length those who wished to speak of any other, and as it was
probably deemed, inferior sort of fidelity, either did not venture to use
so dignified a term, or found it convenient to employ some other in order
to avoid being misunderstood.

§ 2. Cases are not unfrequent in which a circumstance, at first casually
incorporated into the connotation of a word which originally had no
reference to it, in time wholly supersedes the original meaning, and
becomes not merely a part of the connotation, but the whole of it. This is
exemplified in the word pagan, _paganus_; which originally, as its
etymology imports, was equivalent to _villager_; the inhabitant of a
_pagus_, or village. At a particular era in the extension of Christianity
over the Roman empire, the adherents of the old religion, and the
villagers or country people, were nearly the same body of individuals, the
inhabitants of the towns having been earliest converted; as in our own
day, and at all times, the greater activity of social intercourse renders
them the earliest recipients of new opinions and modes, while old habits
and prejudices linger longest among the country people; not to mention
that the towns were more immediately under the direct influence of the
Government, which at that time had embraced Christianity. From this casual
coincidence, the word _paganus_ carried with it, and began more and more
steadily to suggest, the idea of a worshiper of the ancient divinities;
until at length it suggested that idea so forcibly that people who did not
desire to suggest the idea avoided using the word. But when _paganus_ had
come to connote heathenism, the very unimportant circumstance, with
reference to that fact, of the place of residence, was soon disregarded in
the employment of the word. As there was seldom any occasion for making
separate assertions respecting heathens who lived in the country, there
was no need for a separate word to denote them; and pagan came not only to
mean heathen, but to mean that exclusively.

A case still more familiar to most readers is that of the word _villain_
or _villein_. This term, as every body knows, had in the Middle Ages a
connotation as strictly defined as a word could have, being the proper
legal designation for those persons who were the subjects of the less
onerous forms of feudal bondage. The scorn of the semi-barbarous military
aristocracy for these their abject dependants, rendered the act of
likening any person to this class of people a mark of the greatest
contumely; the same scorn led them to ascribe to the same people all
manner of hateful qualities, which doubtless also, in the degrading
situation in which they were held, were often not unjustly imputed to
them. These circumstances combined to attach to the term villain ideas of
crime and guilt, in so forcible a manner that the application of the
epithet even to those to whom it legally belonged became an affront, and
was abstained from whenever no affront was intended. From that time guilt
was part of the connotation; and soon became the whole of it, since
mankind were not prompted by any urgent motive to continue making a
distinction in their language between bad men of servile station and bad
men of any other rank in life.

These and similar instances in which the original signification of a term
is totally lost—another and an entirely distinct meaning being first
ingrafted upon the former, and finally substituted for it—afford examples
of the double movement which is always taking place in language: two
counter-movements, one of Generalization, by which words are perpetually
losing portions of their connotation, and becoming of less meaning and
more general acceptation; the other of Specialization, by which other, or
even these same words, are continually taking on fresh connotation;
acquiring additional meaning by being restricted in their employment to a
part only of the occasions on which they might properly be used before.
This double movement is of sufficient importance in the natural history of
language (to which natural history the artificial modifications ought
always to have some degree of reference), to justify our dwelling a little
longer on the nature of the twofold phenomenon, and the causes to which it
owes its existence.

§ 3. To begin with the movement of generalization. It might seem
unnecessary to dwell on the changes in the meaning of names which take
place merely from their being used ignorantly, by persons who, not having
properly mastered the received connotation of a word, apply it in a looser
and wider sense than belongs to it. This, however, is a real source of
alterations in the language; for when a word, from being often employed in
cases where one of the qualities which it connotes does not exist, ceases
to suggest that quality with certainty, then even those who are under no
mistake as to the proper meaning of the word, prefer expressing that
meaning in some other way, and leave the original word to its fate. The
word ’Squire, as standing for an owner of a landed estate; Parson, as
denoting not the rector of the parish, but clergymen in general; Artist,
to denote only a painter or sculptor; are cases in point. Such cases give
a clear insight into the process of the degeneration of languages in
periods of history when literary culture was suspended; and we are now in
danger of experiencing a similar evil through the superficial extension of
the same culture. So many persons without any thing deserving the name of
education have become writers by profession, that written language may
almost be said to be principally wielded by persons ignorant of the proper
use of the instrument, and who are spoiling it more and more for those who
understand it. Vulgarisms, which creep in nobody knows how, are daily
depriving the English language of valuable modes of expressing thought. To
take a present instance: the verb _transpire_ formerly conveyed very
expressively its correct meaning, viz., to _become known_ through
unnoticed channels—to exhale, as it were, into publicity through invisible
pores, like a vapor or gas disengaging itself. But of late a practice has
commenced of employing this word, for the sake of finery, as a mere
synonym of _to happen_: “the events which have _transpired_ in the
Crimea,” meaning the incidents of the war. This vile specimen of bad
English is already seen in the dispatches of noblemen and viceroys; and
the time is apparently not far distant when nobody will understand the
word if used in its proper sense. In other cases it is not the love of
finery, but simple want of education, which makes writers employ words in
senses unknown to genuine English. The use of “aggravating” for
“provoking,” in my boyhood a vulgarism of the nursery, has crept into
almost all newspapers, and into many books; and when the word is used in
its proper sense, as when writers on criminal law speak of aggravating and
extenuating circumstances, their meaning, it is probable, is already
misunderstood. It is a great error to think that these corruptions of
language do no harm. Those who are struggling with the difficulty (and who
know by experience how great it already is) of expressing one’s self
clearly with precision, find their resources continually narrowed by
illiterate writers, who seize and twist from its purpose some form of
speech which once served to convey briefly and compactly an unambiguous
meaning. It would hardly be believed how often a writer is compelled to a
circumlocution by the single vulgarism, introduced during the last few
years, of using the word _alone_ as an adverb, _only_ not being fine
enough for the rhetoric of ambitious ignorance. A man will say “to which I
am not alone bound by honor but also by law,” unaware that what he has
unintentionally said is, that he is _not alone_ bound, some other person
being bound with him. Formerly, if any one said, “I am not alone
responsible for this,” he was understood to mean (what alone his words
mean in correct English), that he is not the sole person responsible; but
if he now used such an expression, the reader would be confused between
that and two other meanings: that he is not _only responsible_ but
something more; or that he is responsible _not only for this_ but for
something besides. The time is coming when Tennyson’s Œnone could not say,
“I will not die alone,” lest she should be supposed to mean that she would
not only die but do something else.

The blunder of writing _predicate_ for _predict_ has become so widely
diffused that it bids fair to render one of the most useful terms in the
scientific vocabulary of Logic unintelligible. The mathematical and
logical term “to eliminate” is undergoing a similar destruction. All who
are acquainted either with the proper use of the word or with its
etymology know that to eliminate a thing is to thrust it out: but those
who know nothing about it, except that it is a fine-looking phrase, use it
in a sense precisely the reverse, to denote, not turning any thing out,
but bringing it in. They talk of _eliminating_ some truth, or other useful
result, from a mass of details.(220) A similar permanent deterioration in
the language is in danger of being produced by the blunders of
translators. The writers of telegrams, and the foreign correspondents of
newspapers, have gone on so long translating _demander_ by “to demand,”
without a suspicion that it means only to ask, that (the context generally
showing that nothing else is meant) English readers are gradually
associating the English word demand with simple asking, thus leaving the
language without a term to express a demand in its proper sense. In like
manner, “transaction,” the French word for a compromise, is translated
into the English word transaction; while, curiously enough, the inverse
change is taking place in France, where the word “compromis” has lately
begun to be used for expressing the same idea. If this continues, the two
countries will have exchanged phrases.

Independently, however, of the generalization of names through their
ignorant misuse, there is a tendency in the same direction consistently
with a perfect knowledge of their meaning; arising from the fact, that the
number of things known to us, and of which we feel a desire to speak,
multiply faster than the names for them. Except on subjects for which
there has been constructed a scientific terminology, with which
unscientific persons do not meddle, great difficulty is generally found in
bringing a new name into use; and independently of that difficulty, it is
natural to prefer giving to a new object a name which at least expresses
its resemblance to something already known, since by predicating of it a
name entirely new we at first convey no information. In this manner the
name of a species often becomes the name of a genus; as _salt_, for
example, or _oil_; the former of which words originally denoted only the
muriate of soda, the latter, as its etymology indicates, only olive-oil;
but which now denote large and diversified classes of substances
resembling these in some of their qualities, and connote only those common
qualities, instead of the whole of the distinctive properties of olive-oil
and sea-salt. The words _glass_ and _soap_ are used by modern chemists in
a similar manner, to denote genera of which the substances vulgarly so
called are single species. And it often happens, as in those instances,
that the term keeps its special signification in addition to its more
general one, and becomes ambiguous, that is, two names instead of one.

These changes, by which words in ordinary use become more and more
generalized, and less and less expressive, take place in a still greater
degree with the words which express the complicated phenomena of mind and
society. Historians, travelers, and in general those who speak or write
concerning moral and social phenomena with which they are not familiarly
acquainted, are the great agents in this modification of language. The
vocabulary of all except unusually instructed as well as thinking persons,
is, on such subjects, eminently scanty. They have a certain small set of
words to which they are accustomed, and which they employ to express
phenomena the most heterogeneous, because they have never sufficiently
analyzed the facts to which those words correspond in their own country,
to have attached perfectly definite ideas to the words. The first English
conquerors of Bengal, for example, carried with them the phrase _landed
proprietor_ into a country where the rights of individuals over the soil
were extremely different in degree, and even in nature, from those
recognized in England. Applying the term with all its English associations
in such a state of things; to one who had only a limited right they gave
an absolute right, from another because he had not an absolute right they
took away all right, drove whole classes of people to ruin and despair,
filled the country with banditti, created a feeling that nothing was
secure, and produced, with the best intentions, a disorganization of
society which had not been produced in that country by the most ruthless
of its barbarian invaders. Yet the usage of persons capable of so gross a
misapprehension determines the meaning of language; and the words they
thus misuse grow in generality, until the instructed are obliged to
acquiesce; and to employ those words (first freeing them from vagueness by
giving them a definite connotation) as generic terms, subdividing the
genera into species.

§ 4. While the more rapid growth of ideas than of names thus creates a
perpetual necessity for making the same names serve, even if imperfectly,
on a greater number of occasions; a counter-operation is going on, by
which names become on the contrary restricted to fewer occasions, by
taking on, as it were, additional connotation, from circumstances not
originally included in the meaning, but which have become connected with
it in the mind by some accidental cause. We have seen above, in the words
_pagan_ and _villain_, remarkable examples of the specialization of the
meaning of words from casual associations, as well as of the
generalization of it in a new direction, which often follows.

Similar specializations are of frequent occurrence in the history even of
scientific nomenclature. “It is by no means uncommon,” says Dr. Paris, in
his _Pharmacologia_,(221) “to find a word which is used to express general
characters subsequently become the name of a specific substance in which
such characters are predominant; and we shall find that some important
anomalies in nomenclature may be thus explained. The term Αρσενίκον, from
which the word Arsenic is derived, was an ancient epithet applied to those
natural substances which possessed strong and acrimonious properties; and
as the poisonous quality of arsenic was found to be remarkably powerful,
the term was especially applied to Orpiment, the form in which this metal
most usually occurred. So the term _Verbena_ (quasi _Herbena_) originally
denoted all those herbs that were held sacred on account of their being
employed in the rites of sacrifice, as we learn from the poets; but as
_one_ herb was usually adopted upon these occasions, the word Verbena came
to denote that particular herb _only_, and it is transmitted to us to this
day under the same title, viz., Verbena or Vervain, and indeed until
lately it enjoyed the medical reputation which its sacred origin conferred
upon it, for it was worn suspended around the neck as an amulet.
_Vitriol_, in the original application of the word, denoted _any_
crystalline body with a certain degree of transparency (_vitrum_); it is
hardly necessary to observe that the term is now appropriated to a
particular species: in the same manner, Bark, which is a general term, is
applied to express _one_ genus, and by way of eminence it has the article
_The_ prefixed, as _The_ bark; the same observation will apply to the word
Opium, which, in its primitive sense, signifies _any_ juice (ὀπὸς,
_Succus_), while it now only denotes _one_ species, viz., that of the
poppy. So, again, _Elaterium_ was used by Hippocrates to signify various
internal applications, especially purgatives, of a violent and drastic
nature (from the word ἐλαύνω, _agito_, _moveo_, _stimulo_), but by
succeeding authors it was exclusively applied to denote the active matter
which subsides from the juice of the wild cucumber. The word _Fecula_,
again, originally meant to imply _any_ substance which was derived by
spontaneous subsidence from a liquid (from _fæx_, the grounds or
settlement of _any_ liquor); afterward it was applied to Starch, which is
deposited in this manner by agitating the flour of wheat in water; and,
lastly, it has been applied to a peculiar vegetable principle, which, like
starch, is insoluble in cold, but completely soluble in boiling water,
with which it forms a gelatinous solution. This indefinite meaning of the
word _fecula_ has created numerous mistakes in pharmaceutic chemistry;
Elaterium, for instance, is said to be _fecula_, and, in the original
sense of the word, it is properly so called, inasmuch as it is procured
from a vegetable juice by spontaneous subsidence, but in the limited and
modern acceptation of the term it conveys an erroneous idea; for instead
of the active principle of the juice residing in _fecula_, it is a
peculiar proximate principle, _sui generis_, to which I have ventured to
bestow the name of _Elatin_. For the same reason, much doubt and obscurity
involve the meaning of the word _Extract_, because it is applied
_generally_ to any substance obtained by the evaporation of a vegetable
solution, and _specifically_ to a peculiar proximate principle, possessed
of certain characters, by which it is distinguished from every other
elementary body.”

A generic term is always liable to become thus limited to a single
species, or even individual, if people have occasion to think and speak of
that individual or species much oftener than of any thing else which is
contained in the genus. Thus by cattle, a stage-coachman will understand
horses; beasts, in the language of agriculturists, stands for oxen; and
birds, with some sportsmen, for partridges only. The law of language which
operates in these trivial instances is the very same in conformity to
which the terms Θεός, Deus, and God, were adopted from Polytheism by
Christianity, to express the single object of its own adoration. Almost
all the terminology of the Christian Church is made up of words originally
used in a much more general acceptation: _Ecclesia_, Assembly; _Bishop_,
Episcopus, Overseer; _Priest_, Presbyter, Elder; _Deacon_, Diaconus,
Administrator; _Sacrament_, a vow of allegiance; _Evangelium_, good
tidings; and some words, as _Minister_, are still used both in the general
and in the limited sense. It would be interesting to trace the progress by
which _author_ came, in its most familiar sense, to signify a writer, and
ποίητης, or maker, a poet.

Of the incorporation into the meaning of a term, of circumstances
accidentally connected with it at some particular period, as in the case
of Pagan, instances might easily be multiplied. Physician (φυσίκος, or
naturalist) became, in England, synonymous with a healer of diseases,
because until a comparatively late period medical practitioners were the
only naturalists. _Clerc_, or clericus, a scholar, came to signify an
ecclesiastic, because the clergy were for many centuries the only
scholars.

Of all ideas, however, the most liable to cling by association to any
thing with which they have ever been connected by proximity, are those of
our pleasures and pains, or of the things which we habitually contemplate
as sources of our pleasures or pains. The additional connotation,
therefore, which a word soonest and most readily takes on, is that of
agreeableness or painfulness, in their various kinds and degrees; of being
a good or bad thing; desirable or to be avoided; an object of hatred, of
dread, contempt, admiration, hope, or love. Accordingly there is hardly a
single name, expressive of any moral or social fact calculated to call
forth strong affections either of a favorable or of a hostile nature,
which does not carry with it decidedly and irresistibly a connotation of
those strong affections, or, at the least, of approbation or censure;
insomuch that to employ those names in conjunction with others by which
the contrary sentiments were expressed, would produce the effect of a
paradox, or even a contradiction in terms. The baneful influence of a
connotation thus acquired, on the prevailing habits of thought, especially
in morals and politics, has been well pointed out on many occasions by
Bentham. It gives rise to the fallacy of “question-begging names.” The
very property which we are inquiring whether a thing possesses or not, has
become so associated with the name of the thing as to be part of its
meaning, insomuch that by merely uttering the name we assume the point
which was to be made out; one of the most frequent sources of apparently
self-evident propositions.

Without any further multiplication of examples to illustrate the changes
which usage is continually making in the signification of terms, I shall
add, as a practical rule, that the logician, not being able to prevent
such transformations, should submit to them with a good grace when they
are irrevocably effected, and if a definition is necessary, define the
word according to its new meaning; retaining the former as a second
signification, if it is needed, and if there is any chance of being able
to preserve it either in the language of philosophy or in common use.
Logicians can not _make_ the meaning of any but scientific terms; that of
all other words is made by the collective human race. But logicians can
ascertain clearly what it is which, working obscurely, has guided the
general mind to a particular employment of a name; and when they have
found this, they can clothe it in such distinct and permanent terms, that
mankind shall see the meaning which before they only felt, and shall not
suffer it to be afterward forgotten or misapprehended.



                               Chapter VI.


The Principles Of A Philosophical Language Further Considered.


§ 1. We have, thus far, considered only one of the requisites of a
language adapted for the investigation of truth; that its terms shall each
of them convey a determinate and unmistakable meaning. There are, however,
as we have already remarked, other requisites; some of them important only
in the second degree, but one which is fundamental, and barely yields in
point of importance, if it yields at all, to the quality which we have
already discussed at so much length. That the language may be fitted for
its purposes, not only should every word perfectly express its meaning,
but there should be no important meaning without its word. Whatever we
have occasion to think of often, and for scientific purposes, ought to
have a name appropriated to it.

This requisite of philosophical language may be considered under three
different heads; that number of separate conditions being involved in it.

§ 2. First, there ought to be all such names, as are needful for making
such a record of individual observations that the words of the record
shall exactly show what fact it is which has been observed. In other
words, there should be an accurate Descriptive Terminology.

The only things which we can observe directly being our own sensations, or
other feelings, a complete descriptive language would be one in which
there should be a name for every variety of elementary sensation or
feeling. Combinations of sensations or feelings may always be described,
if we have a name for each of the elementary feelings which compose them;
but brevity of description, and clearness (which often depends very much
on brevity), are greatly promoted by giving distinctive names not to the
elements alone, but also to all combinations which are of frequent
recurrence. On this occasion I can not do better than quote from Dr.
Whewell(222) some of the excellent remarks which he has made on this
important branch of our subject.

“The meaning of [descriptive] technical terms can be fixed in the first
instance only by convention, and can be made intelligible only by
presenting to the senses that which the terms are to signify. The
knowledge of a color by its name can only be taught through the eye. No
description can convey to a hearer what we mean by _apple-green_ or
_French gray_. It might, perhaps, be supposed that, in the first example,
the term _apple_, referring to so familiar an object, sufficiently
suggests the color intended. But it may easily be seen that this is not
true; for apples are of many different hues of green, and it is only by a
conventional selection that we can appropriate the term to one special
shade. When this appropriation is once made, the term refers to the
sensation, and not to the parts of the term; for these enter into the
compound merely as a help to the memory, whether the suggestion be a
natural connection as in ‘apple-green,’ or a casual one as in ‘French
gray.’ In order to derive due advantage from technical terms of the kind,
they must be associated _immediately_ with the perception to which they
belong; and not connected with it through the vague usages of common
language. The memory must retain the sensation; and the technical word
must be understood as directly as the most familiar word, and more
distinctly. When we find such terms as _tin-white_ or _pinchbeck-brown_,
the metallic color so denoted ought to start up in our memory without
delay or search.

“This, which it is most important to recollect with respect to the simpler
properties of bodies, as color and form, is no less true with respect to
more compound notions. In all cases the term is fixed to a peculiar
meaning by convention; and the student, in order to use the word, must be
completely familiar with the convention, so that he has no need to frame
conjectures from the word itself. Such conjectures would always be
insecure, and often erroneous. Thus the term _papilionaceous_ applied to a
flower is employed to indicate, not only a resemblance to a butterfly, but
a resemblance arising from five petals of a certain-peculiar shape and
arrangement; and even if the resemblance were much stronger than it is in
such cases, yet, if it were produced in a different way, as, for example,
by one petal, or two only, instead of a ‘standard,’ two ‘wings,’ and a
‘keel’ consisting of two parts more or less united into one, we should be
no longer justified in speaking of it as a ‘papilionaceous’ flower.”

When, however, the thing named is, as in this last case, a combination of
simple sensations, it is not necessary, in order to learn the meaning of
the word, that the student should refer back to the sensations themselves;
it may be communicated to him through the medium of other words; the
terms, in short, may be defined. But the names of elementary sensations,
or elementary feelings of any sort, can not be defined; nor is there any
mode of making their signification known but by making the learner
experience the sensation, or referring him, through some known mark, to
his remembrance of having experienced it before. Hence it is only the
impressions on the outward senses, or those inward feelings which are
connected in a very obvious and uniform manner with outward objects, that
are really susceptible of an exact descriptive language. The countless
variety of sensations which arise, for instance, from disease, or from
peculiar physiological states, it would be in vain to attempt to name; for
as no one can judge whether the sensation I have is the same with his, the
name can not have, to us two, real community of meaning. The same may be
said, to a considerable extent, of purely mental feelings. But in some of
the sciences which are conversant with external objects, it is scarcely
possible to surpass the perfection to which this quality of a
philosophical language has been carried.

“The formation(223) of an exact and extensive descriptive language for
botany has been executed with a degree of skill and felicity, which,
before it was attained, could hardly have been dreamed of as attainable.
Every part of a plant has been named; and the form of every part, even the
most minute, has had a large assemblage of descriptive terms appropriated
to it, by means of which the botanist can convey and receive knowledge of
form and structure, as exactly as if each minute part were presented to
him vastly magnified. This acquisition was part of the Linnæan reform....
‘Tournefort,’ says Decandolle, ‘appears to have been the first who really
perceived the utility of fixing the sense of terms in such a way as always
to employ the same word in the same sense, and always to express the same
idea by the same words; but it was Linnæus who really created and fixed
this botanical language, and this is his fairest claim to glory, for by
this fixation of language he has shed clearness and precision over all
parts of the science.’

“It is not necessary here to give any detailed account of the terms of
botany. The fundamental ones have been gradually introduced, as the parts
of plants were more carefully and minutely examined. Thus the flower was
necessarily distinguished into the _calyx_, the _corolla_, the _stamens_,
and the _pistils_; the sections of the corolla were termed _petals_ by
Columna; those of the calyx were called _sepals_ by Necker. Sometimes
terms of greater generality were devised; as _perianth_, to include the
calyx and corolla, whether one or both of these were present; _pericarp_,
for the part inclosing the grain, of whatever kind it be, fruit, nut, pod,
etc. And it may easily be imagined, that descriptive terms may, by
definition and combination, become very numerous and distinct. Thus leaves
may be called _pinnatifid_, _pinnatipartite_, _pinnatisect_,
_pinnatilobate_, _palmatifid_, _palmatipartite_, etc., and each of these
words designates different combinations of the modes and extent of the
divisions of the leaf with the divisions of its outline. In some cases,
arbitrary numerical relations are introduced into the definition: thus, a
leaf is called _bilobate_, when it is divided into two parts by a notch;
but if the notch go to the middle of its length, it is _bifid_; if it go
near the base of the leaf, it is _bipartite_; if to the base, it is
_bisect_. Thus, too, a pod of a cruciferous plant is a _siliqua_, if it is
four times as long as it is broad, but if it be shorter than this it is a
_silicula_. Such terms being established, the form of the very complex
leaf or frond of a fern (Hymenophyllum Wilsoni) is exactly conveyed by the
following phrase: ‘fronds rigid pinnate, pinnæ recurved subunilateral,
pinnatifid, the segments linear undivided or bifid, spinuloso-serrate.’

“Other characters, as well as form, are conveyed with the like precision:
Color by means of a classified scale of colors.... This was done with most
precision by Werner, and his scale of colors is still the most usual
standard of naturalists. Werner also introduced a more exact terminology
with regard to other characters which are important in mineralogy, as
lustre, hardness. But Mohs improved upon this step by giving a numerical
scale of hardness, in which talc is 1, gypsum 2, calc spar 3, and so
on.... Some properties, as specific gravity, by their definition give at
once a numerical measure; and others, as crystalline form, require a very
considerable array of mathematical calculation and reasoning, to point out
their relations and gradations.”

§ 3. Thus far of Descriptive Terminology, or of the language requisite for
placing on record our observation of individual instances. But when we
proceed from this to Induction, or rather to that comparison of observed
instances which is the preparatory step toward it, we stand in need of an
additional and a different sort of general names.

Whenever, for purposes of Induction, we find it necessary to introduce (in
Dr. Whewell’s phraseology) some new general conception; that is, whenever
the comparison of a set of phenomena leads to the recognition in them of
some common circumstance, which, our attention not having been directed to
it on any former occasion, is to us a new phenomenon; it is of importance
that this new conception, or this new result of abstraction, should have a
name appropriated to it; especially if the circumstance it involves be one
which leads to many consequences, or which is likely to be found also in
other classes of phenomena. No doubt, in most cases of the kind, the
meaning might be conveyed by joining together several words already in
use. But when a thing has to be often spoken of, there are more reasons
than the saving of time and space, for speaking of it in the most concise
manner possible. What darkness would be spread over geometrical
demonstrations, if wherever the word _circle_ is used, the definition of a
circle were inserted instead of it. In mathematics and its applications,
where the nature of the processes demands that the attention should be
strongly concentrated, but does not require that it should be widely
diffused, the importance of concentration also in the expressions has
always been duly felt; and a mathematician no sooner finds that he shall
often have occasion to speak of the same two things together, than he at
once creates a term to express them whenever combined: just as, in his
algebraical operations, he substitutes for (_a_m + _b_n) p/q, or for
_a_/_b_ + _b_/_c_ + _c_/_d_ + etc., the single letter P, Q, or S; not
solely to shorten his symbolical expressions, but to simplify the purely
intellectual part of his operations, by enabling the mind to give its
exclusive attention to the relation between the quantity S and the other
quantities which enter into the equation, without being distracted by
thinking unnecessarily of the parts of which S is itself composed.

But there is another reason, in addition to that of promoting perspicuity,
for giving a brief and compact name to each of the more considerable
results of abstraction which are obtained in the course of our
intellectual phenomena. By naming them, we fix our attention upon them; we
keep them more constantly before the mind. The names are remembered, and
being remembered, suggest their definition; while if instead of specific
and characteristic names, the meaning had been expressed by putting
together a number of other names, that particular combination of words
already in common use for other purposes would have had nothing to make
itself remembered by. If we want to render a particular combination of
ideas permanent in the mind, there is nothing which clinches it like a
name specially devoted to express it. If mathematicians had been obliged
to speak of “that to which a quantity, in increasing or diminishing, is
always approaching nearer, so that the difference becomes less than any
assignable quantity, but to which it never becomes exactly equal,” instead
of expressing all this by the simple phrase, “the limit of a quantity,” we
should probably have long remained without most of the important truths
which have been discovered by means of the relation between quantities of
various kinds and their limits. If instead of speaking of _momentum_, it
had been necessary to say, “the product of the number of units of velocity
in the velocity by the number of units of mass in the mass,” many of the
dynamical truths now apprehended by means of this complex idea would
probably have escaped notice, for want of recalling the idea itself with
sufficient readiness and familiarity. And on subjects less remote from the
topics of popular discussion, whoever wishes to draw attention to some new
or unfamiliar distinction among things, will find no way so sure as to
invent or select suitable names for the express purpose of marking it.

A volume devoted to explaining what the writer means by civilization, does
not raise so vivid a conception of it as the single expression, that
Civilization is a different thing from Cultivation; the compactness of
that brief designation for the contrasted quality being an equivalent for
a long discussion. So, if we would impress forcibly upon the understanding
and memory the distinction between the two different conceptions of a
representative government, we can not more effectually do so than by
saying that Delegation is not Representation. Hardly any original thoughts
on mental or social subjects ever make their way among mankind, or assume
their proper importance in the minds even of their inventors, until
aptly-selected words or phrases have, as it were, nailed them down and
held them fast.

§ 4. Of the three essential parts of a philosophical language, we have now
mentioned two: a terminology suited for describing with precision the
individual facts observed; and a name for every common property of any
importance or interest, which we detect by comparing those facts;
including (as the concretes corresponding to those abstract terms) names
for the classes which we artificially construct in virtue of those
properties, or as many of them, at least, as we have frequent occasion to
predicate any thing of.

But there is a sort of classes, for the recognition of which no such
elaborate process is necessary; because each of them is marked out from
all others not by some one property, the detection of which may depend on
a difficult act of abstraction, but by its properties generally. I mean,
the Kinds of things, in the sense which, in this treatise, has been
specially attached to that term. By a Kind, it will be remembered, we mean
one of those classes which are distinguished from all others not by one or
a few definite properties, but by an unknown multitude of them; the
combination of properties on which the class is grounded, being a mere
index to an indefinite number of other distinctive attributes. The class
horse is a Kind, because the things which agree in possessing the
characters by which we recognize a horse, agree in a great number of other
properties, as we know, and, it can not be doubted, in many more than we
know. Animal, again, is a Kind, because no definition that could be given
of the name animal could either exhaust the properties common to all
animals, or supply premises from which the remainder of those properties
could be inferred. But a combination of properties which does not give
evidence of the existence of any other independent peculiarities, does not
constitute a Kind. White horse, therefore, is not a Kind; because horses
which agree in whiteness, do not agree in any thing else, except the
qualities common to all horses, and whatever may be the causes or effects
of that particular color.

On the principle that there should be a name for every thing which we have
frequent occasion to make assertions about, there ought evidently to be a
name for every Kind; for as it is the very meaning of a Kind that the
individuals composing it have an indefinite multitude of properties in
common, it follows that, if not with our present knowledge, yet with that
which we may hereafter acquire, the Kind is a subject to which there will
have to be applied many predicates. The third component element of a
philosophical language, therefore, is that there shall be a name for every
Kind. In other words, there must not only be a terminology, but also a
nomenclature.

The words Nomenclature and Terminology are employed by most authors almost
indiscriminately; Dr. Whewell being, as far as I am aware, the first
writer who has regularly assigned to the two words different meanings. The
distinction, however, which he has drawn between them being real and
important, his example is likely to be followed; and (as is apt to be the
case when such innovations in language are felicitously made) a vague
sense of the distinction is found to have influenced the employment of the
terms in common practice, before the expediency had been pointed out of
discriminating them philosophically. Every one would say that the reform
effected by Lavoisier and Guyton-Morveau in the language of chemistry
consisted in the introduction of a new nomenclature, not of a new
terminology. Linear, lanceolate, oval, or oblong, serrated, dentate, or
crenate leaves, are expressions forming part of the terminology of botany,
while the names “Viola odorata,” and “Ulex Europæus,” belong to its
nomenclature.

A nomenclature may be defined, the collection of the names of all the
Kinds with which any branch of knowledge is conversant; or more properly,
of all the lowest Kinds, or _infirmæ species_—those which may be
subdivided indeed, but not into Kinds, and which generally accord with
what in natural history are termed simply species. Science possesses two
splendid examples of a systematic nomenclature; that of plants and
animals, constructed by Linnæus and his successors, and that of chemistry,
which we owe to the illustrious group of chemists who flourished in France
toward the close of the eighteenth century. In these two departments, not
only has every known species, or lowest Kind, a name assigned to it, but
when new lowest Kinds are discovered, names are at once given to them on a
uniform principle. In other sciences the nomenclature is not at present
constructed on any system, either because the species to be named are not
numerous enough to require one (as in geometry, for example), or because
no one has yet suggested a suitable principle for such a system, as in
mineralogy; in which the want of a scientifically constructed nomenclature
is now the principal cause which retards the progress of the science.

§ 5. A word which carries on its face that it belongs to a nomenclature,
seems at first sight to differ from other concrete general names in
this—that its meaning does not reside in its connotation, in the
attributes implied in it, but in its denotation, that is, in the
particular group of things which it is appointed to designate; and can
not, therefore, be unfolded by means of a definition, but must be made
known in another way. This opinion, however, appears to me erroneous.
Words belonging to a nomenclature differ, I conceive, from other words
mainly in this, that besides the ordinary connotation, they have a
peculiar one of their own: besides connoting certain attributes, they also
connote that those attributes are distinctive of a Kind. The term
“peroxide of iron,” for example, belonging by its form to the systematic
nomenclature of chemistry, bears on its face that it is the name of a
peculiar Kind of substance. It moreover connotes, like the name of any
other class, some portion of the properties common to the class; in this
instance the property of being a compound of iron and the largest dose of
oxygen with which iron will combine. These two things, the fact of being
such a compound, and the fact of being a Kind, constitute the connotation
of the name peroxide of iron. When we say of the substance before us, that
it is the peroxide of iron, we thereby assert, first, that it is a
compound of iron and a maximum of oxygen, and next, that the substance so
composed is a peculiar Kind of substance.

Now, this second part of the connotation of any word belonging to a
nomenclature is as essential a portion of its meaning as the first part,
while the definition only declares the first; and hence the appearance
that the signification of such terms can not be conveyed by a definition:
which appearance, however, is fallacious. The name Viola odorata denotes a
Kind, of which a certain number of characters, sufficient to distinguish
it, are enunciated in botanical works. This enumeration of characters is
surely, as in other cases, a definition of the name. No, say some, it is
not a definition, for the name Viola odorata does not mean those
characters; it means that particular group of plants, and the characters
are selected from among a much greater number, merely as marks by which to
recognize the group. But to this I reply, that the name does not mean that
group, for it would be applied to that group no longer than while the
group is believed to be an _infima species_; if it were to be discovered
that several distinct Kinds have been confounded under this one name, no
one would any longer apply the name Viola odorata to the whole of the
group, but would apply it, if retained at all, to one only of the Kinds
retained therein. What is imperative, therefore, is not that the name
shall denote one particular collection of objects, but that it shall
denote a Kind, and a lowest Kind. The form of the name declares that,
happen what will, it is to denote an _infima species_; and that,
therefore, the properties which it connotes, and which are expressed in
the definition, are to be connoted by it no longer than while we continue
to believe that those properties, when found together, indicate a Kind,
and that the whole of them are found in no more than one Kind.

With the addition of this peculiar connotation, implied in the form of
every word which belongs to a systematic nomenclature; the set of
characters which is employed to discriminate each Kind from all other
Kinds (and which is a real definition) constitutes as completely as in any
other case the whole meaning of the term. It is no objection to say that
(as is often the case in natural history) the set of characters may be
changed, and another substituted as being better suited for the purpose of
distinction, while the word, still continuing to denote the same group or
things, is not considered to have changed its meaning. For this is no more
than may happen in the case of any other general name: we may, in
reforming its connotation, leave its denotation untouched; and it is
generally desirable to do so. The connotation, however, is not the less
for this the real meaning, for we at once apply the name wherever the
characters set down in the definition are found; and that which
exclusively guides us in applying the term, must constitute its
signification. If we find, contrary to our previous belief, that the
characters are not peculiar to one species, we cease to use the term
co-extensively with the characters; but then it is because the other
portion of the connotation fails; the condition that the class must be a
Kind. The connotation, therefore, is still the meaning; the set of
descriptive characters is a true definition; and the meaning is unfolded,
not indeed (as in other cases) by the definition alone, but by the
definition and the form of the word taken together.

§ 6. We have now analyzed what is implied in the two principal requisites
of a philosophical language; first, precision, or definiteness; and,
secondly, completeness. Any further remarks on the mode of constructing a
nomenclature must be deferred until we treat of Classification; the mode
of naming the Kinds of things being necessarily subordinate to the mode of
arranging those Kinds into larger classes. With respect to the minor
requisites of terminology, some of them are well stated and illustrated in
the “Aphorisms concerning the Language of Science,” included in Dr.
Whewell’s _Philosophy of the Inductive Sciences_. These, as being of
secondary importance in the peculiar point of view of Logic, I shall not
further refer to, but shall confine my observations to one more quality,
which, next to the two already treated of, appears to be the most valuable
which the language of science can possess. Of this quality a general
notion may be conveyed by the following aphorism:

Whenever the nature of the subject permits our reasoning processes to be,
without danger, carried on mechanically, the language should be
constructed on as mechanical principles as possible; while, in the
contrary case, it should be so constructed that there shall be the
greatest possible obstacles to a merely mechanical use of it.

I am aware that this maxim requires much explanation, which I shall at
once proceed to give. At first, as to what is meant by using a language
mechanically. The complete or extreme case of the mechanical use of
language, is when it is used without any consciousness of a meaning, and
with only the consciousness of using certain visible or audible marks in
conformity to technical rules previously laid down. This extreme case is
nowhere realized except in the figures of arithmetic, and still more the
symbols of algebra, a language unique in its kind, and approaching as
nearly to perfection, for the purposes to which it is destined, as can,
perhaps, be said of any creation of the human mind. Its perfection
consists in the completeness of its adaptation to a purely mechanical use.
The symbols are mere counters, without even the semblance of a meaning
apart from the convention which is renewed each time they are employed,
and which is altered at each renewal, the same symbol _a_ or _x_ being
used on different occasions to represent things which (except that, like
all things, they are susceptible of being numbered) have no property in
common. There is nothing, therefore, to distract the mind from the set of
mechanical operations which are to be performed upon the symbols, such as
squaring both sides of the equation, multiplying or dividing them by the
same or by equivalent symbols, and so forth. Each of these operations, it
is true, corresponds to a syllogism; represents one step of a
ratiocination relating not to the symbols, but to the things signified by
them. But as it has been found practicable to frame a technical form, by
conforming to which we can make sure of finding the conclusion of the
ratiocination, our end can be completely attained without our ever
thinking of any thing but the symbols. Being thus intended to work merely
as mechanism, they have the qualities which mechanism ought to have. They
are of the least possible bulk, so that they take up scarcely any room,
and waste no time in their manipulation; they are compact, and fit so
closely together that the eye can take in the whole at once of almost
every operation which they are employed to perform.

These admirable properties of the symbolical language of mathematics have
made so strong an impression on the minds of many thinkers, as to have led
them to consider the symbolical language in question as the ideal type of
philosophical language generally; to think that names in general, or (as
they are fond of calling them) signs, are fitted for the purposes of
thought in proportion as they can be made to approximate to the
compactness, the entire unmeaningness, and the capability of being used as
counters without a thought of what they represent, which are
characteristic of the _a_ and _b_, the _x_ and _y_, of algebra. This
notion has led to sanguine views of the acceleration of the progress of
science by means which, I conceive, can not possibly conduce to that end,
and forms part of that exaggerated estimate of the influence of signs,
which has contributed in no small degree to prevent the real laws of our
intellectual operations from being rightly understood.

In the first place, a set of signs by which we reason without
consciousness of their meaning, can be serviceable, at most, only in our
deductive operations. In our direct inductions we can not for a moment
dispense with a distinct mental image of the phenomena, since the whole
operation turns on a perception of the particulars in which those
phenomena agree and differ. But, further, this reasoning by counters is
only suitable to a very limited portion even of our deductive processes.
In our reasonings respecting numbers, the only general principles which we
ever have occasion to introduce are these, Things which are equal to the
same thing are equal to one another, and The sums or differences of equal
things are equal; with their various corollaries. Not only can no
hesitation ever arise respecting the applicability of these principles,
since they are true of all magnitudes whatever; but every possible
application of which they are susceptible, may be reduced to a technical
rule; and such, in fact, the rules of the calculus are. But if the symbols
represent any other things than mere numbers, let us say even straight or
curve lines, we have then to apply theorems of geometry not true of all
lines without exception, and to select those which are true of the lines
we are reasoning about. And how can we do this unless we keep completely
in mind what particular lines these are? Since additional geometrical
truths may be introduced into the ratiocination in any stage of its
progress, we can not suffer ourselves, during even the smallest part of
it, to use the names mechanically (as we use algebraical symbols) without
an image annexed to them. It is only after ascertaining that the solution
of a question concerning lines can be made to depend on a previous
question concerning numbers, or, in other words, after the question has
been (to speak technically) reduced to an equation, that the unmeaning
signs become available, and that the nature of the facts themselves to
which the investigation relates can be dismissed from the mind. Up to the
establishment of the equation, the language in which mathematicians carry
on their reasoning does not differ in character from that employed by
close reasoners on any other kind of subject.

I do not deny that every correct ratiocination, when thrown into the
syllogistic shape, is conclusive from the mere form of the expression,
provided none of the terms used be ambiguous; and this is one of the
circumstances which have led some writers to think that if all names were
so judiciously constructed and so carefully defined as not to admit of any
ambiguity, the improvement thus made in language would not only give to
the conclusions of every deductive science the same certainty with those
of mathematics, but would reduce all reasonings to the application of a
technical form, and enable their conclusiveness to be rationally assented
to after a merely mechanical process, as is undoubtedly the case in
algebra. But, if we except geometry, the conclusions of which are already
as certain and exact as they can be made, there is no science but that of
number, in which the practical validity of a reasoning can be apparent to
any person who has looked only at the reasoning itself. Whoever has
assented to what was said in the last Book concerning the case of the
Composition of Causes, and the still stronger case of the entire
supersession of one set of laws by another, is aware that geometry and
algebra are the only sciences of which the propositions are categorically
true; the general propositions of all other sciences are true only
hypothetically, supposing that no counteracting cause happens to
interfere. A conclusion, therefore, however correctly deduced, in point of
form, from admitted laws of nature, will have no other than an
hypothetical certainty. At every step we must assure ourselves that no
other law of nature has superseded, or intermingled its operation with,
those which are the premises of the reasoning; and how can this be done by
merely looking at the words? We must not only be constantly thinking of
the phenomena themselves, but we must be constantly studying them; making
ourselves acquainted with the peculiarities of every case to which we
attempt to apply our general principles.

The algebraic notation, considered as a philosophical language, is perfect
in its adaptation to the subjects for which it is commonly employed,
namely those of which the investigations have already been reduced to the
ascertainment of a relation between numbers. But, admirable as it is for
its own purpose, the properties by which it is rendered such are so far
from constituting it the ideal model of philosophical language in general,
that the more nearly the language of any other branch of science
approaches to it, the less fit that language is for its own proper
functions. On all other subjects, instead of contrivances to prevent our
attention from being distracted by thinking of the meaning of our signs,
we ought to wish for contrivances to make it impossible that we should
ever lose sight of that meaning even for an instant.

With this view, as much meaning as possible should be thrown into the
formation of the word itself; the aids of derivation and analogy being
made available to keep alive a consciousness of all that is signified by
it. In this respect those languages have an immense advantage which form
their compounds and derivatives from native roots, like the German, and
not from those of a foreign or dead language, as is so much the case with
English, French, and Italian; and the best are those which form them
according to fixed analogies, corresponding to the relations between the
ideas to be expressed. All languages do this more or less, but especially,
among modern European languages, the German; while even that is inferior
to the Greek, in which the relation between the meaning of a derivative
word and that of its primitive is in general clearly marked by its mode of
formation, except in the case of words compounded with prepositions, which
are often, in both those languages, extremely anomalous.

But all that can be done, by the mode of constructing words, to prevent
them from degenerating into sounds passing through the mind without any
distinct apprehension of what they signify, is far too little for the
necessity of the case. Words, however well constructed originally, are
always tending, like coins, to have their inscription worn off by passing
from hand to hand; and the only possible mode of reviving it is to be ever
stamping it afresh, by living in the habitual contemplation of the
phenomena themselves, and not resting in our familiarity with the words
that express them. If any one, having possessed himself of the laws of
phenomena as recorded in words, whether delivered to him originally by
others, or even found out by himself, is content from thenceforth to live
among these formulæ, to think exclusively of them, and of applying them to
cases as they arise, without keeping up his acquaintance with the
realities from which these laws were collected—not only will he
continually fail in his practical efforts, because he will apply his
formulæ without duly considering whether, in this case and in that, other
laws of nature do not modify or supersede them; but the formulæ themselves
will progressively lose their meaning to him, and he will cease at last
even to be capable of recognizing with certainty whether a case falls
within the contemplation of his formula or not. It is, in short, as
necessary, on all subjects not mathematical, that the things on which we
reason should be conceived by us in the concrete, and “clothed in
circumstances,” as it is in algebra that we should keep all
individualizing peculiarities sedulously out of view.

With this remark we close our observations on the Philosophy of Language.



                               Chapter VII.


Of Classification, As Subsidiary To Induction.


§ 1. There is, as has been frequently remarked in this work, a
classification of things, which is inseparable from the fact of giving
them general names. Every name which connotes an attribute, divides, by
that very fact, all things whatever into two classes, those which have the
attribute and those which have it not; those of which the name can be
predicated, and those of which it can not. And the division thus made is
not merely a division of such things as actually exist, or are known to
exist, but of all such as may hereafter be discovered, and even of all
which can be imagined.

On this kind of Classification we have nothing to add to what has
previously been said. The Classification which requires to be discussed as
a separate act of the mind, is altogether different. In the one, the
arrangement of objects in groups, and distribution of them into
compartments, is a mere incidental effect consequent on the use of names
given for another purpose, namely that of simply expressing some of their
qualities. In the other, the arrangement and distribution are the main
object, and the naming is secondary to, and purposely conforms itself to,
instead of governing, that more important operation.

Classification, thus regarded, is a contrivance for the best possible
ordering of the ideas of objects in our minds; for causing the ideas to
accompany or succeed one another in such a way as shall give us the
greatest command over our knowledge already acquired, and lead most
directly to the acquisition of more. The general problem of
Classification, in reference to these purposes, may be stated as follows:
To provide that things shall be thought of in such groups, and those
groups in such an order, as will best conduce to the remembrance and to
the ascertainment of their laws.

Classification thus considered, differs from classification in the wider
sense, in having reference to real objects exclusively, and not to all
that are imaginable: its object being the due co-ordination in our minds
of those things only, with the properties of which we have actually
occasion to make ourselves acquainted. But, on the other hand, it embraces
_all_ really existing objects. We can not constitute any one class
properly, except in reference to a general division of the whole of
nature; we can not determine the group in which any one object can most
conveniently be placed, without taking into consideration all the
varieties of existing objects, all at least which have any degree of
affinity with it. No one family of plants or animals could have been
rationally constituted, except as part of a systematic arrangement of all
plants or animals; nor could such a general arrangement have been properly
made, without first determining the exact place of plants and animals in a
general division of nature.

§ 2. There is no property of objects which may not be taken, if we please,
as the foundation for a classification or mental grouping of those
objects; and in our first attempts we are likely to select for that
purpose properties which are simple, easily conceived, and perceptible on
a first view, without any previous process of thought. Thus Tournefort’s
arrangement of plants was founded on the shape and divisions of the
corolla; and that which is commonly called the Linnæan (though Linnæus
also suggested another and more scientific arrangement) was grounded
chiefly on the number of the stamens and pistils.

But these classifications, which are at first recommended by the facility
they afford of ascertaining to what class any individual belongs, are
seldom much adapted to the ends of that Classification which is the
subject of our present remarks. The Linnæan arrangement answers the
purpose of making us think together of all those kinds of plants which
possess the same number of stamens and pistils; but to think of them in
that manner is of little use, since we seldom have any thing to affirm in
common of the plants which have a given number of stamens and pistils. If
plants of the class Pentandria, order Monogynia, agreed in any other
properties, the habit of thinking and speaking of the plants under a
common designation would conduce to our remembering those common
properties so far as they were ascertained, and would dispose us to be on
the lookout for such of them as were not yet known. But since this is not
the case, the only purpose of thought which the Linnæan classification
serves is that of causing us to remember, better than we should otherwise
have done, the exact number of stamens and pistils of every species of
plants. Now, as this property is of little importance or interest, the
remembering it with any particular accuracy is of no moment. And, inasmuch
as, by habitually thinking of plants in those groups, we are prevented
from habitually thinking of them in groups which have a greater number of
properties in common, the effect of such a classification, when
systematically adhered to, upon our habits of thought, must be regarded as
mischievous.

The ends of scientific classification are best answered, when the objects
are formed into groups respecting which a greater number of general
propositions can be made, and those propositions more important, than
could be made respecting any other groups into which the same things could
be distributed. The properties, therefore, according to which objects are
classified, should, if possible, be those which are causes of many other
properties; or, at any rate, which are sure marks of them. Causes are
preferable, both as being the surest and most direct of marks, and as
being themselves the properties on which it is of most use that our
attention should be strongly fixed. But the property which is the cause of
the chief peculiarities of a class, is unfortunately seldom fitted to
serve also as the diagnostic of the class. Instead of the cause, we must
generally select some of its more prominent effects, which may serve as
marks of the other effects and of the cause.

A classification thus formed is properly scientific or philosophical, and
is commonly called a Natural, in contradistinction to a Technical or
Artificial, classification or arrangement. The phrase Natural
Classification seems most peculiarly appropriate to such arrangements as
correspond, in the groups which they form, to the spontaneous tendencies
of the mind, by placing together the objects most similar in their general
aspect; in opposition to those technical systems which, arranging things
according to their agreement in some circumstance arbitrarily selected,
often throw into the same group objects which in the general aggregate of
their properties present no resemblance, and into different and remote
groups, others which have the closest similarity. It is one of the most
valid recommendations of any classification to the character of a
scientific one, that it shall be a natural classification in this sense
also; for the test of its scientific character is the number and
importance of the properties which can be asserted in common of all
objects included in a group; and properties on which the general aspect of
the things depends are, if only on that ground, important, as well as, in
most cases, numerous. But, though a strong recommendation, this
circumstance is not a _sine qua non_; since the most obvious properties of
things may be of trifling importance compared with others that are not
obvious. I have seen it mentioned as a great absurdity in the Linnæan
classification, that it places (which by-the-way it does not) the violet
by the side of the oak; it certainly dissevers natural affinities, and
brings together things quite as unlike as the oak and the violet are. But
the difference, apparently so wide, which renders the juxtaposition of
those two vegetables so suitable an illustration of a bad arrangement,
depends, to the common eye, mainly on mere size and texture; now if we
made it our study to adopt the classification which would involve the
least peril of similar _rapprochements_, we should return to the obsolete
division into trees, shrubs, and herbs, which though of primary importance
with regard to mere general aspect, yet (compared even with so petty and
unobvious a distinction as that into dicotyledons and monocotyledons)
answers to so few differences in the other properties of plants, that a
classification founded on it (independently of the indistinctness of the
lines of demarcation) would be as completely artificial and technical as
the Linnæan.

Our natural groups, therefore, must often be founded not on the obvious
but on the unobvious properties of things, when these are of greater
importance. But in such cases it is essential that there should be some
other property or set of properties, more readily recognizable by the
observer, which co-exist with, and may be received as marks of, the
properties which are the real groundwork of the classification. A natural
arrangement, for example, of animals, must be founded in the main on their
internal structure, but (as M. Comte remarks) it would be absurd that we
should not be able to determine the genus and species of an animal without
first killing it. On this ground, the preference, among zoological
classifications, is probably due to that of M. De Blainville, founded on
the differences in the external integuments; differences which correspond,
much more accurately than might be supposed, to the really important
varieties, both in the other parts of the structure, and in the habits and
history of the animals.

This shows, more strongly than ever, how extensive a knowledge of the
properties of objects is necessary for making a good classification of
them. And as it is one of the uses of such a classification that by
drawing attention to the properties on which it is founded, and which, if
the classification be good, are marks of many others, it facilitates the
discovery of those others; we see in what manner our knowledge of things,
and our classification of them, tend mutually and indefinitely to the
improvement of each other.

We said just now that the classification of objects should follow those of
their properties which indicate not only the most numerous, but also the
most important peculiarities. What is here meant by importance? It has
reference to the particular end in view; and the same objects, therefore,
may admit with propriety of several different classifications. Each
science or art forms its classification of things according to the
properties which fall within its special cognizance, or of which it must
take account in order to accomplish its peculiar practical end. A farmer
does not divide plants, like a botanist, into dicotyledonous and
monocotyledonous, but into useful plants and weeds. A geologist divides
fossils, not like a zoologist, into families corresponding to those of
living species, but into fossils of the paleozoic, mesozoic, and tertiary
periods, above the coal and below the coal, etc. Whales are or are not
fish according to the purpose for which we are considering them. “If we
are speaking of the internal structure and physiology of the animal, we
must not call them fish; for in these respects they deviate widely from
fishes; they have warm blood, and produce and suckle their young as land
quadrupeds do. But this would not prevent our speaking of the
_whale-fishery_, and calling such animals _fish_ on all occasions
connected with this employment; for the relations thus arising depend upon
the animal’s living in the water, and being caught in a manner similar to
other fishes. A plea that human laws which mention fish do not apply to
whales, would be rejected at once by an intelligent judge.”(224)

These different classifications are all good, for the purposes of their
own particular departments of knowledge or practice. But when we are
studying objects not for any special practical end, but for the sake of
extending our knowledge of the whole of their properties and relations, we
must consider as the most important attributes those which contribute
most, either by themselves or by their effects, to render the things like
one another, and unlike other things; which give to the class composed of
them the most marked individuality; which fill, as it were, the largest
space in their existence, and would most impress the attention of a
spectator who knew all their properties but was not specially interested
in any. Classes formed on this principle may be called, in a more emphatic
manner than any others, natural groups.

§ 3. On the subject of these groups Dr. Whewell lays down a theory,
grounded on an important truth, which he has, in some respects, expressed
and illustrated very felicitously, but also, as it appears to me, with
some admixture of error. It will be advantageous, for both these reasons,
to extract the statement of his doctrine in the very words he has used.

“Natural groups,” according to this theory,(225) are “given by Type, not
by Definition.” And this consideration accounts for that “indefiniteness
and indecision which we frequently find in the descriptions of such
groups, and which must appear so strange and inconsistent to any one who
does not suppose these descriptions to assume any deeper ground of
connection than an arbitrary choice of the botanist. Thus in the family of
the rose-tree, we are told that the _ovules_ are _very rarely_ erect, the
_stigmata usually_ simple. Of what use, it might be asked, can such loose
accounts be? To which the answer is, that they are not inserted in order
to distinguish the species, but in order to describe the family, and the
total relations of the ovules and the stigmata of the family are better
known by this general statement. A similar observation may be made with
regard to the Anomalies of each group, which occur so commonly, that Dr.
Lindley, in his _Introduction to the Natural System of Botany_, makes the
‘Anomalies’ an article in each family. Thus, part of the character of the
Rosaceæ is, that they have alternate _stipulate_ leaves, and that the
_albumen_ is _obliterated_; but yet in _Lowea_, one of the genera of this
family, the stipulæ are _absent_; and the albumen is _present_ in another,
_Neillia_. This implies, as we have already seen, that the artificial
character (or _diagnosis_, as Mr. Lindley calls it) is imperfect. It is,
though very nearly, yet not exactly, commensurate with the natural group;
and hence in certain cases this character is made to yield to the general
weight of natural affinities.

“These views—of classes determined by characters which can not be
expressed in words—of propositions which state, not what happens in all
cases, but only usually—of particulars which are included in a class,
though they transgress the definition of it, may probably surprise the
reader. They are so contrary to many of the received opinions respecting
the use of definitions, and the nature of scientific propositions, that
they will probably appear to many persons highly illogical and
unphilosophical. But a disposition to such a judgment arises in a great
measure from this, that the mathematical and mathematico-physical sciences
have, in a great degree, determined men’s views of the general nature and
form of scientific truth; while Natural History has not yet had time or
opportunity to exert its due influence upon the current habits of
philosophizing. The apparent indefiniteness and inconsistency of the
classifications and definitions of Natural History belongs, in a far
higher degree, to all other except mathematical speculations; and the
modes in which approximations to exact distinctions and general truths
have been made in Natural History, may be worthy our attention, even for
the light they throw upon the best modes of pursuing truth of all kinds.

“Though in a Natural group of objects a definition can no longer be of any
use as a regulative principle, classes are not therefore left quite loose,
without any certain standard or guide. The class is steadily fixed, though
not precisely limited; it is given, though not circumscribed; it is
determined, not by a boundary-line without, but by a central point within;
not by what it strictly excludes, but by what it eminently includes; by an
example, not by a precept; in short, instead of a Definition we have a
Type for our director.

“A Type is an example of any class, for instance a species of a genus,
which is considered as eminently possessing the character of the class.
All the species which have a greater affinity with this type-species than
with any others, form the genus, and are arranged about it, deviating from
it in various directions and different degrees. Thus a genus may consist
of several species which approach very near the type, and of which the
claim to a place with it is obvious; while there may be other species
which straggle farther from this central knot, and which yet are clearly
more connected with it than with any other. And even if there should be
some species of which the place is dubious, and which appear to be equally
bound to two generic types, it is easily seen that this would not destroy
the reality of the generic groups, any more than the scattered trees of
the intervening plain prevent our speaking intelligibly of the distinct
forests of two separate hills.

“The type-species of every genus, the type-genus of every family, is then,
one which possesses all the characters and properties of the genus in a
marked and prominent manner. The type of the Rose family has alternate
stipulate leaves, wants the albumen, has the ovules not erect, has the
stigmata simple, and besides these features, which distinguish it from the
exceptions or varieties of its class, it has the features which make it
prominent in its class. It is one of those which possess clearly several
leading attributes; and thus, though we can not say of any one genus that
it _must_ be the type of the family, or of any one species that it _must_
be the type of the genus, we are still not wholly to seek; the type must
be connected by many affinities with most of the others of its group; it
must be near the centre of the crowd, and not one of the stragglers.”

In this passage (the latter part of which especially I can not help
noticing as an admirable example of philosophic style) Dr. Whewell has
stated very clearly and forcibly, but (I think) without making all
necessary distinctions, one of the principles of a Natural Classification.
What this principle is, what are its limits, and in what manner he seems
to me to have overstepped them, will appear when we have laid down another
rule of Natural Arrangement, which appears to me still more fundamental.

§ 4. The reader is by this time familiar with the general truth (which I
restate so often on account of the great confusion in which it is commonly
involved), that there are in nature distinctions of Kind; distinctions not
consisting in a given number of definite properties _plus_ the effects
which follow from those properties, but running through the whole nature,
through the attributes generally, of the things so distinguished. Our
knowledge of the properties of a Kind is never complete. We are always
discovering, and expecting to discover, new ones. Where the distinction
between two classes of things is not one of Kind, we expect to find their
properties alike, except where there is some reason for their being
different. On the contrary, when the distinction is in Kind, we expect to
find the properties different unless there be some cause for their being
the same. All knowledge of a Kind must be obtained by observation and
experiment upon the Kind itself; no inference respecting its properties
from the properties of things not connected with it by Kind, goes for more
than the sort of presumption usually characterized as an analogy, and
generally in one of its fainter degrees.

Since the common properties of a true Kind, and consequently the general
assertions which can be made respecting it, or which are certain to be
made hereafter as our knowledge extends, are indefinite and inexhaustible;
and since the very first principle of natural classification is that of
forming the classes so that the objects composing each may have the
greatest number of properties in common; this principle prescribes that
every such classification shall recognize and adopt into itself all
distinctions of Kind, which exist among the objects it professes to
classify. To pass over any distinctions of Kind, and substitute definite
distinctions, which, however considerable they may be, do not point to
ulterior unknown differences, would be to replace classes with more by
classes with fewer attributes in common; and would be subversive of the
Natural Method of Classification.

Accordingly all natural arrangements, whether the reality of the
distinction of Kinds was felt or not by their framers, have been led, by
the mere pursuit of their own proper end, to conform themselves to the
distinctions of Kind, so far as these have been ascertained at the time.
The species of Plants are not only real Kinds, but are probably, all of
them, real lowest Kinds, Infimæ Species; which, if we were to subdivide,
as of course it is open to us to do, into sub-classes, the subdivision
would necessarily be founded on _definite_ distinctions, not pointing
(apart from what may be known of their causes or effects) to any
difference beyond themselves.

In so far as a natural classification is grounded on real Kinds, its
groups are certainly not conventional: it is perfectly true that they do
not depend upon an arbitrary choice of the naturalist. But it does not
follow, nor, I conceive, is it true, that these classes are determined by
a type, and not by characters. To determine them by a type would be as
sure a way of missing the Kind, as if we were to select a set of
characters arbitrarily. They are determined by characters, but these are
not arbitrary. The problem is, to find a few definite characters which
point to the multitude of indefinite ones. Kinds are Classes between which
there is an impassable barrier; and what we have to seek is, marks whereby
we may determine on which side of the barrier an object takes its place.
The characters which will best do this should be chosen: if they are also
important in themselves, so much the better. When we have selected the
characters, we parcel out the objects according to those characters, and
not, I conceive, according to resemblance to a type. We do not compose the
species Ranunculus acris, of all plants which bear a satisfactory degree
of resemblance to a model buttercup, but of those which possess certain
characters selected as marks by which we might recognize the possibility
of a common parentage; and the enumeration of those characters is the
definition of the species.

The question next arises, whether, as all Kinds must have a place among
the classes, so all the classes in a natural arrangement must be Kinds?
And to this I answer, certainly not. The distinctions of Kinds are not
numerous enough to make up the whole of a classification. Very few of the
genera of plants, or even of the families, can be pronounced with
certainty to be Kinds. The great distinctions of Vascular and Cellular,
Dicotyledonous or Exogenous and Monocotyledonous or Endogenous plants, are
perhaps differences of kind; the lines of demarcation which divide those
classes seem (though even on this I would not pronounce positively) to go
through the whole nature of the plants. But the different species of a
genus, or genera of a family, usually have in common only a limited number
of characters. A Rose does not seem to differ from a Rubus, or the
Umbelliferæ from the Ranunculaceæ, in much else than the characters
botanically assigned to those genera or those families. Unenumerated
differences certainly do exist in some cases; there are families of plants
which have peculiarities of chemical composition, or yield products having
peculiar effects on the animal economy. The Cruciferæ and Fungi contain an
unusual proportion of nitrogen; the Labiatæ are the chief sources of
essential oils, the Solaneæ are very commonly narcotic, etc. In these and
similar cases there are possibly distinctions of Kind; but it is by no
means indispensable that there should be. Genera and Families may be
eminently natural, though marked out from one another by properties
limited in number; provided those properties are important, and the
objects contained in each genus or family resemble each other more than
they resemble any thing which is excluded from the genus or family.

After the recognition and definition, then, of the _infimæ species_, the
next step is to arrange those _infimæ species_ into larger groups: making
these groups correspond to Kinds wherever it is possible, but in most
cases without any such guidance. And in doing this it is true that we are
naturally and properly guided, in most cases at least, by resemblance to a
type. We form our groups round certain selected Kinds, each of which
serves as a sort of exemplar of its group. But though the groups are
suggested by types, I can not think that a group when formed is
_determined_ by the type; that in deciding whether a species belongs to
the group, a reference is made to the type, and not to the characters;
that the characters “can not be expressed in words.” This assertion is
inconsistent with Dr. Whewell’s own statement of the fundamental principle
of classification, namely, that “general assertions shall be possible.” If
the class did not possess any characters in common, what general
assertions would be possible respecting it? Except that they all resemble
each other more than they resemble any thing else, nothing whatever could
be predicated of the class.

The truth is, on the contrary, that every genus or family is framed with
distinct reference to certain characters, and is composed, first and
principally, of species which agree in possessing all those characters. To
these are added, as a sort of appendix, such other species, generally in
small number, as possess _nearly_ all the properties selected; wanting
some of them one property, some another, and which, while they agree with
the rest _almost_ as much as these agree with one another, do not resemble
in an equal degree any other group. Our conception of the class continues
to be grounded on the characters; and the class might be defined, those
things which _either_ possess that set of characters, _or_ resemble the
things that do so, more than they resemble any thing else.

And this resemblance itself is not, like resemblance between simple
sensations, an ultimate fact, unsusceptible of analysis. Even the inferior
degree of resemblance is created by the possession of common characters.
Whatever resembles the genus Rose more than it resembles any other genus,
does so because it possesses a greater number of the characters of that
genus than of the characters of any other genus. Nor can there be any real
difficulty in representing, by an enumeration of characters, the nature
and degree of the resemblance which is strictly sufficient to include any
object in the class. There are always some properties common to all things
which are included. Others there often are, to which some things, which
are nevertheless included, are exceptions. But the objects which are
exceptions to one character are not exceptions to another; the resemblance
which fails in some particulars must be made up for in others. The class,
therefore, is constituted by the possession of _all_ the characters which
are universal, and _most_ of those which admit of exceptions. If a plant
had the ovules erect, the stigmata divided, possessed the albumen, and was
without stipules, it possibly would not be classed among the Rosaceæ. But
it may want any one, or more than one of these characters, and not be
excluded. The ends of a scientific classification are better answered by
including it. Since it agrees so nearly, in its known properties, with the
sum of the characters of the class, it is likely to resemble that class
more than any other in those of its properties which are still
undiscovered.

Not only, therefore, are natural groups, no less than any artificial
classes, determined by characters; they are constituted in contemplation
of, and by reason of, characters. But it is in contemplation not of those
characters only which are rigorously common to all the objects included in
the group, but of the entire body of characters, all of which are found in
most of those objects, and most of them in all. And hence our conception
of the class, the image in our minds which is representative of it, is
that of a specimen complete in all the characters; most naturally a
specimen which, by possessing them all in the greatest degree in which
they are ever found, is the best fitted to exhibit clearly, and in a
marked manner, what they are. It is by a mental reference to this
standard, not instead of, but in illustration of, the definition of the
class, that we usually and advantageously determine whether any individual
or species belongs to the class or not. And this, as it seems to me, is
the amount of truth contained in the doctrine of Types.

We shall see presently that where the classification is made for the
express purpose of a special inductive inquiry, it is not optional, but
necessary for fulfilling the conditions of a correct Inductive Method,
that we should establish a type-species or genus, namely, the one which
exhibits in the most eminent degree the particular phenomenon under
investigation. But of this hereafter. It remains, for completing the
theory of natural groups, that a few words should be said on the
principles of the nomenclature adapted to them.

§ 5. A Nomenclature in science is, as we have said, a system of the names
of Kinds. These names, like other class-names, are defined by the
enumeration of the characters distinctive of the class. The only merit
which a set of names can have beyond this, is to convey, by the mode of
their construction, as much information as possible: so that a person who
knows the thing, may receive all the assistance which the name can give in
remembering what he knows; while he who knows it not, may receive as much
knowledge respecting it as the case admits of, by merely being told its
name.

There are two modes of giving to the name of a Kind this sort of
significance. The best, but which unfortunately is seldom practicable, is
when the word can be made to indicate, by its formation, the very
properties which it is designed to connote. The name of a Kind does not,
of course, connote all the properties of the Kind, since these are
inexhaustible, but such of them as are sufficient to distinguish it; such
as are sure marks of all the rest. Now, it is very rarely that one
property, or even any two or three properties, can answer this purpose. To
distinguish the common daisy from all other species of plants would
require the specification of many characters. And a name can not, without
being too cumbrous for use, give indication, by its etymology or mode of
construction, of more than a very small number of these. The possibility,
therefore, of an ideally perfect Nomenclature, is probably confined to the
one case in which we are happily in possession of something approaching to
it—the Nomenclature of elementary Chemistry. The substances, whether
simple or compound, with which chemistry is conversant, are Kinds, and, as
such, the properties which distinguish each of them from the rest are
innumerable; but in the case of compound substances (the simple ones are
not numerous enough to require a systematic nomenclature), there is one
property, the chemical composition, which is of itself sufficient to
distinguish the Kind; and is (with certain reservations not yet thoroughly
understood) a sure mark of all the other properties of the compound. All
that was needful, therefore, was to make the name of every compound
express, on the first hearing, its chemical composition; that is, to form
the name of the compound, in some uniform manner, from the names of the
simple substances which enter into it as elements. This was done, most
skillfully and successfully, by the French chemists, though their
nomenclature has become inadequate to the convenient expression of the
very complicated compounds now known to chemists. The only thing left
unexpressed by them was the exact proportion in which the elements were
combined; and even this, since the establishment of the atomic theory, it
has been found possible to express by a simple adaptation of their
phraseology.

But where the characters which must be taken into consideration, in order
sufficiently to designate the Kind, are too numerous to be all signified
in the derivation of the name, and where no one of them is of such
preponderant importance as to justify its being singled out to be so
indicated, we may avail ourselves of a subsidiary resource. Though we can
not indicate the distinctive properties of the Kind, we may indicate its
nearest natural affinities, by incorporating into its name the name of the
proximate natural group of which it is one of the species. On this
principle is founded the admirable binary nomenclature of botany and
zoology. In this nomenclature the name of every species consists of the
name of the genus, or natural group next above it, with a word added to
distinguish the particular species. The last portion of the compound name
is sometimes taken from some _one_ of the peculiarities in which that
species differs from others of the genus; as Clematis _integrifolia_,
Potentilla _alba_, Viola _palustris_, Artemisia _vulgaris_; sometimes from
a circumstance of an historical nature, as Narcissus _poeticus_,
Potentilla _tormentilla_ (indicating that the plant is that which was
formerly known by the latter name), Exacum _Candollii_ (from the fact that
De Candolle was its first discoverer); and sometimes the word is purely
conventional, as Thlaspi _bursapastoris_, Ranunculus _thora_; it is of
little consequence which; since the second, or, as it is usually called,
the specific name, could at most express, independently of convention, no
more than a very small portion of the connotation of the term. But by
adding to this the name of the superior genus, we may make the best amends
we can for the impossibility of so contriving the name as to express all
the distinctive characters of the Kind. We make it, at all events, express
as many of those characters as are common to the proximate natural group
in which the Kind is included. If even those common characters are so
numerous or so little familiar as to require a further extension of the
same resource, we might, instead of a binary, adopt a ternary
nomenclature, employing not only the name of the genus, but that of the
next natural group in order of generality above the genus, commonly called
the Family. This was done in the mineralogical nomenclature proposed by
Professor Mohs. “The names framed by him were not composed of two, but of
three elements, designating respectively the Species, the Genus, and the
Order; thus he has such species as _Rhombohedral Lime Haloide_,
_Octohedral Fluor Haloide_, _Prismatic Hal Baryte_.”(226) The binary
construction, however, has been found sufficient in botany and zoology,
the only sciences in which this general principle has hitherto been
successfully adopted in the construction of a nomenclature.

Besides the advantage which this principle of nomenclature possesses, in
giving to the names of species the greatest quantity of independent
significance which the circumstances of the case admit of, it answers the
further end of immensely economizing the use of names, and preventing an
otherwise intolerable burden on the memory. When the names of species
become extremely numerous, some artifice (as Dr. Whewell(227) observes)
becomes absolutely necessary to make it possible to recollect or apply
them. “The known species of plants, for example, were ten thousand in the
time of Linnæus, and are now probably sixty thousand. It would be useless
to endeavor to frame and employ separate names for each of these species.
The division of the objects into a subordinated system of classification
enables us to introduce a Nomenclature which does not require this
enormous number of names. Each of the genera has its name, and the species
are marked by the addition of some epithet to the name of the genus. In
this manner about seventeen hundred generic names, with a moderate number
of specific names, were found by Linnæus sufficient to designate with
precision all the species of vegetables known at his time.” And though the
number of generic names has since greatly increased, it has not increased
in any thing like the proportion of the multiplication of known species.



                              Chapter VIII.


Of Classification By Series.


§ 1. Thus far, we have considered the principles of scientific
classification so far only as relates to the formation of natural groups;
and at this point most of those who have attempted a theory of natural
arrangement, including, among the rest, Dr. Whewell, have stopped. There
remains, however, another, and a not less important portion of the theory,
which has not yet, as far as I am aware, been systematically treated of by
any writer except M. Comte. This is, the arrangement of the natural groups
into a natural series.(228)

The end of Classification, as an instrument for the investigation of
nature, is (as before stated) to make us think of those objects together
which have the greatest number of important common properties; and which,
therefore, we have oftenest occasion, in the course of our inductions, for
taking into joint consideration. Our ideas of objects are thus brought
into the order most conducive to the successful prosecution of inductive
inquiries generally. But when the purpose is to facilitate some particular
inductive inquiry, more is required. To be instrumental to that purpose,
the classification must bring those objects together, the simultaneous
contemplation of which is likely to throw most light upon the particular
subject. That subject being the laws of some phenomenon or some set of
connected phenomena; the very phenomenon or set of phenomena in question
must be chosen as the groundwork of the classification.

The requisites of a classification intended to facilitate the study of a
particular phenomenon, are, first to bring into one class all Kinds of
things which exhibit that phenomenon, in whatever variety of forms or
degrees; and, secondly, to arrange those Kinds in a series according to
the degree in which they exhibit it, beginning with those which exhibit
most of it, and terminating with those which exhibit least. The principal
example, as yet, of such a classification, is afforded by comparative
anatomy and physiology, from which, therefore, our illustrations shall be
taken.

§ 2. The object being supposed to be, the investigation of the laws of
animal life; the first step, after forming the most distinct conception of
the phenomenon itself, possible in the existing state of our knowledge, is
to erect into one great class (that of animals) all the known Kinds of
beings where that phenomenon presents itself; in however various
combinations with other properties, and in however different degrees. As
some of these Kinds manifest the general phenomenon of animal life in a
very high degree, and others in an insignificant degree, barely sufficient
for recognition; we must, in the next place, arrange the various Kinds in
a series, following one another according to the degrees in which they
severally exhibit the phenomenon; beginning therefore with man, and ending
with the most imperfect kinds of zoophytes.

This is merely saying that we should put the instances, from which the law
is to be inductively collected, into the order which is implied in one of
the four Methods of Experimental Inquiry discussed in the preceding Book;
the fourth Method, that of Concomitant Variations. As formerly remarked,
this is often the only method to which recourse can be had, with assurance
of a true conclusion, in cases in which we have but limited means of
effecting, by artificial experiments, a separation of circumstances
usually conjoined. The principle of the method is, that facts which
increase or diminish together, and disappear together, are either cause
and effect, or effects of a common cause. When it has been ascertained
that this relation really subsists between the variations, a connection
between the facts themselves may be confidently laid down, either as a law
of nature or only as an empirical law, according to circumstances.

That the application of this Method must be preceded by the formation of
such a series as we have described, is too obvious to need being pointed
out; and the mere arrangement of a set of objects in a series, according
to the degrees in which they exhibit some fact of which we are seeking the
law, is too naturally suggested by the necessities of our inductive
operations, to require any lengthened illustration here. But there are
cases in which the arrangement required for the special purpose becomes
the determining principle of the classification of the same objects for
general purposes. This will naturally and properly happen, when those laws
of the objects which are sought in the special inquiry enact so principal
a part in the general character and history of those objects—exercise so
much influence in determining all the phenomena of which they are either
the agents or the theatre—that all other differences existing among the
objects are fittingly regarded as mere modifications of the one phenomenon
sought; effects determined by the co-operation of some incidental
circumstance with the laws of that phenomenon. Thus in the case of
animated beings, the differences between one class of animals and another
may reasonably be considered as mere modifications of the general
phenomenon, animal life; modifications arising either from the different
degrees in which that phenomenon is manifested in different animals, or
from the intermixture of the effects of incidental causes peculiar to the
nature of each, with the effects produced by the general laws of life;
those laws still exercising a predominant influence over the result. Such
being the case, no other inductive inquiry respecting animals can be
successfully carried on, except in subordination to the great inquiry into
the universal laws of animal life; and the classification of animals best
suited to that one purpose, is the most suitable to all the other purposes
of zoological science.

§ 3. To establish a classification of this sort, or even to apprehend it
when established, requires the power of recognizing the essential
similarity of a phenomenon, in its minuter degrees and obscurer forms,
with what is called the _same_ phenomenon in the greatest perfection of
its development; that is, of identifying with each other all phenomena
which differ only in degree, and in properties which we suppose to be
caused by difference of degree. In order to recognize this identity, or,
in other words, this exact similarity of quality, the assumption of a
type-species is indispensable. We must consider as the type of the class,
that among the Kinds included in it, which exhibits the properties
constitutive of the class, in the highest degree; conceiving the other
varieties as instances of degeneracy, as it were, from that type;
deviations from it by inferior intensity of the characteristic property or
properties. For every phenomenon is best studied (_cæteris paribus_) where
it exists in the greatest intensity. It is there that the effects which
either depend on it, or depend on the same causes with it, will also exist
in the greatest degree. It is there, consequently, and only there, that
those effects of it, or joint effects with it, can become fully known to
us, so that we may learn to recognize their smaller degrees, or even their
mere rudiments, in cases in which the direct study would have been
difficult or even impossible. Not to mention that the phenomenon in its
higher degrees may be attended by effects or collateral circumstances
which in its smaller degrees do not occur at all, requiring for their
production in any sensible amount a greater degree of intensity of the
cause than is there met with. In man, for example (the species in which
both the phenomenon of animal and that of organic life exist in the
highest degree), many subordinate phenomena develop themselves in the
course of his animated existence, which the inferior varieties of animals
do not show. The knowledge of these properties may nevertheless be of
great avail toward the discovery of the conditions and laws of the general
phenomenon of life, which is common to man with those inferior animals.
And they are, even, rightly considered as properties of animated nature
itself; because they may evidently be affiliated to the general laws of
animated nature; because we may fairly presume that some rudiments or
feeble degrees of those properties would be recognized in all animals by
more perfect organs, or even by more perfect instruments, than ours; and
because those may be correctly termed properties of a class, which a thing
exhibits exactly in proportion as it belongs to the class, that is, in
proportion as it possesses the main attributes constitutive of the class.

§ 4. It remains to consider how the internal distribution of the series
may most properly take place; in what manner it should be divided into
Orders, Families, and Genera.

The main principle of division must of course be natural affinity; the
classes formed must be natural groups; and the formation of these has
already been sufficiently treated of. But the principles of natural
grouping must be applied in subordination to the principle of a natural
series. The groups must not be so constituted as to place in the same
group things which ought to occupy different points of the general scale.
The precaution necessary to be observed for this purpose is, that the
_primary_ divisions must be grounded not on all distinctions
indiscriminately, but on those which correspond to variations in the
degree of the main phenomenon. The series of Animated Nature should be
broken into parts at the points where the variation in the degree of
intensity of the main phenomenon (as marked by its principal characters,
Sensation, Thought, Voluntary Motion, etc.) begins to be attended by
conspicuous changes in the miscellaneous properties of the animal. Such
well-marked changes take place, for example, where the class Mammalia
ends; at the points where Fishes are separated from Insects, Insects from
Mollusca, etc. When so formed, the primary natural groups will compose the
series by mere juxtaposition, without redistribution; each of them
corresponding to a definite portion of the scale. In like manner each
family should, if possible, be so subdivided, that one portion of it shall
stand higher and the other lower, though of course contiguous, in the
general scale; and only when this is impossible is it allowable to ground
the remaining subdivisions on characters having no determinable connection
with the main phenomenon.

Where the principal phenomenon so far transcends in importance all other
properties on which a classification could be grounded, as it does in the
case of animated existence, any considerable deviation from the rule last
laid down is in general sufficiently guarded against by the first
principle of a natural arrangement, that of forming the groups according
to the most important characters. All attempts at a scientific
classification of animals, since first their anatomy and physiology were
successfully studied, have been framed with a certain degree of
instinctive reference to a natural series, and have accorded in many more
points than they have differed, with the classification which would most
naturally have been grounded on such a series. But the accordance has not
always been complete; and it still is often a matter of discussion, which
of several classifications best accords with the true scale of intensity
of the main phenomenon. Cuvier, for example, has been justly criticised
for having formed his natural groups, with an undue degree of reference to
the mode of alimentation, a circumstance directly connected only with
organic life, and not leading to the arrangement most appropriate for the
purposes of an investigation of the laws of animal life, since both
carnivorous and herbivorous or frugivorous animals are found at almost
every degree in the scale of animal perfection. Blainville’s
classification has been considered by high authorities to be free from
this defect; as representing correctly, by the mere order of the principal
groups, the successive degeneracy of animal nature from its highest to its
most imperfect exemplification.

§ 5. A classification of any large portion of the field of nature in
conformity to the foregoing principles, has hitherto been found
practicable only in one great instance, that of animals. In the case even
of vegetables, the natural arrangement has not been carried beyond the
formation of natural groups. Naturalists have found, and probably will
continue to find it impossible to form those groups into any series, the
terms of which correspond to real gradations in the phenomenon of
vegetative or organic life. Such a difference of degree may be traced
between the class of Vascular Plants and that of Cellular, which includes
lichens, algæ, and other substances whose organization is simpler and more
rudimentary than that of the higher order of vegetables, and which
therefore approach nearer to mere inorganic nature. But when we rise much
above this point, we do not find any sufficient difference in the degree
in which different plants possess the properties of organization and life.
The dicotyledons are of more complex structure, and somewhat more perfect
organization, than the monocotyledons; and some dicotyledonous families,
such as the Compositæ, are rather more complex in their organization than
the rest. But the differences are not of a marked character, and do not
promise to throw any particular light upon the conditions and laws of
vegetable life and development. If they did, the classification of
vegetables would have to be made, like that of animals, with reference to
the scale or series indicated.

Although the scientific arrangements of organic nature afford as yet the
only complete example of the true principles of rational classification,
whether as to the formation of groups or of series, those principles are
applicable to all cases in which mankind are called upon to bring the
various parts of any extensive subject into mental co-ordination. They are
as much to the point when objects are to be classed for purposes of art or
business, as for those of science. The proper arrangement, for example, of
a code of laws, depends on the same scientific conditions as the
classifications in natural history; nor could there be a better
preparatory discipline for that important function, than the study of the
principles of a natural arrangement, not only in the abstract, but in
their actual application to the class of phenomena for which they were
first elaborated, and which are still the best school for learning their
use. Of this the great authority on codification, Bentham, was perfectly
aware; and his early _Fragment on Government_, the admirable introduction
to a series of writings unequaled in their department, contains clear and
just views (as far as they go) on the meaning of a natural arrangement,
such as could scarcely have occurred to any one who lived anterior to the
age of Linnæus and Bernard de Jussieu.



                                 Book V.


ON FALLACIES.


    “Errare non modo affirmando et negando, sed etiam sentiendo, et in
    tacitâ hominum cogitatione contingit.”—HOBBES, _Computatio sive
    Logica_, chap. v.

    “Il leur semble qu’il n’y a qu’à douter par fantaisie, et qu’il
    n’y a qu’à dire en général que notre nature est infirme; que notre
    esprit est plein d’aveuglement: qu’il faut avoir un grand soin de
    se défaire de ses préjugés, et autres choses semblables. Ils
    pensent que cela suffit pour ne plus se laisser séduire à ses
    sens, et pour ne plus se tromper du tout. Il ne suffit pas de dire
    que l’esprit est foible, il faut lui faire sentir ses foiblesses.
    Ce n’est pas assez de dire qu’il est sujet à l’erreur, il faut lui
    découvrir en quoi consistent ses erreurs.”—MALEBRANCHE, _Recherche
    de la Vérité_.



                                Chapter I.


Of Fallacies In General.


§ 1. It is a maxim of the school-men, that “contrariorum eadem est
scientia:” we never really know what a thing is, unless we are also able
to give a sufficient account of its opposite. Conformably to this maxim,
one considerable section, in most treatises on Logic, is devoted to the
subject of Fallacies; and the practice is too well worthy of observance,
to allow of our departing from it. The philosophy of reasoning, to be
complete, ought to comprise the theory of bad as well as of good
reasoning.

We have endeavored to ascertain the principles by which the sufficiency of
any proof can be tested, and by which the nature and amount of evidence
needful to prove any given conclusion can be determined beforehand. If
these principles were adhered to, then although the number and value of
the truths ascertained would be limited by the opportunities, or by the
industry, ingenuity, and patience, of the individual inquirer, at least
error would not be embraced instead of truth. But the general consent of
mankind, founded on their experience, vouches for their being far indeed
from even this negative kind of perfection in the employment of their
reasoning powers.

In the conduct of life—in the practical business of mankind—wrong
inferences, incorrect interpretations of experience, unless after much
culture of the thinking faculty, are absolutely inevitable; and with most
people, after the highest degree of culture they ever attain, such
erroneous inferences, producing corresponding errors in conduct, are
lamentably frequent. Even in the speculations to which eminent intellects
have systematically devoted themselves, and in reference to which the
collective mind of the scientific world is always at hand to aid the
efforts and correct the aberrations of individuals, it is only from the
more perfect sciences, from those of which the subject-matter is the least
complicated, that opinions not resting on a correct induction have at
length, generally speaking, been expelled. In the departments of inquiry
relating to the more complex phenomena of nature, and especially those of
which the subject is man, whether as a moral and intellectual, a social,
or even as a physical being; the diversity of opinions still prevalent
among instructed persons, and the equal confidence with which those of the
most contrary ways of thinking cling to their respective tenets, are proof
not only that right modes of philosophizing are not yet generally adopted
on those subjects, but that wrong ones are; that inquirers have not only
in general missed the truth, but have often embraced error; that even the
most cultivated portion of our species have not yet learned to abstain
from drawing conclusions which the evidence does not warrant.

The only complete safeguard against reasoning ill, is the habit of
reasoning well; familiarity with the principles of correct reasoning, and
practice in applying those principles. It is, however, not unimportant to
consider what are the most common modes of bad reasoning; by what
appearances the mind is most likely to be seduced from the observance of
true principles of induction; what, in short, are the most common and most
dangerous varieties of Apparent Evidence, whereby persons are misled into
opinions for which there does not exist evidence really conclusive.

A catalogue of the varieties of apparent evidence which are not real
evidence, is an enumeration of Fallacies. Without such an enumeration,
therefore, the present work would be wanting in an essential point. And
while writers who included in their theory of reasoning nothing more than
ratiocination, have in consistency with this limitation, confined their
remarks to the fallacies which have their seat in that portion of the
process of investigation; we, who profess to treat of the whole process,
must add to our directions for performing it rightly, warnings against
performing it wrongly in any of its parts: whether the ratiocinative or
the experimental portion of it be in fault, or the fault lie in dispensing
with ratiocination and induction altogether.

§ 2. In considering the sources of unfounded inference, it is unnecessary
to reckon the errors which arise, not from a wrong method, nor even from
ignorance of the right one, but from a casual lapse, through hurry or
inattention, in the application of the true principles of induction. Such
errors, like the accidental mistakes in casting up a sum, do not call for
philosophical analysis or classification; theoretical considerations can
throw no light upon the means of avoiding them. In the present treatise
our attention is required, not to mere inexpertness in performing the
operation in the right way (the only remedies for which are increased
attention and more sedulous practice), but to the modes of performing it
in a way fundamentally wrong; the conditions under which the human mind
persuades itself that it has sufficient grounds for a conclusion which it
has not arrived at by any of the legitimate methods of induction—which it
has not, even carelessly or overhastily, endeavored to test by those
legitimate methods.

§ 3. There is another branch of what may be called the Philosophy of
Error, which must be mentioned here, though only to be excluded from our
subject. The sources of erroneous opinions are twofold, moral and
intellectual. Of these, the moral do not fall within the compass of this
work. They may be classed under two general heads: Indifference to the
attainment of truth, and Bias; of which last the most common case is that
in which we are biased by our wishes; but the liability is almost as great
to the undue adoption of a conclusion which is disagreeable to us, as of
one which is agreeable, if it be of a nature to bring into action any of
the stronger passions. Persons of timid character are the more predisposed
to believe any statement, the more it is calculated to alarm them. Indeed
it is a psychological law, deducible from the most general laws of the
mental constitution of man, that any strong passion renders us credulous
as to the existence of objects suitable to excite it.

But the moral causes of opinions, though with most persons the most
powerful of all, are but remote causes; they do not act directly, but by
means of the intellectual causes; to which they bear the same relation
that the circumstances called, in the theory of medicine, _predisposing_
causes, bear to _exciting_ causes. Indifference to truth can not, in and
by itself, produce erroneous belief; it operates by preventing the mind
from collecting the proper evidences, or from applying to them the test of
a legitimate and rigid induction; by which omission it is exposed
unprotected to the influence of any species of apparent evidence which
offers itself spontaneously, or which is elicited by that smaller quantity
of trouble which the mind may be willing to take. As little is Bias a
direct source of wrong conclusions. We can not believe a proposition only
by wishing, or only by dreading, to believe it. The most violent
inclination to find a set of propositions true, will not enable the
weakest of mankind to believe them without a vestige of intellectual
grounds—without any, even apparent, evidence. It acts indirectly, by
placing the intellectual grounds of belief in an incomplete or distorted
shape before his eyes. It makes him shrink from the irksome labor of a
rigorous induction, when he has a misgiving that its result may be
disagreeable; and in such examination as he does institute, it makes him
exert that which _is_ in a certain measure voluntary, his attention,
unfairly, giving a larger share of it to the evidence which seems
favorable to the desired conclusion, a smaller to that which seems
unfavorable. It operates, too, by making him look out eagerly for reasons,
or apparent reasons, to support opinions which are conformable, or resist
those which are repugnant, to his interests or feelings; and when the
interests or feelings are common to great numbers of persons, reasons are
accepted and pass current, which would not for a moment be listened to in
that character if the conclusion had nothing more powerful than its
reasons to speak in its behalf. The natural or acquired partialities of
mankind are continually throwing up philosophical theories, the sole
recommendation of which consists in the premises they afford for proving
cherished doctrines, or justifying favorite feelings; and when any one of
these theories has been so thoroughly discredited as no longer to serve
the purpose, another is always ready to take its place. This propensity,
when exercised in favor of any widely-spread persuasion or sentiment, is
often decorated with complimentary epithets; and the contrary habit of
keeping the judgment in complete subordination to evidence, is stigmatized
by various hard names, as skepticism, immorality, coldness,
hard-heartedness, and similar expressions according to the nature of the
case. But though the opinions of the generality of mankind, when not
dependent on mere habit and inculcation, have their root much more in the
inclinations than in the intellect, it is a necessary condition to the
triumph of the moral bias that it should first pervert the understanding.
Every erroneous inference, though originating in moral causes, involves
the intellectual operation of admitting insufficient evidence as
sufficient; and whoever was on his guard against all kinds of inconclusive
evidence which can be mistaken for conclusive, would be in no danger of
being led into error even by the strongest bias. There are minds so
strongly fortified on the intellectual side, that they could not blind
themselves to the light of truth, however really desirous of doing so;
they could not, with all the inclination in the world, pass off upon
themselves bad arguments for good ones. If the sophistry of the intellect
could be rendered impossible, that of the feelings, having no instrument
to work with, would be powerless. A comprehensive classification of all
those things which, not being evidence, are liable to appear such to the
understanding, will, therefore, of itself include all errors of judgment
arising from moral causes, to the exclusion only of errors of practice
committed against better knowledge.

To examine, then, the various kinds of apparent evidence which are not
evidence at all, and of apparently conclusive evidence which do not really
amount to conclusiveness, is the object of that part of our inquiry into
which we are about to enter.

The subject is not beyond the compass of classification and comprehensive
survey. The things, indeed, which are not evidence of any given
conclusion, are manifestly endless, and this negative property, having no
dependence on any positive ones, can not be made the groundwork of a real
classification. But the things which, not being evidence, are susceptible
of being mistaken for it, are capable of a classification having reference
to the positive property which they possess of appearing to be evidence.
We may arrange them, at our choice, on either of two principles; according
to the cause which makes them appear to be evidence, not being so; or
according to the particular kind of evidence which they simulate. The
Classification of Fallacies which will be attempted in the ensuing
chapter, is founded on these considerations jointly.



                               Chapter II.


Classification Of Fallacies.


§ 1. In attempting to establish certain general distinctions which shall
mark out from one another the various kinds of Fallacious Evidence, we
propose to ourselves an altogether different aim from that of several
eminent thinkers, who have given, under the name of Political or other
Fallacies, a mere enumeration of a certain number of erroneous opinions;
false general propositions which happen to be often met with; _loci
communes_ of bad arguments on some particular subject. Logic is not
concerned with the false opinions which people happen to entertain, but
with the manner in which they come to entertain them. The question is not,
what facts have at any time been erroneously supposed to be proof of
certain other facts, but what property in the facts it was which led any
one to this mistaken supposition.

When a fact is supposed, though incorrectly, to be evidentiary of, or a
mark of, some other fact, there must be a cause of the error; the supposed
evidentiary fact must be connected in some particular manner with the fact
of which it is deemed evidentiary—must stand in some particular relation
to it, without which relation it would not be regarded in that light. The
relation may either be one resulting from the simple contemplation of the
two facts side by side with one another, or it may depend on some process
of mind, by which a previous association has been established between
them. Some peculiarity of relation, however, there must be; the fact which
can, even by the wildest aberration, be supposed to prove another fact,
must stand in some special position with regard to it; and if we could
ascertain and define that special position, we should perceive the origin
of the error.

We can not regard one fact as evidentiary of another, unless we believe
that the two are always, or in the majority of cases, conjoined. If we
believe A to be evidentiary of B, if when we see A we are inclined to
infer B from it, the reason is because we believe that wherever A is, B
also either always or for the most part exists, either as an antecedent, a
consequent, or a concomitant. If when we see A we are inclined not to
expect B—if we believe A to be evidentiary of the absence of B—it is
because we believe that where A is, B either is never, or at least seldom,
found. Erroneous conclusions, in short, no less than correct conclusions,
have an invariable relation to a general formula, either expressed or
tacitly implied. When we infer some fact from some other fact which does
not really prove it, we either have admitted, or, if we maintained
consistency, ought to admit, some groundless general proposition
respecting the conjunction of the two phenomena.

For every property, therefore, in facts, or in our mode of considering
facts, which leads us to believe that they are habitually conjoined when
they are not, or that they are not when in reality they are, there is a
corresponding kind of Fallacy; and an enumeration of fallacies would
consist in a specification of those properties in facts, and those
peculiarities in our mode of considering them, which give rise to this
erroneous opinion.

§ 2. To begin, then; the supposed connection, or repugnance, between the
two facts, may either be a conclusion from evidence (that is, from some
other proposition or propositions), or may be admitted without any such
ground; admitted, as the phrase is, on its own evidence; embraced as
self-evident, as an axiomatic truth. This gives rise to the first great
distinction, that between Fallacies of Inference and Fallacies of Simple
Inspection. In the latter division must be included not only all cases in
which a proposition is believed and held for true, literally without any
extrinsic evidence, either of specific experience or general reasoning;
but those more frequent cases in which simple inspection creates a
_presumption_ in favor of a proposition; not sufficient for belief, but
sufficient to cause the strict principles of a regular induction to be
dispensed with, and creating a predisposition to believe it on evidence
which would be seen to be insufficient if no such presumption existed.
This class, comprehending the whole of what may be termed Natural
Prejudices, and which I shall call indiscriminately Fallacies of Simple
Inspection or Fallacies _a priori_, shall be placed at the head of our
list.

Fallacies of Inference, or erroneous conclusions from supposed evidence,
must be subdivided according to the nature of the apparent evidence from
which the conclusions are drawn; or (what is the same thing) according to
the particular kind of sound argument which the fallacy in question
simulates. But there is a distinction to be first drawn, which does not
answer to any of the divisions of sound arguments, but arises out of the
nature of bad ones. We may know exactly what our evidence is, and yet draw
a false conclusion from it; we may conceive precisely what our premises
are, what alleged matters of fact, or general principles, are the
foundation of our inference; and yet, because the premises are false, or
because we have inferred from them what they will not support, our
conclusion may be erroneous. But a case, perhaps even more frequent, is
that in which the error arises from not conceiving our premises with due
clearness, that is (as shown in the preceding Book(229)), with due fixity:
forming one conception of our evidence when we collect or receive it, and
another when we make use of it; or unadvisedly, and in general
unconsciously, substituting, as we proceed, different premises in the
place of those with which we set out, or a different conclusion for that
which we undertook to prove. This gives existence to a class of fallacies
which may be justly termed (in a phrase borrowed from Bentham) Fallacies
of Confusion; comprehending, among others, all those which have their
source in language, whether arising from the vagueness or ambiguity of our
terms, or from casual associations with them.

When the fallacy is not one of Confusion, that is, when the proposition
believed, and the evidence on which it is believed, are steadily
apprehended and unambiguously expressed, there remain to be made two cross
divisions. The Apparent Evidence may be either particular facts, or
foregone generalizations; that is, the process may simulate either simple
Induction or Deduction; and again, the evidence, whether consisting of
supposed facts or of general propositions, may be false in itself, or,
being true, may fail to bear out the conclusion attempted to be founded on
it. This gives us first, Fallacies of Induction and Fallacies of
Deduction, and then a subdivision of each of these, according as the
supposed evidence is false, or true but inconclusive.

Fallacies of Induction, where the facts on which the induction proceeds
are erroneous, may be termed Fallacies of Observation. The term is not
strictly accurate, or, rather, not accurately co-extensive with the class
of fallacies which I propose to designate by it. Induction is not always
grounded on facts immediately observed, but sometimes on facts inferred;
and when these last are erroneous, the error may not be, in the literal
sense of the term, an instance of bad observation, but of bad inference.
It will be convenient, however, to make only one class of all the
inductions of which the error lies in not sufficiently ascertaining the
facts on which the theory is grounded; whether the cause of failure be
malobservation, or simple non-observation, and whether the malobservation
be direct, or by means of intermediate marks which do not prove what they
are supposed to prove. And in the absence of any comprehensive term to
denote the ascertainment, by whatever means, of the facts on which an
induction is grounded, I will venture to retain for this class of
fallacies, under the explanation now given, the title of Fallacies of
Observation.

The other class of inductive fallacies, in which the facts are correct,
but the conclusion not warranted by them, are properly denominated
Fallacies of Generalization; and these, again, fall into various
subordinate classes or natural groups, some of which will be enumerated in
their proper place.

When we now turn to Fallacies of Deduction, namely those modes of
incorrect argumentation in which the premises, or some of them, are
general propositions, and the argument a ratiocination; we may of course
subdivide these also into two species similar to the two preceding,
namely, those which proceed on false premises, and those of which the
premises, though true, do not support the conclusion. But of these
species, the first must necessarily fall under some one of the heads
already enumerated. For the error must be either in those premises which
are general propositions, or in those which assert individual facts. In
the former case it is an Inductive Fallacy, of one or the other class; in
the latter it is a Fallacy of Observation; unless, in either case, the
erroneous premise has been assumed on simple inspection, in which case the
fallacy is _a priori_. Or, finally, the premises, of whichever kind they
are, may never have been conceived in so distinct a manner as to produce
any clear consciousness by what means they were arrived at; as in the case
of what is called reasoning in a circle; and then the fallacy is one of
Confusion.

There remain, therefore, as the only class of fallacies having properly
their seat in deduction, those in which the premises of the ratiocination
do not bear out its conclusion; the various cases, in short, of vicious
argumentation, provided against by the rules of the syllogism. We shall
call these, Fallacies of Ratiocination.

§ 3. We must not, however, expect to find that men’s actual errors always,
or even commonly, fall so unmistakably under some one of these classes, as
to be incapable of being referred to any other. Erroneous arguments do not
admit of such a sharply cut division as valid arguments do. An argument
fully stated, with all its steps distinctly set out, in language not
susceptible of misunderstanding, must, if it be erroneous, be so in some
one of these five modes unequivocally; or indeed of the first four, since
the fifth, on such a supposition, would vanish. But it is not in the
nature of bad reasoning to express itself thus unambiguously. When a
sophist, whether he is imposing on himself or attempting to impose on
others, can be constrained to throw his sophistry into so distinct a form,
it needs, in a large proportion of cases, no further exposure.

In all arguments, everywhere but in the schools, some of the links are
suppressed; _a fortiori_ when the arguer either intends to deceive, or is
a lame and inexpert thinker, little accustomed to bring his reasoning
processes to any test; and it is in those steps of the reasoning which are
made in this tacit and half-conscious, or even wholly unconscious manner,
that the error oftenest lurks. In order to detect the fallacy, the
proposition thus silently assumed must be supplied; but the reasoner, most
likely, has never really asked himself what he was assuming; his confuter,
unless permitted to extort it from him by the Socratic mode of
interrogation, must himself judge what the suppressed premise ought to be
in order to support the conclusion. And hence, in the words of Archbishop
Whately, “it must be often a matter of doubt, or, rather, of arbitrary
choice, not only to which genus each _kind_ of fallacy should be referred,
but even to which kind to refer any one _individual_ fallacy; for since,
in any course of argument, _one_ premise is usually suppressed, it
frequently happens in the case of a fallacy, that the hearers are left to
the alternative of supplying _either_ a premise which is _not true_, or
_else_, one which _does not prove_ the conclusion; _e.g._, if a man
expatiates on the distress of the country, and thence argues that the
government is tyrannical, we must suppose him to assume _either_ that
‘every distressed country is under a tyranny,’ which is a manifest
falsehood, _or_ merely that ‘every country under a tyranny is distressed,’
which, however true, proves nothing, the middle term being undistributed.”
The former would be ranked, in our distribution, among fallacies of
generalization, the latter among those of ratiocination. “Which are we to
suppose the speaker meant us to understand? Surely” (if he understood
himself) “just whichever each of his hearers might happen to prefer: some
might assent to the false premise; others allow the unsound syllogism.”

Almost all fallacies, therefore, might in strictness be brought under our
fifth class, Fallacies of Confusion. A fallacy can seldom be absolutely
referred to any of the other classes; we can only say, that if all the
links were filled up which should be capable of being supplied in a valid
argument, it would either stand thus (forming a fallacy of one class), or
thus (a fallacy of another); or at furthest we may say, that the
conclusion is most _likely_ to have originated in a fallacy of such and
such a class. Thus, in the illustration just quoted, the error committed
may be traced with most probability to a fallacy of generalization; that
of mistaking an uncertain mark, or piece of evidence, for a certain one;
concluding from an effect to some one of its possible causes, when there
are others which would have been equally capable of producing it.

Yet, though the five classes run into each other, and a particular error
often seems to be arbitrarily assigned to one of them rather than to any
of the rest, there is considerable use in so distinguishing them. We shall
find it convenient to set apart, as Fallacies of Confusion, those of which
confusion is the most obvious characteristic; in which no other cause can
be assigned for the mistake committed, than neglect or inability to state
the question properly, and to apprehend the evidence with definiteness and
precision. In the remaining four classes I shall place not only the cases
in which the evidence is clearly seen to be what it is, and yet a wrong
conclusion drawn from it, but also those in which, although there be
confusion, the confusion is not the sole cause of the error, but there is
some shadow of a ground for it in the nature of the evidence itself. And
in distributing these cases of partial confusion among the four classes, I
shall, when there can be any hesitation as to the precise seat of the
fallacy, suppose it to be in that part of the process in which, from the
nature of the case, and the tendencies of the human mind, an error would
in the particular circumstances be the most probable.

After these observations we shall proceed, without further preamble, to
consider the five classes in their order.



                               Chapter III.


Fallacies Of Simple Inspection; Or _A Priori_ Fallacies.


§ 1. The tribe of errors of which we are to treat in the first instance,
are those in which no actual inference takes place at all; the proposition
(it can not in such cases be called a conclusion) being embraced, not as
proved, but as requiring no proof; as a self-evident truth; or else as
having such intrinsic verisimilitude, that external evidence not in itself
amounting to proof, is sufficient in aid of the antecedent presumption.

An attempt to treat this subject comprehensively would be a transgression
of the bounds prescribed to this work, since it would necessitate the
inquiry which, more than any other, is the grand question of what is
called metaphysics, viz., What are the propositions which may reasonably
be received without proof? That there must be some such propositions all
are agreed, since there can not be an infinite series of proof, a chain
suspended from nothing. But to determine what these propositions are, is
the _opus magnum_ of the more recondite mental philosophy. Two principal
divisions of opinion on the subject have divided the schools of philosophy
from its first dawn. The one recognizes no ultimate premises but the facts
of our subjective consciousness; our sensations, emotions, intellectual
states of mind, and volitions. These, and whatever by strict rules of
induction can be derived from these, it is possible, according to this
theory, for us to know; of all else we must remain in ignorance. The
opposite school hold that there are other existences, suggested indeed to
our minds by these subjective phenomena, but not inferable from them, by
any process either of deduction or of induction; which, however, we must,
by the constitution of our mental nature, recognize as realities; and
realities, too, of a higher order than the phenomena of our consciousness,
being the efficient causes and necessary substrata of all Phenomena. Among
these entities they reckon Substances, whether matter or spirit; from the
dust under our feet to the soul, and from that to Deity. All these,
according to them, are preternatural or supernatural beings, having no
likeness in experience, though experience is entirely a manifestation of
their agency. Their existence, together with more or less of the laws to
which they conform in their operations, are, on this theory, apprehended
and recognized as real by the mind itself intuitively; experience (whether
in the form of sensation or of mental feeling) having no other part in the
matter than as affording facts which are consistent with these necessary
postulates of reason, and which are explained and accounted for by them.

As it is foreign to the purpose of the present treatise to decide between
these conflicting theories, we are precluded from inquiring into the
existence, or defining the extent and limits, of knowledge _a priori_, and
from characterizing the kind of correct assumption which the fallacy of
incorrect assumption, now under consideration, simulates. Yet since it is
allowed on both sides that such assumptions are often made improperly, we
may find it practicable, without entering into the ultimate metaphysical
grounds of the discussion, to state some speculative propositions, and
suggest some practical cautions, respecting the forms in which such
unwarranted assumptions are most likely to be made.

§ 2. In the cases in which, according to the thinkers of the ontological
school, the mind apprehends, by intuition, things, and the laws of things,
not cognizable by our sensitive faculty; those intuitive, or supposed
intuitive, perceptions are undistinguishable from what the opposite school
are accustomed to call ideas of the mind. When they themselves say that
they perceive the things by an immediate act of a faculty given for that
purpose by their Creator, it would be said of them by their opponents that
they find an idea or conception in their own minds, and from the idea or
conception, infer the existence of a corresponding objective reality. Nor
would this be an unfair statement, but a mere version into other words of
the account given by many of themselves; and one to which the more
clear-sighted of them might, and generally do, without hesitation,
subscribe. Since, therefore, in the cases which lay the strongest claims
to be examples of knowledge _a priori_, the mind proceeds from the idea of
a thing to the reality of the thing itself, we can not be surprised by
finding that illicit assumptions _a priori_ consist in doing the same
thing erroneously; in mistaking subjective facts for objective, laws of
the percipient mind for laws of the perceived object, properties of the
ideas or conceptions for properties of the things conceived.

Accordingly, a large proportion of the erroneous thinking which exists in
the world proceeds on a tacit assumption, that the same order must obtain
among the objects in nature which obtains among our ideas of them. That if
we always think of two things together, the two things must always exist
together. That if one thing makes us think of another as preceding or
following it, that other must precede it or follow it in actual fact. And
conversely, that when we can not conceive two things together they can not
exist together, and that their combination may, without further evidence,
be rejected from the list of possible occurrences.

Few persons, I am inclined to think, have reflected on the great extent to
which this fallacy has prevailed, and prevails, in the actual beliefs and
actions of mankind. For a first illustration of it we may refer to a large
class of popular superstitions. If any one will examine in what
circumstances most of those things agree, which in different ages and by
different portions of the human race have been considered as omens or
prognostics of some interesting event, whether calamitous or fortunate;
they will be found very generally characterized by this peculiarity, that
they cause the mind to _think_ of that, of which they are therefore
supposed to forbode the actual occurrence. “Talk of the devil and he will
appear,” has passed into a proverb. Talk of the devil, that is, raise the
idea, and the reality will follow. In times when the appearance of that
personage in a visible form was thought to be no unfrequent occurrence, it
has doubtless often happened to persons of vivid imagination and
susceptible nerves, that talking of the devil has caused them to fancy
they saw him; as even in our more incredulous days, listening to ghost
stories predisposes us to see ghosts; and thus, as a prop to the _a
priori_ fallacy, there might come to be added an auxiliary fallacy of
malobservation, with one of false generalization grounded on it. Fallacies
of different orders often herd or cluster together in this fashion, one
smoothing the way for another. But the origin of the superstition is
evidently that which we have assigned. In like manner, it has been
universally considered unlucky to speak of misfortune.

The day on which any calamity happened has been considered an unfortunate
day, and there has been a feeling everywhere, and in some nations a
religious obligation, against transacting any important business on that
day. For on such a day our thoughts are likely to be of misfortune. For a
similar reason, any untoward occurrence in commencing an undertaking has
been considered ominous of failure; and often, doubtless, has really
contributed to it by putting the persons engaged in the enterprise more or
less out of spirits; but the belief has equally prevailed where the
disagreeable circumstance was, independently of superstition, too
insignificant to depress the spirits by any influence of its own. All know
the story of Cæsar’s accidentally stumbling in the act of landing on the
African coast; and the presence of mind with which he converted the
direful presage into a favorable one by exclaiming, “Africa, I embrace
thee.” Such omens, it is true, were often conceived as warnings of the
future, given by a friendly or a hostile deity; but this very superstition
grew out of a pre-existing tendency; the god was supposed to send, as an
indication of what was to come, something which people were already
disposed to consider in that light. So in the case of lucky or unlucky
names. Herodotus tells us how the Greeks, on the way to Mycale, were
encouraged in their enterprise by the arrival of a deputation from Samos,
one of the members of which was named Hegesistratus, the leader of armies.

Cases may be pointed out in which something which could have no real
effect but to make persons _think_ of misfortune, was regarded not merely
as a prognostic, but as something approaching to an actual cause of it.
The εὐφήμει of the Greeks, and _favete linguis_, or _bona verba quæso_, of
the Romans, evince the care with which they endeavored to repress the
utterance of any word expressive or suggestive of ill fortune; not from
notions of delicate politeness, to which their general mode of conduct and
feeling had very little reference, but from _bona fide_ alarm lest the
event so suggested to the imagination should in fact occur. Some vestige
of a similar superstition has been known to exist among uneducated persons
even in our own day: it is thought an unchristian thing to talk of, or
suppose, the death of any person while he is alive. It is known how
careful the Romans were to avoid, by an indirect mode of speech, the
utterance of any word directly expressive of death or other calamity; how
instead of _mortuus est_ they said _vixit_; and “be the event fortunate or
_otherwise_” instead of _adverse_. The name Maleventum, of which Salmasius
so sagaciously detected the Thessalian origin (Μαλόεις, Μαλοέντος), they
changed into the highly propitious denomination, Beneventum; Egesta into
Segesta; and Epidamnus, a name so interesting in its associations to the
reader of Thucydides, they exchanged for Dyrrhachium, to escape the perils
of a word suggestive of _damnum_ or detriment.

“If a hare cross the highway,” says Sir Thomas Browne,(230) “there are few
above threescore that are not perplexed thereat; which notwithstanding is
but an augurial terror, according to that received expression,
_Inauspicatum dat iter oblatus lepus_. And the ground of the conceit was
probably no greater than this, that a fearful animal passing by us
portended unto us something to be feared; as upon the like consideration
the meeting of a fox presaged some future imposture.” Such superstitions
as these last must be the result of study; they are too recondite for
natural or spontaneous growth. But when the attempt was once made to
construct a science of predictions, any association, though ever so faint
or remote, by which an object could be connected in however far-fetched a
manner with ideas either of prosperity or of danger and misfortune, was
enough to determine its being classed among good or evil omens.

An example of rather a different kind from any of these, but falling under
the same principle, is the famous attempt on which so much labor and
ingenuity were expended by the alchemists, to make gold potable. The
motive to this was a conceit that potable gold could be no other than the
universal medicine; and why gold? Because it was so precious. It must have
all marvelous properties as a physical substance, because the mind was
already accustomed to marvel at it.

From a similar feeling, “every substance,” says Dr. Paris,(231) “whose
origin is involved in mystery, has at different times been eagerly applied
to the purposes of medicine. Not long since, one of those showers which
are now known to consist of the excrements of insects, fell in the north
of Italy; the inhabitants regarded it as manna, or some supernatural
panacea, and they swallowed it with such avidity, that it was only by
extreme address that a small quantity was obtained for a chemical
examination.” The superstition, in this instance, though doubtless partly
of a religious character, probably in part also arose from the prejudice
that a wonderful thing must of course have wonderful properties.

§ 3. The instances of _a priori_ fallacy which we have hitherto cited
belong to the class of vulgar errors, and do not now, nor in any but a
rude age ever could, impose upon minds of any considerable attainments.
But those to which we are about to proceed, have been, and still are, all
but universally prevalent among thinkers. The same disposition to give
objectivity to a law of the mind—to suppose that what is true of our ideas
of things must be true of the things themselves—exhibits itself in many of
the most accredited modes of philosophical investigation, both on physical
and on metaphysical subjects. In one of its most undisguised
manifestations, it embodies itself in two maxims, which lay claim to
axiomatic truth: Things which we can not think of together, can not
co-exist; and Things which we can not help thinking of together, must
co-exist. I am not sure that the maxims were ever expressed in these
precise words, but the history both of philosophy and of popular opinions
abounds with exemplifications of both forms of the doctrine.

To begin with the latter of them: Things which we can not think of except
together, must exist together. This is assumed in the generally received
and accredited mode of reasoning which concludes that A must accompany B
in point of fact, because “it is involved in the idea.” Such thinkers do
not reflect that the idea, being a result of abstraction, ought to conform
to the facts, and can not make the facts conform to it. The argument is at
most admissible as an appeal to authority; a surmise, that what is now
part of the idea, must, before it became so, have been found by previous
inquirers in the facts. Nevertheless, the philosopher who more than all
others made professions of rejecting authority, Descartes, constructed his
system on this very basis. His favorite device for arriving at truth, even
in regard to outward things, was by looking into his own mind for it.
“Credidi me,” says his celebrated maxim, “pro regulâ generali sumere
posse, omne id quod valdè dilucidè et distinctè concipiebam, verum esse;”
whatever can be very clearly conceived must certainly exist; that is, as
he afterward explains it, if the idea includes existence. And on this
ground he infers that geometrical figures really exist, because they can
be distinctly conceived. Whenever existence is “involved in an idea,” a
thing conformable to the idea must really exist; which is as much as to
say, whatever the idea contains must have its equivalent in the thing; and
what we are not able to leave out of the idea can not be absent from the
reality.(232) This assumption pervades the philosophy not only of
Descartes, but of all the thinkers who received their impulse mainly from
him, in particular the two most remarkable among them, Spinoza and
Leibnitz, from whom the modern German metaphysical philosophy is
essentially an emanation. I am indeed disposed to think that the fallacy
now under consideration has been the cause of two-thirds of the bad
philosophy, and especially of the bad metaphysics, which the human mind
has never ceased to produce. Our general ideas contain nothing but what
has been put into them, either by our passive experience, or by our active
habits of thought; and the metaphysicians in all ages, who have attempted
to construct the laws of the universe by reasoning from our supposed
necessities of thought, have always proceeded, and only could proceed, by
laboriously finding in their own minds what they themselves had formerly
put there, and evolving from their ideas of things what they had first
involved in those ideas. In this way all deeply-rooted opinions and
feelings are enabled to create apparent demonstrations of their truth and
reasonableness, as it were, out of their own substance.

The other form of the fallacy: Things which we can not think of together
can not exist together—including as one of its branches, that what we can
not think of as existing can not exist at all—may thus be briefly
expressed: Whatever is inconceivable must be false.

Against this prevalent doctrine I have sufficiently argued in a former
Book,(233) and nothing is required in this place but examples. It was long
held that Antipodes were impossible because of the difficulty which was
found in conceiving persons with their heads in the same direction as our
feet. And it was one of the received arguments against the Copernican
system, that we can not conceive so great a void space as that system
supposes to exist in the celestial regions. When men’s imaginations had
always been used to conceive the stars as firmly set in solid spheres,
they naturally found much difficulty in imagining them in so different,
and, as it doubtless appeared to them, so precarious a situation. But they
had no right to mistake the limitation (whether natural, or, as it in fact
proved, only artificial) of their own faculties, for an inherent
limitation of the possible modes of existence in the universe.

It may be said in objection, that the error in these cases was in the
minor premise, not the major; an error of fact, not of principle; that it
did not consist in supposing that what is inconceivable can not be true,
but in supposing antipodes to be inconceivable, when present experience
proves that they can be conceived. Even if this objection were allowed,
and the proposition that what is inconceivable can not be true were
suffered to remain unquestioned as a speculative truth, it would be a
truth on which no practical consequence could ever be founded, since, on
this showing, it is impossible to affirm of any proposition, not being a
contradiction in terms, that it is inconceivable. Antipodes were really,
not fictitiously, inconceivable to our ancestors: they are indeed
conceivable to us; and as the limits of our power of conception have been
so largely extended, by the extension of our experience and the more
varied exercise of our imagination, so may posterity find many
combinations perfectly conceivable to them which are inconceivable to us.
But, as beings of limited experience, we must always and necessarily have
limited conceptive powers; while it does not by any means follow that the
same limitation obtains in the possibilities of Nature, nor even in her
actual manifestations.

Rather more than a century and a half ago it was a scientific maxim,
disputed by no one, and which no one deemed to require any proof, that “a
thing can not act where it is not.”(234) With this weapon the Cartesians
waged a formidable war against the theory of gravitation, which, according
to them, involving so obvious an absurdity, must be rejected _in limine_:
the sun could not possibly act upon the earth, not being there. It was not
surprising that the adherents of the old systems of astronomy should urge
this objection against the new; but the false assumption imposed equally
on Newton himself, who, in order to turn the edge of the objection,
imagined a subtle ether which filled up the space between the sun and the
earth, and by its intermediate agency was the proximate cause of the
phenomena of gravitation. “It is inconceivable,” said Newton, in one of
his letters to Dr. Bentley,(235) “that inanimate brute matter should,
without the mediation of something else, which is not material, operate
upon and affect other matter _without mutual contact_.... That gravity
should be innate, inherent, and essential to matter, so that one body may
act on another, at a distance, through a vacuum, without the mediation of
any thing else, by and through which their action and force may be
conveyed from one to another, is to me so great an absurdity, that I
believe no man, who in philosophical matters has a competent faculty of
thinking, can ever fall into it.” This passage should be hung up in the
cabinet of every cultivator of science who is ever tempted to pronounce a
fact impossible because it appears to him inconceivable. In our own day
one would be more tempted, though with equal injustice, to reverse the
concluding observation, and consider the seeing any absurdity at all in a
thing so simple and natural, to be what really marks the absence of “a
competent faculty of thinking.” No one now feels any difficulty in
conceiving gravity to be, as much as any other property is, “inherent and
essential to matter,” nor finds the comprehension of it facilitated in the
smallest degree by the supposition of an ether (though some recent
inquirers do give this as an explanation of it); nor thinks it at all
incredible that the celestial bodies can and do act where they, in actual
bodily presence, are not. To us it is not more wonderful that bodies
should act upon one another “without mutual contact,” than that they
should do so when in contact; we are familiar with both these facts, and
we find them equally inexplicable, but equally easy to believe. To Newton,
the one, because his imagination was familiar with it, appeared natural
and a matter of course, while the other, for the contrary reason, seemed
too absurd to be credited.

It is strange that any one, after such a warning, should rely implicitly
on the evidence _a priori_ of such propositions as these, that matter can
not think; that space, or extension, is infinite; that nothing can be made
out of nothing (_ex nihilo nihil fit_). Whether these propositions are
true or not this is not the place to determine, nor even whether the
questions are soluble by the human faculties. But such doctrines are no
more self-evident truths, than the ancient maxim that a thing can not act
where it is not, which probably is not now believed by any educated person
in Europe.(236) Matter can not think; why? because we _can not conceive_
thought to be annexed to any arrangement of material particles. Space is
infinite, because having never known any part of it which had not other
parts beyond it, we _can not conceive_ an absolute termination. _Ex nihilo
nihil fit_, because having never known any physical product without a
pre-existing physical material, we _can not_, or think we can not,
_imagine_ a creation out of nothing. But these things may in themselves be
as conceivable as gravitation without an intervening medium, which Newton
thought too great an absurdity for any person of a competent faculty of
philosophical thinking to admit: and even supposing them not conceivable,
this, for aught we know, may be merely one of the limitations of our very
limited minds, and not in nature at all.

No writer has more directly identified himself with the fallacy now under
consideration, or has embodied it in more distinct terms, than Leibnitz.
In his view, unless a thing was not merely conceivable, but even
explainable, it could not exist in nature. All _natural_ phenomena,
according to him, must be susceptible of being accounted for _a priori_.
The only facts of which no explanation could be given but the will of God,
were miracles properly so called. “Je reconnais,” says he,(237) “qu’il
n’est pas permis de nier ce qu’on n’entend pas; mais j’ajoute qu’on a
droit de nier (au moins dans l’ordre naturel) ce que absolument n’est
point intelligible ni explicable. Je soutiens aussi ... qu’enfin la
conception des créatures n’est pas la mesure du pouvoir de Dieu, mais que
leur conceptivité, ou force de concevoir, est la mesure du pouvoir de la
nature, tout ce qui est conforme à l’ordre naturel pouvant être conçu ou
entendu par quelque créature.”

Not content with assuming that nothing can be true which we are unable to
conceive, scientific inquirers have frequently given a still further
extension to the doctrine, and held that, even of things not altogether
inconceivable, that which we can conceive with the greatest ease is
likeliest to be true. It was long an admitted axiom, and is not yet
entirely discredited, that “nature always acts by the simplest means,”
_i.e._, by those which are most easily conceivable.(238) A large
proportion of all the errors ever committed in the investigation of the
laws of nature, have arisen from the assumption that the most familiar
explanation or hypothesis must be the truest.

One of the most instructive facts in scientific history is the pertinacity
with which the human mind clung to the belief that the heavenly bodies
must move in circles, or be carried round by the revolution of spheres;
merely because those were in themselves the simplest suppositions: though,
to make them accord with the facts which were ever contradicting them more
and more, it became necessary to add sphere to sphere and circle to
circle, until the original simplicity was converted into almost
inextricable complication.

§ 4. We pass to another _a priori_ fallacy or natural prejudice, allied to
the former, and originating, as that does, in the tendency to presume an
exact correspondence between the laws of the mind and those of things
external to it. The fallacy may be enunciated in this general
form—Whatever can be thought of apart exists apart: and its most
remarkable manifestation consists in the personification of abstractions.
Mankind in all ages have had a strong propensity to conclude that wherever
there is a name, there must be a distinguishable separate entity
corresponding to the name; and every complex idea which the mind has
formed for itself by operating upon its conceptions of individual things,
was considered to have an outward objective reality answering to it. Fate,
Chance, Nature, Time, Space, were real beings, nay, even gods. If the
analysis of qualities in the earlier part of this work be correct, names
of qualities and names of substances stand for the very same sets of facts
or phenomena; _whiteness_ and _a white thing_ are only different phrases,
required by convenience for speaking of the same external fact under
different relations. Not such, however, was the notion which this verbal
distinction suggested of old, either to the vulgar or to the scientific.
Whiteness was an entity, inhering or sticking in the white substance: and
so of all other qualities. So far was this carried, that even concrete
general terms were supposed to be, not names of indefinite numbers of
individual substances, but names of a peculiar kind of entities termed
Universal Substances. Because we can think and speak of man in general,
that is, of all persons in so far as possessing the common attributes of
the species, without fastening our thoughts permanently on some one
individual person; therefore man in general was supposed to be, not an
aggregate of individual persons, but an abstract or universal man,
distinct from these.

It may be imagined what havoc metaphysicians trained in these habits made
with philosophy, when they came to the largest generalizations of all.
_Substantiæ Secundæ_ of any kind were bad enough, but such Substantiæ
Secundæ as τὸ ὄν, for example, and τὸ ἔν, standing for peculiar entities
supposed to be inherent in all things which _exist_, or in all which are
said to be _one_, were enough to put an end to all intelligible
discussion; especially since, with a just perception that the truths which
philosophy pursues are _general_ truths, it was soon laid down that these
general substances were the only subjects of science, being immutable,
while individual substances cognizable by the senses, being in a perpetual
flux, could not be the subject of real knowledge. This misapprehension of
the import of general language constitutes Mysticism, a word so much
oftener written and spoken than understood. Whether in the Vedas, in the
Platonists, or in the Hegelians, mysticism is neither more nor less than
ascribing objective existence to the subjective creations of our own
faculties, to ideas or feelings of the mind; and believing that by
watching and contemplating these ideas of its own making, it can read in
them what takes place in the world without.

§ 5. Proceeding with the enumeration of _a priori_ fallacies, and
endeavoring to arrange them with as much reference as possible to their
natural affinities, we come to another, which is also nearly allied to the
fallacy preceding the last, standing in the same relation to one variety
of it as the fallacy last mentioned does to the other. This, too,
represents nature as under incapacities corresponding to those of our
intellect; but instead of only asserting that nature can not do a thing
because we can not conceive it done, goes the still greater length of
averring that nature does a particular thing, on the sole ground that we
can see no reason why she should not. Absurd as this seems when so plainly
stated, it is a received principle among scientific authorities for
demonstrating _a priori_ the laws of physical phenomena. A phenomenon must
follow a certain law, because we see no reason why it should deviate from
that law in one way rather than in another. This is called the Principle
of the Sufficient Reason;(239) and by means of it philosophers often
flatter themselves that they are able to establish, without any appeal to
experience, the most general truths of experimental physics.

Take, for example, two of the most elementary of all laws, the law of
inertia and the first law of motion. A body at rest can not, it is
affirmed, begin to move unless acted upon by some external force; because,
if it did, it must either move up or down, forward or backward, and so
forth; but if no outward force acts upon it, there can be _no reason_ for
its moving up rather than down, or down rather than up, etc., _ergo_, it
will not move at all.

This reasoning I conceive to be entirely fallacious, as indeed Dr. Brown,
in his treatise on Cause and Effect, has shown with great acuteness and
justness of thought. We have before remarked, that almost every fallacy
may be referred to different genera by different modes of filling up the
suppressed steps; and this particular one may, at our option, be brought
under _petitio principii_. It supposes that nothing can be a “sufficient
reason” for a body’s moving in one particular direction, except some
external force. But this is the very thing to be proved. Why not some
_internal_ force? Why not the law of the thing’s own nature? Since these
philosophers think it necessary to prove the law of inertia, they of
course do not suppose _it_ to be self-evident; they must, therefore, be of
opinion that previously to all proof, the supposition of a body’s moving
by internal impulse is an admissible hypothesis; but if so, why is not the
hypothesis also admissible, that the internal impulse acts naturally in
some one particular direction, not in another? If spontaneous motion might
have been the law of matter, why not spontaneous motion toward the sun,
toward the earth, or toward the zenith? Why not, as the ancients supposed,
toward a particular place in the universe, appropriated to each particular
kind of substance? Surely it is not allowable to say that spontaneity of
motion is credible in itself, but not credible if supposed to take place
in any determinate direction.

Indeed, if any one chose to assert that all bodies when uncontrolled set
out in a direct line toward the North Pole, he might equally prove his
point by the principle of the Sufficient Reason. By what right is it
assumed that a state of rest is the particular state which can not be
deviated from without special cause? Why not a state of motion, and of
some particular sort of motion? Why may we not say that the natural state
of a horse left to himself is to amble, because otherwise he must either
trot, gallop, or stand still, and because we know no reason why he should
do one of these rather than another? If this is to be called an unfair use
of the “sufficient reason,” and the other a fair one, there must be a
tacit assumption that a state of rest is more natural to a horse than a
state of ambling. If this means that it is the state which the animal will
assume when left to himself, that is the very point to be proved; and if
it does not mean this, it can only mean that a state of rest is the
simplest state, and therefore the most likely to prevail in nature, which
is one of the fallacies or natural prejudices we have already examined.

So again of the First Law of Motion; that a body once moving will, if left
to itself, continue to move uniformly in a straight line. An attempt is
made to prove this law by saying, that if not, the body must deviate
either to the right or to the left, and that there is no reason why it
should do one more than the other. But who could know, antecedently to
experience, whether there was a reason or not? Might it not be the nature
of bodies, or of some particular bodies, to deviate toward the right? or
if the supposition is preferred, toward the east, or south? It was long
thought that bodies, terrestrial ones at least, had a natural tendency to
deflect downward; and there is no shadow of any thing objectionable in the
supposition, except that it is not true. The pretended proof of the law of
motion is even more manifestly untenable than that of the law of inertia,
for it is flagrantly inconsistent; it assumes that the continuance of
motion in the direction first taken is more natural than deviation either
to the right or to the left, but denies that one of these can possibly be
more natural than the other. All these fancies of the possibility of
knowing what is natural or not natural by any other means than experience,
are, in truth, entirely futile. The real and only proof of the laws of
motion, or of any other law of the universe, is experience; it is simply
that no other suppositions explain or are consistent with the facts of
universal nature.

Geometers have, in all ages, been open to the imputation of endeavoring to
prove the most general facts of the outward world by sophistical
reasoning, in order to avoid appeals to the senses. Archimedes, says
Professor Playfair,(240) established some of the elementary propositions
of statics by a process in which he “borrows no principle from experiment,
but establishes his conclusion entirely by reasoning _a priori_. He
assumes, indeed, that equal bodies, at the ends of the equal arms of a
lever, will balance one another; and also that a cylinder or
parallelopiped of homogeneous matter, will be balanced about its centre of
magnitude. These, however, are not inferences from experience; they are,
properly speaking, conclusions deduced from the principle of the
Sufficient Reason.” And to this day there are few geometers who would not
think it far more scientific to establish these or any other premises in
this way, than to rest their evidence on that familiar experience which in
the case in question might have been so safely appealed to.

§ 6. Another natural prejudice, of most extensive prevalence, and which
had a great share in producing the errors fallen into by the ancients in
their physical inquiries, was this: That the differences in nature must
correspond to our received distinctions: that effects which we are
accustomed, in popular language, to call by different names, and arrange
in different classes, must be of different natures, and have different
causes. This prejudice, so evidently of the same origin with those already
treated of, marks more especially the earliest stage of science, when it
has not yet broken loose from the trammels of every-day phraseology. The
extraordinary prevalence of the fallacy among the Greek philosophers may
be accounted for by their generally knowing no other language than their
own; from which it was a consequence that their ideas followed the
accidental or arbitrary combinations of that language, more completely
than can happen among the moderns to any but illiterate persons. They had
great difficulty in distinguishing between things which their language
confounded, or in putting mentally together things which it distinguished;
and could hardly combine the objects in nature, into any classes but those
which were made for them by the popular phrases of their own country; or
at least could not help fancying those classes to be natural and all
others arbitrary and artificial. Accordingly, scientific investigation
among the Greek schools of speculation and their followers in the Middle
Ages, was little more than a mere sifting and analyzing of the notions
attached to common language. They thought that by determining the meaning
of words, they could become acquainted with facts. “They took for
granted,” says Dr. Whewell,(241) “that philosophy must result from the
relations of those notions which are involved in the common use of
language, and they proceeded to seek it by studying such notions.” In his
next chapter, Dr. Whewell has so well illustrated and exemplified this
error, that I shall take the liberty of quoting him at some length.

“The propensity to seek for principles in the common usages of language
may be discerned at a very early period. Thus we have an example of it in
a saying which is reported of Thales, the founder of Greek philosophy.
When he was asked, ‘What is the _greatest_ thing?’ he replied ‘_Place_;
for all other things are _in_ the world, but the world is _in_ it.’ In
Aristotle we have the consummation of this mode of speculation. The usual
point from which he starts in his inquiries is, that _we say_ thus or thus
in common language. Thus, when he has to discuss the question whether
there be, in any part of the universe, a void, or space in which there is
nothing, he inquires first in how many senses we say that one thing is
_in_ another. He enumerates many of these; we say the part is in the
whole, as the finger is _in_ the hand; again we say, the species is in the
genus, as man is included _in_ animal; again, the government of Greece is
_in_ the king; and various other senses are described and exemplified, but
of all these _the most proper_ is when we say a thing is _in_ a vessel,
and generally _in place_. He next examines what _place_ is, and comes to
this conclusion, that ‘if about a body there be another body including it,
it is in place, and if not, not.’ A body moves when it changes its place;
but he adds, that if water be in a vessel, the vessel being at rest, the
parts of the water may still move, for they are included by each other; so
that while the whole does not change its place, the parts may change their
place in a circular order. Proceeding then to the question of a _void_, he
as usual examines the different senses in which the term is used, and
adopts as the most proper, _place without matter_, with no useful result.

“Again, in a question concerning mechanical action, he says, ‘When a man
moves a stone by pushing it with a stick, _we_ say both that the man moves
the stone, and that the stick moves the stone, but the latter _more
properly_.’

“Again, we find the Greek philosophers applying themselves to extract
their dogmas from the most general and abstract notions which they could
detect; for example, from the conception of the Universe as One or as Many
things. They tried to determine how far we may, or must, combine with
these conceptions that of a whole, of parts, of number, of limits, of
place, of beginning or end, of full or void, of rest or motion, of cause
and effect, and the like. The analysis of such conceptions with such a
view, occupies, for instance, almost the whole of Aristotle’s Treatise on
the Heavens.”

The following paragraph merits particular attention: “Another mode of
reasoning, very widely applied in these attempts, was the _doctrine of
contrarieties_, in which it was assumed that adjectives or substances
which are in common language, or in some abstract mode of conception,
opposed to each other, must point at some fundamental antithesis in
nature, which it is important to study. Thus Aristotle says that the
Pythagoreans, from the contrasts which number suggests, collected ten
principles—Limited and Unlimited, Odd and Even, One and Many, Right and
Left, Male and Female, Rest and Motion, Straight and Curved, Light and
Darkness, Good and Evil, Square and Oblong.... Aristotle himself deduced
the doctrine of four elements and other dogmas by oppositions of the same
kind.”

Of the manner in which, from premises obtained in this way, the ancients
attempted to deduce laws of nature, an example is given in the same work a
few pages further on. “Aristotle decides that there is no void on such
arguments as this. In a void there could be no difference of up and down;
for as in nothing there are no differences, so there are none in a
privation or negation; but a void is merely a privation or negation of
matter; therefore, in a void, bodies could not move up and down, which it
is in their nature to do. It is easily seen” (Dr. Whewell very justly
adds) “that such a mode of reasoning elevates the familiar forms of
language, and the intellectual connections of terms, to a supremacy over
facts; making truth depend upon whether terms are or are not privative,
and whether we say that bodies fall _naturally_.”

The propensity to assume that the same relations obtain between objects
themselves, which obtain between our ideas of them, is here seen in the
extreme stage of its development. For the mode of philosophizing,
exemplified in the foregoing instances, assumes no less than that the
proper way of arriving at knowledge of nature, is to study nature itself
subjectively; to apply our observation and analysis not to the facts, but
to the common notions entertained of the facts.

Many other equally striking examples may be given of the tendency to
assume that things which for the convenience of common life are placed in
different classes, must differ in every respect. Of this nature was the
universal and deeply-rooted prejudice of antiquity and the Middle Ages,
that celestial and terrestrial phenomena must be essentially different,
and could in no manner or degree depend on the same laws. Of the same
kind, also, was the prejudice against which Bacon contended, that nothing
produced by nature could be successfully imitated by man: “Calorem solis
et ignis toto genere differre; ne scilicet homines putent se per opera
ignis, aliquid simile iis quæ in Natura fiunt, educere et formare posse;”
and again, “Compositionem tantum opus Hominis, Mistionem vero opus solius
Naturæ esse: ne scilicet homines sperent aliquam ex arte Corporum
naturalium generationem aut transformationem.”(242) The grand distinction
in the ancient scientific speculations, between natural and violent
motions, though not without a plausible foundation in the appearances
themselves, was doubtless greatly recommended to adoption by its
conformity to this prejudice.

§ 7. From the fundamental error of the scientific inquirers of antiquity,
we pass, by a natural association, to a scarcely less fundamental one of
their great rival and successor, Bacon. It has excited the surprise of
philosophers that the detailed system of inductive logic, which this
extraordinary man labored to construct, has been turned to so little
direct use by subsequent inquirers, having neither continued, except in a
few of its generalities, to be recognized as a theory, nor having
conducted in practice to any great scientific results. But this, though
not unfrequently remarked, has scarcely received any plausible
explanation; and some, indeed, have preferred to assert that all rules of
induction are useless, rather than suppose that Bacon’s rules are grounded
on an insufficient analysis of the inductive process. Such, however, will
be seen to be the fact, as soon as it is considered, that Bacon entirely
overlooked Plurality of Causes. All his rules tacitly imply the
assumption, so contrary to all we now know of nature, that a phenomenon
can not have more than one cause.

When he is inquiring into what he terms the forma _calidi aut frigidi,
gravis aut levis, sicci aut humidi_, and the like, he never for an instant
doubts that there is some one thing, some invariable condition or set of
conditions, which is present in all cases of heat, or cold, or whatever
other phenomenon he is considering; the only difficulty being to find what
it is; which accordingly he tries to do by a process of elimination,
rejecting or excluding, by negative instances, whatever is not the _forma_
or cause, in order to arrive at what is. But, that this _forma_ or cause
is _one_ thing, and that it is the same in all hot objects, he has no more
doubt of, than another person has that there is always some cause _or
other_. In the present state of knowledge it could not be necessary, even
if we had not already treated so fully of the question, to point out how
widely this supposition is at variance with the truth. It is particularly
unfortunate for Bacon that, falling into this error, he should have fixed
almost exclusively upon a class of inquiries in which it was especially
fatal; namely, inquiries into the causes of the sensible qualities of
objects. For his assumption, groundless in every case, is false in a
peculiar degree with respect to those sensible qualities. In regard to
scarcely any of them has it been found possible to trace any unity of
cause, any set of conditions invariably accompanying the quality. The
conjunctions of such qualities with one another constitute the variety of
Kinds, in which, as already remarked, it has not been found possible to
trace any law. Bacon was seeking for what did not exist. The phenomenon of
which he sought for the one cause has oftenest no cause at all, and when
it has, depends (as far as hitherto ascertained) on an unassignable
variety of distinct causes.

And on this rock every one must split, who represents to himself as the
first and fundamental problem of science to ascertain what is the cause of
a given effect, rather than what are the effects of a given cause. It was
shown, in an early stage of our inquiry into the nature of Induction,(243)
how much more ample are the resources which science commands for the
latter than for the former inquiry, since it is upon the latter only that
we can throw any direct light by means of experiment; the power of
artificially producing an effect, implying a previous knowledge of at
least one of its causes. If we discover the causes of effects, it is
generally by having previously discovered the effects of causes; the
greatest skill in devising crucial instances for the former purpose may
only end, as Bacon’s physical inquiries did, in no result at all. Was it
that his eagerness to acquire the power of producing for man’s benefit
effects of practical importance to human life, rendering him impatient of
pursuing that end by a circuitous route, made even him, the champion of
experiment, prefer the direct mode, though one of mere observation, to the
indirect, in which alone experiment was possible? Or had even Bacon not
entirely cleared his mind from the notion of the ancients, that “rerum
cognoscere _causas_” was the sole object of philosophy, and that to
inquire into the _effects_ of things belonged to servile and mechanical
arts?

It is worth remarking that, while the only efficient mode of cultivating
speculative science was missed from an undue contempt of manual
operations, the false speculative views thus engendered gave in their turn
a false direction to such practical and mechanical aims as were suffered
to exist. The assumption universal among the ancients and in the Middle
Ages, that there were _principles_ of heat and cold, dryness and moisture,
etc., led directly to a belief in alchemy; in a transmutation of
substances, a change from one Kind into another. Why should it not be
possible to make gold? Each of the characteristic properties of gold has
its _forma_, its essence, its set of conditions, which if we could
discover, and learn how to realize, we could superinduce that particular
property upon any other substance, upon wood, or iron, or lime, or clay.
If, then, we could effect this with respect to every one of the essential
properties of the precious metal, we should have converted the other
substance into gold. Nor did this, if once the premises were granted,
appear to transcend the real powers of mankind. For daily experience
showed that almost every one of the distinctive sensible properties of any
object, its consistence, its color, its taste, its smell, its shape,
admitted of being totally changed by fire, or water, or some other
chemical agent. The _formæ_ of all those qualities seeming, therefore, to
be within human power either to produce or to annihilate, not only did the
transmutation of substances appear abstractedly possible, but the
employment of the power, at our choice, for practical ends, seemed by no
means hopeless.(244)

A prejudice, universal in the ancient world, and from which Bacon was so
far from being free, that it pervaded and vitiated the whole practical
part of his system of logic, may with good reason be ranked high in the
order of Fallacies of which we are now treating.

§ 8. There remains one _a priori_ fallacy or natural prejudice, the most
deeply-rooted, perhaps, of all which we have enumerated; one which not
only reigned supreme in the ancient world, but still possesses almost
undisputed dominion over many of the most cultivated minds; and some of
the most remarkable of the numerous instances by which I shall think it
necessary to exemplify it, will be taken from recent thinkers. This is,
that the conditions of a phenomenon must, or at least probably will,
resemble the phenomenon itself.

Conformably to what we have before remarked to be of frequent occurrence,
this fallacy might without much impropriety have been placed in a
different class, among Fallacies of Generalization; for experience does
afford a certain degree of countenance to the assumption. The cause does,
in very many cases, resemble its effect; like produces like. Many
phenomena have a direct tendency to perpetuate their own existence, or to
give rise to other phenomena similar to themselves. Not to mention forms
actually moulded on one another, as impressions on wax and the like, in
which the closest resemblance between the effect and its cause is the very
law of the phenomenon; all motion tends to continue itself, with its own
velocity, and in its own original direction; and the motion of one body
tends to set others in motion, which is indeed the most common of the
modes in which the motions of bodies originate. We need scarcely refer to
contagion, fermentation, and the like; or to the production of effects by
the growth or expansion of a germ or rudiment resembling on a smaller
scale the completed phenomenon, as in the growth of a plant or animal from
an embryo, that embryo itself deriving its origin from another plant or
animal of the same kind. Again, the thoughts or reminiscences, which are
effects of our past sensations, resemble those sensations; feelings
produce similar feelings by way of sympathy; acts produce similar acts by
involuntary or voluntary imitation. With so many appearances in its favor,
no wonder if a presumption naturally grew up, that causes must
_necessarily_ resemble their effects, and that like could _only_ be
produced by like.

This principle of fallacy has usually presided over the fantastical
attempts to influence the course of nature by conjectural means, the
choice of which was not directed by previous observation and experiment.
The guess almost always fixed upon some means which possessed features of
real or apparent resemblance to the end in view. If a charm was wanted, as
by Ovid’s Medea, to prolong life, all long-lived animals, or what were
esteemed such, were collected and brewed into a broth:


           nec defuit illic
    Squamea Cinyphii tenuis membrana chelydri
    Vivacisque jecur cervi: quibus insuper addit
    Ora caputque novem cornicis sæcula passæ.


A similar notion was embodied in the celebrated medical theory called the
“Doctrine of Signatures,” “which is no less,” says Dr. Paris,(245) “than a
belief that every natural substance which possesses any medicinal virtue
indicates by an obvious and well-marked external character the disease for
which it is a remedy, or the object for which it should be employed.” This
outward character was generally some feature of resemblance, real or
fantastical, either to the effect it was supposed to produce, or to the
phenomenon over which its power was thought to be exercised. “Thus the
lungs of a fox must be a specific for asthma, because that animal is
remarkable for its strong powers of respiration. Turmeric has a brilliant
yellow color, which indicates that it has the power of curing the
jaundice; for the same reason, poppies must relieve diseases of the head;
Agaricus those of the bladder; _Cassia fistula_ the affections of the
intestines, and Aristolochia the disorders of the uterus: the polished
surface and stony hardness which so eminently characterize the seeds of
the Lithospermum officinale (common gromwell) were deemed a certain
indication of their efficacy in calculous and gravelly disorders; for a
similar reason, the roots of the Saxifraga granulata (white saxifrage)
gained reputation in the cure of the same disease; and the Euphrasia
(eye-bright) acquired fame, as an application in complaints of the eye,
because it exhibits a black spot in its corolla resembling the pupil. The
blood-stone, the Heliotropium of the ancients, from the occasional small
specks or points of a blood-red color exhibited on its green surface, is
even at this very day employed in many parts of England and Scotland to
stop a bleeding from the nose; and nettle tea continues a popular remedy
for the cure of _Urticaria_. It is also asserted that some substances bear
the _signatures_ of the humors, as the petals of the red rose that of the
blood, and the roots of rhubarb and the flowers of saffron that of the
bile.”

The early speculations respecting the chemical composition of bodies were
rendered abortive by no circumstance more than by their invariably taking
for granted that the properties of the elements must resemble those of the
compounds which were formed from them.

To descend to more modern instances; it was long thought, and was stoutly
maintained by the Cartesians and even by Leibnitz against the Newtonian
system (nor did Newton himself, as we have seen, contest the assumption,
but eluded it by an arbitrary hypothesis), that nothing (of a physical
nature at least) could account for motion, except previous motion; the
impulse or impact of some other body. It was very long before the
scientific world could prevail upon itself to admit attraction and
repulsion (_i.e._, spontaneous tendencies of particles to approach or
recede from one another) as ultimate laws, no more requiring to be
accounted for than impulse itself, if indeed the latter were not, in
truth, resolvable into the former. From the same source arose the
innumerable hypotheses devised to explain those classes of motion which
appeared more mysterious than others because there was no obvious mode of
attributing them to impulse, as for example the voluntary motions of the
human body. Such were the interminable systems of vibrations propagated
along the nerves, or animal spirits rushing up and down between the
muscles and the brain; which, if the facts could have been proved, would
have been an important addition to our knowledge of physiological laws;
but the mere invention, or arbitrary supposition of them, could not unless
by the strongest delusion be supposed to render the phenomena of animal
life more comprehensible, or less mysterious. Nothing, however, seemed
satisfactory, but to make out that motion was caused by motion; by
something like itself. If it was not one kind of motion, it must be
another. In like manner it was supposed that the physical qualities of
objects must arise from some similar quality, or perhaps only some quality
bearing the same name, in the particles or atoms of which the objects were
composed; that a sharp taste, for example, must arise from sharp
particles. And reversing the inference, the effects produced by a
phenomenon must, it was supposed, resemble in their physical attributes
the phenomenon itself. The influences of the planets were supposed to be
analogous to their visible peculiarities: Mars, being of a red color,
portended fire and slaughter; and the like.

Passing from physics to metaphysics, we may notice among the most
remarkable fruits of this _a priori_ fallacy two closely analogous
theories, employed in ancient and modern times to bridge over the chasm
between the world of mind and that of matter; the _species sensibiles_ of
the Epicureans, and the modern doctrine of perception by means of ideas.
These theories are indeed, probably, indebted for their existence not
solely to the fallacy in question, but to that fallacy combined with
another natural prejudice already adverted to, that a thing can not act
where it is not. In both doctrines it is assumed that the phenomenon which
takes place _in us_ when we see or touch an object, and which we regard as
an effect of that object, or rather of its presence to our organs, must of
necessity resemble very closely the outward object itself. To fulfill this
condition, the Epicureans supposed that objects were constantly projecting
in all directions impalpable images of themselves, which entered at the
eyes and penetrated to the mind; while modern metaphysicians, though they
rejected this hypothesis, agreed in deeming it necessary to suppose that
not the thing itself, but a mental image or representation of it, was the
direct object of perception. Dr. Reid had to employ a world of argument
and illustration to familiarize people with the truth, that the sensations
or impressions on our minds need not necessarily be copies of, or bear any
resemblance to, the causes which produce them; in opposition to the
natural prejudice which led people to assimilate the action of bodies upon
our senses, and through them upon our minds, to the transfer of a given
form from one object to another by actual moulding. The works of Dr. Reid
are even now the most effectual course of study for detaching the mind
from the prejudice of which this was an example. And the value of the
service which he thus rendered to popular philosophy is not much
diminished, although we may hold, with Brown, that he went too far in
imputing the “ideal theory” as an actual tenet, to the generality of the
philosophers who preceded him, and especially to Locke and Hume; for if
they did not themselves consciously fall into the error, unquestionably
they often led their readers into it.

The prejudice, that the conditions of a phenomenon must resemble the
phenomenon, is occasionally exaggerated, at least verbally, into a still
more palpable absurdity; the conditions of the thing are spoken of as if
they _were_ the very thing itself. In Bacon’s model inquiry, which
occupies so great a space in the _Novum Organum_, the _inquisitio in
formam calidi_, the conclusion which he favors is that heat is a kind of
motion; meaning of course not the feeling of heat, but the conditions of
the feeling; meaning, therefore, only that wherever there is heat, there
must first be a particular kind of motion; but he makes no distinction in
his language between these two ideas, expressing himself as if heat, and
the conditions of heat, were one and the same thing. So the elder Darwin,
in the beginning of his _Zoonomia_, says, “The word _idea_ has various
meanings in the writers of metaphysics; it is here used simply for those
notions of external things which our organs of sense bring us acquainted
with originally” (thus far the proposition, though vague, is
unexceptionable in meaning), “and is defined a contraction, a motion, or
configuration, of the fibres which constitute the immediate organ of
sense.” Our _notions_, a configuration of the fibres! What kind of
logician must he be who thinks that a phenomenon is _defined_ to _be_ the
condition on which he supposes it to depend? Accordingly he says soon
after, not that our ideas are caused by, or consequent on, certain organic
phenomena, but “our ideas _are_ animal motions of the organs of sense.”
And this confusion runs through the four volumes of the _Zoonomia_; the
reader never knows whether the writer is speaking of the effect, or of its
supposed cause; of the idea, a state of mental consciousness, or of the
state of the nerves and brain which he considers it to presuppose.

I have given a variety of instances in which the natural prejudice, that
causes and their effects must resemble one another, has operated in
practice so as to give rise to serious errors. I shall now go further, and
produce from writings even of the present or very recent times, instances
in which this prejudice is laid down as an established principle. M.
Victor Cousin, in the last of his celebrated lectures on Locke, enunciates
the maxim in the following unqualified terms: “Tout ce qui est vrai de
l’effet, est vrai de la cause.” A doctrine to which, unless in some
peculiar and technical meaning of the words cause and effect, it is not to
be imagined that any person would literally adhere; but he who could so
write must be far enough from seeing that the very reverse might be the
effect; that there is nothing impossible in the supposition that no one
property which is true of the effect might be true of the cause. Without
going quite so far in point of expression, Coleridge, in his _Biographia
Literaria_,(246) affirms as an “evident truth,” that “the law of causality
holds only between homogeneous things, _i.e._, things having some common
property,” and therefore “can not extend from one world into another, its
opposite;” hence, as mind and matter have no common property, mind can not
act upon matter, nor matter upon mind. What is this but the _a priori_
fallacy of which we are speaking? The doctrine, like many others of
Coleridge, is taken from Spinoza, in the first book of whose _Ethica_ (_De
Deo_) it stands as the Third Proposition, “Quæ res nihil commune inter se
habent, earum una alterius causa esse non potest,” and is there proved
from two so-called axioms, equally gratuitous with itself; but Spinoza
ever systematically consistent, pursued the doctrine to its inevitable
consequence, the materiality of God.

The same conception of impossibility led the ingenious and subtle mind of
Leibnitz to his celebrated doctrine of a pre-established harmony. He, too,
thought that mind could not act upon matter, nor matter upon mind, and
that the two, therefore, must have been arranged by their Maker like two
clocks, which, though unconnected with one another, strike simultaneously,
and always point to the same hour. Malebranche’s equally famous theory of
Occasional Causes was another form of the same conception; instead of
supposing the clocks originally arranged to strike together, he held that
when the one strikes, God interposes, and makes the other strike in
correspondence with it.

Descartes, in like manner, whose works are a rich mine of almost every
description of _a priori_ fallacy, says that the Efficient Cause must at
least have all the perfections of the effect, and for this singular
reason: “Si enim ponamus aliquid in ideâ reperiri quod non fuerit in ejus
causâ, hoc igitur habet a nihilo;” of which it is scarcely a parody to
say, that if there be pepper in the soup there must be pepper in the cook
who made it, since otherwise the pepper would be without a cause. A
similar fallacy is committed by Cicero, in his second book _De Finibus_,
where, speaking in his own person against the Epicureans, he charges them
with inconsistency in saying that the pleasures of the mind had their
origin from those of the body, and yet that the former were more valuable,
as if the effect could surpass the cause. “Animi voluptas oritur propter
voluptatem corporis, et major est animi voluptas quam corporis? ita fit ut
gratulator, lætior sit quam is cui gratulatur.” Even that, surely, is not
an impossibility; a person’s good fortune has often given more pleasure to
others than it gave to the person himself.

Descartes, with no less readiness, applies the same principle the converse
way, and infers the nature of the effects from the assumption that they
must, in this or that property or in all their properties, resemble their
cause. To this class belong his speculations, and those of so many others
after him, tending to infer the order of the universe, not from
observation, but by _a priori_ reasoning from supposed qualities of the
Godhead. This sort of inference was probably never carried to a greater
length than it was in one particular instance by Descartes, when, as a
proof of one of his physical principles, that the quantity of motion in
the universe is invariable, he had recourse to the immutability of the
Divine Nature. Reasoning of a very similar character is, however, nearly
as common now as it was in his time, and does duty largely as a means of
fencing off disagreeable conclusions. Writers have not yet ceased to
oppose the theory of divine benevolence to the evidence of physical facts,
to the principle of population for example. And people seem in general to
think that they have used a very powerful argument, when they have said,
that to suppose some proposition true, would be a reflection on the
goodness or wisdom of the Deity. Put into the simplest possible terms,
their argument is, “If it had depended on me, I would not have made the
proposition true, therefore it is not true.” Put into other words, it
stands thus: “God is perfect, therefore (what I think) perfection must
obtain in nature.” But since in reality every one feels that nature is
very far from perfect, the doctrine is never applied consistently. It
furnishes an argument which (like many others of a similar character)
people like to appeal to when it makes for their own side. Nobody is
convinced by it, but each appears to think that it puts religion on his
side of the question, and that it is a useful weapon of offense for
wounding an adversary.

Although several other varieties of _a priori_ fallacy might probably be
added to those here specified, these are all against which it seems
necessary to give any special caution. Our object is to open, without
attempting or affecting to exhaust, the subject. Having illustrated,
therefore, this first class of Fallacies at sufficient length, I shall
proceed to the second.



                               Chapter IV.


Fallacies Of Observation.


§ 1. From the Fallacies which are properly Prejudices, or presumptions
antecedent to, and superseding, proof, we pass to those which lie in the
incorrect performance of the proving process. And as Proof, in its widest
extent, embraces one or more, or all, of three processes, Observation,
Generalization, and Deduction, we shall consider in their order the errors
capable of being committed in these three operations. And first, of the
first mentioned.

A fallacy of misobservation may be either negative or positive; either
Non-observation or Mal-observation. It is non-observation, when all the
error consists in overlooking, or neglecting, facts or particulars which
ought to have been observed. It is mal-observation, when something is not
simply unseen, but seen wrong; when the fact or phenomenon, instead of
being recognized for what it is in reality, is mistaken for something
else.

§ 2. Non-observation may either take place by overlooking instances, or by
overlooking some of the circumstances of a given instance. If we were to
conclude that a fortune-teller was a true prophet, from not adverting to
the cases in which his predictions had been falsified by the event, this
would be non-observation of instances; but if we overlooked or remained
ignorant of the fact that in cases where the predictions had been
fulfilled, he had been in collusion with some one who had given him the
information on which they were grounded, this would be non-observation of
circumstances.

The former case, in so far as the act of induction from insufficient
evidence is concerned, does not fall under this second class of Fallacies,
but under the third, Fallacies of Generalization. In every such case,
however, there are two defects or errors instead of one; there is the
error of treating the insufficient evidence as if it were sufficient,
which is a Fallacy of the third class; and there is the insufficiency
itself; the not having better evidence; which, when such evidence, or, in
other words, when other instances, were to be had, is Non-observation; and
the erroneous inference, so far as it is to be attributed to this cause,
is a Fallacy of the second class.

It belongs not to our purpose to treat of non-observation as arising from
casual inattention, from general slovenliness of mental habits, want of
due practice in the use of the observing faculties, or insufficient
interest in the subject. The question pertinent to logic is—Granting the
want of complete competency in the observer, on what point is that
insufficiency on his part likely to lead him wrong? or rather, what sorts
of instances, or of circumstances in any given instance, are most likely
to escape the notice of observers generally; of mankind at large.

§ 3. First, then, it is evident that when the instances on one side of a
question are more likely to be remembered and recorded than those on the
other; especially if there be any strong motive to preserve the memory of
the first, but not of the latter; these last are likely to be overlooked,
and escape the observation of the mass of mankind. This is the recognized
explanation of the credit given, in spite of reason and evidence, to many
classes of impostors; to quack-doctors, and fortune-tellers in all ages;
to the “cunning man” of modern times, and the oracles of old. Few have
considered the extent to which this fallacy operates in practice, even in
the teeth of the most palpable negative evidence. A striking example of it
is the faith which the uneducated portion of the agricultural classes, in
this and other countries, continue to repose in the prophecies as to
weather supplied by almanac-makers; though every season affords to them
numerous cases of completely erroneous prediction; but as every season
also furnishes some cases in which the prediction is fulfilled, this is
enough to keep up the credit of the prophet, with people who do not
reflect on the number of instances requisite for what we have called, in
our inductive terminology, the Elimination of Chance; since a certain
number of casual coincidences not only may but will happen, between any
two unconnected events.

Coleridge, in one of the essays in the _Friend_, has illustrated the
matter we are now considering, in discussing the origin of a proverb,
“which, differently worded, is to be found in all the languages of
Europe,” viz., “Fortune favors fools.” He ascribes it partly to the
“tendency to exaggerate all effects that seem disproportionate to their
visible cause, and all circumstances that are in any way strongly
contrasted with our notions of the persons under them.” Omitting some
explanations which would refer the error to mal-observation, or to the
other species of non-observation (that of circumstances), I take up the
quotation further on. “Unforeseen coincidences may have greatly helped a
man, yet if they have done for him only what possibly from his own
abilities he might have effected for himself, his good luck will excite
less attention, and the instances be less remembered. That clever men
should attain their objects seems natural, and we neglect the
circumstances that perhaps produced that success of themselves without the
intervention of skill or foresight; but we dwell on the fact and remember
it, as something strange, when the same happens to a weak or ignorant man.
So too, though the latter should fail in his undertakings from
concurrences that might have happened to the wisest man, yet his failure
being no more than might have been expected and accounted for from his
folly, it lays no hold on our attention, but fleets away among the other
undistinguished waves in which the stream of ordinary life murmurs by us,
and is forgotten. Had it been as true as it was notoriously false, that
those all-embracing discoveries, which have shed a dawn of _science_ on
the _art_ of chemistry, and give no obscure promise of some one great
constitutive law, in the light of which dwell dominion and the power of
prophecy; if these discoveries, instead of having been, as they really
were, preconcerted by meditation, and evolved out of his own intellect,
had occurred by a set of lucky _accidents_ to the illustrious father and
founder of philosophic alchemy; if they had presented themselves to
Professor Davy exclusively in consequence of his _luck_ in possessing a
particular galvanic battery; if this battery, as far as Davy was
concerned, had itself been an _accident_, and not (as in point of fact it
was) desired and obtained by him for the purpose of insuring the testimony
of experience to his principles, and in order to bind down material nature
under the inquisition of reason, and force from her, as by torture,
unequivocal answers to _prepared_ and _preconceived_ questions—yet still
they would not have been talked of or described as instances of _luck_,
but as the natural results of his admitted genius and known skill. But
should an accident have disclosed similar discoveries to a mechanic at
Birmingham or Sheffield, and if the man should grow rich in consequence,
and partly by the envy of his neighbors and partly with good reason, be
considered by them as a man _below par_ in the general powers of his
understanding; then, ‘Oh, what a lucky fellow! Well, Fortune _does_ favor
fools—that’s for certain! It is always so!’ And forthwith the exclaimer
relates half a dozen similar instances. Thus accumulating the one sort of
facts and never collecting the other, we do, as poets in their diction,
and quacks of all denominations do in their reasoning, put a part for the
whole.”

This passage very happily sets forth the manner in which, under the loose
mode of induction which proceeds _per enumerationem simplicem_, not
seeking for instances of such a kind as to be decisive of the question,
but generalizing from any which occur, or rather which are remembered,
opinions grow up with the apparent sanction of experience, which have no
foundation in the laws of nature at all. “Itaque recte respondit ille” (we
may say with Bacon(247)), “qui cum suspensa tabula in templo ei
monstraretur eorum, qui vota solverant, quod naufragii periculo elapsi
sint, atque interrogando premeretur, anne tum quidem Deorum numen
agnosceret, quæsivit denuo, _At ubi sunt illi depicti qui post vota
nuncupata perierunt_? Eadem ratio est fere omnis superstitionis, ut in
Astrologicis, in Somniis, Ominibus, Nemesibus, et hujusmodi; in quibus,
homines delectati hujusmodi vanitatibus, advertunt eventus, ubi implentur;
ast ubi fallunt, licet multo frequentius, tamen negligunt, et prætereunt.”
And he proceeds to say that, independently of the love of the marvelous,
or any other bias in the inclinations, there is a natural tendency in the
intellect itself to this kind of fallacy; since the mind is more moved by
affirmative instances, though negative ones are of most use in philosophy:
“Is tamen humano intellectui error est proprius et perpetuus, ut magis
moveatur et excitetur Affirmativis quam Negativis; cum rite et ordine
æquum se utrique præbere debeat; quin contra, in omni Axiomate vero
constituendo, major vis est instantiæ negativæ.”

But the greatest of all causes of non-observation is a preconceived
opinion. This it is which, in all ages, has made the whole race of
mankind, and every separate section of it, for the most part unobservant
of all facts, however abundant, even when passing under their own eyes,
which are contradictory to any first appearance, or any received tenet. It
is worth while to recall occasionally to the oblivious memory of mankind
some of the striking instances in which opinions that the simplest
experiment would have shown to be erroneous, continued to be entertained
because nobody ever thought of trying that experiment. One of the most
remarkable of these was exhibited in the Copernican controversy. The
opponents of Copernicus argued that the earth did not move, because if it
did, a stone let fall from the top of a high tower would not reach the
ground at the foot of the tower, but at a little distance from it, in a
contrary direction to the earth’s course; in the same manner (said they)
as, if a ball is let drop from the mast-head while the ship is in full
sail, it does not fall exactly at the foot of the mast, but nearer to the
stern of the vessel. The Copernicans would have silenced these objectors
at once if they had _tried_ dropping a ball from the mast-head, since they
would have found that it does fall exactly at the foot, as the theory
requires; but no; they admitted the spurious fact, and struggled vainly to
make out a difference between the two cases. “The ball was no _part_ of
the ship—and the motion forward was not _natural_, either to the ship or
to the ball. The stone, on the other hand, let fall from the top of the
tower, was a _part_ of the earth; and therefore, the diurnal and annular
revolutions which were _natural_ to the earth, were also _natural_ to the
stone; the stone would, therefore, retain the same motion with the tower,
and strike the ground precisely at the bottom of it.”(248)

Other examples, scarcely less striking, are recorded by Dr. Whewell,(249)
where imaginary laws of nature have continued to be received as real,
merely because no person had steadily looked at facts which almost every
one had the opportunity of observing. “A vague and loose mode of looking
at facts very easily observable, left men for a long time under the belief
that a body ten times as heavy as another falls ten times as fast; that
objects immersed in water are always magnified, without regard to the form
of the surface; that the magnet exerts an irresistible force; that crystal
is always found associated with ice; and the like. These and many others
are examples how blind and careless man can be even in observation of the
plainest and commonest appearances; and they show us that the mere
faculties of perception, although constantly exercised upon innumerable
objects, may long fail in leading to any exact knowledge.”

If even on physical facts, and these of the most obvious character, the
observing faculties of mankind can be to this degree the passive slaves of
their preconceived impressions, we need not be surprised that this should
be so lamentably true as all experience attests it to be, on things more
nearly connected with their stronger feelings—on moral, social, and
religious subjects. The information which an ordinary traveler brings back
from a foreign country, as the result of the evidence of his senses, is
almost always such as exactly confirms the opinions with which he set out.
He has had eyes and ears for such things only as he expected to see. Men
read the sacred books of their religion, and pass unobserved therein
multitudes of things utterly irreconcilable with even their own notions of
moral excellence. With the same authorities before them, different
historians, alike innocent of intentional misrepresentation, see only what
is favorable to Protestants or Catholics, royalists or republicans,
Charles I. or Cromwell; while others, having set out with the
preconception that extremes must be in the wrong, are incapable of seeing
truth and justice when these are wholly on one side.

The influence of a preconceived theory is well exemplified in the
superstitions of barbarians respecting the virtues of medicaments and
charms. The negroes, among whom coral, as of old among ourselves, is worn
as an amulet, affirm, according to Dr. Paris,(250) that its color “is
always affected by the state of health of the wearer, it becoming paler in
disease.” On a matter open to universal observation, a general proposition
which has not the smallest vestige of truth is received as a result of
experience; the preconceived opinion preventing, it would seem, any
observation whatever on the subject.

§ 4. For illustration of the first species of non-observation, that of
Instances, what has now been stated may suffice. But there may also be
non-observation of some material circumstances, in instances which have
not been altogether overlooked—nay, which may be the very instances on
which the whole superstructure of a theory has been founded. As, in the
cases hitherto examined, a general proposition was too rashly adopted, on
the evidence of particulars, true indeed, but insufficient to support it;
so in the cases to which we now turn, the particulars themselves have been
imperfectly observed, and the singular propositions on which the
generalization is grounded, or some at least of those singular
propositions, are false.

Such, for instance, was one of the mistakes committed in the celebrated
phlogistic theory; a doctrine which accounted for combustion by the
extrication of a substance called phlogiston, supposed to be contained in
all combustible matter. The hypothesis accorded tolerably well with
superficial appearances; the ascent of flame naturally suggests the escape
of a substance; and the visible residuum of ashes, in bulk and weight,
generally falls extremely short of the combustible material. The error
was, non-observation of an important portion of the actual residue,
namely, the gaseous products of combustion. When these were at last
noticed and brought into account, it appeared to be a universal law, that
all substances gain instead of losing weight by undergoing combustion; and
after the usual attempt to accommodate the old theory to the new fact by
means of an arbitrary hypothesis (that phlogiston had the quality of
positive levity instead of gravity), chemists were conducted to the true
explanation, namely, that instead of a substance separated, there was, on
the contrary, a substance absorbed.

Many of the absurd practices which have been deemed to possess medicinal
efficacy, have been indebted for their reputation to non-observance of
some accompanying circumstance which was the real agent in the cures
ascribed to them. Thus, of the sympathetic powder of Sir Kenelm Digby:
“Whenever any wound had been inflicted, this powder was applied to the
weapon that had inflicted it, which was, moreover, covered with ointment,
and dressed two or three times a day. The wound itself, in the mean time,
was directed to be brought together, and carefully bound up with clean
linen rags, but, _above all, to be let alone_ for seven days, at the end
of which period the bandages were removed, when the wound was generally
found perfectly united. The triumph of the cure was decreed to the
mysterious agency of the sympathetic powder which had been so assiduously
applied to the weapon, whereas it is hardly necessary to observe that the
promptness of the cure depended on the total exclusion of air from the
wound, and upon the sanative operations of nature not having received any
disturbance from the officious interference of art. The result, beyond all
doubt, furnished the first hint which led surgeons to the improved
practice of healing wounds by what is technically called the _first
intention_.”(251) “In all records,” adds Dr. Paris, of “extraordinary
cures performed by mysterious agents, there is a great desire to conceal
the remedies and other curative means which were simultaneously
administered with them; thus Oribasius commends in high terms a necklace
of Pæony root for the cure of epilepsy; but we learn that he always took
care to accompany its use with copious evacuations, although he assigns to
them no share of credit in the cure. In later times we have a good
specimen of this species of deception, presented to us in a work on
scrofula by Mr. Morley, written, as we are informed, for the sole purpose
of restoring the much-injured character and use of the Vervain; in which
the author directs the root of this plant to be tied with a yard of white
satin ribbon around the neck, where it is to remain until the patient is
cured; but mark—during this interval he calls to his aid the most active
medicines in the materia medica.”(252)

In other cases, the cures really produced by rest, regimen, and amusement
have been ascribed to the medicinal, or occasionally to the supernatural,
means which were put in requisition. “The celebrated John Wesley, while he
commemorates the triumph of sulphur and supplication over his bodily
infirmity, forgets to appreciate the resuscitating influence of four
months’ repose from his apostolic labors; and such is the disposition of
the human mind to place confidence in the operation of mysterious agents,
that we find him more disposed to attribute his cure to a brown paper
plaster of egg and brimstone, than to Dr. Fothergill’s salutary
prescription of country air, rest, asses’ milk, and horse exercise.”(253)

In the following example, the circumstance overlooked was of a somewhat
different character. “When the yellow fever raged in America, the
practitioners trusted exclusively to the copious use of mercury; at first
this plan was deemed so universally efficacious, that, in the enthusiasm
of the moment, it was triumphantly proclaimed that death never took place
after the mercury had evinced its effect upon the system: all this was
very true, but it furnished no proof of the efficacy of that metal, since
the disease in its aggravated form was so rapid in its career, that it
swept away its victims long before the system could be brought under
mercurial influence, while in its milder shape it passed off equally well
without any assistance from art.”(254)

In these examples the circumstance overlooked was cognizable by the
senses. In other cases, it is one the knowledge of which could only be
arrived at by reasoning; but the fallacy may still be classed under the
head to which, for want of a more appropriate name, we have given the
appellation Fallacies of Non-observation. It is not the nature of the
faculties which ought to have been employed, but the non-employment of
them, which constitutes this Natural Order of Fallacies. Wherever the
error is negative, not positive; wherever it consists especially in
_overlooking_, in being ignorant or unmindful of some fact which, if known
and attended to, would have made a difference in the conclusion arrived
at; the error is properly placed in the Class which we are considering. In
this Class, there is not, as in all other fallacies there is, a positive
misestimate of evidence actually had. The conclusion would be just, if the
portion which is seen of the case were the whole of it; but there is
another portion overlooked, which vitiates the result.

For instance, there is a remarkable doctrine which has occasionally found
a vent in the public speeches of unwise legislators, but which only in one
instance that I am aware of has received the sanction of a philosophical
writer, namely, M. Cousin, who in his preface to the _Gorgias_ of Plato,
contending that punishment must have some other and higher justification
than the prevention of crime, makes use of this argument—that if
punishment were only for the sake of example, it would be indifferent
whether we punished the innocent or the guilty, since the punishment,
considered as an example, is equally efficacious in either case. Now we
must, in order to go along with this reasoning, suppose, that the person
who feels himself under temptation, observing somebody punished, concludes
himself to be in danger of being punished likewise, and is terrified
accordingly. But it is forgotten that if the person punished is supposed
to be innocent, or even if there be any doubt of his guilt, the spectator
will reflect that his own danger, whatever it may be, is not contingent on
his guiltiness, but threatens him equally if he remains innocent, and how,
therefore, is he deterred from guilt by the apprehension of such
punishment? M. Cousin supposes that people will be dissuaded from guilt by
whatever renders the condition of the guilty more perilous, forgetting
that the condition of the innocent (also one of the elements in the
calculation) is, in the case supposed, made perilous in precisely an equal
degree. This is a fallacy of overlooking; or of non-observation, within
the intent of our classification.

Fallacies of this description are the great stumbling-block to correct
thinking in political economy. The economical workings of society afford
numerous cases in which the effects of a cause consist of two sets of
phenomena: the one immediate, concentrated, obvious to all eyes, and
passing, in common apprehension, for the whole effect; the other widely
diffused, or lying deeper under the surface, and which is exactly contrary
to the former. Take, for instance, the common notion so plausible at the
first glance, of the encouragement given to industry by lavish
expenditure. A, who spends his whole income, and even his capital, in
expensive living, is supposed to give great employment to labor. B, who
lives on a small portion, and invests the remainder in the funds, is
thought to give little or no employment. For every body sees the gains
which are made by A’s tradesmen, servants, and others, while his money is
spending. B’s savings, on the contrary, pass into the hands of the person
whose stock he purchased, who with it pays a debt he owed to some banker,
who lends it again to some merchant or manufacturer; and the capital being
laid out in hiring spinners and weavers, or carriers and the crews of
merchant vessels, not only gives immediate employment to at least as much
industry as A employs during the whole of his career, but coming back with
increase by the sale of the goods which have been manufactured or
imported, forms a fund for the employment of the same and perhaps a
greater quantity of labor in perpetuity. But the observer does not see,
and therefore does not consider, what becomes of B’s money; he does see
what is done with A’s; he observes the amount of industry which A’s
profusion feeds; he observes not the far greater quantity which it
prevents from being fed; and thence the prejudice, universal to the time
of Adam Smith, that prodigality encourages industry, and parsimony is a
discouragement to it.

The common argument against free trade was a fallacy of the same nature.
The purchaser of British silk encourages British industry; the purchaser
of Lyons silk encourages only French; the former conduct is patriotic, the
latter ought to be prevented by law. The circumstance is overlooked, that
the purchaser of any foreign commodity necessarily causes, directly or
indirectly, the export of an equivalent value of some article of home
production (beyond what would otherwise be exported), either to the same
foreign country or to some other; which fact, though from the complication
of the circumstances it can not always be verified by specific
observation, no observation can possibly be brought to contradict, while
the evidence of reasoning on which it rests is irrefragable. The fallacy
is, therefore, the same as in the preceding case, that of seeing a part
only of the phenomena, and imagining that part to be the whole; and may be
ranked among Fallacies of Non-observation.

§ 5. To complete the examination of the second of our five classes, we
have now to speak of Mal-observation; in which the error does not lie in
the fact that something is unseen, but that something seen is seen wrong.

Perception being infallible evidence of whatever is really perceived, the
error now under consideration can be committed no otherwise than by
mistaking for conception what is, in fact, inference. We have formerly
shown how intimately the two are blended in almost every thing which is
called observation, and still more in every Description.(255) What is
actually on any occasion perceived by our senses being so minute in
amount, and generally so unimportant a portion of the state of facts which
we wish to ascertain or to communicate; it would be absurd to say that
either in our observations, or in conveying their result to others, we
ought not to mingle inference with fact; all that can be said is, that
when we do so we ought to be aware of what we are doing, and to know what
part of the assertion rests on consciousness, and is therefore
indisputable, what part on inference, and is therefore questionable.

One of the most celebrated examples of a universal error produced by
mistaking an inference for the direct evidence of the senses, was the
resistance made, on the ground of common sense, to the Copernican system.
People fancied they _saw_ the sun rise and set, the stars revolve in
circles round the pole. We now know that they saw no such thing; what they
really saw was a set of appearances, equally reconcilable with the theory
they held and with a totally different one. It seems strange that such an
instance as this of the testimony of the senses pleaded with the most
entire conviction in favor of something which was a mere inference of the
judgment, and, as it turned out, a false inference, should not have opened
the eyes of the bigots of common sense, and inspired them with a more
modest distrust of the competency of mere ignorance to judge the
conclusions of cultivated thought.

In proportion to any person’s deficiency of knowledge and mental
cultivation is, generally, his inability to discriminate between his
inferences and the perceptions on which they were grounded. Many a
marvelous tale, many a scandalous anecdote, owes its origin to this
incapacity. The narrator relates, not what he saw or heard, but the
impression which he derived from what he saw or heard, and of which
perhaps the greater part consisted of inference, though the whole is
related, not as inference but as matter of fact. The difficulty of
inducing witnesses to restrain within any moderate limits the intermixture
of their inferences with the narrative of their perceptions, is well known
to experienced cross-examiners; and still more is this the case when
ignorant persons attempt to describe any natural phenomenon. “The simplest
narrative,” says Dugald Stewart,(256) “of the most illiterate observer
involves more or less of hypothesis; nay, in general, it will be found
that, in proportion to his ignorance, the greater is the number of
conjectural principles involved in his statements. A village apothecary
(and, if possible, in a still greater degree, an experienced nurse) is
seldom able to describe the plainest case, without employing a phraseology
of which every word is a theory: whereas a simple and genuine
specification of the phenomena which mark a particular disease; a
specification unsophisticated by fancy, or by preconceived opinions, may
be regarded as unequivocal evidence of a mind trained by long and
successful study to the most difficult of all arts, that of the faithful
_interpretation_ of nature.”

The universality of the confusion between perceptions and the inferences
drawn from them, and the rarity of the power to discriminate the one from
the other, ceases to surprise us when we consider that in the far greater
number of instances the actual perceptions of our senses are of no
importance or interest to us except as marks from which we infer something
beyond them. It is not the color and superficial extension perceived by
the eye that are important to us, but the object, of which those visible
appearances testify the presence; and where the sensation itself is
indifferent, as it generally is, we have no motive to attend particularly
to it, but acquire a habit of passing it over without distinct
consciousness, and going on at once to the inference. So that to know what
the sensation actually was, is a study in itself, to which painters, for
example, have to train themselves by special and long-continued discipline
and application. In things farther removed from the dominion of the
outward senses, no one who has not great experience in psychological
analysis is competent to break this intense association; and when such
analytic habits do not exist in the requisite degree, it is hardly
possible to mention any of the habitual judgments of mankind on subjects
of a high degree of abstraction, from the being of a God and the
immortality of the soul down to the multiplication table, which are not,
or have not been, considered as matter of direct intuition. So strong is
the tendency to ascribe an intuitive character to judgments which are mere
inferences, and often false ones. No one can doubt that many a deluded
visionary has actually believed that he was directly inspired from Heaven,
and that the Almighty had conversed with him face to face; which yet was
only, on his part, a conclusion drawn from appearances to his senses, or
feelings in his internal consciousness, which afforded no warrant for any
such belief. A caution, therefore, against this class of errors, is not
only needful but indispensable; though to determine whether, on any of the
great questions of metaphysics, such errors are actually committed,
belongs not to this place, but, as I have so often said, to a different
science.



                                Chapter V.


Fallacies Of Generalization.


§ 1. The class of Fallacies of which we are now to speak, is the most
extensive of all; embracing a greater number and variety of unfounded
inferences than any of the other classes, and which it is even more
difficult to reduce to sub-classes or species. If the attempt made in the
preceding books to define the principles of well-grounded generalization
has been successful, all generalizations not conformable to those
principles might, in a certain sense, be brought under the present class;
when, however, the rules are known and kept in view, but a casual lapse
committed in the application of them, this is a blunder, not a fallacy. To
entitle an error of generalization to the latter epithet, it must be
committed on principle; there must lie in it some erroneous general
conception of the inductive process; the legitimate mode of drawing
conclusions from observation and experiment must be fundamentally
misconceived.

Without attempting any thing so chimerical as an exhaustive classification
of all the misconceptions which can exist on the subject, let us content
ourselves with noting, among the cautions which might be suggested, a few
of the most useful and needful.

§ 2. In the first place, there are certain kinds of generalization which,
if the principles already laid down be correct, _must_ be groundless;
experience can not afford the necessary conditions for establishing them
by a correct induction. Such, for instance, are all inferences from the
order of nature existing on the earth, or in the solar system, to that
which may exist in remote parts of the universe; where the phenomena, for
aught we know, may be entirely different, or may succeed one another
according to different laws, or even according to no fixed law at all.
Such, again, in matters dependent on causation, are all universal
negatives, all propositions that assert impossibility. The non-existence
of any given phenomenon, however uniformly experience may as yet have
testified to the fact, proves at most that no cause, adequate to its
production, has yet manifested itself; but that no such causes exist in
nature can only be inferred if we are so foolish as to suppose that we
know all the forces in nature. The supposition would at least be premature
while our acquaintance with some even of those which we do know is so
extremely recent. And however much our knowledge of nature may hereafter
be extended, it is not easy to see how that knowledge could ever be
complete, or how, if it were, we could ever be assured of its being so.

The only laws of nature which afford sufficient warrant for attributing
impossibility (even with reference to the existing order of nature, and to
our own region of the universe) are, first, those of number and extension,
which are paramount to the laws of the succession of phenomena, and not
exposed to the agency of counteracting causes; and, secondly, the
universal law of causality itself. That no valuation in any effect or
consequent will take place while the whole of the antecedents remain the
same, may be affirmed with full assurance. But, that the addition of some
new antecedent might not entirely alter and subvert the accustomed
consequent, or that antecedents competent to do this do not exist in
nature, we are in no case empowered positively to conclude.

§ 3. It is next to be remarked that all generalizations which profess,
like the theories of Thales, Democritus, and others of the early Greek
speculators, to resolve all things into some one element, or like many
modern theories, to resolve phenomena radically different into the same,
are necessarily false. By radically different phenomena I mean impressions
on our senses which differ in quality, and not merely in degree. On this
subject what appeared necessary was said in the chapter on the Limits to
the Explanation of Laws of Nature; but as the fallacy is even in our own
times a common one, I shall touch on it somewhat further in this place.

When we say that the force which retains the planets in their orbits is
resolved into gravity, or that the force which makes substances combine
chemically is resolved into electricity, we assert in the one case what
is, and in the other case what might, and probably will ultimately, be a
legitimate result of induction. In both these cases motion is resolved
into motion. The assertion is, that a case of motion, which was supposed
to be special, and to follow a distinct law of its own, conforms to and is
included in the general law which regulates another class of motions. But,
from these and similar generalizations, countenance and currency have been
given to attempts to resolve, not motion into motion, but heat into
motion, light into motion, sensation itself into motion; states of
consciousness into states of the nervous system, as in the ruder forms of
the materialist philosophy; vital phenomena into mechanical or chemical
processes, as in some schools of physiology.

Now I am far from pretending that it may not be capable of proof, or that
it is not an important addition to our knowledge if proved, that certain
motions in the particles of bodies are the _conditions_ of the production
of heat or light; that certain assignable physical modifications of the
nerves may be the conditions not only of our sensations or emotions, but
even of our thoughts; that certain mechanical and chemical conditions may,
in the order of nature, be sufficient to determine to action the
physiological laws of life. All I insist upon, in common with every
thinker who entertains any clear idea of the logic of science, is, that it
shall not be supposed that by proving these things one step would be made
toward a real explanation of heat, light, or sensation; or that the
generic peculiarity of those phenomena can be in the least degree evaded
by any such discoveries, however well established. Let it be shown, for
instance, that the most complex series of physical causes and effects
succeed one another in the eye and in the brain to produce a sensation of
color; rays falling on the eye, refracted, converging, crossing one
another, making an inverted image on the retina, and after this a
motion—let it be a vibration, or a rush of nervous fluid, or whatever else
you are pleased to suppose, along the optic nerve—a propagation of this
motion to the brain itself, and as many more different motions as you
choose; still, at the end of these motions, there is something which is
not motion, there is a feeling or sensation of color. Whatever number of
motions we may be able to interpolate, and whether they be real or
imaginary, we shall still find, at the end of the series, a motion
antecedent and a color consequent. The mode in which any one of the
motions produces the next, may possibly be susceptible of explanation by
some general law of motion: but the mode in which the last motion produces
the sensation of color, can not be explained by any law of motion; it is
the law of color: which is, and must always remain, a peculiar thing.
Where our consciousness recognizes between two phenomena an inherent
distinction; where we are sensible of a difference which is not merely of
degree, and feel that no adding one of the phenomena to itself would
produce the other; any theory which attempts to bring either under the
laws of the other must be false; though a theory which merely treats the
one as a cause or condition of the other, may possibly be true.

§ 4. Among the remaining forms of erroneous generalization, several of
those most worthy of and most requiring notice have fallen under our
examination in former places, where, in investigating the rules of correct
induction, we have had occasion to advert to the distinction between it
and some common mode of the incorrect. In this number is what I have
formerly called the natural Induction of uninquiring minds, the induction
of the ancients, which proceeds _per enumerationem simplicem_: “This,
that, and the other A are B, I can not think of any A which is not B,
therefore every A is B.” As a final condemnation of this rude and slovenly
mode of generalization, I will quote Bacon’s emphatic denunciation of it;
the most important part, as I have more than once ventured to assert, of
the permanent service rendered by him to philosophy. “Inductio quæ
procedit per enumerationem simplicem, res puerilis est, et precario
concludit” (concludes only _by your leave_, or provisionally), “et
periculo exponitur ab instantiâ contradictoriâ, et plerumque secundum
pauciora quam par est, et _ex his tantummodo quæ præsto sunt pronunciat_.
At Inductio quæ ad inventionem et demonstrationem Scientiarum et Artium
erit utilis, Naturam separare debet, per rejectiones et exclusiones
debitas; ac deinde post negativas tot quot sufficiunt, super affirmativas
concludere.”

I have already said that the mode of Simple Enumeration is still the
common and received method of Induction in whatever relates to man and
society. Of this a very few instances, more by way of memento than of
instruction, may suffice. What, for example, is to be thought of all the
“common-sense” maxims for which the following may serve as the universal
formula, “Whatsoever has never been, will never be.” As for example:
negroes have never been as civilized as whites sometimes are, therefore it
is impossible they should be so. Women, as a class, are supposed not to
have hitherto been equal in intellect to men, therefore they are
necessarily inferior. Society can not prosper without this or the other
institution; _e.g._, in Aristotle’s time, without slavery; in later times,
without an established priesthood, without artificial distinctions of
rank, etc. One poor person in a thousand, educated, while the nine hundred
and ninety-nine remain uneducated, has usually aimed at raising himself
out of his class, therefore education makes people dissatisfied with the
condition of a laborer. Bookish men, taken from speculative pursuits and
set to work on something they know nothing about, have generally been
found or thought to do it ill; therefore philosophers are unfit for
business, etc., etc. All these are inductions by simple enumeration.
Reasons having some reference to the canons of scientific investigation
have been attempted to be given, however unsuccessfully, for some of these
propositions; but to the multitude of those who parrot them, the
_enumeratio simplex, ex __ his tantummodo quæ præsto sunt pronuncians_, is
the sole evidence. Their fallacy consists in this, that they are
inductions without elimination: there has been no real comparison of
instances, nor even ascertainment of the material facts in any given
instance. There is also the further error, of forgetting that such
generalizations, even if well established, could not be ultimate truths,
but must be results of laws much more elementary; and therefore, until
deduced from such, could at most be admitted as empirical laws, holding
good within the limits of space and time by which the particular
observations that suggested the generalization were bounded.

This error, of placing mere empirical laws, and laws in which there is no
direct evidence of causation, on the same footing of certainty as laws of
cause and effect, an error which is at the root of perhaps the greater
number of bad inductions, is exemplified only in its grossest form in the
kind of generalizations to which we have now referred. These, indeed, do
not possess even the degree of evidence which pertains to a
well-ascertained empirical law; but admit of refutation on the empirical
ground itself, without ascending to casual laws. A little reflection,
indeed, will show that mere negations can only form the ground of the
lowest and least valuable kind of empirical law. A phenomenon has never
been noticed; this only proves that the conditions of that phenomenon have
not yet occurred in experience, but does not prove that they may not occur
hereafter. There is a better kind of empirical law than this, namely, when
a phenomenon which is observed presents within the limits of observation a
series of gradations, in which a regularity, or something like a
mathematical law, is perceptible; from which, therefore, something may be
rationally presumed as to those terms of the series which are beyond the
limits of observation. But in negation there are no gradations, and no
series; the generalizations, therefore, which deny the possibility of any
given condition of man and society merely because it has never yet been
witnessed, can not possess this higher degree of validity even as
empirical laws. What is more, the minuter examination which that higher
order of empirical laws presupposes, being applied to the subject-matter
of these, not only does not confirm but actually refutes them. For in
reality the past history of Man and Society, instead of exhibiting them as
immovable, unchangeable, incapable of ever presenting new phenomena, shows
them, on the contrary, to be, in many most important particulars, not only
changeable, but actually undergoing a progressive change. The empirical
law, therefore, best expressive, in most cases, of the genuine result of
observation, would be, not that such and such a phenomenon will continue
unchanged, but that it will continue to change in some particular manner.

Accordingly, while almost all generalizations relating to Man and Society,
antecedent to the last fifty or sixty years, have erred in the gross way
which we have attempted to characterize, namely, by implicitly assuming
that nature and society will forever revolve in the same orbit, and
exhibit essentially the same phenomena; which is also the vulgar error of
the ostentatiously practical, the votaries of so-called common sense, in
our day, especially in Great Britain; the more thinking minds of the
present age, having applied a more minute analysis to the past records of
our race, have for the most part adopted a contrary opinion, that the
human species is in a state of necessary progression, and that from the
terms of the series which are past we may infer positively those which are
yet to come. Of this doctrine, considered as a philosophical tenet, we
shall have occasion to speak more fully in the concluding Book. If not, in
all its forms, free from error, it is at least free from the gross and
error which we previously exemplified. But, in all except the most
eminently philosophical minds, it is infected with precisely the same
_kind_ of fallacy as that is. For we must remember that even this other
and better generalization, the progressive change in the condition of the
human species, is, after all, but an empirical law; to which, too, it is
not difficult to point out exceedingly large exceptions; and even if these
could be got rid of, either by disputing the facts or by explaining and
limiting the theory, the general objection remains valid against the
supposed law, as applicable to any other than what, in our third book,
were termed Adjacent Cases. For not only is it no ultimate, but not even a
causal law. Changes do indeed take place in human affairs, but every one
of those changes depends on determinate causes; the “progressiveness of
the species” is not a cause, but a summary expression for the general
result of all the causes. So soon as, by a quite different sort of
induction, it shall be ascertained what causes have produced these
successive changes, from the beginning of history, in so far as they have
really taken place, and by what causes of a contrary tendency they have
been occasionally checked or entirely counteracted, we may then be
prepared to predict the future with reasonable foresight; we may be in
possession of the real _law_ of the future; and may be able to declare on
what circumstances the continuance of the same onward movement will
eventually depend. But this it is the error of many of the more advanced
thinkers, in the present age, to overlook; and to imagine that the
empirical law collected from a mere comparison of the condition of our
species at different past times, is a real law, is _the_ law of its
changes, not only past but also to come. The truth is, that the causes on
which the phenomena of the moral world depend, are in every age, and
almost in every country, combined in some different proportion; so that it
is scarcely to be expected that the general result of them all should
conform very closely, in its details at least, to any uniformly
progressive series. And all generalizations which affirm that mankind have
a tendency to grow better or worse, richer or poorer, more cultivated or
more barbarous, that population increases faster than subsistence, or
subsistence than population, that inequality of fortune has a tendency to
increase or to break down, and the like, propositions of considerable
value as empirical laws within certain (but generally rather narrow)
limits, are in reality true or false according to times and circumstances.

What we have said of empirical generalizations from times past to times
still to come, holds equally true of similar generalizations from present
times to times past; when persons whose acquaintance with moral and social
facts is confined to their own age, take the men and the things of that
age for the type of men and things in general, and apply without scruple
to the interpretation of the events of history, the empirical laws which
represent sufficiently for daily guidance the common phenomena of human
nature at that time and in that particular state of society. If examples
are wanted, almost every historical work, until a very recent period,
abounded in them. The same may be said of those who generalize empirically
from the people of their own country to the people of other countries, as
if human beings felt, judged, and acted everywhere in the same manner.

§ 5. In the foregoing instances, the distinction is confounded between
empirical laws, which express merely the customary order of the succession
of effects, and the laws of causation on which the effects depend. There
may, however, be incorrect generalization when this mistake is not
committed; when the investigation takes its proper direction, that of
causes, and the result erroneously obtained purports to be a really causal
law.

The most vulgar form of this fallacy is that which is commonly called
_post hoc, ergo propter hoc_, or, _cum hoc, ergo propter hoc_. As when it
was inferred that England owed her industrial pre-eminence to her
restrictions on commerce; as when the old school of financiers, and some
speculative writers, maintained that the national debt was one of the
causes of national prosperity; as when the excellence of the Church, of
the Houses of Lords and Commons, of the procedure of the law courts, etc.,
were inferred from the mere fact that the country had prospered under
them. In such cases as these, if it can be rendered probable by other
evidence that the supposed causes have some tendency to produce the effect
ascribed to them, the fact of its having been produced, though only in one
instance, is of some value as a verification by specific experience; but
in itself it goes scarcely any way at all toward establishing such a
tendency, since, admitting the effect, a hundred other antecedents could
show an equally strong title of _that_ kind to be considered as the cause.

In these examples we see bad generalization _a posteriori_, or empiricism
properly so called; causation inferred from casual conjunction, without
either due elimination, or any presumption arising from known properties
of the supposed agent. But bad generalization _a priori_ is fully as
common; which is properly called false theory; conclusions drawn, by way
of deduction, from properties of some one agent which is known or supposed
to be present, all other co-existing agents being overlooked. As the
former is the error of sheer ignorance, so the latter is especially that
of semi-instructed minds; and is mainly committed in attempting to explain
complicated phenomena by a simpler theory than their nature admits of. As
when one school of physicians sought for the universal principle of all
disease in “lentor and morbid viscidity of the blood,” and imputing most
bodily derangements to mechanical obstructions, thought to cure them by
mechanical remedies;(257) while another, the chemical school,
“acknowledged no source of disease but the presence of some hostile acid
or alkali, or some deranged condition in the chemical composition of the
fluid or solid parts,” and conceived, therefore, that “all remedies must
act by producing chemical changes in the body.” We find Tournefort busily
engaged in testing every vegetable juice, in order to discover in it some
traces of an acid or alkaline ingredient, which might confer upon it
medicinal activity. The fatal errors into which such an hypothesis was
liable to betray the practitioner, received an awful illustration in the
history of the memorable fever that raged at Leyden in the year 1699, and
which consigned two-thirds of the population of that city to an untimely
grave; an event which in a great measure depended upon the Professor
Sylvius de la Boe, who having just embraced the chemical doctrines of Van
Helmont, assigned the origin of the distemper to a prevailing acid, and
declared that its cure could alone [only] be effected by the copious
administration of absorbent and testaceous medicines.(258)

These aberrations in medical theory have their exact parallels in
politics. All the doctrines which ascribe absolute goodness to particular
forms of government, particular social arrangements, and even to
particular modes of education, without reference to the state of
civilization and the various distinguishing characters of the society for
which they are intended, are open to the same objection—that of assuming
one class of influencing circumstances to be the paramount rulers of
phenomena which depend in an equal or greater degree on many others. But
on these considerations it is the less necessary that we should now dwell,
as they will occupy our attention more largely in the concluding Book.

§ 6. The last of the modes of erroneous generalization to which I shall
advert, is that to which we may give the name of False Analogies. This
Fallacy stands distinguished from those already treated of by the
peculiarity that it does not even simulate a complete and conclusive
induction, but consists in the misapplication of an argument which is at
best only admissible as an inconclusive presumption, where real proof is
unattainable.

An argument from analogy, is an inference that what is true in a certain
case is true in a case known to be somewhat similar, but not known to be
exactly parallel, that is, to be similar in all the material
circumstances. An object has the property B: another object is not known
to have that property, but resembles the first in a property A, not known
to be connected with B; and the conclusion to which the analogy points, is
that this object has the property B also. As, for example, that the
planets are inhabited, because the earth is so. The planets resemble the
earth in describing elliptical orbits round the sun, in being attracted by
it and by one another, in being nearly spherical, revolving on their axes,
etc.; and, as we have now reason to believe from the revelations of the
spectroscope, are composed, in great part at least, of similar materials;
but it is not known that any of these properties, or all of them together,
are the conditions on which the possession of inhabitants is dependent, or
are marks of those conditions. Nevertheless, so long as we do not know
what the conditions are, they _may_ be connected by some law of nature
with those common properties; and to the extent of that possibility the
planets are more likely to be inhabited than if they did not resemble the
earth at all. This non-assignable and generally small increase of
probability, beyond what would otherwise exist, is all the evidence which
a conclusion can derive from analogy. For if we have the slightest reason
to suppose any real connection between the two properties A and B, the
argument is no longer one of analogy. If it had been ascertained (I
purposely put an absurd supposition) that there was a connection by
causation between the fact of revolving on an axis and the existence of
animated beings, or if there were any reasonable ground for even
suspecting such a connection, a probability would arise of the existence
of inhabitants in the planets, which might be of any degree of strength,
up to a complete induction; but we should then infer the fact from the
ascertained or presumed law of causation, and not from the analogy of the
earth.

The name analogy, however, is sometimes employed by extension to denote
those arguments of an inductive character but not amounting to a real
induction, which are employed to strengthen the argument drawn from a
simple resemblance. Though A, the property common to the two cases, can
not be shown to be the cause or effect of B, the analogical reasoner will
endeavor to show that there is some less close degree of connection
between them; that A is one of a set of conditions from which, when all
united, B would result; or is an occasional effect of some cause which has
been known also to produce B; and the like. Any of which things, if shown,
would render the existence of B by so much more probable, than if there
had not been even that amount of known connection between B and A.

Now an error or fallacy of analogy may occur in two ways. Sometimes it
consists in employing an argument of either of the above kinds with
correctness indeed, but overrating its probative force. This very common
aberration is sometimes supposed to be particularly incident to persons
distinguished for their imagination; but in reality it is the
characteristic intellectual vice of those whose imaginations are barren,
either from want of exercise, natural defect, or the narrowness of their
range of ideas. To such minds objects present themselves clothed in but
few properties; and as, therefore, few analogies between one object and
another occur to them, they almost invariably overrate the degree of
importance of those few: while one whose fancy takes a wider range,
perceives and remembers so many analogies tending to conflicting
conclusions, that he is much less likely to lay undue stress on any of
them. We always find that those are the greatest slaves to metaphorical
language who have but one set of metaphors.

But this is only one of the modes of error in the employment of arguments
of analogy. There is another, more properly deserving the name of fallacy;
namely, when resemblance in one point is inferred from resemblance in
another point, though there is not only no evidence to connect the two
circumstances by way of causation, but the evidence tends positively to
disconnect them. This is properly the Fallacy of False Analogies.

As a first instance, we may cite that favorite argument in defense of
absolute power, drawn from the analogy of paternal government in a family,
which government, however much in need of control, is not and can not be
controlled by the children themselves, while they remain children.
Paternal government, says the argument, works well; therefore, despotic
government in a state will work well. I waive, as not pertinent in this
place, all that could be said in qualification of the alleged excellence
of paternal government. However this might be, the argument from the
family to the state would not the less proceed on a false analogy;
implying that the beneficial working of parental government depends, in
the family, on the only point which it has in common with political
despotism, namely, irresponsibility. Whereas it depends, when real, not on
that but on two other circumstances of the case, the affection of the
parent for the children, and the superiority of the parent in wisdom and
experience; neither of which properties can be reckoned on, or are at all
likely to exist, between a political despot and his subjects; and when
either of these circumstances fails even in the family, and the influence
of the irresponsibility is allowed to work uncorrected, the result is any
thing but good government. This, therefore, is a false analogy.

Another example is the not uncommon _dictum_ that bodies politic have
youth, maturity, old age, and death, like bodies natural; that after a
certain duration of prosperity, they tend spontaneously to decay. This
also is a false analogy, because the decay of the vital powers in an
animated body can be distinctly traced to the natural progress of those
very changes of structure which, in their earlier stages, constitutes its
growth to maturity; while in the body politic the progress of those
changes can not, generally speaking, have any effect but the still further
continuance of growth: it is the stoppage of that progress, and the
commencement of retrogression, that alone would constitute decay. Bodies
politic die, but it is of disease, or violent death; they have no old age.

The following sentence from Hooker’s _Ecclesiastical Polity_ is an
instance of a false analogy from physical bodies to what are called bodies
politic. “As there could be in natural bodies no motion of any thing
unless there were some which moveth all things, and continueth immovable;
even so in politic societies there must be some unpunishable, or else no
man shall suffer punishment.” There is a double fallacy here, for not only
the analogy, but the premise from which it is drawn, is untenable. The
notion that there must be something immovable which moves all other
things, is the old scholastic error of a _primum mobile_.

The following instance I quote from Archbishop Whately’s _Rhetoric_: “It
would be admitted that a great and permanent diminution in the quantity of
some useful commodity, such as corn, or coal, or iron, throughout the
world, would be a serious and lasting loss; and again, that if the fields
and coal-mines yielded regularly double quantities, with the same labor,
we should be so much the richer; hence it might be inferred, that if the
quantity of gold and silver in the world were diminished one-half, or were
doubled, like results would follow; the utility of these metals, for the
purposes of coin, being very great. Now there are many points of
resemblance and many of difference, between the precious metals on the one
hand, and corn, coal, etc., on the other; but the important circumstance
to the supposed argument is, that the _utility_ of gold and silver (as
coin, which is far the chief) _depends on their value_, which is regulated
by their scarcity; or rather, to speak strictly, by the difficulty of
obtaining them; whereas, if corn and coal were ten times as abundant
(_i.e._, more easily obtained), a bushel of either would still be as
useful as now. But if it were twice as easy to procure gold as it is, a
sovereign would be twice as large; if only half as easy, it would be of
the size of a half-sovereign, and this (besides the trifling circumstance
of the cheapness or dearness of gold ornaments) would be all the
difference. The analogy, therefore, fails in the point essential to the
argument.”

The same author notices, after Bishop Copleston, the case of False Analogy
which consists in inferring from the similarity in many respects between
the metropolis of a country and the heart of the animal body, that the
increased size of the metropolis is a disease.

Some of the false analogies on which systems of physics were confidently
grounded in the time of the Greek philosophers, are such as we now call
fanciful, not that the resemblances are not often real, but that it is
long since any one has been inclined to draw from them the inferences
which were then drawn. Such, for instance, are the curious speculations of
the Pythagoreans on the subject of numbers. Finding that the distances of
the planets bore, or seemed to bear, to one another a proportion not
varying much from that of the divisions of the monochord, they inferred
from it the existence of an inaudible music, that of the spheres; as if
the music of a harp had depended solely on the numerical proportions, and
not on the material, nor even on the existence of any material, any
strings at all. It has been similarly imagined that certain combinations
of numbers, which were found to prevail in some natural phenomena, must
run through the whole of nature: as that there must be four elements,
because there are four possible combinations of hot and cold, wet and dry;
that there must be seven planets, because there were seven metals, and
even because there were seven days of the week. Kepler himself thought
that there could be only six planets, because there were only five regular
solids. With these we may class the reasonings, so common in the
speculations of the ancients, founded on a supposed _perfection_ in
nature; meaning by nature the customary order of events as they take place
of themselves without human interference. This also is a rude guess at an
analogy supposed to pervade all phenomena, however dissimilar. Since what
was thought to be perfection appeared to obtain in some phenomena, it was
inferred (in opposition to the plainest evidence) to obtain in all. “We
always suppose that which is better to take place in nature, if it be
possible,” says Aristotle; and the vaguest and most heterogeneous
qualities being confounded together under the notion of being _better_,
there was no limit to the wildness of the inferences. Thus, because the
heavenly bodies were “perfect,” they must move in circles and uniformly.
For “they” (the Pythagoreans) “would not allow,” says Geminus,(259) “of
any such disorder among divine and eternal things, as that they should
sometimes move quicker and sometimes slower, and sometimes stand still;
for no one would tolerate such anomaly in the movements even of a man, who
was decent and orderly. The occasions of life, however, are often reasons
for men going quicker or slower; but in the incorruptible nature of the
stars, it is not possible that any cause can be alleged of quickness or
slowness.” It is seeking an argument of analogy very far, to suppose that
the stars must observe the rules of decorum in gait and carriage
prescribed for themselves by the long-bearded philosophers satirized by
Lucian.

As late as the Copernican controversy it was urged as an argument in favor
of the true theory of the solar system, that it placed the fire, the
noblest element, in the centre of the universe. This was a remnant of the
notion that the order of nature must be perfect, and that perfection
consisted in conformity to rules of precedency in dignity, either real or
conventional. Again, reverting to numbers: certain numbers were _perfect_,
therefore those numbers must obtain in the great phenomena of nature. Six
was a perfect number, that is, equal to the sum of all its factors; an
additional reason why there must be exactly six planets. The Pythagoreans,
on the other hand, attributed perfection to the number ten; but agreed in
thinking that the perfect number must be somehow realized in the heavens;
and knowing only of nine heavenly bodies, to make up the enumeration, they
asserted “that there was an _antichthon_, or counter-earth, on the other
side of the sun, invisible to us.”(260) Even Huygens was persuaded that
when the number of the heavenly bodies had reached twelve, it could not
admit of any further increase. Creative power could not go beyond that
sacred number.

Some curious instances of false analogy are to be found in the arguments
of the Stoics to prove the equality of all crimes, and the equal
wretchedness of all who had not realized their idea of perfect virtue.
Cicero, toward the end of his Fourth Book, _De Finibus_, states some of
these as follows: “Ut, inquit, in fidibus plurimis, si nulla earum ita
contenta numeris sit, ut concentum servare possit, omnes æque incontentæ
sunt; sic peccata, quia discrepant, æque discrepant; paria sunt igitur.”
To which Cicero himself aptly answers, “æque contingit omnibus fidibus, ut
incontentæ sint; illud non continuo, ut æque incontentæ.” The Stoic
resumes: “Ut enim, inquit, gubernator æque peccat, si palearum navem
evertit, et si auri; item æque peccat qui parentem, et qui servum, injuriâ
verberat;” assuming, that because the magnitude of the interest at stake
makes no difference in the mere defect of skill, it can make none in the
moral defect: a false analogy. Again, “Quis ignorat, si plures ex alto
emergere velint, propius fore eos quidem ad respirandum, qui ad summam jam
aquam appropinquant, sed nihilo magis respirare posse, quam eos, qui sunt
in profundo? Nihil ergo adjuvat procedere, et progredi in virtute,
quominus miserrimus sit, antequam ad eam pervenerit, quoniam in aquâ nihil
adjuvat: et quoniam catuli, qui jam despecturi sunt, cæci æque, et ii qui
modo nati; Platonem quoque necesse est, quoniam nondum videbat sapientiam,
æque cæcum animo, ac Phalarim fuisse.” Cicero, in his own person, combats
these false analogies by other analogies tending to an opposite
conclusion. “Ista similia non sunt, Cato.... Illa sunt similia; hebes
acies est cuipiam oculorum: corpore alius languescit: hi curatione
adhibitâ levantur in dies: alter valet plus quotidie: alter videt. Hi
similes sunt omnibus, qui virtuti student; levantur vitiis, levantur
erroribus.”

§ 7. In these and all other arguments drawn from remote analogies, and
from metaphors, which are cases of analogy, it is apparent (especially
when we consider the extreme facility of raising up contrary analogies and
conflicting metaphors) that, so far from the metaphor or analogy proving
any thing, the applicability of the metaphor is the very thing to be made
out. It has to be shown that in the two cases asserted to be analogous,
the same law is really operating; that between the known resemblance and
the inferred one there is some connection by means of causation. Cicero
and Cato might have bandied opposite analogies forever; it rested with
each of them to prove by just induction, or at least to render probable,
that the case resembled the one set of analogous cases and not the other,
in the circumstances on which the disputed question really hinged.
Metaphors, for the most part, therefore, assume the proposition which they
are brought to prove: their use is, to aid the apprehension of it; to make
clearly and vividly comprehended what it is that the person who employs
the metaphor is proposing to make out; and sometimes also, by what media
he proposes to do so. For an apt metaphor, though it can not prove, often
suggests the proof.

For instance, when D’Alembert (I believe) remarked that in certain
governments only two creatures find their way to the highest places, the
eagle and the serpent, the metaphor not only conveys with great vividness
the assertion intended, but contributes toward substantiating it, by
suggesting, in a lively manner, the means by which the two opposite
characters thus typified effect their rise. When it is said that a certain
person misunderstands another because the lesser of two objects can not
comprehend the greater, the application of what is true in the literal
sense of the word _comprehend_, to its metaphorical sense, points to the
fact which is the ground and justification of the assertion, viz., that
one mind can not thoroughly understand another unless it can contain it in
itself, that is, unless it possesses all that is contained in the other.
When it is urged as an argument for education, that if the soil is left
uncultivated, weeds will spring up, the metaphor, though no proof, but a
statement of the thing to be proved, states it in terms which, by
suggesting a parallel case, put the mind upon the track of the real proof.
For, the reason why weeds grow in an uncultivated soil, is that the seeds
of worthless products exist everywhere, and can germinate and grow in
almost all circumstances, while the reverse is the case with those which
are valuable; and this being equally true of mental products, this mode of
conveying an argument, independently of its rhetorical advantages, has a
logical value; since it not only suggests the grounds of the conclusion,
but points to another case in which those grounds have been found, or at
least deemed to be, sufficient.

On the other hand, when Bacon, who is equally conspicuous in the use and
abuse of figurative illustration, says that the stream of time has brought
down to us only the least valuable part of the writings of the ancients,
as a river carries froth and straws floating on its surface, while more
weighty objects sink to the bottom; this, even if the assertion
illustrated by it were true, would be no good illustration, there being no
parity of cause. The levity by which substances float on a stream, and the
levity which is synonymous with worthlessness, have nothing in common
except the name; and (to show how little value there is in the metaphor)
we need only change the word into _buoyancy_, to turn the semblance of
argument involved in Bacon’s illustration against himself.

A metaphor, then, is not to be considered as an argument, but as an
assertion that an argument exists; that a parity subsists between the case
from which the metaphor is drawn and that to which it is applied. This
parity may exist though the two cases be apparently very remote from one
another; the only resemblance existing between them may be a resemblance
of relations, an analogy in Ferguson’s and Archbishop Whately’s sense: as
in the preceding instance, in which an illustration from agriculture was
applied to mental cultivation.

§ 8. To terminate the subject of Fallacies of Generalization, it remains
to be said, that the most fertile source of them is bad classification:
bringing together in one group, and under one name, things which have no
common properties, or none but such as are too unimportant to allow
general propositions of any considerable value to be made respecting the
class. The misleading effect is greatest, when a word which in common use
expresses some definite fact, is extended by slight links of connection to
cases in which that fact does not exist, but some other or others, only
slightly resembling it. Thus Bacon,(261) in speaking of the _Idola_ or
Fallacies arising from notions _temere et inæqualiter à rebus abstractæ_,
exemplifies them by the notion of Humidum or Wet, so familiar in the
physics of antiquity and of the Middle Ages. “Invenietur verbum istud,
Humidum, nihil aliud quam nota confusa diversarum actionum, quæ nullam
constantiam aut reductionem patiuntur. Significat enim, et quod circa
aliud corpus facile se circumfundit; et quod in se est indeterminabile,
nec consistere potest; et quod facile cedit undique; et quod facile se
dividit et dispergit; et quod facile se unit et colligit; et quod facile
fluit, et in motu ponitur; et quod alteri corpori facile adhæret, idque
madefacit; et quod facile reducitur in liquidum, sive colliquatur, cum
antea consisteret. Itaque quum ad hujus nominis prædicationem et
impositionem ventum sit; si alia accipias, flamma humida est; si alia
accipias, aer humidus non est; si alia, pulvis minutus humidus est; si
alia, vitrum humidum est: ut facile appareat, istam notionem ex aquâ
tantum, et communibus et vulgaribus liquoribus, absque ullâ debitâ
verificatione, temere abstractam esse.”

Bacon himself is not exempt from a similar accusation when inquiring into
the nature of heat: where he occasionally proceeds like one who, seeking
for the cause of hardness, after examining that quality in iron, flint,
and diamond, should expect to find that it is something which can be
traced also in hard water, a hard knot, and a hard heart.

The word κίνησις in the Greek philosophy, and the words Generation and
Corruption, both then and long afterward, denoted such a multitude of
heterogeneous phenomena, that any attempt at philosophizing in which those
words were used was almost as necessarily abortive as if the word _hard_
had been taken to denote a class including all the things mentioned above.
Κίνησις, for instance, which properly signified motion, was taken to
denote not only all motion but even all change: ἀλλοίωσις being recognized
as one of the modes of κίνησις. The effect was, to connect with every form
of ἀλλοίωσις or change, ideas drawn from motion in the proper and literal
sense, and which had no real connection with any other kind of κίνησις
than that. Aristotle and Plato labored under a continual embarrassment
from this misuse of terms. But if we proceed further in this direction we
shall encroach upon the Fallacy of Ambiguity, which belongs to a different
class, the last in order of our classification, Fallacies of Confusion.



                               Chapter VI.


Fallacies Of Ratiocination.


§ 1. We have now, in our progress through the classes of Fallacies,
arrived at those to which, in the common books of logic, the appellation
is in general exclusively appropriated; those which have their seat in the
ratiocinative or deductive part of the investigation of truth. Of these
fallacies it is the less necessary for us to insist at any length, as they
have been most satisfactorily treated in a work familiar to almost all, in
this country at least, who feel any interest in these speculations,
Archbishop Whately’s _Logic_. Against the more obvious forms of this class
of fallacies, the rules of the syllogism are a complete protection. Not
(as we have so often said) that ratiocination can not be good unless it be
in the form of a syllogism; but that, by showing it in that form, we are
sure to discover if it be bad, or at least if it contain any fallacy of
this class.

§ 2. Among Fallacies of Ratiocination, we ought perhaps to include the
errors committed in processes which have the appearance only, not the
reality, of an inference from premises; the fallacies connected with the
conversion and æquipollency of propositions. I believe errors of this
description to be far more frequently committed than is generally
supposed, or than their extreme obviousness might seem to admit of. For
example, the simple conversion of a universal affirmative proposition, All
A are B, therefore all B are A, I take to be a very common form of error:
though committed, like many other fallacies, oftener in the silence of
thought than in express words, for it can scarcely be clearly enunciated
without being detected. And so with another form of fallacy, not
substantially different from the preceding: the erroneous conversion of an
hypothetical proposition. The proper converse of an hypothetical
proposition is this: If the consequent be false, the antecedent is false;
but this, If the consequent be true, the antecedent is true, by no means
holds good, but is an error corresponding to the simple conversion of a
universal affirmative. Yet hardly any thing is more common than for
people, in their private thoughts, to draw this inference. As when the
conclusion is accepted, which it so often is, for proof of the premises.
That the premises can not be true if the conclusion is false, is the
unexceptionable foundation of the legitimate mode of reasoning called
_reductio ad absurdum_. But people continually think and express
themselves, as if they also believed that the premises can not be false if
the conclusion is true. The truth, or supposed truth, of the inferences
which follow from a doctrine, often enables it to find acceptance in spite
of gross absurdities in it. How many philosophical systems which had
scarcely any intrinsic recommendation, have been received by thoughtful
men because they were supposed to lend additional support to religion,
morality, some favorite view of politics, or some other cherished
persuasion: not merely because their wishes were thereby enlisted on its
side, but because its leading to what they deemed sound conclusions
appeared to them a strong presumption in favor of its truth: though the
presumption, when viewed in its true light, amounted only to the absence
of that particular evidence of falsehood, which would have resulted from
its leading by correct inference to something already known to be false.

Again, the very frequent error in conduct, of mistaking reverse of wrong
for right, is the practical form of a logical error with respect to the
Opposition of Propositions. It is committed for want of the habit of
distinguishing the _contrary_ of a proposition from the _contradictory_ of
it, and of attending to the logical canon, that contrary propositions,
though they can not both be true, may both be false. If the error were to
express itself in words, it would run distinctly counter to this canon. It
generally, however, does not so express itself, and to compel it to do so
is the most effectual method of detecting and exposing it.

§ 3. Among Fallacies of Ratiocination are to be ranked, in the first
place, all the cases of vicious syllogism laid down in the books. These
generally resolve themselves into having more than three terms to the
syllogism, either avowedly, or in the covert mode of an undistributed
middle term, or an _illicit process_ of one of the two extremes. It is
not, indeed, very easy fully to convict an argument of falling under any
one of these vicious cases in particular; for the reason already more than
once referred to, that the premises are seldom formally set out: if they
were, the fallacy would impose upon nobody; and while they are not, it is
almost always to a certain degree optional in what manner the suppressed
link shall be filled up. The rules of the syllogism are rules for
compelling a person to be aware of the whole of what he must undertake to
defend if he persists in maintaining his conclusion. He has it almost
always in his power to make his syllogism good by introducing a false
premise; and hence it is scarcely ever possible decidedly to affirm that
any argument involves a bad syllogism: but this detracts nothing from the
value of the syllogistic rules, since it is by them that a reasoner is
compelled distinctly to make his election what premises he is prepared to
maintain. The election made, there is generally so little difficulty in
seeing whether the conclusion follows from the premises set out, that we
might without much logical impropriety have merged this fourth class of
fallacies in the fifth, or Fallacies of Confusion.

§ 4. Perhaps, however, the commonest, and certainly the most dangerous
fallacies of this class, are those which do not lie in a single syllogism,
but slip in between one syllogism and another in a chain of argument, and
are committed by _changing the premises_. A proposition is proved, or an
acknowledged truth laid down, in the first part of an argumentation, and
in the second a further argument is founded not on the same proposition,
but on some other, resembling it sufficiently to be mistaken for it.
Instances of this fallacy will be found in almost all the argumentative
discourses of unprecise thinkers; and we need only here advert to one of
the obscurer forms of it, recognized by the school-men as the fallacy _à
dicto secundum quid ad dictum simpliciter_. This is committed when, in the
premises, a proposition is asserted with a qualification, and the
qualification lost sight of in the conclusion; or oftener, when a
limitation or condition, though not asserted, is necessary to the truth of
the proposition, but is forgotten when that proposition comes to be
employed as a premise. Many of the bad arguments in vogue belong to this
class of error. The premise is some admitted truth, some common maxim, the
reasons or evidence for which have been forgotten, or are not thought of
at the time, but if they had been thought of would have shown the
necessity of so limiting the premise that it would no longer have
supported the conclusion drawn from it.

Of this nature is the fallacy in what is called, by Adam Smith and others,
the Mercantile Theory in Political Economy. That theory sets out from the
common maxim, that whatever brings in money enriches; or that every one is
rich in proportion to the quantity of money he obtains. From this it is
concluded that the value of any branch of trade, or of the trade of the
country altogether, consists in the balance of money it brings in; that
any trade which carries more money out of the country than it draws into
it is a losing trade; that therefore money should be attracted into the
country and kept there, by prohibitions and bounties; and a train of
similar corollaries. All for want of reflecting that if the riches of an
individual are in proportion to the quantity of money he can command, it
is because that is the measure of his power of purchasing money’s worth;
and is therefore subject to the proviso that he is not debarred from
employing his money in such purchases. The premise, therefore, is only
true _secundum quid_; but the theory assumes it to be true absolutely, and
infers that increase of money is increase of riches, even when produced by
means subversive of the condition under which alone money can be riches.

A second instance is, the argument by which it used to be contended,
before the commutation of tithe, that tithes fell on the landlord, and
were a deduction from rent; because the rent of tithe-free land was always
higher than that of land of the same quality, and the same advantages of
situation, subject to tithe. Whether it be true or not that a tithe falls
on rent, a treatise on Logic is not the place to examine; but it is
certain that this is no proof of it. Whether the proposition be true or
false, tithe-free land must, by the necessity of the case, pay a higher
rent. For if tithes do not fall on rent, it must be because they fall on
the consumer; because they raise the price of agricultural produce. But if
the produce be raised in price, the farmer of tithe-free as well as the
farmer of tithed land gets the benefit. To the latter the rise is but a
compensation for the tithe he pays; to the first, who pays none, it is
clear gain, and therefore enables him, and if there be freedom of
competition, forces him, to pay so much more rent to his landlord. The
question remains, to what class of fallacies this belongs. The premise is,
that the owner of tithed land receives less rent than the owner of
tithe-free land; the conclusion is, that therefore he receives less than
he himself would receive if tithe were abolished. But the premise is only
true conditionally; the owner of tithed land receives less than what the
owner of tithe-free land is enabled to receive _when other lands are
tithed_; while the conclusion is applied to a state of circumstances in
which that condition fails, and in which, by consequence, the premise will
not be true. The fallacy, therefore, is _à dicto secundum quid ad dictum
simpliciter_.

A third example is the opposition sometimes made to legitimate
interferences of government in the economical affairs of society, grounded
on a misapplication of the maxim, that an individual is a better judge
than the government of what is for his own pecuniary interest. This
objection was urged to Mr. Wakefield’s principle of colonization; the
concentration of the settlers, by fixing such a price on unoccupied land
as may preserve the most desirable proportion between the quantity of land
in culture and the laboring population. Against this it was argued, that
if individuals found it for their advantage to occupy extensive tracts of
land, they, being better judges of their own interest than the legislature
(which can only proceed on general rules), ought not to be restrained from
doing so. But in this argument it was forgotten that the fact of a
person’s taking a large tract of land is evidence only that it is his
interest to take as much as other people, but not that it might not be for
his interest to content himself with less, if he could be assured that
other people would do so too; an assurance which nothing but a government
regulation can give. If all other people took much, and he only a little,
he would reap none of the advantages derived from the concentration of the
population and the consequent possibility of procuring labor for hire, but
would have placed himself, without equivalent, in a situation of voluntary
inferiority. The proposition, therefore, that the quantity of land which
people will take when left to themselves is that which is most for their
interest to take, is true only _secundum quid_: it is only their interest
while they have no guarantee for the conduct of one another. But the
arrangement disregards the limitation, and takes the proposition for true
_simpliciter_.

One of the conditions oftenest dropped, when what would otherwise be a
true proposition is employed as a premise for proving others, is the
condition of _time_. It is a principle of political economy that prices,
profits, wages, etc., “always find their level;” but this is often
interpreted as if it meant that they are always, or generally, _at_ their
level, while the truth is, as Coleridge epigrammatically expresses it,
that they are always _finding_ their level, “which might be taken as a
paraphrase or ironical definition of a storm.”

Under the same head of fallacy (_à dicto secundum quid ad dictum
simpliciter_) might be placed all the errors which are vulgarly called
misapplications of abstract truths; that is, where a principle, true (as
the common expression is) _in the abstract_, that is, all modifying causes
being supposed absent, is reasoned on as if it were true absolutely, and
no modifying circumstance could ever by possibility exist. This very
common form of error it is not requisite that we should exemplify here, as
it will be particularly treated of hereafter in its application to the
subjects on which it is most frequent and most fatal, those of politics
and society.(262)



                               Chapter VII.


Fallacies Of Confusion.


§ 1. Under this fifth and last class it is convenient to arrange all those
fallacies in which the source of error is not so much a false estimate of
the probative force of known evidence, as an indistinct, indefinite, and
fluctuating conception of what the evidence is.

At the head of these stands that multitudinous body of fallacious
reasonings in which the source of error is the ambiguity of terms: when
something which is true if a word be used in a particular sense, is
reasoned on as if it were true in another sense. In such a case there is
not a mal-estimation of evidence, because there is not properly any
evidence to the point at all; there is evidence, but to a different point,
which from a confused apprehension of the meaning of the terms used, is
supposed to be the same. This error will naturally be oftener committed in
our ratiocinations than in our direct inductions, because in the former we
are deciphering our own or other people’s notes, while in the latter we
have the things themselves present, either to the senses or to the memory.
Except, indeed, when the induction is not from individual cases to a
generality, but from generalities to a still higher generalization; in
that case the fallacy of ambiguity may affect the inductive process as
well as the ratiocinative. It occurs in ratiocination in two ways: when
the middle term is ambiguous, or when one of the terms of the syllogism is
taken in one sense in the premises, and in another sense in the
conclusion.

Some good exemplifications of this fallacy are given by Archbishop
Whately. “One case,” says he, “which may be regarded as coming under the
head of Ambiguous Middle, is (what I believe logical writers mean by
‘_Fallacia Figuræ Dictionis_’) the fallacy built on the grammatical
structure of language, from men’s usually taking for granted that
_paronymous_ (or _conjugate_) words, _i.e._, those belonging to each
other, as the substantive, adjective, verb, etc., of the same root, have a
precisely corresponding meaning; which is by no means universally the
case. Such a fallacy could not indeed be even exhibited in strict logical
form, which would preclude even the attempt at it, since it has two middle
terms in sound as well as sense. But nothing is more common in practice
than to vary continually the terms employed, with a view to grammatical
convenience; nor is there any thing unfair in such a practice, as long as
the _meaning_ is preserved unaltered; _e.g._, ‘murder should be punished
with death; this man is a murderer, therefore he deserves to die,’ etc.
Here we proceed on the assumption (in this case just) that to commit
murder, and to be a murderer—to deserve death, and to be one who ought to
die, are, respectively, equivalent expressions; and it would frequently
prove a heavy inconvenience to be debarred this kind of liberty; but the
abuse of it gives rise to the Fallacy in question; _e.g._, _projectors_
are unfit to be trusted; this man has formed a _project_, therefore he is
unfit to be trusted: here the sophist proceeds on the hypothesis that he
who forms a _project_ must be a _projector_: whereas the bad sense that
commonly attaches to the latter word, is not at all implied in the former.
This fallacy may often be considered as lying not in the Middle, but in
one of the terms of the Conclusion; so that the conclusion drawn shall not
be, in reality, at all warranted by the premises, though it will appear to
be so, by means of the grammatical affinity of the words; _e.g._, to be
acquainted with the guilty is a _presumption_ of guilt; this man is so
acquainted, therefore we may _presume_ that he is guilty: this argument
proceeds on the supposition of an exact correspondence between _presume_
and _presumption_, which, however, does not really exist; for
‘presumption’ is commonly used to express a kind of _slight suspicion_;
whereas, ‘to presume’ amounts to actual belief. There are innumerable
instances of a non-correspondence in paronymous words, similar to that
above instanced; as between _art_ and _artful_, _design_ and _designing_,
_faith_ and _faithful_, etc.; and the more slight the variation of the
meaning, the more likely is the fallacy to be successful; for when the
words have become so widely removed in sense as ‘pity’ and ‘pitiful,’
every one would perceive such a fallacy, nor would it be employed but in
jest.(263)

“The present Fallacy is nearly allied to, or rather, perhaps, may be
regarded as a branch of, that founded on _etymology_—viz., when a term is
used, at one time in its customary, and at another in its etymological
sense. Perhaps no example of this can be found that is more extensively
and mischievously employed than in the case of the word _representative_:
assuming that its right meaning must correspond exactly with the strict
and original sense of the verb ‘represent,’ the sophist persuades the
multitude that a member of the House of Commons is bound to be guided in
all points by the opinion of his constituents; and, in short, to be merely
their _spokesman_; whereas law and custom, which in this case may be
considered as fixing the meaning of the term, require no such thing, but
enjoin the representative to act according to the best of his _own_
judgment, and on his own responsibility.”

The following are instances of great practical importance, in which
arguments are habitually founded on a verbal ambiguity.

The mercantile public are frequently led into this fallacy by the phrase
“scarcity of money.” In the language of commerce, “money” has two
meanings: _currency_, or the circulating medium; and _capital seeking
investment_, especially investment on loan. In this last sense the word is
used when the “money market” is spoken of, and when the “value of money”
is said to be high or low, the rate of interest being meant. The
consequence of this ambiguity is, that as soon as scarcity of money in the
latter of these senses begins to be felt—as soon as there is difficulty of
obtaining loans, and the rate of interest is high—it is concluded that
this must arise from causes acting upon the quantity of money in the other
and more popular sense; that the circulating medium must have diminished
in quantity, or ought to be increased. I am aware that, independently of
the double meaning of the term, there are in the facts themselves some
peculiarities, giving an apparent support to this error; but the ambiguity
of the language stands on the very threshold of the subject, and
intercepts all attempts to throw light upon it.

Another ambiguous expression which continually meets us in the political
controversies of the present time, especially in those which relate to
organic changes, is the phrase “influence of property”—which is sometimes
used for the influence of respect for superior intelligence or gratitude
for the kind offices which persons of large property have it so much in
their power to bestow; at other times for the influence of fear; fear of
the worst sort of power, which large property also gives to its possessor,
the power of doing mischief to dependents. To confound these two, is the
standing fallacy of ambiguity brought against those who seek to purify the
electoral system from corruption and intimidation. Persuasive influence,
acting through the conscience of the voter, and carrying his heart and
mind with it, is beneficial—therefore (it is pretended) coercive
influence, which compels him to forget that he is a moral agent, or to act
in opposition to his moral convictions, ought not to be placed under
restraint.

Another word which is often turned into an instrument of the fallacy of
ambiguity, is Theory. In its most proper acceptation, theory means the
completed result of philosophical induction from experience. In that
sense, there are erroneous as well as true theories, for induction may be
incorrectly performed, but theory of some sort is the necessary result of
knowing any thing of a subject, and having put one’s knowledge into the
form of general propositions for the guidance of practice. In this, the
proper sense of the word, Theory is the explanation of practice. In
another and a more vulgar sense, theory means any mere fiction of the
imagination, endeavoring to conceive how a thing may possibly have been
produced, instead of examining how it was produced. In this sense only are
theory and theorists unsafe guides; but because of this, ridicule or
discredit is attempted to be attached to theory in its proper sense, that
is, to legitimate generalization, the end and aim of all philosophy; and a
conclusion is represented as worthless, just because that has been done
which, if done correctly, constitutes the highest worth that a principle
for the guidance of practice can possess, namely, to comprehend in a few
words the real law on which a phenomenon depends, or some property or
relation which is universally true of it.

“The Church” is sometimes understood to mean the clergy alone, sometimes
the whole body of believers, or at least of communicants. The declamations
respecting the inviolability of church property are indebted for the
greater part of their apparent force to this ambiguity. The clergy, being
called the church, are supposed to be the real owners of what is called
church property; whereas they are in truth only the managing members of a
much larger body of proprietors, and enjoy on their own part a mere
usufruct, not extending beyond a life interest.

The following is a Stoical argument taken from Cicero, _De Finibus_, book
the third: “Quod est bonum, omne laudabile est. Quod autem laudabile est,
omne honestum est. Bonum igitur quod est, honestum est.” Here the
ambiguous word is _laudabile_, which in the minor premise means any thing
which mankind are accustomed, on good grounds, to admire or value; as
beauty, for instance, or good fortune: but in the major, it denotes
exclusively moral qualities. In much the same manner the Stoics endeavored
logically to justify as philosophical truths, their figurative and
rhetorical expressions of ethical sentiment: as that the virtuous man is
alone free, alone beautiful, alone a king, etc. Whoever has virtue has
Good (because it has been previously determined not to call any thing else
good); but, again, Good necessarily includes freedom, beauty, and even
kingship, all these being good things; therefore whoever has virtue has
all these.

The following is an argument of Descartes to prove, in his _a priori_
manner, the being of a God. The conception, says he, of an infinite Being
proves the real existence of such a being. For if there is not really any
such being, _I_ must have made the conception; but if I could make it, I
can also unmake it; which evidently is not true; therefore there must be,
externally to myself, an archetype, from which the conception was derived.
In this argument (which, it may be observed, would equally prove the real
existence of ghosts and of witches) the ambiguity is in the pronoun _I_,
by which, in one place, is to be understood my _will_, in another the
_laws of my nature_. If the conception, existing as it does in my mind,
had no original without, the conclusion would unquestionably follow that
_I_ made it; that is, the laws of my nature must have somehow evolved it:
but that my _will_ made it, would not follow. Now when Descartes afterward
adds that I can not unmake the conception, he means that I can not get rid
of it by an act of my will: which is true, but is not the proposition
required. I can as much unmake this conception as I can any other: no
conception which I have once had, can I ever dismiss by mere volition; but
what some of the laws of my nature have produced, other laws, or those
same laws in other circumstances, may, and often do, subsequently efface.

Analogous to this are some of the ambiguities in the free-will
controversy; which, as they will come under special consideration in the
concluding Book, I only mention _memoriæ causâ_. In that discussion, too,
the word _I_ is often shifted from one meaning to another, at one time
standing for my volitions, at another time for the actions which are the
consequences of them, or the mental dispositions from which they proceed.
The latter ambiguity is exemplified in an argument of Coleridge (in his
_Aids to Reflection_), in support of the freedom of the will. It is not
true, he says, that a man is governed by motives; “the man makes the
motive, not the motive the man;” the proof being that “what is a strong
motive to one man is no motive at all to another.” The premise is true,
but only amounts to this, that different persons have different degrees of
susceptibility to the same motive; as they have also to the same
intoxicating liquid, which, however, does not prove that they are free to
be drunk or not drunk, whatever quantity of the fluid they may drink. What
is proved is, that certain mental conditions in the person himself must
co-operate, in the production of the act, with the external inducement;
but those mental conditions also are the effect of causes; and there is
nothing in the argument to prove that they can arise without a cause—that
a spontaneous determination of the will, without any cause at all, ever
takes place, as the free-will doctrine supposes.

The double use, in the free-will controversy, of the word Necessity, which
sometimes stands only for Certainty, at other times for Compulsion;
sometimes for what _can not_ be prevented, at other times only for what we
have reason to be assured _will_ not; we shall have occasion hereafter to
pursue to some of its ulterior consequences.

A most important ambiguity, both in common and in metaphysical language,
is thus pointed out by Archbishop Whately in the Appendix to his Logic:
“_Same_ (as well as _One_, _Identical_, and other words derived from them)
is used frequently in a sense very different from its primary one, as
applicable to a _single_ object; being employed to denote great
_similarity_. When several objects are undistinguishably alike, _one
single description_ will apply equally to any of them; and thence they are
said to be all of _one and the same_ nature, appearance, etc. As, _e.g._,
when we say ‘this house is built of the _same_ stone with such another,’
we only mean that the stones are undistinguishable in their qualities; not
that the one building was pulled down, and the other constructed with the
materials. Whereas _sameness_, in the primary sense, does not even
necessarily imply similarity; for if we say of any man that he is greatly
altered since such a time, we understand, and indeed imply by the very
expression, that he is _one person_, though different in several
qualities. It is worth observing also, that Same, in the secondary sense,
admits, according to popular usage, of degrees: we speak of two things
being _nearly_ the same, but not entirely: personal identity does not
admit of degrees. Nothing, perhaps, has contributed more to the error of
Realism than inattention to this ambiguity. When several persons are said
to have _one and the same_ opinion, thought, or idea, many men,
overlooking the true simple statement of the case, which is, that they are
_all thinking alike_, look for something more abstruse and mystical, and
imagine there must be some _One Thing_, in the primary sense, though not
an individual which is present at once in the mind of each of these
persons; and thence readily sprung Plato’s theory of Ideas, each of which
was, according to him, one real, eternal object, existing entire and
complete in each of the individual objects that are known by one name.”

It is, indeed, not a matter of inference, but of authentic history, that
Plato’s doctrine of Ideas, and the Aristotelian doctrine (in this respect
similar to the Platonic) of substantial forms and second substances, grew
up in the precise way here pointed out; from the supposed necessity of
finding, in things which were said to have the _same_ nature, or the
_same_ qualities, something which was the _same_ in the very sense in
which a man is the same as himself. All the idle speculations respecting
τὸ ὄν, τὸ ἕν, τὸ ὅμοιον, and similar abstractions, so common in the
ancient and in some modern schools of thought, sprang from the same
source. The Aristotelian logicians saw, however, one case of the
ambiguity, and provided against it with their peculiar felicity in the
invention of technical language, when they distinguished things which
differed both _specie_ and _numero_, from those which differed _numero
tantum_, that is, which were exactly alike (in some particular respect at
least) but were distinct individuals. An extension of this distinction to
the two meanings of the word Same, namely, things which are the same
_specie tantum_, and a thing which is the same _numero_ as well as
_specie_, would have prevented the confusion which has been a source of so
much darkness and such an abundance of positive error in metaphysical
philosophy.

One of the most singular examples of the length to which a thinker of
eminence may be led away by an ambiguity of language, is afforded by this
very case. I refer to the famous argument by which Bishop Berkeley
flattered himself that he had forever put an end to “skepticism, atheism,
and irreligion.” It is briefly as follows: I thought of a thing yesterday;
I ceased to think of it; I think of it again to-day. I had, therefore, in
my mind yesterday an _idea_ of the object; I have also an idea of it
to-day; this idea is evidently not another, but the very same idea. Yet an
intervening time elapsed in which I had it not. Where was the idea during
this interval? It must have been somewhere; it did not cease to exist;
otherwise the idea I had yesterday could not be the _same_ idea; no more
than the man I see alive to-day can be the same whom I saw yesterday if
the man has died in the mean while. Now an idea can not be conceived to
exist anywhere except in a mind; and hence there must exist a Universal
Mind, in which all ideas have their permanent residence during the
intervals of their conscious presence in our own minds.

It is evident that Berkeley here confounded sameness _numero_ with
sameness _specie_, that is, with exact resemblance, and assumed the former
where there was only the latter; not perceiving that when we say we have
the same thought to-day which we had yesterday, we do not mean the same
individual thought, but a thought exactly similar: as we say that we have
the same illness which we had last year, meaning only the same sort of
illness.

In one remarkable instance the scientific world was divided into two
furiously hostile parties by an ambiguity of language affecting a branch
of science which, more completely than most others, enjoys the advantage
of a precise and well-defined terminology. I refer to the famous dispute
respecting the vis viva, the history of which is given at large in
Professor Playfair’s Dissertation. The question was, whether the _force_
of a moving body was proportional (its mass being given) to its velocity
simply, or to the square of its velocity: and the ambiguity was in the
word Force. “One of the effects,” says Playfair, “produced by a moving
body is proportional to the square of the velocity, while another is
proportional to the velocity simply:” from whence clearer thinkers were
subsequently led to establish a double measure of the efficiency of a
moving power, one being called _vis viva_, and the other _momentum_. About
the facts, both parties were from the first agreed: the only question was,
with which of the two effects the term _force_ should be, or could most
conveniently be, associated. But the disputants were by no means aware
that this was all; they thought that force was one thing, the production
of effects another; and the question, by which set of effects the force
which produced both the one and the other should be measured, was supposed
to be a question not of terminology, but of fact.

The ambiguity of the word Infinite is the real fallacy in the amusing
logical puzzle of Achilles and the Tortoise, a puzzle which has been too
hard for the ingenuity or patience of many philosophers, and which no less
a thinker than Sir William Hamilton considered as insoluble; as a sound
argument, though leading to a palpable falsehood. The fallacy, as Hobbes
hinted, lies in the tacit assumption that whatever is infinitely divisible
is infinite; but the following solution (to the invention of which I have
no claim) is more precise and satisfactory.

The argument is, let Achilles run ten times as fast as the tortoise, yet
if the tortoise has the start, Achilles will never overtake him. For
suppose them to be at first separated by an interval of a thousand feet:
when Achilles has run these thousand feet, the tortoise will have got on a
hundred; when Achilles has run those hundred, the tortoise will have run
ten, and so on forever: therefore Achilles may run forever without
overtaking the tortoise.

Now the “forever,” in the conclusion, means, for any length of time that
can be supposed; but in the premises, “ever” does not mean any _length_ of
time; it means any _number of subdivisions_ of time. It means that we may
divide a thousand feet by ten, and that quotient again by ten, and so on
as often as we please; that there never needs be an end to the
subdivisions of the distance, nor consequently to those of the time in
which it is performed. But an unlimited number of subdivisions may be made
of that which is itself limited. The argument proves no other infinity of
duration than may be embraced within five minutes. As long as the five
minutes are not expired, what remains of them may be divided by ten, and
again by ten, as often as we like, which is perfectly compatible with
their being only five minutes altogether. It proves, in short, that to
pass through this finite space requires a time which is infinitely
divisible, but not an infinite time; the confounding of which distinction
Hobbes had already seen to be the gist of the fallacy.

The following ambiguities of the word _right_ (in addition to the obvious
and familiar one of _a_ right and the _adjective_ right) are extracted
from a forgotten paper of my own, in a periodical:

“Speaking morally, you are said to have a right to do a thing, if all
persons are morally bound not to hinder you from doing it. But, in another
sense, to have a right to do a thing is the opposite of having _no_ right
to do it, _i.e._, of being under a moral obligation to forbear doing it.
In this sense, to say that you have a right to do a thing, means that you
may do it without any breach of duty on your part; that other persons not
only ought not to hinder you, but have no cause to think worse of you for
doing it. This is a perfectly distinct proposition from the preceding. The
right which you have by virtue of a duty incumbent upon other persons, is
obviously quite a different thing from a right consisting in the absence
of any duty incumbent upon yourself. Yet the two things are perpetually
confounded. Thus, a man will say he has a right to publish his opinions;
which may be true in this sense, that it would be a breach of duty in any
other person to interfere and prevent the publication: but he assumes
thereupon that, in publishing his opinions, he himself violates no duty;
which may either be true or false, depending, as it does, on his having
taken due pains to satisfy himself, first, that the opinions are true, and
next, that their publication in this manner, and at this particular
juncture, will probably be beneficial to the interests of truth on the
whole.

“The second ambiguity is that of confounding a right of any kind, with a
right to enforce that right by resisting or punishing a violation of it.
People will say, for example, that they have a right to good government,
which is undeniably true, it being the moral duty of their governors to
govern them well. But in granting this, you are supposed to have admitted
their right or liberty to turn out their governors, and perhaps to punish
them, for having failed in the performance of this duty; which, far from
being the same thing, is by no means universally true, but depends on an
immense number of varying circumstances,” requiring to be conscientiously
weighed before adopting or acting on such a resolution. This last example
is (like others which have been cited) a case of fallacy within fallacy;
it involves not only the second of the two ambiguities pointed out, but
the first likewise.

One not unusual form of the Fallacy of Ambiguous Terms is known
technically as the Fallacy of Composition and Division; when the same term
is collective in the premises, distributive in the conclusion, or _vicè __
versa_; or when the middle term is collective in one premise, distributive
in the other. As if one were to say (I quote from Archbishop Whately),
“All the angles of a triangle are equal to two right angles: A B C is an
angle of a triangle; therefore A B C is equal to two right angles....
There is no fallacy more common, or more likely to deceive, than the one
now before us. The form in which it is most usually employed is to
establish some truth, separately, concerning _each single_ member of a
certain class, and thence to infer the same of the _whole collectively_.”
As in the argument one sometimes hears, to prove that the world could do
without great men. If Columbus (it is said) had never lived, America would
still have been discovered, at most only a few years later; if Newton had
never lived, some other person would have discovered the law of
gravitation; and so forth. Most true: these things would have been done,
but in all probability not till some one had again been found with the
qualities of Columbus or Newton. Because any one great man might have had
his place supplied by other great men, the argument concludes that all
great men could have been dispensed with. The term “great men” is
distributive in the premises and collective in the conclusion.

“Such also is the fallacy which probably operates on most adventurers in
lotteries; _e.g._, ‘the gaining of a high prize is no uncommon occurrence;
and what is no uncommon occurrence may reasonably be expected; therefore
the gaining of a high prize may reasonably be expected;’ the conclusion,
when applied to the individual (as in practice it is), must be understood
in the sense of ‘reasonably expected _by a certain individual_;’ therefore
for the major premise to be true, the middle term must be understood to
mean, ‘no uncommon occurrence to some one _particular_ person;’ whereas
for the minor (which has been placed first) to be true, you must
understand it of ‘no uncommon occurrence to _some one or other_;’ and thus
you will have the Fallacy of Composition.

“This is a Fallacy with which men are extremely apt to deceive
_themselves_; for when a multitude of particulars are presented to the
mind, many are too weak or too indolent to take a comprehensive view of
them, but confine their attention to each single point, by turns; and then
decide, infer, and act accordingly; _e.g._, the imprudent spendthrift,
finding that he is able to afford this, _or_ that, _or_ the other expense,
forgets that _all of them together_ will ruin him.” The debauchee destroys
his health by successive acts of intemperance, because no _one_ of those
acts would be of itself sufficient to do him any serious harm. A sick
person reasons with himself, “one, and another, and another, of my
symptoms do not prove that I have a fatal disease;” and practically
concludes that all taken together do not prove it.

§ 2. We have now sufficiently exemplified one of the principal Genera in
this Order of Fallacies; where, the source of error being the ambiguity of
terms, the premises are verbally what is required to support the
conclusion, but not really so. In the second great Fallacy of Confusion
they are neither verbally nor really sufficient, though, from their
multiplicity and confused arrangement, and still oftener from defect of
memory, they are not seen to be what they are. The fallacy I mean is that
of Petitio Principii, or begging the question; including the more complex
and not uncommon variety of it, which is termed Reasoning in a Circle.

Petitio Principii, as defined by Archbishop Whately, is the fallacy “in
which the premise either appears manifestly to be the same as the
conclusion, or is actually proved from the conclusion, or is such as would
naturally and properly so be proved.” By the last clause I presume is
meant, that it is not susceptible of any other proof; for otherwise, there
would be no fallacy. To deduce from a proposition propositions from which
it would itself more naturally be deduced, is often an allowable deviation
from the usual didactic order; or at most, what, by an adaptation of a
phrase familiar to mathematicians, may be called a logical
_inelegance_.(264)

The employment of a proposition to prove that on which it is itself
dependent for proof, by no means implies the degree of mental imbecility
which might at first be supposed. The difficulty of comprehending how this
fallacy could possibly be committed, disappears when we reflect that all
persons, even the instructed, hold a great number of opinions without
exactly recollecting how they came by them. Believing that they have at
some former time verified them by sufficient evidence, but having
forgotten what the evidence was, they may easily be betrayed into deducing
from them the very propositions which are alone capable of serving as
premises for their establishment. “As if,” says Archbishop Whately, “one
should attempt to prove the being of a God from the authority of Holy
Writ;” which might easily happen to one with whom both doctrines, as
fundamental tenets of his religious creed, stand on the same ground of
familiar and traditional belief.

Arguing in a circle, however, is a stronger case of the fallacy, and
implies more than the mere passive reception of a premise by one who does
not remember how it is to be proved. It implies an actual attempt to prove
two propositions reciprocally from one another; and is seldom resorted to,
at least in express terms, by any person in his own speculations, but is
committed by those who, being hard pressed by an adversary, are forced
into giving reasons for an opinion of which, when they began to argue,
they had not sufficiently considered the grounds. As in the following
example from Archbishop Whately: “Some mechanicians attempt to prove (what
they ought to lay down as a probable but doubtful hypothesis)(265) that
every particle of matter gravitates equally: ‘why?’ ‘because those bodies
which contain more particles ever gravitate more strongly, _i.e._, are
heavier:’ ‘but (it may be urged) those which are heaviest are not always
more bulky;’ ‘no, but they contain more particles, though more closely
condensed:’ ‘how do you know that?’ ‘because they are heavier:’ ‘how does
that prove it?’ ‘because all particles of matter gravitating equally, that
mass which is specifically the heavier must needs have the more of them in
the same space.’ ” It appears to me that the fallacious reasoner, in his
private thoughts, would not be likely to proceed beyond the first step. He
would acquiesce in the sufficiency of the reason first given, “bodies
which contain more particles are heavier.” It is when he finds this
questioned, and is called upon to prove it, without knowing how, that he
tries to establish his premise by supposing proved what he is attempting
to prove by it. The most effectual way, in fact, of exposing a petitio
principii, when circumstances allow of it, is by challenging the reasoner
to prove his premises; which if he attempts to do, he is necessarily
driven into arguing in a circle.

It is not uncommon, however, for thinkers, and those not of the lowest
description, to be led even in their own thoughts, not indeed into
formally proving each of two propositions from the other, but into
admitting propositions which can only be so proved. In the preceding
example the two together form a complete and consistent, though
hypothetical, explanation of the facts concerned. And the tendency to
mistake mutual coherency for truth—to trust one’s safety to a strong chain
though it has no point of support—is at the bottom of much which, when
reduced to the strict forms of argumentation, can exhibit itself no
otherwise than as reasoning in a circle. All experience bears testimony to
the enthralling effect of neat concatenation in a system of doctrines, and
the difficulty with which people admit the persuasion that any thing which
holds so well together can possibly fall.

Since every case where a conclusion which can only be proved from certain
premises is used for the proof of those premises, is a case of _petitio
principii_, that fallacy includes a very great proportion of all incorrect
reasoning. It is necessary, for completing our view of the fallacy, to
exemplify some of the disguises under which it is accustomed to mask
itself, and to escape exposure.

A proposition would not be admitted by any person in his senses as a
corollary from itself, unless it were expressed in language which made it
seem different. One of the commonest modes of so expressing it, is to
present the proposition itself in abstract terms, as a proof of the same
proposition expressed in concrete language. This is a very frequent mode,
not only of pretended proof, but of pretended explanation; and is parodied
when Molière (_Le Malade Imaginaire_) makes one of his absurd physicians
say,


      Mihi a docto doctore,
      Demandatur causam et rationem quare
    Opium facit dormire.
      A quoi respondeo,
      Quia est in eo
      Virtus dormitiva,
    Cujus est natura
      Sensus assoupire.


The words Nature and Essence are grand instruments of this mode of begging
the question, as in the well-known argument of the scholastic theologians,
that the mind thinks always, because the _essence_ of the mind is to
think. Locke had to point out, that if by essence is here meant some
property which must manifest itself by actual exercise at all times, the
premise is a direct assumption of the conclusion; while if it only means
that to think is the distinctive property of a mind, there is no
connection between the premise and the conclusion, since it is not
necessary that a distinctive property should be perpetually in action.

The following is one of the modes in which these abstract terms, Nature
and Essence, are used as instruments of this fallacy. Some particular
properties of a thing are selected, more or less arbitrarily, to be termed
its nature or essence; and when this has been done, these properties are
supposed to be invested with a kind of indefeasibleness; to have become
paramount to all the other properties of the thing, and incapable of being
prevailed over or counteracted by them. As when Aristotle, in a passage
already cited, “decides that there is no void on such arguments as this:
in a void there could be no difference of up and down; for as in nothing
there are no differences, so there are none in a privation or negation;
but a void is merely a privation or negation of matter; therefore, in a
void, bodies could not move up and down, which it is in their _nature_ to
do.”(266) In other words, it is in the _nature_ of bodies to move up and
down, _ergo_ any physical fact which supposes them not so to move, can not
be authentic. This mode of reasoning, by which a bad generalization is
made to overrule all facts which contradict it, is Petitio Principii in
one of its most palpable forms.

None of the modes of assuming what should be proved are in more frequent
use than what are termed by Bentham “question-begging appellatives;” names
which beg the question under the disguise of stating it. The most potent
of these are such as have a laudatory or vituperative character. For
instance, in politics, the word Innovation. The dictionary meaning of this
term being merely “a change to something new,” it is difficult for the
defenders even of the most salutary improvement to deny that it is an
innovation; yet the word having acquired in common usage a vituperative
connotation in addition to its dictionary meaning, the admission is always
construed as a large concession to the disadvantage of the thing proposed.

The following passage from the argument in refutation of the Epicureans,
in the second book of Cicero, “De Finibus,” affords a fine example of this
sort of fallacy: “Et quidem illud ipsum non nimium probo (et tantum
patior) philosophum loqui de cupiditatibus finiendis. An potest cupiditas
finiri? tollenda est, atque extrahenda radicitus. Quis est enim, in quo
sit cupiditas, quin recte cupidus dici possit? Ergo et avarus erit, sed
finite: adulter, verum habebit modum: et luxuriosus eodem modo. Qualis
ista philosophia est, quæ non interitum afferat pravitatis, sed sit
contenta mediocritate vitiorum?” The question was, whether certain
desires, when kept within bounds, are vices or not; and the argument
decides the point by applying to them a word (_cupiditas_) which _implies_
vice. It is shown, however, in the remarks which follow, that Cicero did
not intend this as a serious argument, but as a criticism on what he
deemed an inappropriate expression. “Rem ipsam prorsus probo: elegantiam
desidero. Appellet hæc _desideria naturæ_; cupiditatis nomen servet alio,”
etc. But many persons, both ancient and modern, have employed this, or
something equivalent to it, as a real and conclusive argument. We may
remark that the passage respecting _cupiditas_ and _cupidus_ is also an
example of another fallacy already noticed, that of Paronymous Terms.

Many more of the arguments of the ancient moralists, and especially of the
Stoics, fall within the definition of Petitio Principii. In the “De
Finibus,” for example, which I continue to quote as being probably the
best extant exemplification at once of the doctrines and the methods of
the schools of philosophy existing at that time; of what value as
arguments are such pleas as those of Cato in the third book: That if
virtue were not happiness, it could not be a thing to _boast_ of: That if
death or pain were evils, it would be impossible not to fear them, and it
could not, therefore, be laudable to despise them, etc. In one way of
viewing these arguments, they may be regarded as appeals to the authority
of the general sentiment of mankind which had stamped its approval upon
certain actions and characters by the phrases referred to; but that such
could have been the meaning intended is very unlikely, considering the
contempt of the ancient philosophers for vulgar opinion. In any other
sense they are clear cases of Petitio Principii, since the word laudable,
and the idea of boasting, imply principles of conduct; and practical
maxims can only be proved from speculative truths, namely, from the
properties of the subject-matter, and can not, therefore, be employed to
prove those properties. As well might it be argued that a government is
good because we ought to support it, or that there is a God because it is
our duty to pray to him.

It is assumed by all the disputants in the “De Finibus” as the foundation
of the inquiry into the _summum bonum_, that “sapiens semper beatus est.”
Not simply that wisdom gives the best chance of happiness, or that wisdom
consists in knowing what happiness is, and by what things it is promoted;
these propositions would not have been enough for them; but that the sage
always is, and must of necessity be, happy. The idea that wisdom could be
consistent with unhappiness, was always rejected as inadmissible: the
reason assigned by one of the interlocutors, near the beginning of the
third book, being, that if the wise could be unhappy, there was little use
in pursuing wisdom. But by unhappiness they did not mean pain or
suffering; to that it was granted that the wisest person was liable in
common with others: he was happy, because in possessing wisdom he had the
most valuable of all possessions, the most to be sought and prized of all
things, and to possess the most valuable thing was to be the most happy.
By laying it down, therefore, at the commencement of the inquiry, that the
sage must be happy, the disputed question respecting the _summum bonum_
was in fact begged; with the further assumption, that pain and suffering,
so far as they can co-exist with wisdom, are not unhappiness, and are no
evil.

The following are additional instances of Petitio Principii, under more or
less of disguise.

Plato, in the _Sophistes_, attempts to prove that things may exist which
are incorporeal, by the argument that justice and wisdom are incorporeal,
and justice and wisdom must be something. Here, if by _something_ be
meant, as Plato did in fact mean, a thing capable of existing in and by
itself, and not as a quality of some other thing, he begs the question in
asserting that justice and wisdom must be something; if he means any thing
else, his conclusion is not proved. This fallacy might also be classed
under ambiguous middleterm; _something_, in the one premise, meaning some
substance, in the other merely some object of thought, whether substance
or attribute.

It was formerly an argument employed in proof of what is now no longer a
popular doctrine, the infinite divisibility of matter, that every portion
of matter however small, must at least have an upper and an under surface.
Those who used this argument did not see that it assumed the very point in
dispute, the impossibility of arriving at a minimum of thickness; for if
there be a minimum, its upper and under surface will of course be one; it
will be itself a surface, and no more. The argument owes its very
considerable plausibility to this, that the premise does actually seem
more obvious than the conclusion, though really identical with it. As
expressed in the premise, the proposition appeals directly and in concrete
language to the incapacity of the human imagination for conceiving a
minimum. Viewed in this light, it becomes a case of the _a priori_ fallacy
or natural prejudice, that whatever can not be conceived can not exist.
Every fallacy of Confusion (it is almost unnecessary to repeat) will, if
cleared up, become a fallacy of some other sort; and it will be found of
deductive or ratiocinative fallacies generally, that when they mislead,
there is mostly, as in this case, a fallacy of some other description
lurking under them, by virtue of which chiefly it is that the verbal
juggle, which is the outside or body of this kind of fallacy, passes
undetected.

Euler’s Algebra, a book otherwise of great merit, but full, to
overflowing, of logical errors in respect to the foundation of the
science, contains the following argument to prove that _minus_ multiplied
by _minus_ gives _plus_, a doctrine the opprobrium of all mere
mathematicians, and which Euler had not a glimpse of the true method of
proving. He says _minus_ multiplied by _minus_ can not give _minus_; for
_minus_ multiplied by _plus_ gives _minus_, and _minus_ multiplied by
_minus_ can not give the same product as _minus_ multiplied by _plus_. Now
one is obliged to ask, why minus multiplied by minus must give any product
at all? and if it does, why its product can not be the same as that of
minus multiplied by plus? for this would seem, at the first glance, not
more absurd than that minus by minus should give the same as plus by plus,
the proposition which Euler prefers to it. The premise requires proof, as
much as the conclusion; nor can it be proved, except by that more
comprehensive view of the nature of multiplication, and of algebraic
processes in general, which would also supply a far better proof of the
mysterious doctrine which Euler is here endeavoring to demonstrate.

A striking instance of reasoning in a circle is that of some ethical
writers, who first take for their standard of moral truth what, being the
general, they deem to be the natural or instinctive sentiments and
perceptions of mankind, and then explain away the numerous instances of
divergence from their assumed standard, by representing them as cases in
which the perceptions are unhealthy. Some particular mode of conduct or
feeling is affirmed to be _unnatural_; why? because it is abhorrent to the
universal and natural sentiments of mankind. Finding no such sentiment in
yourself, you question the fact; and the answer is (if your antagonist is
polite), that you are an exception, a peculiar case. But neither (say you)
do I find in the people of some other country, or of some former age, any
such feeling of abhorrence; “ay, but their feelings were sophisticated and
unhealthy.”

One of the most notable specimens of reasoning in a circle is the doctrine
of Hobbes, Rousseau, and others, which rests the obligations by which
human beings are bound as members of society, on a supposed social
compact. I waive the consideration of the fictitious nature of the compact
itself; but when Hobbes, through the whole Leviathan, elaborately deduces
the obligation of obeying the sovereign, not from the necessity or utility
of doing so, but from a promise supposed to have been made by our
ancestors, on renouncing savage life and agreeing to establish political
society, it is impossible not to retort by the question, Why are we bound
to keep a promise made for us by others? or why bound to keep a promise at
all? No satisfactory ground can be assigned for the obligation, except the
mischievous consequences of the absence of faith and mutual confidence
among mankind. We are, therefore, brought round to the interests of
society, as the ultimate ground of the obligation of a promise; and yet
those interests are not admitted to be a sufficient justification for the
existence of government and law. Without a promise it is thought that we
should not be bound to that which is implied in all modes of living in
society, namely, to yield a general obedience to the laws therein
established; and so necessary is the promise deemed, that if none has
actually been made, some additional safety is supposed to be given to the
foundations of society by feigning one.

§ 3. Two principal subdivisions of the class of Fallacies of Confusion
having been disposed of; there remains a third, in which the confusion is
not, as in the Fallacy of Ambiguity, in misconceiving the import of the
premises, nor, as in Petitio Principii, in forgetting what the premises
are, but in mistaking the conclusion which is to be proved. This is the
fallacy of Ignoratio Elenchi, in the widest sense of the phrase; also
called by Archbishop Whately the Fallacy of Irrelevant Conclusion. His
examples and remarks are highly worthy of citation.

“Various kinds of propositions are, according to the occasion, substituted
for the one of which proof is required; sometimes the particular for the
universal; sometimes a proposition with different terms; and various are
the contrivances employed to effect and to conceal this substitution, and
to make the conclusion which the sophist has drawn, answer practically the
same purpose as the one he ought to have established. We say, ‘practically
the same purpose,’ because it will very often happen that some _emotion_
will be excited, some sentiment impressed on the mind (by a dexterous
employment of this fallacy), such as shall bring men into the
_disposition_ requisite for your purpose; though they may not have
assented to, or even stated distinctly in their own minds, the
_proposition_ which it was your business to establish. Thus if a sophist
has to defend one who has been guilty of some _serious_ offense, which he
wishes to extenuate, though he is unable distinctly to prove that it is
not such, yet if he can succeed in _making the audience laugh_ at some
casual matter, he has gained practically the same point. So also if any
one has pointed out the extenuating circumstances in some particular case
of offense, so as to show that it differs widely from the generality of
the same class, the sophist, if he finds himself unable to disprove these
circumstances, may do away the force of them, by simply _referring the
action to that very class_, which no one can deny that it belongs to, and
the very name of which will excite a feeling of disgust sufficient to
counteract the extenuation; _e.g._, let it be a case of peculation, and
that many _mitigating_ circumstances have been brought forward which can
not be denied; the sophistical opponent will reply, ‘Well, but after all,
the man is a _rogue_, and there is an end of it;’ now in reality this was
(by hypothesis) never the question; and the mere assertion of what was
never denied _ought_ not, in fairness, to be regarded as decisive; but,
practically, the odiousness of the word, arising in great measure from the
association of those very circumstances which belong to most of the class,
but which we have supposed to be _absent_ in _this particular_ instance,
excites precisely that feeling of disgust which, in effect, destroys the
force of the defense. In like manner we may refer to this head all cases
of improper appeal to the passions, and every thing else which is
mentioned by Aristotle as extraneous to the matter in hand (ἔξω τοῦ
πράγματος).”

Again, “instead of proving that ‘this prisoner has committed an atrocious
fraud,’ you prove that the fraud he is accused of is atrocious; instead of
proving (as in the well-known tale of Cyrus and the two coats) that the
taller boy had a right to force the other boy to exchange coats with him,
you prove that the exchange would have been advantageous to both; instead
of proving that the poor ought to be relieved in this way rather than in
that, you prove that the poor ought to be relieved; instead of proving
that the irrational agent—whether a brute or a madman—can never be
deterred from any act by apprehension of punishment (as, for instance, a
dog from sheep-biting, by fear of being beaten), you prove that the
beating of one dog does not operate as an _example_ to _other_ dogs, etc.

“It is evident that Ignoratio Elenchi may be employed as well for the
apparent refutation of your opponent’s proposition, as for the apparent
establishment of your own; for it is substantially the same thing, to
prove what was not denied or to disprove what was not asserted. The latter
practice is not less common, and it is more offensive, because it
frequently amounts to a personal affront, in attributing to a person
opinions, etc., which he perhaps holds in abhorrence. Thus, when in a
discussion one party vindicates, on the ground of general expediency, a
particular instance of resistance to government in a case of intolerable
oppression, the opponent may gravely maintain, ‘that we ought not to do
evil that good may come;’ a proposition which of course had never been
denied, the point in dispute being, ‘whether resistance in this particular
case _were_ doing evil or not.’ Or again, by way of disproving the
assertion of the right of private judgment in religion, one may hear a
grave argument to prove that ‘it is impossible every one can be _right in
his judgment_.’ ”

The works of controversial writers are seldom free from this fallacy. The
attempts, for instance, to disprove the population doctrines of Malthus,
have been mostly cases of _ignoratio elenchi_. Malthus has been supposed
to be refuted if it could be shown that in some countries or ages
population has been nearly stationary; as if he had asserted that
population always increases in a given ratio, or had not expressly
declared that it increases only in so far as it is not restrained by
prudence, or kept down by poverty and disease. Or, perhaps, a collection
of facts is produced to prove that in some one country the people are
better off with a dense population than they are in another country with a
thin one; or that the people have become more numerous and better off at
the same time. As if the assertion were that a dense population could not
possibly be well off; as if it were not part of the very doctrine, and
essential to it, that where there is a more abundant production there may
be a greater population without any increase of poverty, or even with a
diminution of it.

The favorite argument against Berkeley’s theory of the non-existence of
matter, and the most popularly effective, next to a “grin”(267)—an
argument, moreover, which is not confined to “coxcombs,” nor to men like
Samuel Johnson, whose greatly overrated ability certainly did not lie in
the direction of metaphysical speculation, but is the stock argument of
the Scotch school of metaphysicians—is a palpable Ignoratio Elenchi. The
argument is perhaps as frequently expressed by gesture as by words, and
one of its commonest forms consists in knocking a stick against the
ground. This short and easy confutation overlooks the fact, that in
denying matter, Berkeley did not deny any thing to which our senses bear
witness, and therefore can not be answered by any appeal to them. His
skepticism related to the supposed substratum, or hidden cause of the
appearances perceived by our senses; the evidence of which, whatever may
be thought of its conclusiveness, is certainly not the evidence of sense.
And it will always remain a signal proof of the want of metaphysical
profundity of Reid, Stewart, and, I am sorry to add, of Brown, that they
should have persisted in asserting that Berkeley, if he believed his own
doctrine, was bound to walk into the kennel, or run his head against a
post. As if persons who do not recognize an occult cause of their
sensations could not possibly believe that a fixed order subsists among
the sensations themselves. Such a want of comprehension of the distinction
between a thing and its sensible manifestation, or, in metaphysical
language, between the noumenon and the phenomenon, would be impossible to
even the dullest disciple of Kant or Coleridge.

It would be easy to add a greater number of examples of this fallacy, as
well as of the others which I have attempted to characterize. But a more
copious exemplification does not seem to be necessary; and the intelligent
reader will have little difficulty in adding to the catalogue from his own
reading and experience. We shall, therefore, here close our exposition of
the general principles of logic, and proceed to the supplementary inquiry
which is necessary to complete our design.



                                 Book VI.


ON THE LOGIC OF THE MORAL SCIENCES.


    “Si l’homme peut prédire, avec une assurance presque entière, les
    phénomènes dont il connaît les lois; si lors même qu’elles lui
    sont inconnues, il peut, d’après l’expérience, prévoir avec une
    grande probabilité les événements de l’avenir; pourquoi
    regarderait-on comme une entreprise chimérique, celle de tracer
    avec quelque vraisemblance le tableau des destinées futures de
    l’espèce humaine, d’après les résultats de son histoire? Le seul
    fondement de croyance dans les sciences naturelles, est cette
    idée, que les lois générales, connues ou ignorées, qui règlent les
    phénomènes de l’univers, sont nécessaires et constantes; et par
    quelle raison ce principe serait-il moins vrai pour le
    développement des facultés intellectuelles et morales de l’homme,
    que pour les autres opérations de la nature? Enfin, puisque des
    opinions formées d’après l’expérience ... sont la seule règle de
    la conduite des hommes les plus sages, pourquoi interdirait-on au
    philosophe d’appuyer ses conjectures sur cette même base, pourvu
    qu’il ne leur attribue pas une certitude supérieure à celle qui
    peut naître du nombre, de la constance, de l’exactitude des
    observations?”—CONDORCET, _Esquisse d’un Tableau Historique des
    Progrès de l’Esprit Humain_.



                                Chapter I.


Introductory Remarks.


§ 1. Principles of Evidence and Theories of Method are not to be
constructed _a priori_. The laws of our rational faculty, like those of
every other natural agency, are only learned by seeing the agent at work.
The earlier achievements of science were made without the conscious
observance of any Scientific Method; and we should never have known by
what process truth is to be ascertained, if we had not previously
ascertained many truths. But it was only the easier problems which could
be thus resolved: natural sagacity, when it tried its strength against the
more difficult ones, either failed altogether, or, if it succeeded here
and there in obtaining a solution, had no sure means of convincing others
that its solution was correct. In scientific investigation, as in all
other works of human skill, the way of obtaining the end is seen as it
were instinctively by superior minds in some comparatively simple case,
and is then, by judicious generalization, adapted to the variety of
complex cases. We learn to do a thing in difficult circumstances, by
attending to the manner in which we have spontaneously done the same thing
in easier ones.

This truth is exemplified by the history of the various branches of
knowledge which have successively, in the ascending order of their
complication, assumed the character of sciences; and will doubtless
receive fresh confirmation from those of which the final scientific
constitution is yet to come, and which are still abandoned to the
uncertainties of vague and popular discussion. Although several other
sciences have emerged from this state at a comparatively recent date, none
now remain in it except those which relate to man himself, the most
complex and most difficult subject of study on which the human mind can be
engaged.

Concerning the physical nature of man, as an organized being—though there
is still much uncertainty and much controversy, which can only be
terminated by the general acknowledgment and employment of stricter rules
of induction than are commonly recognized—there is, however, a
considerable body of truths which all who have attended to the subject
consider to be fully established; nor is there now any radical
imperfection in the method observed in the department of science by its
most distinguished modern teachers. But the laws of Mind, and, in even a
greater degree, those of Society, are so far from having attained a
similar state of even partial recognition, that it is still a controversy
whether they are capable of becoming subjects of science in the strict
sense of the term: and among those who are agreed on this point, there
reigns the most irreconcilable diversity on almost every other. Here,
therefore, if anywhere, the principles laid down in the preceding Books
may be expected to be useful.

If on matters so much the most important with which human intellect can
occupy itself a more general agreement is ever to exist among thinkers; if
what has been pronounced “the proper study of mankind” is not destined to
remain the only subject which Philosophy can not succeed in rescuing from
Empiricism; the same process through which the laws of many simpler
phenomena have by general acknowledgment been placed beyond dispute, must
be consciously and deliberately applied to those more difficult inquiries.
If there are some subjects on which the results obtained have finally
received the unanimous assent of all who have attended to the proof, and
others on which mankind have not yet been equally successful; on which the
most sagacious minds have occupied themselves from the earliest date, and
have never succeeded in establishing any considerable body of truths, so
as to be beyond denial or doubt; it is by generalizing the methods
successfully followed in the former inquiries, and adapting them to the
latter, that we may hope to remove this blot on the face of science. The
remaining chapters are an endeavor to facilitate this most desirable
object.

§ 2. In attempting this, I am not unmindful how little can be done toward
it in a mere treatise on Logic, or how vague and unsatisfactory all
precepts of Method must necessarily appear when not practically
exemplified in the establishment of a body of doctrine. Doubtless, the
most effectual mode of showing how the sciences of Ethics and Politics may
be constructed would be to construct them: a task which, it needs scarcely
be said, I am not about to undertake. But even if there were no other
examples, the memorable one of Bacon would be sufficient to demonstrate,
that it is sometimes both possible and useful to point out the way, though
without being one’s self prepared to adventure far into it. And if more
were to be attempted, this at least is not a proper place for the attempt.

In substance, whatever can be done in a work like this for the Logic of
the Moral Sciences, has been or ought to have been accomplished in the
five preceding Books; to which the present can be only a kind of
supplement or appendix, since the methods of investigation applicable to
moral and social science must have been already described, if I have
succeeded in enumerating and characterizing those of science in general.
It remains, however, to examine which of those methods are more especially
suited to the various branches of moral inquiry; under what peculiar
facilities or difficulties they are there employed; how far the
unsatisfactory state of those inquiries is owing to a wrong choice of
methods, how far to want of skill in the application of right ones; and
what degree of ultimate success may be attained or hoped for by a better
choice or more careful employment of logical processes appropriate to the
case. In other words, whether moral sciences exist, or can exist; to what
degree of perfection they are susceptible of being carried; and by what
selection or adaptation of the methods brought to view in the previous
part of this work that degree of perfection is attainable.

At the threshold of this inquiry we are met by an objection, which, if not
removed, would be fatal to the attempt to treat human conduct as a subject
of science. Are the actions of human beings, like all other natural
events, subject to invariable laws? Does that constancy of causation,
which is the foundation of every scientific theory of successive
phenomena, really obtain among them? This is often denied; and for the
sake of systematic completeness, if not from any very urgent practical
necessity, the question should receive a deliberate answer in this place.
We shall devote to the subject a chapter apart.



                               Chapter II.


Of Liberty And Necessity.


§ 1. The question, whether the law of causality applies in the same strict
sense to human actions as to other phenomena, is the celebrated
controversy concerning the freedom of the will; which, from at least as
far back as the time of Pelagius, has divided both the philosophical and
the religious world. The affirmative opinion is commonly called the
doctrine of Necessity, as asserting human volitions and actions to be
necessary and inevitable. The negative maintains that the will is not
determined, like other phenomena, by antecedents, but determines itself;
that our volitions are not, properly speaking, the effects of causes, or
at least have no causes which they uniformly and implicitly obey.

I have already made it sufficiently apparent that the former of these
opinions is that which I consider the true one; but the misleading terms
in which it is often expressed, and the indistinct manner in which it is
usually apprehended, have both obstructed its reception, and perverted its
influence when received. The metaphysical theory of free-will, as held by
philosophers (for the practical feeling of it, common in a greater or less
degree to all mankind, is in no way inconsistent with the contrary
theory), was invented because the supposed alternative of admitting human
actions to be _necessary_ was deemed inconsistent with every one’s
instinctive consciousness, as well as humiliating to the pride and even
degrading to the moral nature of man. Nor do I deny that the doctrine, as
sometimes held, is open to these imputations; for the misapprehension in
which I shall be able to show that they originate, unfortunately is not
confined to the opponents of the doctrine, but is participated in by many,
perhaps we might say by most, of its supporters.

§ 2. Correctly conceived, the doctrine called Philosophical Necessity is
simply this: that, given the motives which are present to an individual’s
mind, and given likewise the character and disposition of the individual,
the manner in which he will act might be unerringly inferred; that if we
knew the person thoroughly, and knew all the inducements which are acting
upon him, we could foretell his conduct with as much certainty as we can
predict any physical event. This proposition I take to be a mere
interpretation of universal experience, a statement in words of what every
one is internally convinced of. No one who believed that he knew
thoroughly the circumstances of any case, and the characters of the
different persons concerned, would hesitate to foretell how all of them
would act. Whatever degree of doubt he may in fact feel, arises from the
uncertainty whether he really knows the circumstances, or the character of
some one or other of the persons, with the degree of accuracy required;
but by no means from thinking that if he did know these things, there
could be any uncertainty what the conduct would be. Nor does this full
assurance conflict in the smallest degree with what is called our feeling
of freedom. We do not feel ourselves the less free, because those to whom
we are intimately known are well assured how we shall will to act in a
particular case. We often, on the contrary, regard the doubt what our
conduct will be, as a mark of ignorance of our character, and sometimes
even resent it as an imputation. The religious metaphysicians who have
asserted the freedom of the will, have always maintained it to be
consistent with divine foreknowledge of our actions: and if with divine,
then with any other foreknowledge. We may be free, and yet another may
have reason to be perfectly certain what use we shall make of our freedom.
It is not, therefore, the doctrine that our volitions and actions are
invariable consequents of our antecedent states of mind, that is either
contradicted by our consciousness, or felt to be degrading.

But the doctrine of causation, when considered as obtaining between our
volitions and their antecedents, is almost universally conceived as
involving more than this. Many do not believe, and very few practically
feel, that there is nothing in causation but invariable, certain, and
unconditional sequence. There are few to whom mere constancy of succession
appears a sufficiently stringent bond of union for so peculiar a relation
as that of cause and effect. Even if the reason repudiates, the
imagination retains, the feeling of some more intimate connection, of some
peculiar tie, or mysterious constraint exercised by the antecedent over
the consequent. Now this it is which, considered as applying to the human
will, conflicts with our consciousness, and revolts our feelings. We are
certain that, in the case of our volitions, there is not this mysterious
constraint. We know that we are not compelled, as by a magical spell, to
obey any particular motive. We feel, that if we wished to prove that we
have the power of resisting the motive, we could do so (that wish being,
it needs scarcely be observed, a _new antecedent_); and it would be
humiliating to our pride, and (what is of more importance) paralyzing to
our desire of excellence, if we thought otherwise. But neither is any such
mysterious compulsion now supposed, by the best philosophical authorities,
to be exercised by any other cause over its effect. Those who think that
causes draw their effects after them by a mystical tie, are right in
believing that the relation between volitions and their antecedents is of
another nature. But they should go farther, and admit that this is also
true of all other effects and their antecedents. If such a tie is
considered to be involved in the word Necessity, the doctrine is not true
of human actions; but neither is it then true of inanimate objects. It
would be more correct to say that matter is not bound by necessity, than
that mind is so.

That the free-will metaphysicians, being mostly of the school which
rejects Hume’s and Brown’s analysis of Cause and Effect, should miss their
way for want of the light which that analysis affords, can not surprise
us. The wonder is, that the necessitarians, who usually admit that
philosophical theory, should in practice equally lose sight of it. The
very same misconception of the doctrine called Philosophical Necessity,
which prevents the opposite party from recognizing its truth, I believe to
exist more or less obscurely in the minds of most necessitarians, however
they may in words disavow it. I am much mistaken if they habitually feel
that the necessity which they recognize in actions is but uniformity of
order, and capability of being predicted. They have a feeling as if there
were at bottom a stronger tie between the volitions and their causes; as
if, when they asserted that the will is governed by the balance of
motives, they meant something more cogent than if they had only said, that
whoever knew the motives, and our habitual susceptibilities to them, could
predict how we should will to act. They commit, in opposition to their own
scientific system, the very same mistake which their adversaries commit in
obedience to theirs; and in consequence do really in some instances suffer
those depressing consequences which their opponents erroneously impute to
the doctrine itself.

§ 3. I am inclined to think that this error is almost wholly an effect of
the associations with a word, and that it would be prevented, by
forbearing to employ, for the expression of the simple fact of causation,
so extremely inappropriate a term as Necessity. That word, in its other
acceptations, involves much more than mere uniformity of sequence: it
implies irresistibleness. Applied to the will, it only means that, the
given cause will be followed by the effect, subject to all possibilities
of counteraction by other causes; but in common use it stands for the
operation of those causes exclusively which are supposed too powerful to
be counteracted at all. When we say that all human actions take place of
necessity, we only mean that they will certainly happen if nothing
prevents; when we say that dying of want, to those who can not get food,
is a necessity, we mean that it will certainly happen whatever may be done
to prevent it. The application of the same term to the agencies on which
human actions depend, as is used to express those agencies of nature which
are really uncontrollable, can not fail, when habitual, to create a
feeling of uncontrollableness in the former also. This, however, is a mere
illusion. There are physical sequences which we call necessary, as death
for want of food or air; there are others which, though as much cases of
causation as the former, are not said to be necessary, as death from
poison, which an antidote, or the use of the stomach-pump, will sometimes
avert. It is apt to be forgotten by people’s feelings, even if remembered
by their understandings, that human actions are in this last predicament:
they are never (except in some cases of mania) ruled by any one motive
with such absolute sway that there is no room for the influence of any
other. The causes, therefore, on which action depends, are never
uncontrollable; and any given effect is only necessary provided that the
causes tending to produce it are not controlled. That whatever happens,
could not have happened otherwise, unless something had taken place which
was capable of preventing it, no one surely needs hesitate to admit. But
to call this by the name Necessity is to use the term in a sense so
different from its primitive and familiar meaning, from that which it
bears in the common occasions of life, as to amount almost to a play upon
words. The associations derived from the ordinary sense of the term will
adhere to it in spite of all we can do; and though the doctrine of
Necessity, as stated by most who hold it, is very remote from fatalism, it
is probable that most necessitarians are fatalists, more or less, in their
feelings.

A fatalist believes, or half believes (for nobody is a consistent
fatalist), not only that whatever is about to happen will be the
infallible result of the causes which produce it (which is the true
necessitarian doctrine), but moreover that there is no use in struggling
against it; that it will happen, however we may strive to prevent it. Now,
a necessitarian, believing that our actions follow from our characters,
and that our characters follow from our organization, our education, and
our circumstances, is apt to be, with more or less of consciousness on his
part, a fatalist as to his own actions, and to believe that his nature is
such, or that his education and circumstances have so moulded his
character, that nothing can now prevent him from feeling and acting in a
particular way, or at least that no effort of his own can hinder it. In
the words of the sect which in our own day has most perseveringly
inculcated and most perversely misunderstood this great doctrine, his
character is formed _for_ him, and not _by_ him; therefore his wishing
that it had been formed differently is of no use; he has no power to alter
it. But this is a grand error. He has, to a certain extent, a power to
alter his character. Its being, in the ultimate resort, formed for him, is
not inconsistent with its being, in part, formed _by_ him as one of the
intermediate agents. His character is formed by his circumstances
(including among these his particular organization); but his own desire to
mould it in a particular way, is one of those circumstances, and by no
means one of the least influential. We can not, indeed, directly will to
be different from what we are. But neither did those who are supposed to
have formed our characters directly will that we should be what we are.
Their will had no direct power except over their own actions. They made us
what they did make us, by willing, not the end, but the requisite means;
and we, when our habits are not too inveterate, can, by similarly willing
the requisite means, make ourselves different. If they could place us
under the influence of certain circumstances, we, in like manner, can
place ourselves under the influence of other circumstances. We are exactly
as capable of making our own character, _if we will_, as others are of
making it for us.

Yes (answers the Owenite), but these words, “if we will,” surrender the
whole point: since the will to alter our own character is given us, not by
any efforts of ours, but by circumstances which we can not help, it comes
to us either from external causes, or not at all. Most true: if the
Owenite stops here, he is in a position from which nothing can expel him.
Our character is formed by us as well as for us; but the wish which
induces us to attempt to form it is formed for us; and how? Not, in
general, by our organization, nor wholly by our education, but by our
experience; experience of the painful consequences of the character we
previously had; or by some strong feeling of admiration or aspiration,
accidentally aroused. But to think that we have no power of altering our
character, and to think that we shall not use our power unless we desire
to use it, are very different things, and have a very different effect on
the mind. A person who does not wish to alter his character, can not be
the person who is supposed to feel discouraged or paralyzed by thinking
himself unable to do it. The depressing effect of the fatalist doctrine
can only be felt where there _is_ a wish to do what that doctrine
represents as impossible. It is of no consequence what we think forms our
character, when we have no desire of our own about forming it; but it is
of great consequence that we should not be prevented from forming such a
desire by thinking the attainment impracticable, and that if we have the
desire, we should know that the work is not so irrevocably done as to be
incapable of being altered.

And indeed, if we examine closely, we shall find that this feeling, of our
being able to modify our own character _if we wish_, is itself the feeling
of moral freedom which we are conscious of. A person feels morally free
who feels that his habits or his temptations are not his masters, but he
theirs; who, even in yielding to them, knows that he could resist; that
were he desirous of altogether throwing them off, there would not be
required for that purpose a stronger desire than he knows himself to be
capable of feeling. It is of course necessary, to render our consciousness
of freedom complete, that we should have succeeded in making our character
all we have hitherto attempted to make it; for if we have wished and not
attained, we have, to that extent, not power over our own character; we
are not free. Or at least, we must feel that our wish, if not strong
enough to alter our character, is strong enough to conquer our character
when the two are brought into conflict in any particular case of conduct.
And hence it is said with truth, that none but a person of confirmed
virtue is completely free.

The application of so improper a term as Necessity to the doctrine of
cause and effect in the matter of human character, seems to me one of the
most signal instances in philosophy of the abuse of terms, and its
practical consequences one of the most striking examples of the power of
language over our associations. The subject will never be generally
understood until that objectionable term is dropped. The free-will
doctrine, by keeping in view precisely that portion of the truth which the
word Necessity puts out of sight, namely the power of the mind to
co-operate in the formation of its own character, has given to its
adherents a practical feeling much nearer to the truth than has generally
(I believe) existed in the minds of necessitarians. The latter may have
had a stronger sense of the importance of what human beings can do to
shape the characters of one another; but the free-will doctrine has, I
believe, fostered in its supporters a much stronger spirit of
self-culture.

§ 4. There is still one fact which requires to be noticed (in addition to
the existence of a power of self-formation) before the doctrine of the
causation of human actions can be freed from the confusion and
misapprehensions which surround it in many minds. When the will is said to
be determined by motives, a motive does not mean always, or solely, the
anticipation of a pleasure or of a pain. I shall not here inquire whether
it be true that, in the commencement, all our voluntary actions are mere
means consciously employed to obtain some pleasure or avoid some pain. It
is at least certain that we gradually, through the influence of
association, come to desire the means without thinking of the end; the
action itself becomes an object of desire, and is performed without
reference to any motive beyond itself. Thus far, it may still be objected
that, the action having through association become pleasurable, we are, as
much as before, moved to act by the anticipation of a pleasure, namely,
the pleasure of the action itself. But granting this, the matter does not
end here. As we proceed in the formation of habits, and become accustomed
to will a particular act or a particular course of conduct because it is
pleasurable, we at last continue to will it without any reference to its
being pleasurable. Although, from some change in us or in our
circumstances, we have ceased to find any pleasure in the action, or
perhaps to anticipate any pleasure as the consequence of it, we still
continue to desire the action, and consequently to do it. In this manner
it is that habits of hurtful excess continue to be practiced although they
have ceased to be pleasurable; and in this manner also it is that the
habit of willing to persevere in the course which he has chosen, does not
desert the moral hero, even when the reward, however real, which he
doubtless receives from the consciousness of well-doing, is any thing but
an equivalent for the sufferings he undergoes, or the wishes which he may
have to renounce.

A habit of willing is commonly called a purpose; and among the causes of
our volitions, and of the actions which flow from them, must be reckoned
not only likings and aversions, but also purposes. It is only when our
purposes have become independent of the feelings of pain or pleasure from
which they originally took their rise, that we are said to have a
confirmed character. “A character,” says Novalis, “is a completely
fashioned will:” and the will, once so fashioned, may be steady and
constant, when the passive susceptibilities of pleasure and pain are
greatly weakened or materially changed.

With the corrections and explanations now given, the doctrine of the
causation of our volitions by motives, and of motives by the desirable
objects offered to us, combined with our particular susceptibilities of
desire, may be considered, I hope, as sufficiently established for the
purposes of this treatise.(268)



                               Chapter III.


That There Is, Or May Be, A Science Of Human Nature.


§ 1. It is a common notion, or at least it is implied in many common modes
of speech, that the thoughts, feelings, and actions of sentient beings are
not a subject of science, in the same strict sense in which this is true
of the objects of outward nature. This notion seems to involve some
confusion of ideas, which it is necessary to begin by clearing up.

Any facts are fitted, in themselves, to be a subject of science which
follow one another according to constant laws, although those laws may not
have been discovered, nor even be discoverable by our existing resources.
Take, for instance, the most familiar class of meteorological phenomena,
those of rain and sunshine. Scientific inquiry has not yet succeeded in
ascertaining the order of antecedence and consequence among these
phenomena, so as to be able, at least in our regions of the earth, to
predict them with certainty, or even with any high degree of probability.
Yet no one doubts that the phenomena depend on laws, and that these must
be derivative laws resulting from known ultimate laws, those of heat,
electricity, vaporization, and elastic fluids. Nor can it be doubted that
if we were acquainted with all the antecedent circumstances, we could,
even from those more general laws, predict (saving difficulties of
calculation) the state of the weather at any future time. Meteorology,
therefore, not only has in itself every natural requisite for being, but
actually is, a science; though, from the difficulty of observing the facts
on which the phenomena depend (a difficulty inherent in the peculiar
nature of those phenomena), the science is extremely imperfect; and were
it perfect, might probably be of little avail in practice, since the data
requisite for applying its principles to particular instances would rarely
be procurable.

A case may be conceived, of an intermediate character, between the
perfection of science and this its extreme imperfection. It may happen
that the greater causes, those on which the principal part of the
phenomena depends, are within the reach of observation and measurement; so
that if no other causes intervened, a complete explanation could be given
not only of the phenomena in general, but of all the variations and
modifications which it admits of. But inasmuch as other, perhaps many
other causes, separately insignificant in their effects, co-operate or
conflict in many or in all cases with those greater causes, the effect,
accordingly, presents more or less of aberration from what would be
produced by the greater causes alone. Now if these minor causes are not so
constantly accessible, or not accessible at all, to accurate observation,
the principal mass of the effect may still, as before, be accounted for,
and even predicted; but there will be variations and modifications which
we shall not be competent to explain thoroughly, and our predictions will
not be fulfilled accurately, but only approximately.

It is thus, for example, with the theory of the tides. No one doubts that
Tidology (as Dr. Whewell proposes to call it) is really a science. As much
of the phenomena as depends on the attraction of the sun and moon is
completely understood, and may, in any, even unknown, part of the earth’s
surface, be foretold with certainty; and the far greater part of the
phenomena depends on those causes. But circumstances of a local or casual
nature, such as the configuration of the bottom of the ocean, the degree
of confinement from shores, the direction of the wind, etc., influence, in
many or in all places, the height and time of the tide; and a portion of
these circumstances being either not accurately knowable, not precisely
measurable, or not capable of being certainly foreseen, the tide in known
places commonly varies from the calculated result of general principles by
some difference that we can not explain, and in unknown ones may vary from
it by a difference that we are not able to foresee or conjecture.
Nevertheless, not only is it certain that these variations depend on
causes, and follow their causes by laws of unerring uniformity; not only,
therefore, is tidology a science, like meteorology, but it is, what
hitherto at least meteorology is not, a science largely available in
practice. General laws may be laid down respecting the tides, predictions
may be founded on those laws, and the result will in the main, though
often not with complete accuracy, correspond to the predictions.

And this is what is or ought to be meant by those who speak of sciences
which are not _exact_ sciences. Astronomy was once a science, without
being an exact science. It could not become exact until not only the
general course of the planetary motions, but the perturbations also, were
accounted for, and referred to their causes. It has become an exact
science, because its phenomena have been brought under laws comprehending
the whole of the causes by which the phenomena are influenced, whether in
a great or only in a trifling degree, whether in all or only in some
cases, and assigning to each of those causes the share of effect which
really belongs to it. But in the theory of the tides the only laws as yet
accurately ascertained are those of the causes which affect the phenomenon
in all cases, and in a considerable degree; while others which affect it
in some cases only, or, if in all, only in a slight degree, have not been
sufficiently ascertained and studied to enable us to lay down their laws;
still less to deduce the completed law of the phenomenon, by compounding
the effects of the greater with those of the minor causes. Tidology,
therefore, is not yet an exact science; not from any inherent incapacity
of being so, but from the difficulty of ascertaining with complete
precision the real derivative uniformities. By combining, however, the
exact laws of the greater causes, and of such of the minor ones as are
sufficiently known, with such empirical laws or such approximate
generalizations respecting the miscellaneous variations as can be obtained
by specific observation, we can lay down general propositions which will
be true in the main, and on which, with allowance for the degree of their
probable inaccuracy, we may safely ground our expectations and our
conduct.

§ 2. The science of human nature is of this description. It falls far
short of the standard of exactness now realized in Astronomy; but there is
no reason that it should not be as much a science as Tidology is, or as
Astronomy was when its calculations had only mastered the main phenomena,
but not the perturbations.

The phenomena with which this science is conversant being the thoughts,
feelings, and actions of human beings, it would have attained the ideal
perfection of a science if it enabled us to foretell how an individual
would think, feel, or act throughout life, with the same certainty with
which astronomy enables us to predict the places and the occultations of
the heavenly bodies. It needs scarcely be stated that nothing approaching
to this can be done. The actions of individuals could not be predicted
with scientific accuracy, were it only because we can not foresee the
whole of the circumstances in which those individuals will be placed. But
further, even in any given combination of (present) circumstances, no
assertion, which is both precise and universally true, can be made
respecting the manner in which human beings will think, feel, or act. This
is not, however, because every person’s modes of thinking, feeling, and
acting do not depend on causes; nor can we doubt that if, in the case of
any individual, our data could be complete, we even now know enough of the
ultimate laws by which mental phenomena are determined, to enable us in
many cases to predict, with tolerable certainty, what, in the greater
number of supposable combinations of circumstances, his conduct or
sentiments would be. But the impressions and actions of human beings are
not solely the result of their present circumstances, but the joint result
of those circumstances and of the characters of the individuals; and the
agencies which determine human character are so numerous and diversified
(nothing which has happened to the person throughout life being without
its portion of influence), that in the aggregate they are never in any two
cases exactly similar. Hence, even if our science of human nature were
theoretically perfect, that is, if we could calculate any character as we
can calculate the orbit of any planet, _from given data_; still, as the
data are never all given, nor ever precisely alike in different cases, we
could neither make positive predictions, nor lay down universal
propositions.

Inasmuch, however, as many of those effects which it is of most importance
to render amenable to human foresight and control are determined, like the
tides, in an incomparably greater degree by general causes, than by all
partial causes taken together; depending in the main on those
circumstances and qualities which are common to all mankind, or at least
to large bodies of them, and only in a small degree on the idiosyncrasies
of organization or the peculiar history of individuals; it is evidently
possible with regard to all such effects, to make predictions which will
_almost_ always be verified, and general propositions which are almost
always true. And whenever it is sufficient to know how the great majority
of the human race, or of some nation or class of persons, will think,
feel, and act, these propositions are equivalent to universal ones. For
the purposes of political and social science this _is_ sufficient. As we
formerly remarked,(269) an approximate generalization is, in social
inquiries, for most practical purposes equivalent to an exact one; that
which is only probable when asserted of individual human beings
indiscriminately selected, being certain when affirmed of the character
and collective conduct of masses.

It is no disparagement, therefore, to the science of Human Nature, that
those of its general propositions which descend sufficiently into detail
to serve as a foundation for predicting phenomena in the concrete, are for
the most part only approximately true. But in order to give a genuinely
scientific character to the study, it is indispensable that these
approximate generalizations, which in themselves would amount only to the
lowest kind of empirical laws, should be connected deductively with the
laws of nature from which they result; should be resolved into the
properties of the causes on which the phenomena depend. In other words,
the science of Human Nature may be said to exist in proportion as the
approximate truths, which compose a practical knowledge of mankind, can be
exhibited as corollaries from the universal laws of human nature on which
they rest; whereby the proper limits of those approximate truths would be
shown, and we should be enabled to deduce others for any new state of
circumstances, in anticipation of specific experience.

The proposition now stated is the text on which the two succeeding
chapters will furnish the comment.



                               Chapter IV.


Of The Laws Of Mind.


§ 1. What the Mind is, as well as what Matter is, or any other question
respecting Things in themselves, as distinguished from their sensible
manifestations, it would be foreign to the purposes of this treatise to
consider. Here, as throughout our inquiry, we shall keep clear of all
speculations respecting the mind’s own nature, and shall understand by the
laws of mind those of mental Phenomena; of the various feelings or states
of consciousness of sentient beings. These, according to the
classification we have uniformly followed, consist of Thoughts, Emotions,
Volitions, and Sensations; the last being as truly states of Mind as the
three former. It is usual, indeed, to speak of sensations as states of
body, not of mind. But this is the common confusion, of giving one and the
same name to a phenomenon and to the approximate cause or conditions of
the phenomenon. The immediate antecedent of a sensation is a state of
body, but the sensation itself is a state of mind. If the word Mind means
any thing, it means that which feels. Whatever opinion we hold respecting
the fundamental identity or diversity of matter and mind, in any case the
distinction between mental and physical facts, between the internal and
the external world, will always remain, as a matter of classification; and
in that classification, sensations, like all other feelings, must be
ranked as mental phenomena. The mechanism of their production, both in the
body itself and in what is called outward nature, is all that can with any
propriety be classed as physical.

The phenomena of mind, then, are the various feelings of our nature, both
those improperly called physical and those peculiarly designated as
mental; and by the laws of mind, I mean the laws according to which those
feelings generate one another.

§ 2. All states of mind are immediately caused either by other states of
mind, or by states of body. When a state of mind is produced by a state of
mind, I call the law concerned in the case a law of Mind. When a state of
mind is produced directly by a state of body, the law is a law of Body,
and belongs to physical science.

With regard to those states of mind which are called sensations, all are
agreed that these have for their immediate antecedents, states of body.
Every sensation has for its proximate cause some affection of the portion
of our frame called the nervous system, whether this affection originates
in the action of some external object, or in some pathological condition
of the nervous organization itself. The laws of this portion of our
nature—the varieties of our sensations, and the physical conditions on
which they proximately depend—manifestly belong to the province of
Physiology.

Whether the remainder of our mental states are similarly dependent on
physical conditions, is one of the _vexatæ questiones_ in the science of
human nature. It is still disputed whether our thoughts, emotions, and
volitions are generated through the intervention of material mechanism;
whether we have organs of thought and of emotion, in the same sense in
which we have organs of sensation. Many eminent physiologists hold the
affirmative. These contend that a thought (for example) is as much the
result of nervous agency, as a sensation; that some particular state of
our nervous system, in particular of that central portion of it called the
brain, invariably precedes, and is presupposed by, every state of our
consciousness. According to this theory, one state of mind is never really
produced by another: all are produced by states of body. When one thought
seems to call up another by association, it is not really a thought which
recalls a thought; the association did not exist between the two thoughts,
but between the two states of the brain or nerves which preceded the
thoughts: one of those states recalls the other, each being attended in
its passage by the particular state of consciousness which is consequent
on it. On this theory the uniformities of succession among states of mind
would be mere derivative uniformities, resulting from the laws of
succession of the bodily states which cause them. There would be no
original mental laws, no Laws of Mind in the sense in which I use the
term, at all; and mental science would be a mere branch, though the
highest and most recondite branch, of the science of physiology. M. Comte,
accordingly, claims the scientific cognizance of moral and intellectual
phenomena exclusively for physiologists; and not only denies to
Psychology, or Mental Philosophy properly so called, the character of a
science, but places it, in the chimerical nature of its objects and
pretensions, almost on a par with astrology.

But, after all has been said which can be said, it remains incontestable
that there exist uniformities of succession among states of mind, and that
these can be ascertained by observation and experiment. Further, that
every mental state has a nervous state for its immediate antecedent and
proximate cause, though extremely probable, can not hitherto be said to be
proved, in the conclusive manner in which this can be proved of
sensations; and even were it certain, yet every one must admit that we are
wholly ignorant of the characteristics of these nervous states; we know
not, and at present have no means of knowing, in what respect one of them
differs from another; and our only mode of studying their successions or
co-existences must be by observing the successions and co-existences of
the mental states, of which they are supposed to be the generators or
causes. The successions, therefore, which obtain among mental phenomena,
do not admit of being deduced from the physiological laws of our nervous
organization; and all real knowledge of them must continue, for a long
time at least, if not always, to be sought in the direct study, by
observation and experiment, of the mental successions themselves. Since,
therefore, the order of our mental phenomena must be studied in those
phenomena, and not inferred from the laws of any phenomena more general,
there is a distinct and separate Science of Mind.

The relations, indeed, of that science to the science of physiology must
never be overlooked or undervalued. It must by no means be forgotten that
the laws of mind may be derivative laws resulting from laws of animal
life, and that their truth, therefore, may ultimately depend on physical
conditions; and the influence of physiological states or physiological
changes in altering or counteracting the mental successions, is one of the
most important departments of psychological study. But, on the other hand,
to reject the resource of psychological analysis, and construct the theory
of the mind solely on such data as physiology at present affords, seems to
me as great an error in principle, and an even more serious one in
practice. Imperfect as is the science of mind, I do not scruple to affirm
that it is in a considerably more advanced state than the portion of
physiology which corresponds to it; and to discard the former for the
latter appears, to me an infringement of the true canons of inductive
philosophy, which must produce, and which does produce, erroneous
conclusions in some very important departments of the science of human
nature.

§ 3. The subject, then, of Psychology is the uniformities of succession,
the laws, whether ultimate or derivative, according to which one mental
state succeeds another; is caused by, or at least, is caused to follow,
another. Of these laws some are general, others more special. The
following are examples of the most general laws:

First. Whenever any state of consciousness has once been excited in us, no
matter by what cause, an inferior degree of the same state of
consciousness, a state of consciousness resembling the former, but
inferior in intensity, is capable of being reproduced in us, without the
presence of any such cause as excited it at first. Thus, if we have once
seen or touched an object, we can afterward think of the object though it
be absent from our sight or from our touch. If we have been joyful or
grieved at some event, we can think of or remember our past joy or grief,
though no new event of a happy or painful nature has taken place. When a
poet has put together a mental picture of an imaginary object, a Castle of
Indolence, a Una, or a Hamlet, he can afterward think of the ideal object
he has created, without any fresh act of intellectual combination. This
law is expressed by saying, in the language of Hume, that every mental
_impression_ has its _idea_.

Secondly. These ideas, or secondary mental states, are excited by our
impressions, or by other ideas, according to certain laws which are called
Laws of Association. Of these laws the first is, that similar ideas tend
to excite one another. The second is, that when two impressions have been
frequently experienced (or even thought of) either simultaneously or in
immediate succession, then whenever one of these impressions, or the idea
of it, recurs, it tends to excite the idea of the other. The third law is,
that greater intensity in either or both of the impressions is equivalent,
in rendering them excitable by one another, to a greater frequency of
conjunction. These are the laws of ideas, on which I shall not enlarge in
this place, but refer the reader to works professedly psychological, in
particular to Mr. James Mill’s _Analysis of the Phenomena of the Human
Mind_, where the principal laws of association, along with many of their
applications, are copiously exemplified, and with a masterly hand.(270)

These simple or elementary Laws of Mind have been ascertained by the
ordinary methods of experimental inquiry; nor could they have been
ascertained in any other manner. But a certain number of elementary laws
having thus been obtained, it is a fair subject of scientific inquiry how
far those laws can be made to go in explaining the actual phenomena. It is
obvious that complex laws of thought and feeling not only may, but must,
be generated from these simple laws. And it is to be remarked, that the
case is not always one of Composition of Causes: the effect of concurring
causes is not always precisely the sum of the effects of those causes when
separate, nor even always an effect of the same kind with them. Reverting
to the distinction which occupies so prominent a place in the theory of
induction, the laws of the phenomena of mind are sometimes analogous to
mechanical, but sometimes also to chemical laws. When many impressions or
ideas are operating in the mind together, there sometimes takes place a
process of a similar kind to chemical combination. When impressions have
been so often experienced in conjunction, that each of them calls up
readily and instantaneously the ideas of the whole group, those ideas
sometimes melt and coalesce into one another, and appear not several
ideas, but one; in the same manner as, when the seven prismatic colors are
presented to the eye in rapid succession, the sensation produced is that
of white. But as in this last case it is correct to say that the seven
colors when they rapidly follow one another _generate_ white, but not that
they actually _are_ white; so it appears to me that the Complex Idea,
formed by the blending together of several simpler ones, should, when it
really appears simple (that is, when the separate elements are not
consciously distinguishable in it), be said to _result from_, or _be
generated by_, the simple ideas, not to _consist_ of them. Our idea of an
orange really _consists_ of the simple ideas of a certain color, a certain
form, a certain taste and smell, etc., because we can, by interrogating
our consciousness, perceive all these elements in the idea. But we can not
perceive, in so apparently simple a feeling as our perception of the shape
of an object by the eye, all that multitude of ideas derived from other
senses, without which it is well ascertained that no such visual
perception would ever have had existence; nor, in our idea of Extension,
can we discover those elementary ideas of resistance, derived from our
muscular frame, in which it has been conclusively shown that the idea
originates. These, therefore, are cases of mental chemistry; in which it
is proper to say that the simple ideas generate, rather than that they
compose, the complex ones.

With respect to all the other constituents of the mind, its beliefs, its
abstruser conceptions, its sentiments, emotions, and volitions, there are
some (among whom are Hartley and the author of the _Analysis_) who think
that the whole of these are generated from simple ideas of sensation, by a
chemistry similar to that which we have just exemplified. These
philosophers have made out a great part of their case, but I am not
satisfied that they have established the whole of it. They have shown that
there is such a thing as mental chemistry; that the heterogeneous nature
of a feeling A, considered in relation to B and C, is no conclusive
argument against its being generated from B and C. Having proved this,
they proceed to show, that where A is found, B and C were, or may have
been present, and why, therefore, they ask, should not A have been
generated from B and C? But even if this evidence were carried to the
highest degree of completeness which it admits of; if it were shown (which
hitherto it has not, in all cases, been) that certain groups of associated
ideas not only might have been, but actually were, present whenever the
more recondite mental feeling was experienced; this would amount only to
the Method of Agreement, and could not prove causation until confirmed by
the more conclusive evidence of the Method of Difference. If the question
be whether Belief is a mere case of close association of ideas, it would
be necessary to examine experimentally if it be true that any ideas
whatever, provided they are associated with the required degree of
closeness, give rise to belief. If the inquiry be into the origin of moral
feelings, the feeling for example of moral reprobation, it is necessary to
compare all the varieties of actions or states of mind which are ever
morally disapproved, and see whether in all these cases it can be shown,
or reasonably surmised, that the action or state of mind had become
connected by association, in the disapproving mind, with some particular
class of hateful or disgusting ideas; and the method employed is, thus
far, that of Agreement. But this is not enough. Supposing this proved, we
must try further by the Method of Difference, whether this particular kind
of hateful or disgusting ideas, when it becomes associated with an action
previously indifferent, will render that action a subject of moral
disapproval. If this question can be answered in the affirmative, it is
shown to be a law of the human mind, that an association of that
particular description is the generating cause of moral reprobation. That
all this is the case has been rendered extremely probable, but the
experiments have not been tried with the degree of precision necessary for
a complete and absolutely conclusive induction.(271)

It is further to be remembered, that even if all which this theory of
mental phenomena contends for could be proved, we should not be the more
enabled to resolve the laws of the more complex feelings into those of the
simpler ones. The generation of one class of mental phenomena from
another, whenever it can be made out, is a highly interesting fact in
psychological chemistry; but it no more supersedes the necessity of an
experimental study of the generated phenomenon, than a knowledge of the
properties of oxygen and sulphur enables us to deduce those of sulphuric
acid without specific observation and experiment. Whatever, therefore, may
be the final issue of the attempt to account for the origin of our
judgments, our desires, or our volitions, from simpler mental phenomena,
it is not the less imperative to ascertain the sequences of the complex
phenomena themselves, by special study in conformity to the canons of
Induction. Thus, in respect to Belief, psychologists will always have to
inquire what beliefs we have by direct consciousness, and according to
what laws one belief produces another; what are the laws in virtue of
which one thing is recognized by the mind, either rightly or erroneously,
as evidence of another thing. In regard to Desire, they will have to
examine what objects we desire naturally, and by what causes we are made
to desire things originally indifferent, or even disagreeable to us; and
so forth. It may be remarked that the general laws of association prevail
among these more intricate states of mind, in the same manner as among the
simpler ones. A desire, an emotion, an idea of the higher order of
abstraction, even our judgments and volitions, when they have become
habitual, are called up by association, according to precisely the same
laws as our simple ideas.

§ 4. In the course of these inquiries, it will be natural and necessary to
examine how far the production of one state of mind by another is
influenced by any assignable state of body. The commonest observation
shows that different minds are susceptible in very different degrees to
the action of the same psychological causes. The idea, for example, of a
given desirable object will excite in different minds very different
degrees of intensity of desire. The same subject of meditation, presented
to different minds, will excite in them very unequal degrees of
intellectual action. These differences of mental susceptibility in
different individuals may be, first, original and ultimate facts; or,
secondly, they may be consequences of the previous mental history of those
individuals; or, thirdly and lastly, they may depend on varieties of
physical organization. That the previous mental history of the individuals
must have some share in producing or in modifying the whole of their
mental character, is an inevitable consequence of the laws of mind; but
that differences of bodily structure also co-operate, is the opinion of
all physiologists, confirmed by common experience. It is to be regretted
that hitherto this experience, being accepted in the gross, without due
analysis, has been made the groundwork of empirical generalizations most
detrimental to the progress of real knowledge.

It is certain that the natural differences which really exist in the
mental predispositions or susceptibilities of different persons are often
not unconnected with diversities in their organic constitution. But it
does not therefore follow that these organic differences must in all cases
influence the mental phenomena directly and immediately. They often affect
them through the medium of their psychological causes. For example, the
idea of some particular pleasure may excite in different persons, even
independently of habit or education, very different strengths of desire,
and this may be the effect of their different degrees or kinds of nervous
susceptibility; but these organic differences, we must remember, will
render the pleasurable sensation itself more intense in one of these
persons than in the other; so that the idea of the pleasure will also be
an intenser feeling, and will, by the operation of mere mental laws,
excite an intenser desire, without its being necessary to suppose that the
desire itself is directly influenced by the physical peculiarity. As in
this, so in many cases, such differences in the kind or in the intensity
of the physical sensations as must necessarily result from differences of
bodily organization, will of themselves account for many differences not
only in the degree, but even in the kind, of the other mental phenomena.
So true is this, that even different _qualities_ of mind, different types
of mental character, will naturally be produced by mere differences of
intensity in the sensations generally; as is well pointed out in the able
essay on Dr. Priestley, by Mr. Martineau, mentioned in a former chapter:

“The sensations which form the elements of all knowledge are received
either simultaneously or successively: when several are received
simultaneously, as the smell, the taste, the color, the form, etc., of a
fruit, their association together constitutes our idea of an _object_;
when received successively, their association makes up the idea of an
_event_. Any thing, then, which favors the associations of synchronous
ideas will tend to produce a knowledge of objects, a perception of
qualities; while any thing which favors association in the successive
order, will tend to produce a knowledge of events, of the order of
occurrences, and of the connection of cause and effect: in other words, in
the one case a perceptive mind, with a discriminate feeling of the
pleasurable and painful properties of things, a sense of the grand and the
beautiful will be the result: in the other, a mind attentive to the
movements and phenomena, a ratiocinative and philosophic intellect. Now it
is an acknowledged principle, that all sensations experienced during the
presence of any vivid impression become strongly associated with it, and
with each other; and does it not follow that the synchronous feelings of a
sensitive constitution (_i.e._, the one which has vivid impressions) will
be more intimately blended than in a differently formed mind? If this
suggestion has any foundation in truth, it leads to an inference not
unimportant; that where nature has endowed an individual with great
original susceptibility, he will probably be distinguished by fondness for
natural history, a relish for the beautiful and great, and moral
enthusiasm; where there is but a mediocrity of sensibility, a love of
science, of abstract truth, with a deficiency of taste and of fervor, is
likely to be the result.”

We see from this example, that when the general laws of mind are more
accurately known, and, above all, more skillfully applied to the detailed
explanation of mental peculiarities, they will account for many more of
those peculiarities than is ordinarily supposed. Unfortunately the
reaction of the last and present generation against the philosophy of the
eighteenth century has produced a very general neglect of this great
department of analytical inquiry; of which, consequently, the recent
progress has been by no means proportional to its early promise. The
majority of those who speculate on human nature prefer dogmatically to
assume that the mental differences which they perceive, or think they
perceive, among human beings, are ultimate facts, incapable of being
either explained or altered, rather than take the trouble of fitting
themselves, by the requisite processes of thought, for referring those
mental differences to the outward causes by which they are for the most
part produced, and on the removal of which they would cease to exist. The
German school of metaphysical speculation, which has not yet lost its
temporary predominance in European thought, has had this among many other
injurious influences; and at the opposite extreme of the psychological
scale, no writer, either of early or of recent date, is chargeable in a
higher degree with this aberration from the true scientific spirit, than
M. Comte.

It is certain that, in human beings at least, differences in education and
in outward circumstances are capable of affording an adequate explanation
of by far the greatest portion of character; and that the remainder may be
in great part accounted for by physical differences in the sensations
produced in different individuals by the same external or internal cause.
There are, however, some mental facts which do not seem to admit of these
modes of explanation. Such, to take the strongest case, are the various
instincts of animals, and the portion of human nature which corresponds to
those instincts. No mode has been suggested, even by way of hypothesis, in
which these can receive any satisfactory, or even plausible, explanation
from psychological causes alone; and there is great reason to think that
they have as positive, and even as direct and immediate, a connection with
physical conditions of the brain and nerves as any of our mere sensations
have. A supposition which (it is perhaps not superfluous to add) in no way
conflicts with the indisputable fact that these instincts may be modified
to any extent, or entirely conquered, in human beings, and to no
inconsiderable extent even in some of the domesticated animals, by other
mental influences, and by education.

Whether organic causes exercise a direct influence over any other classes
of mental phenomena, is hitherto as far from being ascertained as is the
precise nature of the organic conditions even in the case of instincts.
The physiology, however, of the brain and nervous system is in a state of
such rapid advance, and is continually bringing forth such new and
interesting results, that if there be really a connection between mental
peculiarities and any varieties cognizable by our senses in the structure
of the cerebral and nervous apparatus, the nature of that connection is
now in a fair way of being found out. The latest discoveries in cerebral
physiology appear to have proved that any such connection which may exist
is of a radically different character from that contended for by Gall and
his followers, and that, whatever may hereafter be found to be the true
theory of the subject, phrenology at least is untenable.



                                Chapter V.


Of Ethology, Or The Science Of The Formation Of Character.


§ 1. The laws of mind as characterized in the preceding chapter, compose
the universal or abstract portion of the philosophy of human nature; and
all the truths of common experience, constituting a practical knowledge of
mankind, must, to the extent to which they are truths, be results or
consequences of these. Such familiar maxims, when collected _a posteriori_
from observation of life, occupy among the truths of the science the place
of what, in our analysis of Induction, have so often been spoken of under
the title of Empirical Laws.

An Empirical Law (it will be remembered) is a uniformity, whether of
succession or of co-existence, which holds true in all instances within
our limits of observation, but is not of a nature to afford any assurance
that it would hold beyond those limits; either because the consequent is
not really the effect of the antecedent, but forms part along with it of a
chain of effects flowing from prior causes not yet ascertained, or because
there is ground to believe that the sequence (though a case of causation)
is resolvable into simpler sequences, and, depending therefore on a
concurrence of several natural agencies, is exposed to an unknown
multitude of possibilities of counteraction. In other words, an empirical
law is a generalization, of which, not content with finding it true, we
are obliged to ask, why is it true? knowing that its truth is not
absolute, but dependent on some more general conditions, and that it can
only be relied on in so far as there is ground of assurance that those
conditions are realized.

Now, the observations concerning human affairs collected from common
experience are precisely of this nature. Even if they were universally and
exactly true within the bounds of experience, which they never are, still
they are not the ultimate laws of human action; they are not the
principles of human nature, but results of those principles under the
circumstances in which mankind have happened to be placed. When the
Psalmist “said in his haste that all men are liars,” he enunciated what in
some ages and countries is borne out by ample experience; but it is not a
law of man’s nature to lie; though it is one of the consequences of the
laws of human nature, that lying is nearly universal when certain external
circumstances exist universally, especially circumstances productive of
habitual distrust and fear. When the character of the old is asserted to
be cautious, and of the young impetuous, this, again, is but an empirical
law; for it is not because of their youth that the young are impetuous,
nor because of their age that the old are cautious. It is chiefly, if not
wholly, because the old, during their many years of life, have generally
had much experience of its various evils, and having suffered or seen
others suffer much from incautious exposure to them, have acquired
associations favorable to circumspection; while the young, as well from
the absence of similar experience as from the greater strength of the
inclinations which urge them to enterprise, engage themselves in it more
readily. Here, then, is the _explanation_ of the empirical law; here are
the conditions which ultimately determine whether the law holds good or
not. If an old man has not been oftener than most young men in contact
with danger and difficulty, he will be equally incautious; if a youth has
not stronger inclinations than an old man, he probably will be as little
enterprising. The empirical law derives whatever truth it has from the
causal laws of which it is a consequence. If we know those laws, we know
what are the limits to the derivative law; while, if we have not yet
accounted for the empirical law—if it rests only on observation—there is
no safety in applying it far beyond the limits of time, place, and
circumstance in which the observations were made.

The really scientific truths, then, are not these empirical laws, but the
causal laws which explain them. The empirical laws of those phenomena
which depend on known causes, and of which a general theory can therefore
be constructed, have, whatever may be their value in practice, no other
function in science than that of verifying the conclusions of theory.
Still more must this be the case when most of the empirical laws amount,
even within the limits of observation, only to approximate
generalizations.

§ 2. This, however, is not, so much as is sometimes supposed, a
peculiarity of the sciences called moral. It is only in the simplest
branches of science that empirical laws are ever exactly true; and not
always in those. Astronomy, for example, is the simplest of all the
sciences which explain, in the concrete, the actual course of natural
events. The causes or forces on which astronomical phenomena depend, are
fewer in number than those which determine any other of the great
phenomena of nature. Accordingly, as each effect results from the conflict
of but few causes, a great degree of regularity and uniformity might be
expected to exist among the effects; and such is really the case: they
have a fixed order, and return in cycles. But propositions which should
express, with absolute correctness, all the successive positions of a
planet until the cycle is completed, would be of almost unmanageable
complexity, and could be obtained from theory alone. The generalizations
which can be collected on the subject from direct observation, even such
as Kepler’s law, are mere approximations; the planets, owing to their
perturbations by one another, do not move in exact ellipses. Thus even in
astronomy, perfect exactness in the mere empirical laws is not to be
looked for; much less, then, in more complex subjects of inquiry.

The same example shows how little can be inferred against the universality
or even the simplicity of the ultimate laws, from the impossibility of
establishing any but approximate empirical laws of the effects. The laws
of causation according to which a class of phenomena are produced may be
very few and simple, and yet the effects themselves may be so various and
complicated that it shall be impossible to trace any regularity whatever
completely through them. For the phenomena in question may be of an
eminently modifiable character; insomuch that innumerable circumstances
are capable of influencing the effect, although they may all do it
according to a very small number of laws. Suppose that all which passes in
the mind of man is determined by a few simple laws; still, if those laws
be such that there is not one of the facts surrounding a human being, or
of the events which happen to him, that does not influence in some mode or
degree his subsequent mental history, and if the circumstances of
different human beings are extremely different, it will be no wonder if
very few propositions can be made respecting the details of their conduct
or feelings, which will be true of all mankind.

Now, without deciding whether the ultimate laws of our mental nature are
few or many, it is at least certain that they are of the above
description. It is certain that our mental states, and our mental
capacities and susceptibilities, are modified, either for a time or
permanently, by every thing which happens to us in life. Considering,
therefore, how much these modifying causes differ in the case of any two
individuals, it would be unreasonable to expect that the empirical laws of
the human mind, the generalizations which can be made respecting the
feelings or actions of mankind without reference to the causes that
determine them, should be any thing but approximate generalizations. They
are the common wisdom of common life, and as such are invaluable;
especially as they are mostly to be applied to cases not very dissimilar
to those from which they were collected. But when maxims of this sort,
collected from Englishmen, come to be applied to Frenchmen, or when those
collected from the present day are applied to past or future generations,
they are apt to be very much at fault. Unless we have resolved the
empirical law into the laws of the causes on which it depends, and
ascertained that those causes extend to the case which we have in view,
there can be no reliance placed in our inferences. For every individual is
surrounded by circumstances different from those of every other
individual; every nation or generation of mankind from every other nation
or generation: and none of these differences are without their influence
in forming a different type of character. There is, indeed, also a certain
general resemblance; but peculiarities of circumstances are continually
constituting exceptions even to the propositions which are true in the
great majority of cases.

Although, however, there is scarcely any mode of feeling or conduct which
is, in the absolute sense, common to all mankind; and though the
generalizations which assert that any given variety of conduct or feeling
will be found universally (however nearly they may approximate to truth
within given limits of observation), will be considered as scientific
propositions by no one who is at all familiar with scientific
investigation; yet all modes of feeling and conduct met with among mankind
have causes which produce them; and in the propositions which assign those
causes will be found the explanation of the empirical laws, and the
limiting principle of our reliance on them. Human beings do not all feel
and act alike in the same circumstances; but it is possible to determine
what makes one person, in a given position, feel or act in one way,
another in another; how any given mode of feeling and conduct, compatible
with the general laws (physical and mental) of human nature, has been, or
may be, formed. In other words, mankind have not one universal character,
but there exist universal laws of the Formation of Character. And since it
is by these laws, combined with the facts of each particular case, that
the whole of the phenomena of human action and feeling are produced, it is
on these that every rational attempt to construct the science of human
nature in the concrete, and for practical purposes, must proceed.

§ 3. The laws, then, of the formation of character being the principal
object of scientific inquiry into human nature, it remains to determine
the method of investigation best fitted for ascertaining them. And the
logical principles according to which this question is to be decided, must
be those which preside over every other attempt to investigate the laws of
very complex phenomena. For it is evident that both the character of any
human being, and the aggregate of the circumstances by which that
character has been formed, are facts of a high order of complexity. Now to
such cases we have seen that the Deductive Method, setting out from
general laws, and verifying their consequences by specific experience, is
alone applicable. The grounds of this great logical doctrine have formerly
been stated; and its truth will derive additional support from a brief
examination of the specialties of the present case.

There are only two modes in which laws of nature can be
ascertained—deductively and experimentally; including under the
denomination of experimental inquiry, observation as well as artificial
experiment. Are the laws of the formation of character susceptible of a
satisfactory investigation by the method of experimentation? Evidently
not; because, even if we suppose unlimited power of varying the experiment
(which is abstractedly possible, though no one but an Oriental despot has
that power, or, if he had, would probably be disposed to exercise it), a
still more essential condition is wanting—the power of performing any of
the experiments with scientific accuracy.

The instances requisite for the prosecution of a directly experimental
inquiry into the formation of character, would be a number of human beings
to bring up and educate, from infancy to mature age. And to perform any
one of these experiments with scientific propriety, it would be necessary
to know and record every sensation or impression received by the young
pupil from a period long before it could speak; including its own notions
respecting the sources of all those sensations and impressions. It is not
only impossible to do this completely, but even to do so much of it as
should constitute a tolerable approximation. One apparently trivial
circumstance which eluded our vigilance might let in a train of
impressions and associations sufficient to vitiate the experiment as an
authentic exhibition of the effects flowing from given causes. No one who
has sufficiently reflected on education is ignorant of this truth; and
whoever has not, will find it most instructively illustrated in the
writings of Rousseau and Helvetius on that great subject.

Under this impossibility of studying the laws of the formation of
character by experiments purposely contrived to elucidate them, there
remains the resource of simple observation. But if it be impossible to
ascertain the influencing circumstances with any approach to completeness
even when we have the shaping of them ourselves, much more impossible is
it when the cases are further removed from our observation, and altogether
out of our control. Consider the difficulty of the very first step—of
ascertaining what actually is the character of the individual, in each
particular case that we examine. There is hardly any person living
concerning some essential part of whose character there are not
differences of opinion even among his intimate acquaintances; and a single
action, or conduct continued only for a short time, goes a very little way
toward ascertaining it. We can only make our observations in a rough way
and _en masse_; not attempting to ascertain completely in any given
instance, what character has been formed, and still less by what causes;
but only observing in what state of previous circumstances it is found
that certain marked mental qualities or deficiencies _oftenest_ exist.
These conclusions, besides that they are mere approximate generalizations,
deserve no reliance, even as such, unless the instances are sufficiently
numerous to eliminate not only chance, but every assignable circumstance
in which a number of the cases examined may happen to have resembled one
another. So numerous and various, too, are the circumstances which form
individual character, that the consequence of any particular combination
is hardly ever some definite and strongly marked character, always found
where that combination exists, and not otherwise. What is obtained, even
after the most extensive and accurate observation, is merely a comparative
result; as, for example, that in a given number of Frenchmen, taken
indiscriminately, there will be found more persons of a particular mental
tendency, and fewer of the contrary tendency, than among an equal number
of Italians or English, similarly taken; or thus: of a hundred Frenchmen
and an equal number of Englishmen, fairly selected, and arranged according
to the degree in which they possess a particular mental characteristic,
each number, 1, 2, 3, etc., of the one series, will be found to possess
more of that characteristic than the corresponding number of the other.
Since, therefore, the comparison is not one of kinds, but of ratios and
degrees; and since, in proportion as the differences are slight, it
requires a greater number of instances to eliminate chance, it can not
often happen to any one to know a sufficient number of cases with the
accuracy requisite for making the sort of comparison last mentioned; less
than which, however, would not constitute a real induction. Accordingly,
there is hardly one current opinion respecting the characters of nations,
classes, or descriptions of persons, which is universally acknowledged as
indisputable.(272)

And finally, if we could even obtain by way of experiment a much more
satisfactory assurance of these generalizations than is really possible,
they would still be only empirical laws. They would show, indeed, that
there was some connection between the type of character formed and the
circumstances existing in the case; but not what the precise connection
was, nor to which of the peculiarities of those circumstances the effect
was really owing. They could only, therefore, be received as results of
causation, requiring to be resolved into the general laws of the causes:
until the determination of which, we could not judge within what limits
the derivative laws might serve as presumptions in cases yet unknown, or
even be depended on as permanent in the very cases from which they were
collected. The French people had, or were supposed to have, a certain
national character; but they drive out their royal family and aristocracy,
alter their institutions, pass through a series of extraordinary events
for the greater part of a century, and at the end of that time their
character is found to have undergone important changes. A long list of
mental and moral differences are observed, or supposed to exist between
men and women; but at some future and, it may be hoped, not distant
period, equal freedom and an equally independent social position come to
be possessed by both, and their differences of character are either
removed or totally altered.

But if the differences which we think we observe between French and
English, or between men and women, can be connected with more general
laws; if they be such as might be expected to be produced by the
differences of government, former customs, and physical peculiarities in
the two nations, and by the diversities of education, occupations,
personal independence, and social privileges, and whatever original
differences there may be in bodily strength and nervous sensibility
between the two sexes; then, indeed, the coincidence of the two kinds of
evidence justifies us in believing that we have both reasoned rightly and
observed rightly. Our observation, though not sufficient as proof, is
ample as verification. And having ascertained not only the empirical laws,
but the causes, of the peculiarities, we need be under no difficulty in
judging how far they may be expected to be permanent, or by what
circumstances they would be modified or destroyed.

§ 4. Since then it is impossible to obtain really accurate propositions
respecting the formation of character from observation and experiment
alone, we are driven perforce to that which, even if it had not been the
indispensable, would have been the most perfect, mode of investigation,
and which it is one of the principal aims of philosophy to extend; namely,
that which tries its experiments not on the complex facts, but on the
simple ones of which they are compounded; and after ascertaining the laws
of the causes, the composition of which gives rise to the complex
phenomena, then considers whether these will not explain and account for
the approximate generalizations which have been framed empirically
respecting the sequences of those complex phenomena. The laws of the
formation of character are, in short, derivative laws, resulting from the
general laws of mind, and are to be obtained by deducing them from those
general laws by supposing any given set of circumstances, and then
considering what, according to the laws of mind, will be the influence of
those circumstances on the formation of character.

A science is thus formed, to which I would propose to give the name of
Ethology, or the Science of Character, from ἦθος, a word more nearly
corresponding to the term “character” as I here use it, than any other
word in the same language. The name is perhaps etymologically applicable
to the entire science of our mental and moral nature; but if, as is usual
and convenient, we employ the name Psychology for the science of the
elementary laws of mind, Ethology will serve for the ulterior science
which determines the kind of character produced in conformity to those
general laws by any set of circumstances, physical and moral. According to
this definition, Ethology is the science which corresponds to the art of
education in the widest sense of the term, including the formation of
national or collective character as well as individual. It would indeed be
vain to expect (however completely the laws of the formation of character
might be ascertained) that we could know so accurately the circumstances
of any given case as to be able positively to predict the character that
would be produced in that case. But we must remember that a degree of
knowledge far short of the power of actual prediction is often of much
practical value. There may be great power of influencing phenomena, with a
very imperfect knowledge of the causes by which they are in any given
instance determined. It is enough that we know that certain means have a
_tendency_ to produce a given effect, and that others have a tendency to
frustrate it. When the circumstances of an individual or of a nation are
in any considerable degree under our control, we may, by our knowledge of
tendencies, be enabled to shape those circumstances in a manner much more
favorable to the ends we desire, than the shape which they would of
themselves assume. This is the limit of our power; but within this limit
the power is a most important one.

This science of Ethology may be called the Exact Science of Human Nature;
for its truths are not, like the empirical laws which depend on them,
approximate generalizations, but real laws. It is, however (as in all
cases of complex phenomena), necessary to the exactness of the
propositions, that they should be hypothetical only, and affirm
tendencies, not facts. They must not assert that something will always, or
certainly, happen; but only that such and such will be the effect of a
given cause, so far as it operates uncounteracted. It is a scientific
proposition, that bodily strength tends to make men courageous; not that
it always makes them so: that an interest on one side of a question tends
to bias the judgment; not that it invariably does so: that experience
tends to give wisdom; not that such is always its effect. These
propositions, being assertive only of tendencies, are not the less
universally true because the tendencies may be frustrated.

§ 5. While, on the one hand, Psychology is altogether, or principally, a
science of observation and experiment, Ethology, as I have conceived it,
is, as I have already remarked, altogether deductive. The one ascertains
the simple laws of Mind in general, the other traces their operation in
complex combinations of circumstances. Ethology stands to Psychology in a
relation very similar to that in which the various branches of natural
philosophy stand to mechanics. The principles of Ethology are properly the
middle principles, the _axiomata media_ (as Bacon would have said) of the
science of mind: as distinguished, on the one hand, from the empirical
laws resulting from simple observation, and, on the other, from the
highest generalizations.

And this seems a suitable place for a logical remark, which, though of
general application, is of peculiar importance in reference to the present
subject. Bacon has judiciously observed that the _axiomata media_ of every
science principally constitute its value. The lowest generalizations,
until explained by and resolved into the middle principles of which they
are the consequences, have only the imperfect accuracy of empirical laws;
while the most general laws are _too_ general, and include too few
circumstances, to give sufficient indication of what happens in individual
cases, where the circumstances are almost always immensely numerous. In
the importance, therefore, which Bacon assigns, in every science, to the
middle principles, it is impossible not to agree with him. But I conceive
him to have been radically wrong in his doctrine respecting the mode in
which these _axiomata media_ should be arrived at; though there is no one
proposition laid down in his works for which he has been more
extravagantly eulogized. He enunciates as a universal rule that induction
should proceed from the lowest to the middle principles, and from those to
the highest, never reversing that order, and, consequently, leaving no
room for the discovery of new principles by way of deduction at all. It is
not to be conceived that a man of his sagacity could have fallen into this
mistake if there had existed in his time, among the sciences which treat
of successive phenomena, one single instance of a deductive science, such
as mechanics, astronomy, optics, acoustics, etc., now are. In those
sciences it is evident that the higher and middle principles are by no
means derived from the lowest, but the reverse. In some of them the very
highest generalizations were those earliest ascertained with any
scientific exactness; as, for example (in mechanics), the laws of motion.
Those general laws had not, indeed, at first the acknowledged universality
which they acquired after having been successfully employed to explain
many classes of phenomena to which they were not originally seen to be
applicable; as when the laws of motion were employed, in conjunction with
other laws, to explain deductively the celestial phenomena. Still, the
fact remains, that the propositions which were afterward recognized as the
most general truths of the science were, of all its accurate
generalizations, those earliest arrived at. Bacon’s greatest merit can not
therefore consist, as we are so often told that it did, in exploding the
vicious method pursued by the ancients of flying to the highest
generalizations first, and deducing the middle principles from them; since
this is neither a vicious nor an exploded, but the universally accredited
method of modern science, and that to which it owes its greatest triumphs.
The error of ancient speculation did not consist in making the largest
generalizations first, but in making them without the aid or warrant of
rigorous inductive methods, and applying them deductively without the
needful use of that important part of the Deductive Method termed
Verification.

The order in which truths of the various degrees of generality should be
ascertained can not, I apprehend, be prescribed by any unbending rule. I
know of no maxim which can be laid down on the subject, but to obtain
those first in respect to which the conditions of a real induction can be
first and most completely realized. Now, wherever our means of
investigation can reach causes, without stopping at the empirical laws of
the effects, the simplest cases, being those in which fewest causes are
simultaneously concerned, will be most amenable to the inductive process;
and these are the cases which elicit laws of the greatest
comprehensiveness. In every science, therefore, which has reached the
stage at which it becomes a science of causes, it will be usual as well as
desirable first to obtain the highest generalizations, and then deduce the
more special ones from them. Nor can I discover any foundation for the
Baconian maxim, so much extolled by subsequent writers, except this: That
before we attempt to explain deductively from more general laws any new
class of phenomena, it is desirable to have gone as far as is practicable
in ascertaining the empirical laws of those phenomena; so as to compare
the results of deduction, not with one individual instance after another,
but with general propositions expressive of the points of agreement which
have been found among many instances. For if Newton had been obliged to
verify the theory of gravitation, not by deducing from it Kepler’s laws,
but by deducing all the observed planetary positions which had served
Kepler to establish those laws, the Newtonian theory would probably never
have emerged from the state of an hypothesis.(273)

The applicability of these remarks to the special case under consideration
can not admit of question. The science of the formation of character is a
science of causes. The subject is one to which those among the canons of
induction, by which laws of causation are ascertained, can be rigorously
applied. It is, therefore, both natural and advisable to ascertain the
simplest, which are necessarily the most general, laws of causation first,
and to deduce the middle principles from them. In other words, Ethology,
the deductive science, is a system of corollaries from Psychology, the
experimental science.

§ 6. Of these, the earlier alone has been, as yet, really conceived or
studied as a science; the other, Ethology, is still to be created. But its
creation has at length become practicable. The empirical laws, destined to
verify its deductions, have been formed in abundance by every successive
age of humanity; and the premises for the deductions are now sufficiently
complete. Excepting the degree of uncertainty which still exists as to the
extent of the natural differences of individual minds, and the physical
circumstances on which these may be dependent (considerations which are of
secondary importance when we are considering mankind in the average, or
_en masse_), I believe most competent judges will agree that the general
laws of the different constituent elements of human nature are even now
sufficiently understood to render it possible for a competent thinker to
deduce from those laws, with a considerable approach to certainty, the
particular type of character which would be formed in mankind generally by
any assumed set of circumstances. A science of Ethology, founded on the
laws of Psychology, is therefore possible; though little has yet been
done, and that little not at all systematically, toward forming it. The
progress of this important but most imperfect science will depend on a
double process: first, that of deducing theoretically the ethological
consequences of particular circumstances of position, and comparing them
with the recognized results of common experience; and, secondly, the
reverse operation; increased study of the various types of human nature
that are to be found in the world; conducted by persons not only capable
of analyzing and recording the circumstances in which these types
severally prevail, but also sufficiently acquainted with psychological
laws to be able to explain and account for the characteristics of the
type, by the peculiarities of the circumstances: the residuum alone, when
there proves to be any, being set down to the account of congenital
predispositions.

For the experimental or _a posteriori_ part of this process, the materials
are continually accumulating by the observation of mankind. So far as
thought is concerned, the great problem of Ethology is to deduce the
requisite middle principles from the general laws of Psychology. The
subject to be studied is, the origin and sources of all those qualities in
human beings which are interesting to us, either as facts to be produced,
to be avoided, or merely to be understood; and the object is, to
determine, from the general laws of mind, combined with the general
position of our species in the universe, what actual or possible
combinations of circumstances are capable of promoting or of preventing
the production of those qualities. A science which possesses middle
principles of this kind, arranged in the order, not of causes, but of the
effects which it is desirable to produce or to prevent, is duly prepared
to be the foundation of the corresponding Art. And when Ethology shall be
thus prepared, practical education will be the mere transformation of
those principles into a parallel system of precepts, and the adaptation of
these to the sum total of the individual circumstances which exist in each
particular case.

It is hardly necessary again to repeat that, as in every other deductive
science, verification _a posteriori_ must proceed _pari passu_ with
deduction _a priori_. The inference given by theory as to the type of
character which would be formed by any given circumstances must be tested
by specific experience of those circumstances whenever obtainable; and the
conclusions of the science as a whole must undergo a perpetual
verification and correction from the general remarks afforded by common
experience respecting human nature in our own age, and by history
respecting times gone by. The conclusions of theory can not be trusted,
unless confirmed by observation; nor those of observation, unless they can
be affiliated to theory, by deducing them from the laws of human nature,
and from a close analysis of the circumstances of the particular
situation. It is the accordance of these two kinds of evidence separately
taken—the consilience of _a priori_ reasoning and specific
experience—which forms the only sufficient ground for the principles of
any science so “immersed in matter,” dealing with such complex and
concrete phenomena, as Ethology.



                               Chapter VI.


General Considerations On The Social Science.


§ 1. Next after the science of individual man comes the science of man in
society—of the actions of collective masses of mankind, and the various
phenomena which constitute social life.

If the formation of individual character is already a complex subject of
study, this subject must be, in appearance at least, still more complex;
because the number of concurrent causes, all exercising more or less
influence on the total effect, is greater, in the proportion in which a
nation, or the species at large, exposes a larger surface to the operation
of agents, psychological and physical, than any single individual. If it
was necessary to prove, in opposition to an existing prejudice, that the
simpler of the two is capable of being a subject of science, the prejudice
is likely to be yet stronger against the possibility of giving a
scientific character to the study of Politics, and of the phenomena of
Society. It is, accordingly, but of yesterday that the conception of a
political or social science has existed anywhere but in the mind of here
and there an insulated thinker, generally very ill prepared for its
realization: though the subject itself has of all others engaged the most
general attention, and been a theme of interested and earnest discussions,
almost from the beginning of recorded time.

The condition, indeed, of politics as a branch of knowledge was, until
very lately, and has scarcely even yet ceased to be, that which Bacon
animadverted on, as the natural state of the sciences while their
cultivation is abandoned to practitioners; not being carried on as a
branch of speculative inquiry, but only with a view to the exigencies of
daily practice, and the _fructifera experimenta_, therefore, being aimed
at, almost to the exclusion of the _lucifera_. Such was medical
investigation, before physiology and natural history began to be
cultivated as branches of general knowledge. The only questions examined
were, what diet is wholesome, or what medicine will cure some given
disease; without any previous systematic inquiry into the laws of
nutrition, and of the healthy and morbid action of the different organs,
on which laws the effect of any diet or medicine must evidently depend.
And in politics the questions which engaged general attention were
similar: Is such an enactment, or such a form of government, beneficial or
the reverse—either universally, or to some particular community? without
any previous inquiry into the general conditions by which the operation of
legislative measures, or the effects produced by forms of government, are
determined. Students in politics thus attempted to study the pathology and
therapeutics of the social body, before they had laid the necessary
foundation in its physiology; to cure disease without understanding the
laws of health. And the result was such as it must always be when persons,
even of ability, attempt to deal with the complex questions of a science
before its simpler and more elementary truths have been established.

No wonder that, when the phenomena of society have so rarely been
contemplated in the point of view characteristic of science, the
philosophy of society should have made little progress; should contain few
general propositions sufficiently precise and certain for common inquirers
to recognize in them a scientific character. The vulgar notion accordingly
is, that all pretension to lay down general truths on politics and society
is quackery; that no universality and no certainty are attainable in such
matters. What partly excuses this common notion is, that it is really not
without foundation in one particular sense. A large proportion of those
who have laid claim to the character of philosophic politicians have
attempted not to ascertain universal sequences, but to frame universal
precepts. They have imagined some one form of government, or system of
laws, to fit all cases—a pretension well meriting the ridicule with which
it is treated by practitioners, and wholly unsupported by the analogy of
the art to which, from the nature of its subject, that of politics must be
the most nearly allied. No one now supposes it possible that one remedy
can cure all diseases, or even the same disease in all constitutions and
habits of body.

It is not necessary even to the perfection of a science, that the
corresponding art should possess universal, or even general, rules. The
phenomena of society might not only be completely dependent on known
causes, but the mode of action of all those causes might be reducible to
laws of considerable simplicity, and yet no two cases might admit of being
treated in precisely the same manner. So great might be the variety of
circumstances on which the results in different cases depend, that the art
might not have a single general precept to give, except that of watching
the circumstances of the particular case, and adapting our measures to the
effects which, according to the principles of the science, result from
those circumstances. But although, in so complicated a class of subjects,
it is impossible to lay down practical maxims of universal application, it
does not follow that the phenomena do not conform to universal laws.

§ 2. All phenomena of society are phenomena of human nature, generated by
the action of outward circumstances upon masses of human beings; and if,
therefore, the phenomena of human thought, feeling, and action are subject
to fixed laws, the phenomena of society can not but conform to fixed laws,
the consequence of the preceding. There is, indeed, no hope that these
laws, though our knowledge of them were as certain and as complete as it
is in astronomy, would enable us to predict the history of society, like
that of the celestial appearances, for thousands of years to come. But the
difference of certainty is not in the laws themselves, it is in the data
to which these laws are to be applied. In astronomy the causes influencing
the result are few, and change little, and that little according to known
laws; we can ascertain what they are now, and thence determine what they
will be at any epoch of a distant future. The data, therefore, in
astronomy are as certain as the laws themselves. The circumstances, on the
contrary, which influence the condition and progress of society are
innumerable, and perpetually changing; and though they all change in
obedience to causes, and therefore to laws, the multitude of the causes is
so great as to defy our limited powers of calculation. Not to say that the
impossibility of applying precise numbers to facts of such a description
would set an impassable limit to the possibility of calculating them
beforehand, even if the powers of the human intellect were otherwise
adequate to the task.

But, as before remarked, an amount of knowledge quite insufficient for
prediction, may be most valuable for guidance. The science of society
would have attained a very high point of perfection if it enabled us, in
any given condition of social affairs, in the condition, for instance, of
Europe or any European country at the present time, to understand by what
causes it had, in any and every particular, been made what it was; whether
it was tending to any, and to what, changes; what effects each feature of
its existing state was likely to produce in the future; and by what means
any of those effects might be prevented, modified, or accelerated, or a
different class of effects superinduced. There is nothing chimerical in
the hope that general laws, sufficient to enable us to answer these
various questions for any country or time with the individual
circumstances of which we are well acquainted, do really admit of being
ascertained; and that the other branches of human knowledge, which this
undertaking presupposes, are so far advanced that the time is ripe for its
commencement. Such is the object of the Social Science.

That the nature of what I consider the true method of the science may be
made more palpable, by first showing what that method is not, it will be
expedient to characterize briefly two radical misconceptions of the proper
mode of philosophizing on society and government, one or other of which
is, either explicitly or more often unconsciously, entertained by almost
all who have meditated or argued respecting the logic of politics, since
the notion of treating it by strict rules, and on Baconian principles, has
been current among the more advanced thinkers. These erroneous methods, if
the word method can be applied to erroneous tendencies arising from the
absence of any sufficiently distinct conception of method, may be termed
the Experimental, or Chemical, mode of investigation, and the Abstract, or
Geometrical, mode. We shall begin with the former.



                               Chapter VII.


Of The Chemical, Or Experimental, Method In The Social Science.


§ 1. The laws of the phenomena of society are, and can be, nothing but the
laws of the actions and passions of human beings united together in the
social state. Men, however, in a state of society are still men; their
actions and passions are obedient to the laws of individual human nature.
Men are not, when brought together, converted into another kind of
substance, with different properties; as hydrogen and oxygen are different
from water, or as hydrogen, oxygen, carbon, and azote, are different from
nerves, muscles, and tendons. Human beings in society have no properties
but those which are derived from, and may be resolved into, the laws of
the nature of individual man. In social phenomena the Composition of
Causes is the universal law.

Now, the method of philosophizing which may be termed chemical overlooks
this fact, and proceeds as if the nature of man as an individual were not
concerned at all, or were concerned in a very inferior degree, in the
operations of human beings in society. All reasoning in political or
social affairs, grounded on principles of human nature, is objected to by
reasoners of this sort, under such names as “abstract theory.” For the
direction of their opinions and conduct, they profess to demand, in all
cases without exception, specific experience.

This mode of thinking is not only general with practitioners in politics,
and with that very numerous class who (on a subject which no one, however
ignorant, thinks himself incompetent to discuss) profess to guide
themselves by common sense rather than by science; but is often
countenanced by persons with greater pretensions to instruction—persons
who, having sufficient acquaintance with books and with the current ideas
to have heard that Bacon taught mankind to follow experience, and to
ground their conclusions on facts instead of metaphysical dogmas, think
that, by treating political facts in as directly experimental a method as
chemical facts, they are showing themselves true Baconians, and proving
their adversaries to be mere syllogizers and school-men. As, however, the
notion of the applicability of experimental methods to political
philosophy can not co-exist with any just conception of these methods
themselves, the kind of arguments from experience which the chemical
theory brings forth as its fruits (and which form the staple, in this
country especially, of parliamentary and hustings oratory), are such as,
at no time since Bacon, would have been admitted to be valid in chemistry
itself, or in any other branch of experimental science. They are such as
these: that the prohibition of foreign commodities must conduce to
national wealth, because England has flourished under it, or because
countries in general which have adopted it have flourished; that our laws,
or our internal administration, or our constitution, are excellent for a
similar reason; and the eternal arguments from historical examples, from
Athens or Rome, from the fires in Smithfield or the French Revolution.

I will not waste time in contending against modes of argumentation which
no person with the smallest practice in estimating evidence could possibly
be betrayed into; which draw conclusions of general application from a
single unanalyzed instance, or arbitrarily refer an effect to some one
among its antecedents, without any process of elimination or comparison of
instances. It is a rule both of justice and of good sense to grapple not
with the absurdest, but with the most reasonable form of a wrong opinion.
We shall suppose our inquirer acquainted with the true conditions of
experimental investigation, and competent in point of acquirements for
realizing them, so far as they can be realized. He shall know as much of
the facts of history as mere erudition can teach—as much as can be proved
by testimony, without the assistance of any theory; and if those mere
facts, properly collated, can fulfill the conditions of a real induction,
he shall be qualified for the task.

But that no such attempt can have the smallest chance of success, has been
abundantly shown in the tenth chapter of the Third Book.(274) We there
examined whether effects which depend on a complication of causes can be
made the subject of a true induction by observation and experiment; and
concluded, on the most convincing grounds, that they can not. Since, of
all effects, none depend on so great a complication of causes as social
phenomena, we might leave our case to rest in safety on that previous
showing. But a logical principle as yet so little familiar to the ordinary
run of thinkers, requires to be insisted on more than once, in order to
make the due impression; and the present being the case which of all
others exemplifies it the most strongly, there will be advantage in
re-stating the grounds of the general maxim, as applied to the specialties
of the class of inquiries now under consideration.

§ 2. The first difficulty which meets us in the attempt to apply
experimental methods for ascertaining the laws of social phenomena, is
that we are without the means of making artificial experiments. Even if we
could contrive experiments at leisure, and try them without limit, we
should do so under immense disadvantage; both from the impossibility of
ascertaining and taking note of all the facts of each case, and because
(those facts being in a perpetual state of change), before sufficient time
had elapsed to ascertain the result of the experiment, some material
circumstances would always have ceased to be the same. But it is
unnecessary to consider the logical objections which would exist to the
conclusiveness of our experiments, since we palpably never have the power
of trying any. We can only watch those which nature produces, or which are
produced for other reasons. We can not adapt our logical means to our
wants, by varying the circumstances as the exigencies of elimination may
require. If the spontaneous instances, formed by contemporary events and
by the successions of phenomena recorded in history, afford a sufficient
variation of circumstances, an induction from specific experience is
attainable; otherwise not. The question to be resolved is, therefore,
whether the requisites for induction respecting the causes of political
effects or the properties of political agents, are to be met with in
history? including under the term, contemporary history. And in order to
give fixity to our conceptions, it will be advisable to suppose this
question asked in reference to some special subject of political inquiry
or controversy; such as that frequent topic of debate in the present
century, the operation of restrictive and prohibitory commercial
legislation upon national wealth. Let this, then, be the scientific
question to be investigated by specific experience.

§ 3. In order to apply to the case the most perfect of the methods of
experimental inquiry, the Method of Difference, we require to find two
instances which tally in every particular except the one which is the
subject of inquiry. If two nations can be found which are alike in all
natural advantages and disadvantages; whose people resemble each other in
every quality, physical and moral, spontaneous and acquired; whose habits,
usages, opinions, laws, and institutions are the same in all respects,
except that one of them has a more protective tariff, or in other respects
interferes more with the freedom of industry; if one of these nations is
found to be rich and the other poor, or one richer than the other, this
will be an _experimentum crucis_: a real proof by experience, which of the
two systems is most favorable to national riches. But the supposition that
two such instances can be met with is manifestly absurd. Nor is such a
concurrence even abstractedly possible. Two nations which agreed in every
thing except their commercial policy would agree also in that. Differences
of legislation are not inherent and ultimate diversities; are not
properties of Kinds. They are effects of pre-existing causes. If the two
nations differ in this portion of their institutions, it is from some
difference in their position, and thence in their apparent interests, or
in some portion or other of their opinions, habits, and tendencies; which
opens a view of further differences without any assignable limit, capable
of operating on their industrial prosperity, as well as on every other
feature of their condition, in more ways than can be enumerated or
imagined. There is thus a demonstrated impossibility of obtaining, in the
investigations of the social science, the conditions required for the most
conclusive form of inquiry by specific experience.

In the absence of the direct, we may next try, as in other cases, the
supplementary resource, called in a former place the Indirect Method of
Difference; which, instead of two instances differing in nothing but the
presence or absence of a given circumstance, compares two _classes_ of
instances respectively agreeing in nothing but the presence of a
circumstance on the one side and its absence on the other. To choose the
most advantageous case conceivable (a case far too advantageous to be ever
obtained), suppose that we compare one nation which has a restrictive
policy with two or more nations agreeing in nothing but in permitting free
trade. We need not now suppose that either of these nations agrees with
the first in all its circumstances; one may agree with it in some of its
circumstances, and another in the remainder. And it may be argued, that if
these nations remain poorer than the restrictive nation, it can not be for
want either of the first or of the second set of circumstances, but it
must be for want of the protective system. If (we might say) the
restrictive nation had prospered from the one set of causes, the first of
the free-trade nations would have prospered equally; if by reason of the
other, the second would; but neither has; therefore the prosperity was
owing to the restrictions. This will be allowed to be a very favorable
specimen of an argument from specific experience in politics, and if this
be inconclusive, it would not be easy to find another preferable to it.

Yet, that it is inconclusive, scarcely requires to be pointed out. Why
must the prosperous nation have prospered from one cause exclusively?
National prosperity is always the collective result of a multitude of
favorable circumstances; and of these, the restrictive nation may unite a
greater number than either of the others, though it may have all of those
circumstances in common with either one or the other of them. Its
prosperity may be partly owing to circumstances common to it with one of
those nations, and partly with the other, while they, having each of them
only half the number of favorable circumstances, have remained inferior.
So that the closest imitation which can be made, in the social science, of
a legitimate induction from direct experience, gives but a specious
semblance of conclusiveness, without any real value.

§ 4. The Method of Difference in either of its forms being thus completely
out of the question, there remains the Method of Agreement. But we are
already aware of how little value this method is, in cases admitting
Plurality of Causes; and social phenomena are those in which the plurality
prevails in the utmost possible extent.

Suppose that the observer makes the luckiest hit which could be given by
any conceivable combination of chances; that he finds two nations which
agree in no circumstance whatever, except in having a restrictive system,
and in being prosperous; or a number of nations, all prosperous, which
have no antecedent circumstances common to them all but that of having a
restrictive policy. It is unnecessary to go into the consideration of the
impossibility of ascertaining from history, or even from contemporary
observation, that such is really the fact; that the nations agree in no
other circumstance capable of influencing the case. Let us suppose this
impossibility vanquished, and the fact ascertained that they agree only in
a restrictive system as an antecedent, and industrial prosperity as a
consequent. What degree of presumption does this raise that the
restrictive system caused the prosperity? One so trifling as to be
equivalent to none at all. That some one antecedent is the cause of a
given effect, because all other antecedents have been found capable of
being eliminated, is a just inference, only if the effect can have but one
cause. If it admits of several, nothing is more natural than that each of
these should separately admit of being eliminated. Now, in the case of
political phenomena, the supposition of unity of cause is not only wide of
the truth, but at an immeasurable distance from it. The causes of every
social phenomenon which we are particularly interested about, security,
wealth, freedom, good government, public virtue, general intelligence, or
their opposites, are infinitely numerous, especially the external or
remote causes, which alone are, for the most part, accessible to direct
observation. No one cause suffices of itself to produce any of these
phenomena; while there are countless causes which have some influence over
them, and may co-operate either in their production or in their
prevention. From the mere fact, therefore, of our having been able to
eliminate some circumstance, we can by no means infer that this
circumstance was not instrumental to the effect in some of the very
instances from which we have eliminated it. We can conclude that the
effect is sometimes produced without it; but not that, when present, it
does not contribute its share.

Similar objections will be found to apply to the Method of Concomitant
Variations. If the causes which act upon the state of any society produced
effects differing from one another in kind; if wealth depended on one
cause, peace on another, a third made people virtuous, a fourth
intelligent; we might, though unable to sever the causes from one another,
refer to each of them that property of the effect which waxed as it waxed,
and which waned as it waned. But every attribute of the social body is
influenced by innumerable causes; and such is the mutual action of the
co-existing elements of society, that whatever affects any one of the more
important of them, will by that alone, if it does not affect the others
directly, affect them indirectly. The effects, therefore, of different
agents not being different in quality, while the quantity of each is the
mixed result of all the agents, the variations of the aggregate can not
bear a uniform proportion to those of any one of its component parts.

§ 5. There remains the Method of Residues; which appears, on the first
view, less foreign to this kind of inquiry than the three other methods,
because it only requires that we should accurately note the circumstances
of some one country, or state of society. Making allowance, thereupon, for
the effect of all causes whose tendencies are known, the residue which
those causes are inadequate to explain may plausibly be imputed to the
remainder of the circumstances which are known to have existed in the
case. Something similar to this is the method which Coleridge(275)
describes himself as having followed in his political essays in the
_Morning Post_. “On every great occurrence I endeavored to discover in
past history the event that most nearly resembled it. I procured, whenever
it was possible, the contemporary historians, memorialists, and
pamphleteers. Then fairly subtracting the points of difference from those
of likeness, as the balance favored the former or the latter, I
conjectured that the result would be the same or different. As, for
instance, in the series of essays entitled ‘A Comparison of France under
Napoleon with Rome under the first Cæsars,’ and in those which followed,
‘on the probable final restoration of the Bourbons.’ The same plan I
pursued at the commencement of the Spanish Revolution, and with the same
success, taking the war of the United Provinces with Philip II. as the
groundwork of the comparison.” In this inquiry he no doubt employed the
Method of Residues; for, in “subtracting the points of difference from
those of likeness,” he doubtless weighed, and did not content himself with
numbering, them: he doubtless took those points of agreement only which he
presumed from their own nature to be capable of influencing the effect,
and, allowing for that influence, concluded that the remainder of the
result would be referable to the points of difference.

Whatever may be the efficacy of this method, it is, as we long ago
remarked, not a method of pure observation and experiment; it concludes,
not from a comparison of instances, but from the comparison of an instance
with the result of a previous deduction. Applied to social phenomena, it
presupposes that the causes from which part of the effect proceeded are
already known; and as we have shown that these can not have been known by
specific experience, they must have been learned by deduction from
principles of human nature; experience being called in only as a
supplementary resource, to determine the causes which produced an
unexplained residue. But if the principles of human nature may be had
recourse to for the establishment of some political truths, they may for
all. If it be admissible to say, England must have prospered by reason of
the prohibitory system, because after allowing for all the other
tendencies which have been operating, there is a portion of prosperity
still to be accounted for; it must be admissible to go to the same source
for the effect of the prohibitory system, and examine what account the
laws of human motives and actions will enable us to give of _its_
tendencies. Nor, in fact, will the experimental argument amount to any
thing, except in verification of a conclusion drawn from those general
laws. For we may subtract the effect of one, two, three, or four causes,
but we shall never succeed in subtracting the effect of all causes except
one; while it would be a curious instance of the dangers of too much
caution if, to avoid depending on _a priori_ reasoning concerning the
effect of a single cause, we should oblige ourselves to depend on as many
separate _a priori_ reasonings as there are causes operating concurrently
with that particular cause in some given instance.

We have now sufficiently characterized the gross misconception of the mode
of investigation proper to political phenomena, which I have termed the
Chemical Method. So lengthened a discussion would not have been necessary,
if the claim to decide authoritatively on political doctrines were
confined to persons who had competently studied any one of the higher
departments of physical science. But since the generality of those who
reason on political subjects, satisfactorily to themselves and to a more
or less numerous body of admirers, know nothing whatever of the methods of
physical investigation beyond a few precepts which they continue to parrot
after Bacon, being entirely unaware that Bacon’s conception of scientific
inquiry has done its work, and that science has now advanced into a higher
stage, there are probably many to whom such remarks as the foregoing may
still be useful. In an age in which chemistry itself, when attempting to
deal with the more complex chemical sequences—those of the animal or even
the vegetable organism—has found it necessary to become, and has succeeded
in becoming, a Deductive Science, it is not to be apprehended that any
person of scientific habits, who has kept pace with the general progress
of the knowledge of nature, can be in danger of applying the methods of
elementary chemistry to explore the sequences of the most complex order of
phenomena in existence.



                              Chapter VIII.


Of The Geometrical, Or Abstract, Method.


§ 1. The misconception discussed in the preceding chapter is, as we said,
chiefly committed by persons not much accustomed to scientific
investigation: practitioners in politics, who rather employ the
commonplaces of philosophy to justify their practice than seek to guide
their practice by philosophic principles; or imperfectly educated persons,
who, in ignorance of the careful selection and elaborate comparison of
instances required for the formation of a sound theory, attempt to found
one upon a few coincidences which they have casually noticed.

The erroneous method of which we are now to treat is, on the contrary,
peculiar to thinking and studious minds. It never could have suggested
itself but to persons of some familiarity with the nature of scientific
research; who, being aware of the impossibility of establishing, by casual
observation or direct experimentation, a true theory of sequences so
complex as are those of the social phenomena, have recourse to the simpler
laws which are immediately operative in those phenomena, and which are no
other than the laws of the nature of the human beings therein concerned,
These thinkers perceive (what the partisans of the chemical or
experimental theory do not) that the science of society must necessarily
be deductive. But, from an insufficient consideration of the specific
nature of the subject-matter—and often because (their own scientific
education having stopped short in too early a stage) geometry stands in
their minds as the type of all deductive science—it is to geometry, rather
than to astronomy and natural philosophy, that they unconsciously
assimilate the deductive science of society.

Among the differences between geometry (a science of co-existent facts,
altogether independent of the laws of the succession of phenomena), and
those physical Sciences of Causation which have been rendered deductive,
the following is one of the most conspicuous: That geometry affords no
room for what so constantly occurs in mechanics and its applications, the
case of conflicting forces; of causes which counteract or modify one
another. In mechanics we continually find two or more moving forces
producing, not motion, but rest; or motion in a different direction from
that which would have been produced by either of the generating forces. It
is true that the effect of the joint forces is the same when they act
simultaneously, as if they had acted one after another, or by turns; and
it is in this that the difference between mechanical and chemical laws
consists. But still the effects, whether produced by successive or by
simultaneous action, do, wholly or in part, cancel one another: what the
one force does, the other, partly, or altogether undoes. There is no
similar state of things in geometry. The result which follows from one
geometrical principle has nothing that conflicts with the result which
follows from another. What is proved true from one geometrical theorem,
what would be true if no other geometrical principles existed, can not be
altered and made no longer true by reason of some other geometrical
principle. What is once proved true is true in all cases, whatever
supposition may be made in regard to any other matter.

Now a conception similar to this last would appear to have been formed of
the social science, in the minds of the earlier of those who have
attempted to cultivate it by a deductive method. Mechanics would be a
science very similar to geometry, if every motion resulted from one force
alone, and not from a conflict of forces. In the geometrical theory of
society, it seems to be supposed that this is really the case with the
social phenomena; that each of them results always from only one force,
one single property of human nature.

At the point which we have now reached, it can not be necessary to say any
thing either in proof or in illustration of the assertion that such is not
the true character of the social phenomena. There is not, among these most
complex and (for that reason) most modifiable of all phenomena, any one
over which innumerable forces do not exercise influence; which does not
depend on a conjunction of very many causes. We have not, therefore, to
prove the notion in question to be an error, but to prove that the error
has been committed; that so mistaken a conception of the mode in which the
phenomena of society are produced has actually been ascertained.

§ 2. One numerous division of the reasoners who have treated social facts
according to geometrical methods, not admitting any modification of one
law by another, must for the present be left out of consideration, because
in them this error is complicated with, and is the effect of, another
fundamental misconception, of which we have already taken some notice, and
which will be further treated of before we conclude. I speak of those who
deduce political conclusions not from laws of nature, not from sequences
of phenomena, real or imaginary, but from unbending practical maxims.
Such, for example, are all who found their theory of politics on what is
called abstract right, that is to say, on universal precepts; a pretension
of which we have already noticed the chimerical nature. Such, in like
manner, are those who make the assumption of a social contract, or any
other kind of original obligation, and apply it to particular cases by
mere interpretation. But in this the fundamental error is the attempt to
treat an art like a science, and to have a deductive art; the
irrationality of which will be shown in a future chapter. It will be
proper to take our exemplification of the geometrical theory from those
thinkers who have avoided this additional error, and who entertain, so
far, a juster idea of the nature of political inquiry.

We may cite, in the first instance, those who assume as the principle of
their political philosophy that government is founded on fear; that the
dread of each other is the one motive by which human beings were
originally brought into a state of society, and are still held in it. Some
of the earlier scientific inquirers into politics, in particular Hobbes,
assumed this proposition, not by implication, but avowedly, as the
foundation of their doctrine, and attempted to build a complete philosophy
of politics thereupon. It is true that Hobbes did not find this one maxim
sufficient to carry him through the whole of his subject, but was obliged
to eke it out by the double sophism of an original contract. I call this a
double sophism; first, as passing off a fiction for a fact, and, secondly,
assuming a practical principle, or precept, as the basis of a theory;
which is a _petitio principii_, since (as we noticed in treating of that
Fallacy) every rule of conduct, even though it be so binding a one as the
observance of a promise, must rest its own foundations on the theory of
the subject; and the theory, therefore, can not rest upon it.

§ 3. Passing over less important instances, I shall come at once to the
most remarkable example afforded by our own times of the geometrical
method in politics; emanating from persons who are well aware of the
distinction between science and art; who knew that rules of conduct must
follow, not precede, the ascertainment of laws of nature, and that the
latter, not the former, is the legitimate field for the application of the
deductive method. I allude to the interest-philosophy of the Bentham
school.

The profound and original thinkers who are commonly known under this
description, founded their general theory of government on one
comprehensive premise, namely, that men’s actions are always determined by
their interests. There is an ambiguity in this last expression; for, as
the same philosophers, especially Bentham, gave the name of an interest to
any thing which a person likes, the proposition may be understood to mean
only this, that men’s actions are always determined by their wishes. In
this sense, however, it would not bear out any of the consequences which
these writers drew from it; and the word, therefore, in their political
reasonings, must be understood to mean (which is also the explanation they
themselves, on such occasions gave of it) what is commonly termed private,
or worldly, interest.

Taking the doctrine, then, in this sense, an objection presents itself _in
limine_ which might be deemed a fatal one, namely, that so sweeping a
proposition is far from being universally true. Human beings are not
governed in all their actions by their worldly interests. This, however,
is by no means so conclusive an objection as it at first appears; because
in politics we are for the most part concerned with the conduct, not of
individual persons, but either of a series of persons (as a succession of
kings), or a body or mass of persons, as a nation, an aristocracy, or a
representative assembly. And whatever is true of a large majority of
mankind, may without much error be taken for true of any succession of
persons, considered as a whole, or of any collection of persons in which
the act of the majority becomes the act of the whole body. Although,
therefore, the maxim is sometimes expressed in a manner unnecessarily
paradoxical, the consequences drawn from it will hold equally good if the
assertion be limited as follows: Any succession of persons, or the
majority of any body of persons, will be governed in the bulk of their
conduct by their personal interests. We are bound to allow to this school
of thinkers the benefit of this more rational statement of their
fundamental maxim, which is also in strict conformity to the explanations
which, when considered to be called for, have been given by themselves.

The theory goes on to infer, quite correctly, that if the actions of
mankind are determined in the main by their selfish interests, the only
rulers who will govern according to the interest of the governed, are
those whose selfish interests are in accordance with it. And to this is
added a third proposition, namely, that no rulers have their selfish
interest identical with that of the governed, unless it be rendered so by
accountability, that is, by dependence on the will of the governed. In
other words (and as the result of the whole), that the desire of retaining
or the fear of losing their power, and whatever is thereon consequent, is
the sole motive which can be relied on for producing on the part of rulers
a course of conduct in accordance with the general interest.

We have thus a fundamental theorem of political science, consisting of
three syllogisms, and depending chiefly on two general premises, in each
of which a certain effect is considered as determined only by one cause,
not by a concurrence of causes. In the one, it is assumed that the actions
of average rulers are determined solely by self-interest; in the other,
that the sense of identity of interest with the governed, is produced and
producible by no other cause than responsibility.

Neither of these propositions is by any means true; the last is extremely
wide of the truth.

It is not true that the actions even of average rulers are wholly, or any
thing approaching to wholly, determined by their personal interest, or
even by their own opinion of their personal interest. I do not speak of
the influence of a sense of duty, or feelings of philanthropy, motives
never to be mainly relied on, though (except in countries or during
periods of great moral debasement) they influence almost all rulers in
some degree, and some rulers in a very great degree. But I insist only on
what is true of all rulers, viz., that the character and course of their
actions is largely influenced (independently of personal calculation) by
the habitual sentiments and feelings, the general modes of thinking and
acting, which prevail throughout the community of which they are members;
as well as by the feelings, habits, and modes of thought which
characterize the particular class in that community to which they
themselves belong. And no one will understand or be able to decipher their
system of conduct, who does not take all these things into account. They
are also much influenced by the maxims and traditions which have descended
to them from other rulers, their predecessors; which maxims and traditions
have been known to retain an ascendancy during long periods, even in
opposition to the private interests of the rulers for the time being. I
put aside the influence of other less general causes. Although, therefore,
the private interest of the rulers or of the ruling class is a very
powerful force, constantly in action, and exercising the most important
influence upon their conduct, there is also, in what they do, a large
portion which that private interest by no means affords a sufficient
explanation of; and even the particulars which constitute the goodness or
badness of their government, are in some, and no small degree, influenced
by those among the circumstances acting upon them, which can not, with any
propriety, be included in the term self-interest.

Turning now to the other proposition, that responsibility to the governed
is the only cause capable of producing in the rulers a sense of identity
of interest with the community, this is still less admissible as a
universal truth, than even the former. I am not speaking of perfect
identity of interest, which is an impracticable chimera; which, most
assuredly, responsibility to the people does not give. I speak of identity
in essentials; and the essentials are different at different places and
times. There are a large number of cases in which those things which it is
most for the general interest that the rulers should do, are also those
which they are prompted to do by their strongest personal interest, the
consolidation of their power. The suppression, for instance, of anarchy
and resistance to law—the complete establishment of the authority of the
central government, in a state of society like that of Europe in the
Middle Ages—is one of the strongest interests of the people, and also of
the rulers simply because they are the rulers; and responsibility on their
part could not strengthen, though in many conceivable ways it might
weaken, the motives prompting them to pursue this object. During the
greater part, of the reign of Queen Elizabeth, and of many other monarchs
who might be named, the sense of identity of interest between the
sovereign and the majority of the people was probably stronger than it
usually is in responsible governments; every thing that the people had
most at heart, the monarch had at heart too. Had Peter the Great, or the
rugged savages whom he began to civilize, the truest inclination toward
the things which were for the real interest of those savages?

I am not here attempting to establish a theory of government, and am not
called upon to determine the proportional weight which ought to be given
to the circumstances which this school of geometrical politicians left out
of their system, and those which they took into it. I am only concerned to
show that their method was unscientific; not to measure the amount of
error which may have affected their practical conclusions.

It is but justice to them, however, to remark, that their mistake was not
so much one of substance as of form, and consisted in presenting in a
systematic shape, and as the scientific treatment of a great philosophical
question, what should have passed for that which it really was, the mere
polemics of the day. Although the actions of rulers are by no means wholly
determined by their selfish interests, it is chiefly as a security against
those selfish interests that constitutional checks are required; and for
that purpose such checks, in England, and the other nations of modern
Europe, can in no manner be dispensed with. It is likewise true, that in
these same nations, and in the present age, responsibility to the governed
is the only means practically available to create a feeling of identity of
interest, in the cases, and on the points, where that feeling does not
sufficiently exist. To all this, and to the arguments which may be founded
on it in favor of measures for the correction of our representative
system, I have nothing to object; but I confess my regret, that the small
though highly important portion of the philosophy of government, which was
wanted for the immediate purpose of serving the cause of parliamentary
reform, should have been held forth by thinkers of such eminence as a
complete theory.

It is not to be imagined possible, nor is it true in point of fact, that
these philosophers regarded the few premises of their theory as including
all that is required for explaining social phenomena, or for determining
the choice of forms of government and measures of legislation and
administration. They were too highly instructed, of too comprehensive
intellect, and some of them of too sober and practical a character, for
such an error. They would have applied, and did apply, their principles
with innumerable allowances. But it is not allowances that are wanted.
There is little chance of making due amends in the superstructure of a
theory for the want of sufficient breadth in its foundations. It is
unphilosophical to construct a science out of a few of the agencies by
which the phenomena are determined, and leave the rest to the routine of
practice or the sagacity of conjecture. We either ought not to pretend to
scientific forms, or we ought to study all the determining agencies
equally, and endeavor, so far as it can be done, to include all of them
within the pale of the science; else we shall infallibly bestow a
disproportionate attention upon those which our theory takes into account,
while we misestimate the rest, and probably underrate their importance.
That the deductions should be from the whole and not from a part only of
the laws of nature that are concerned, would be desirable even if those
omitted were so insignificant in comparison with the others, that they
might, for most purposes and on most occasions, be left out of the
account. But this is far indeed from being true in the social science. The
phenomena of society do not depend, in essentials, on some one agency or
law of human nature, with only inconsiderable modifications from others.
The whole of the qualities of human nature influence those phenomena, and
there is not one which influences them in a small degree. There is not
one, the removal or any great alteration of which would not materially
affect the whole aspect of society, and change more or less the sequences
of social phenomena generally.

The theory which has been the subject of these remarks is, in this country
at least, the principal contemporary example of what I have styled the
geometrical method of philosophizing in the social science; and our
examination of it has, for this reason, been more detailed than would
otherwise have been suitable to a work like the present. Having now
sufficiently illustrated the two erroneous methods, we shall pass without
further preliminary to the true method; that which proceeds (conformably
to the practice of the more complex physical sciences) deductively indeed,
but by deduction from many, not from one or a very few, original premises;
considering each effect as (what it really is) an aggregate result of many
causes, operating sometimes through the same, sometimes through different
mental agencies, or laws of human nature.



                               Chapter IX.


Of The Physical, Or Concrete Deductive, Method.


§ 1. After what has been said to illustrate the nature of the inquiry into
social phenomena, the general character of the method proper to that
inquiry is sufficiently evident, and needs only to be recapitulated, not
proved. However complex the phenomena, all their sequences and
co-existences result from the laws of the separate elements. The effect
produced, in social phenomena, by any complex set of circumstances,
amounts precisely to the sum of the effects of the circumstances taken
singly; and the complexity does not arise from the number of the laws
themselves, which is not remarkably great, but from the extraordinary
number and variety of the data or elements—of the agents which, in
obedience to that small number of laws, co-operate toward the effect. The
Social Science, therefore (which, by a convenient barbarism, has been
termed Sociology), is a deductive science; not, indeed, after the model of
geometry, but after that of the more complex physical sciences. It infers
the law of each effect from the laws of causation on which that effect
depends; not, however, from the law merely of one cause, as in the
geometrical method, but by considering all the causes which conjunctly
influence the effect, and compounding their laws with one another. Its
method, in short, is the Concrete Deductive Method: that of which
astronomy furnishes the most perfect, natural philosophy a somewhat less
perfect, example, and the employment of which, with the adaptations and
precautions required by the subject, is beginning to regenerate
physiology.

Nor does it admit of doubt, that similar adaptations and precautions are
indispensable in sociology. In applying to that most complex of all
studies what is demonstrably the sole method capable of throwing the light
of science even upon phenomena of a far inferior degree of complication,
we ought to be aware that the same superior complexity which renders the
instrument of Deduction more necessary, renders it also more precarious;
and we must be prepared to meet, by appropriate contrivances, this
increase of difficulty.

The actions and feelings of human beings in the social state, are, no
doubt, entirely governed by psychological and ethological laws: whatever
influence any cause exercises upon the social phenomena, it exercises
through those laws. Supposing therefore the laws of human actions and
feelings to be sufficiently known, there is no extraordinary difficulty in
determining from those laws, the nature of the social effects which any
given cause tends to produce. But when the question is that of compounding
several tendencies together, and computing the aggregate result of many
co-existent causes; and especially when, by attempting to predict what
will actually occur in a given case, we incur the obligation of estimating
and compounding the influences of all the causes which happen to exist in
that case, we attempt a task to proceed far in which, surpasses the
compass of the human faculties.

If all the resources of science are not sufficient to enable us to
calculate, _a priori_, with complete precision, the mutual action of three
bodies gravitating toward one another, it may be judged with what prospect
of success we should endeavor to calculate the result of the conflicting
tendencies which are acting in a thousand different directions and
promoting a thousand different changes at a given instant in a given
society; although we might and ought to be able, from the laws of human
nature, to distinguish correctly enough the tendencies themselves, so far
as they depend on causes accessible to our observation; and to determine
the direction which each of them, if acting alone, would impress upon
society, as well as, in a general way at least, to pronounce that some of
these tendencies are more powerful than others.

But, without dissembling the necessary imperfections of the _a priori_
method when applied to such a subject, neither ought we, on the other
hand; to exaggerate them. The same objections which apply to the Method of
Deduction in this its most difficult employment, apply to it, as we
formerly showed,(276) in its easiest; and would even there have been
insuperable, if there had not existed, as was then fully explained, an
appropriate remedy. This remedy consists in the process which, under the
name of Verification, we have characterized as the third essential
constituent part of the Deductive Method; that of collating the
conclusions of the ratiocination either with the concrete phenomena
themselves, or, when such are obtainable, with their empirical laws. The
ground of confidence in any concrete deductive science is not the _a
priori_ reasoning itself, but the accordance between its results and those
of observation _a posteriori_. Either of these processes, apart from the
other, diminishes in value as the subject increases in complication, and
this is in so rapid a ratio as soon to become entirely worthless; but the
reliance to be placed in the concurrence of the two sorts of evidence, not
only does not diminish in any thing like the same proportion, but is not
necessarily much diminished at all. Nothing more results than a
disturbance in the order of precedency of the two processes, sometimes
amounting to its actual inversion: insomuch that instead of deducing our
conclusions by reasoning, and verifying them by observation, we in some
cases begin by obtaining them provisionally from specific experience, and
afterward connect them with the principles of human nature by _a priori_
reasonings, which reasonings are thus a real Verification.

The only thinker who, with a competent knowledge of scientific methods in
general, has attempted to characterize the Method of Sociology, M. Comte,
considers this inverse order as inseparably inherent in the nature of
sociological speculation. He looks upon the social science as essentially
consisting of generalizations from history, verified, not originally
suggested, by deduction from the laws of human nature. Though there is a
truth contained in this opinion, of which I shall presently endeavor to
show the importance, I can not but think that this truth is enunciated in
too unlimited a manner, and that there is considerable scope in
sociological inquiry for the direct, as well as for the inverse, Deductive
Method.

It will, in fact, be shown in the next chapter, that there is a kind of
sociological inquiries to which, from their prodigious complication, the
method of direct deduction is altogether inapplicable, while by a happy
compensation it is precisely in these cases that we are able to obtain the
best empirical laws: to these inquiries, therefore, the Inverse Method is
exclusively adapted. But there are also, as will presently appear, other
cases in which it is impossible to obtain from direct observation any
thing worthy the name of an empirical law; and it fortunately happens that
these are the very cases in which the Direct Method is least affected by
the objection which undoubtedly must always affect it in a certain degree.

We shall begin, then, by looking at the Social Science as a science of
direct Deduction, and considering what can be accomplished in it, and
under what limitations, by that mode of investigation. We shall, then, in
a separate chapter, examine and endeavor to characterize the inverse
process.

§ 2. It is evident, in the first place, that Sociology, considered as a
system of deductions _a priori_, can not be a science of positive
predictions, but only of tendencies. We may be able to conclude, from the
laws of human nature applied to the circumstances of a given state of
society, that a particular cause will operate in a certain manner unless
counteracted; but we can never be assured to what extent or amount it will
so operate, or affirm with certainty that it will not be counteracted;
because we can seldom know, even approximately, all the agencies which may
co-exist with it, and still less calculate the “collective result” of so
many combined elements. The remark, however, must here be once more
repeated, that knowledge insufficient for prediction may be most valuable
for guidance. It is not necessary for the wise conduct of the affairs of
society, no more than of any one’s private concerns, that we should be
able to foresee infallibly the results of what we do. We must seek our
objects by means which may perhaps be defeated, and take precautions
against dangers which possibly may never be realized. The aim of practical
politics is to surround any given society with the greatest possible
number of circumstances of which the tendencies are beneficial, and to
remove or counteract, as far as practicable, those of which the tendencies
are injurious. A knowledge of the tendencies only, though without the
power of accurately predicting their conjunct result, gives us to a
considerable extent this power.

It would, however, be an error to suppose that even with respect to
tendencies we could arrive in this manner at any great number of
propositions which will be true in all societies without exception. Such a
supposition would be inconsistent with the eminently modifiable nature of
the social phenomena, and the multitude and variety of the circumstances
by which they are modified—circumstances never the same, or even nearly
the same, in two different societies, or in two different periods of the
same society. This would not be so serious an obstacle if, though the
causes acting upon society in general are numerous, those which influence
any one feature of society were limited in number; for we might then
insulate any particular social phenomenon, and investigate its laws
without disturbance from the rest. But the truth is the very opposite of
this. Whatever affects, in an appreciable degree, any one element of the
social state, affects through it all the other elements. The mode of
production of all social phenomena is one great case of Intermixture of
Laws. We can never either understand in theory or command in practice the
condition of a society in any one respect, without taking into
consideration its condition in all other respects. There is no social
phenomenon which is not more or less influenced by every other part of the
condition of the same society, and therefore by every cause which is
influencing any other of the contemporaneous social phenomena. There is,
in short, what physiologists term a _consensus_, similar to that existing
among the various organs and functions of the physical frame of man and
the more perfect animals; and constituting one of the many analogies which
have rendered universal such expressions as the “body politic” and “body
natural.” It follows from this _consensus_, that unless two societies
could be alike in all the circumstances which surround and influence them
(which would imply their being alike in their previous history), no
portion whatever of the phenomena will, unless by accident, precisely
correspond; no one cause will produce exactly the same effects in both.
Every cause, as its effect spreads through society, comes somewhere in
contact with different sets of agencies, and thus has its effects on some
of the social phenomena differently modified; and these differences, by
their reaction, produce a difference even in those of the effects which
would otherwise have been the same. We can never, therefore, affirm with
certainty that a cause which has a particular tendency in one people or in
one age will have exactly the same tendency in another, without referring
back to our premises, and performing over again for the second age or
nation, that analysis of the whole of its influencing circumstances which
we had already performed for the first. The deductive science of society
will not lay down a theorem, asserting in a universal manner the effect of
any cause; but will rather teach us how to frame the proper theorem for
the circumstances of any given case. It will not give the laws of society
in general, but the means of determining the phenomena of any given
society from the particular elements or data of that society.

All the general propositions which can be framed by the deductive science,
are therefore, in the strictest sense of the word, hypothetical. They are
grounded on some suppositious set of circumstances, and declare how some
given cause would operate in those circumstances, supposing that no others
were combined with them. If the set of circumstances supposed have been
copied from those of any existing society, the conclusions will be true of
that society, provided, and in as far as, the effect of those
circumstances shall not be modified by others which have not been taken
into the account. If we desire a nearer approach to concrete truth, we can
only aim at it by taking, or endeavoring to take, a greater number of
individualizing circumstances into the computation.

Considering, however, in how accelerating a ratio the uncertainty of our
conclusions increases as we attempt to take the effect of a greater number
of concurrent causes into our calculations, the hypothetical combinations
of circumstances on which we construct the general theorems of the
science, can not be made very complex, without so rapidly accumulating a
liability to error as must soon deprive our conclusions of all value. This
mode of inquiry, considered as a means of obtaining general propositions,
must, therefore, on pain of frivolity, be limited to those classes of
social facts which, though influenced like the rest by all sociological
agents, are under the _immediate_ influence, principally at least, of a
few only.

§ 3. Notwithstanding the universal _consensus_ of the social phenomena,
whereby nothing which takes place in any part of the operations of society
is without its share of influence on every other part; and notwithstanding
the paramount ascendancy which the general state of civilization and
social progress in any given society must hence exercise over all the
partial and subordinate phenomena; it is not the less true that different
species of social facts are in the main dependent, immediately and in the
first resort, on different kinds of causes; and therefore not only may
with advantage, but must, be studied apart: just as in the natural body we
study separately the physiology and pathology of each of the principal
organs and tissues, though every one is acted upon by the state of all the
others; and though the peculiar constitution and general state of health
of the organism co-operates with, and often preponderates over, the local
causes, in determining the state of any particular organ.

On these considerations is grounded the existence of distinct and
separate, though not independent, branches or departments of sociological
speculation.

There is, for example, one large class of social phenomena in which the
immediately determining causes are principally those which act through the
desire of wealth, and in which the psychological law mainly concerned is
the familiar one, that a greater gain is preferred to a smaller. I mean,
of course, that portion of the phenomena of society which emanate from the
industrial, or productive, operations of mankind; and from those of their
acts through which the distribution of the products of those industrial
operations takes place, in so far as not effected by force, or modified by
voluntary gift. By reasoning from that one law of human nature, and from
the principal outward circumstances (whether universal or confined to
particular states of society) which operate upon the human mind through
that law, we may be enabled to explain and predict this portion of the
phenomena of society, so far as they depend on that class of circumstances
only; overlooking the influence of any other of the circumstances of
society; and therefore neither tracing back the circumstances which we do
take into account, to their possible origin in some other facts in the
social state, nor making allowance for the manner in which any of those
other circumstances may interfere with, and counteract or modify, the
effect of the former. A department of science may thus be constructed,
which has received the name of Political Economy.

The motive which suggests the separation of this portion of the social
phenomena from the rest, and the creation of a distinct branch of science
relating to them is—that they do _mainly_ depend, at least in the first
resort, on one class of circumstances only; and that even when other
circumstances interfere, the ascertainment of the effect due to the one
class of circumstances alone, is a sufficiently intricate and difficult
business to make it expedient to perform it once for all, and then allow
for the effect of the modifying circumstances; especially as certain fixed
combinations of the former are apt to recur often, in conjunction with
ever-varying circumstances of the latter class.

Political Economy, as I have said on another occasion, concerns itself
only with “such of the phenomena of the social state as take place in
consequence of the pursuit of wealth. It makes entire abstraction of every
other human passion or motive; except those which may be regarded as
perpetually antagonizing principles to the desire of wealth, namely,
aversion to labor, and desire of the present enjoyment of costly
indulgences. These it takes, to a certain extent, into its calculations,
because these do not merely, like our other desires, occasionally conflict
with the pursuit of wealth, but accompany it always as a drag or
impediment, and are therefore inseparably mixed up in the consideration of
it. Political Economy considers mankind as occupied solely in acquiring
and consuming wealth; and aims at showing what is the course of action
into which mankind, living in a state of society, would be impelled, if
that motive, except in the degree in which it is checked by the two
perpetual counter-motives above adverted to, were absolute ruler of all
their actions. Under the influence of this desire, it shows mankind
accumulating wealth, and employing that wealth in the production of other
wealth; sanctioning by mutual agreement the institution of property;
establishing laws to prevent individuals from encroaching upon the
property of others by force or fraud; adopting various contrivances for
increasing the productiveness of their labor; settling the division of the
produce by agreement, under the influence of competition (competition
itself being governed by certain laws, which laws are therefore the
ultimate regulators of the division of the produce); and employing certain
expedients (as money, credit, etc.) to facilitate the distribution. All
these operations, though many of them are really the result of a plurality
of motives, are considered by political economy as flowing solely from the
desire of wealth. The science then proceeds to investigate the laws which
govern these several operations, under the supposition that man is a being
who is determined, by the necessity of his nature, to prefer a greater
portion of wealth to a smaller, in all cases, without any other exception
than that constituted by the two counter-motives already specified. Not
that any political economist was ever so absurd as to suppose that mankind
are really thus constituted, but because this is the mode in which science
must necessarily proceed. When an effect depends on a concurrence of
causes, these causes must be studied one at a time, and their laws
separately investigated, if we wish, through the causes, to obtain the
power of either predicting or controlling the effect; since the law of the
effect is compounded of the laws of all the causes which determine it. The
law of the centripetal and that of the projectile force must have been
known, before the motions of the earth and planets could be explained, or
many of them predicted. The same is the case with the conduct of man in
society. In order to judge how he will act under the variety of desires
and aversions which are concurrently operating upon him, we must know how
he would act under the exclusive influence of each one in particular.
There is, perhaps, no action of a man’s life in which he is neither under
the immediate nor under the remote influence of any impulse but the mere
desire of wealth. With respect to those parts of human conduct of which
wealth is not even the principal object, to these political economy does
not pretend that its conclusions are applicable. But there are also
certain departments of human affairs, in which the acquisition of wealth
is the main and acknowledged end. It is only of these that political
economy takes notice. The manner in which it necessarily proceeds is that
of treating the main and acknowledged end as if it were the sole end;
which, of all hypotheses equally simple, is the nearest to the truth. The
political economist inquires, what are the actions which would be produced
by this desire, if within the departments in question it were unimpeded by
any other. In this way a nearer approximation is obtained than would
otherwise be practicable to the real order of human affairs in those
departments. This approximation has then to be corrected by making proper
allowance for the effects of any impulses of a different description,
which can be shown to interfere with the result in any particular case.
Only in a few of the most striking cases (such as the important one of the
principle of population) are these corrections interpolated into the
expositions of political economy itself; the strictness of purely
scientific arrangement being thereby somewhat departed from, for the sake
of practical utility. So far as it is known, or may be presumed, that the
conduct of mankind in the pursuit of wealth is under the collateral
influence of any other of the properties of our nature than the desire of
obtaining the greatest quantity of wealth with the least labor and
self-denial, the conclusions of political economy will so far fail of
being applicable to the explanation or prediction of real events, until
they are modified by a correct allowance for the degree of influence
exercised by the other cause.”(277)

Extensive and important practical guidance may be derived, in any given
state of society, from general propositions such as those above indicated;
even though the modifying influence of the miscellaneous causes which the
theory does not take into account, as well as the effect of the general
social changes in progress, be provisionally overlooked. And though it has
been a very common error of political economists to draw conclusions from
the elements of one state of society, and apply them to other states in
which many of the elements are not the same, it is even then not
difficult, by tracing back the demonstrations, and introducing the new
premises in their proper places, to make the same general course of
argument which served for the one case, serve for the others too.

For example, it has been greatly the custom of English political
economists to discuss the laws of the distribution of the produce of
industry, on a supposition which is scarcely realized anywhere out of
England and Scotland, namely, that the produce is “shared among three
classes, altogether distinct from one another, laborers, capitalists, and
landlords; and that all these are free agents, permitted in law and in
fact to set upon their labor, their capital, and their land, whatever
price they are able to get for it. The conclusions of the science, being
all adapted to a society thus constituted, require to be revised whenever
they are applied to any other. They are inapplicable where the only
capitalists are the landlords, and the laborers are their property, as in
slave countries. They are inapplicable where the almost universal landlord
is the state, as in India. They are inapplicable where the agricultural
laborer is generally the owner both of the land itself and of the capital,
as frequently in France, or of the capital only, as in Ireland.” But
though it may often be very justly objected to the existing race of
political economists “that they attempt to construct a permanent fabric
out of transitory materials; that they take for granted the immutability
of arrangements of society, many of which are in their nature fluctuating
or progressive, and enunciate with as little qualification as if they were
universal and absolute truths, propositions which are perhaps applicable
to no state of society except the particular one in which the writer
happened to live;” this does not take away the value of the propositions,
considered with reference to the state of society from which they were
drawn. And even as applicable to other states of society, “it must not be
supposed that the science is so incomplete and unsatisfactory as this
might seem to prove. Though many of its conclusions are only locally true,
its method of investigation is applicable universally; and as whoever has
solved a certain number of algebraic equations, can without difficulty
solve all others of the same kind, so whoever knows the political economy
of England, or even of Yorkshire, knows that of all nations, actual or
possible, provided he have good sense enough not to expect the same
conclusion to issue from varying premises.” Whoever has mastered with the
degree of precision which is attainable the laws which, under free
competition, determine the rent, profits, and wages, received by
landlords, capitalists, and laborers, in a state of society in which the
three classes are completely separate, will have no difficulty in
determining the very different laws which regulate the distribution of the
produce among the classes interested in it in any of the states of
cultivation and landed property set forth in the foregoing extract.(278)

§ 4. I would not here undertake to decide what other hypothetical or
abstract sciences similar to Political Economy, may admit of being carved
out of the general body of the social science; what other portions of the
social phenomena are in a sufficiently close and complete dependence, in
the first resort, on a peculiar class of causes, to make it convenient to
create a preliminary science of those causes; postponing the consideration
of the causes which act through them, or in concurrence with them, to a
later period of the inquiry. There is, however, among these separate
departments one which can not be passed over in silence, being of a more
comprehensive and commanding character than any of the other branches into
which the social science may admit of being divided. Like them, it is
directly conversant with the causes of only one class of social facts, but
a class which exercises, immediately or remotely, a paramount influence
over the test. I allude to what may be termed Political Ethology, or the
theory of the causes which determine the type of character belonging to a
people or to an age. Of all the subordinate branches of the social
science, this is the most completely in its infancy. The causes of
national character are scarcely at all understood, and the effect of
institutions or social arrangements upon the character of the people is
generally that portion of their effects which is least attended to, and
least comprehended. Nor is this wonderful, when we consider the infant
state of the science of Ethology itself, from whence the laws must be
drawn, of which the truths of political ethology can be but results and
exemplifications.

Yet, to whoever well considers the matter, it must appear that the laws of
national (or collective) character are by far the most important class of
sociological laws. In the first place, the character which is formed by
any state of social circumstances is in itself the most interesting
phenomenon which that state of society can possibly present. Secondly, it
is also a fact which enters largely into the production of all the other
phenomena. And above all, the character, that is, the opinions, feelings,
and habits, of the people, though greatly the results of the state of
society which precedes them, are also greatly the causes of the state of
society which follows them; and are the power by which all those of the
circumstances of society which are artificial, laws and customs for
instance, are altogether moulded: customs evidently, laws no less really,
either by the direct influence of public sentiment upon the ruling powers,
or by the effect which the state of national opinion and feeling has in
determining the form of government and shaping the character of the
governors.

As might be expected, the most imperfect part of those branches of social
inquiry which have been cultivated as separate sciences, is the theory of
the manner in which their conclusions are affected by ethological
considerations. The omission is no defect in them as abstract or
hypothetical sciences, but it vitiates them in their practical application
as branches of a comprehensive social science. In political economy, for
instance, empirical laws of human nature are tacitly assumed by English
thinkers, which are calculated only for Great Britain and the United
States. Among other things, an intensity of competition is constantly
supposed, which, as a general mercantile fact, exists in no country in the
world except those two. An English political economist, like his
countrymen in general, has seldom learned that it is possible that men, in
conducting the business of selling their goods over a counter, should care
more about their ease or their vanity than about their pecuniary gain. Yet
those who know the habits of the continent of Europe are aware how
apparently small a motive often outweighs the desire of money getting,
even in the operations which have money getting for their direct object.
The more highly the science of ethology is cultivated, and the better the
diversities of individual and national character are understood, the
smaller, probably, will the number of propositions become, which it will
be considered safe to build on as universal principles of human nature.

These considerations show that the process of dividing off the social
science into compartments, in order that each may be studied separately,
and its conclusions afterward corrected for practice by the modifications
supplied by the others, must be subject to at least one important
limitation. Those portions alone of the social phenomena can with
advantage be made the subjects, even provisionally, of distinct branches
of science, into which the diversities of character between different
nations or different times enter as influencing causes only in a secondary
degree. Those phenomena, on the contrary, with which the influences of the
ethological state of the people are mixed up at every step (so that the
connection of effects and causes can not be even rudely marked out without
taking those influences into consideration) could not with any advantage,
nor without great disadvantage, be treated independently of political
ethology, nor, therefore, of all the circumstances by which the qualities
of a people are influenced. For this reason (as well as for others which
will hereafter appear) there can be no separate Science of Government;
that being the fact which, of all others, is most mixed up, both as cause
and effect, with the qualities of the particular people or of the
particular age. All questions respecting the tendencies of forms of
government must stand part of the general science of society, not of any
separate branch of it.

This general Science of Society, as distinguished from the separate
departments of the science (each of which asserts its conclusions only
conditionally, subject to the paramount control of the laws of the general
science) now remains to be characterized. And as will be shown presently,
nothing of a really scientific character is here possible, except by the
inverse deductive method. But before we quit the subject of those
sociological speculations which proceed by way of direct deduction, we
must examine in what relation they stand to that indispensable element in
all deductive sciences, Verification by Specific Experience—comparison
between the conclusions of reasoning and the results of observation.

§ 5. We have seen that, in most deductive sciences, and among the rest in
Ethology itself, which is the immediate foundation of the Social Science,
a preliminary work of preparation is performed on the observed facts, to
fit them for being rapidly and accurately collated (sometimes even for
being collated at all) with the conclusions of theory. This preparatory
treatment consists in finding general propositions which express concisely
what is common to large classes of observed facts; and these are called
the empirical laws of the phenomena. We have, therefore, to inquire,
whether any similar preparatory process can be performed on the facts of
the social science; whether there are any empirical laws in history or
statistics.

In statistics, it is evident that empirical laws may sometimes be traced;
and the tracing them forms an important part of that system of indirect
observation on which we must often rely for the data of the Deductive
Science. The process of the science consists in inferring effects from
their causes; but we have often no means of observing the causes, except
through the medium of their effects. In such cases the deductive science
is unable to predict the effects, for want of the necessary data; it can
determine what causes are capable of producing any given effect, but not
with what frequency and in what quantities those causes exist. An instance
in point is afforded by a newspaper now lying before me. A statement was
furnished by one of the official assignees in bankruptcy showing among the
various bankruptcies which it had been his duty to investigate, in how
many cases the losses had been caused by misconduct of different kinds,
and in how many by unavoidable misfortunes. The result was, that the
number of failures caused by misconduct greatly preponderated over those
arising from all other causes whatever. Nothing but specific experience
could have given sufficient ground for a conclusion to this purport. To
collect, therefore, such empirical laws (which are never more than
approximate generalizations) from direct observation, is an important part
of the process of sociological inquiry.

The experimental process is not here to be regarded as a distinct road to
the truth, but as a means (happening accidentally to be the only, or the
best, available) for obtaining the necessary data for the deductive
science. When the immediate causes of social facts are not open to direct
observation, the empirical law of the effects gives us the empirical law
(which in that case is all that we can obtain) of the causes likewise. But
those immediate causes depend on remote causes; and the empirical law,
obtained by this indirect mode of observation, can only be relied on as
applicable to unobserved cases, so long as there is reason to think that
no change has taken place in any of the remote causes on which the
immediate causes depend. In making use, therefore, of even the best
statistical generalizations for the purpose of inferring (though it be
only conjecturally) that the same empirical laws will hold in any new
case, it is necessary that we be well acquainted with the remoter causes,
in order that we may avoid applying the empirical law to cases which
differ in any of the circumstances on which the truth of the law
ultimately depends. And thus, even where conclusions derived from specific
observation are available for practical inferences in new cases, it is
necessary that the deductive science should stand sentinel over the whole
process; that it should be constantly referred to, and its sanction
obtained to every inference.

The same thing holds true of all generalizations which can be grounded on
history. Not only there are such generalizations, but it will presently be
shown that the general science of society, which inquires into the laws of
succession and co-existence of the great facts constituting the state of
society and civilization at any time, can proceed in no other manner than
by making such generalizations—afterward to be confirmed by connecting
them with the psychological and ethological laws on which they must really
depend.

§ 6. But (reserving this question for its proper place) in those more
special inquiries which form the subject of the separate branches of the
social science, this twofold logical process and reciprocal verification
is not possible; specific experience affords nothing amounting to
empirical laws. This is particularly the case where the object is to
determine the effect of any one social cause among a great number acting
simultaneously; the effect, for example, of corn laws, or of a prohibitive
commercial system generally. Though it may be perfectly certain, from
theory, what _kind_ of effects corn laws must produce, and in what general
direction their influence must tell upon industrial prosperity, their
effect is yet of necessity so much disguised by the similar or contrary
effects of other influencing agents, that specific experience can at most
only show that on the average of some great number of instances, the cases
where there were corn laws exhibited the effect in a greater degree than
those where there were not. Now the number of instances necessary to
exhaust the whole round of combinations of the various influential
circumstances, and thus afford a fair average, never can be obtained. Not
only we can never learn with sufficient authenticity the facts of so many
instances, but the world itself does not afford them in sufficient
numbers, within the limits of the given state of society and civilization
which such inquiries always presuppose. Having thus no previous empirical
generalizations with which to collate the conclusions of theory, the only
mode of direct verification which remains is to compare those conclusions
with the result of an individual experiment or instance. But here the
difficulty is equally great. For in order to verify a theory by an
experiment, the circumstances of the experiment must be exactly the same
with those contemplated in the theory. But in social phenomena the
circumstances of no two cases are exactly alike. A trial of corn laws in
another country, or in a former generation, would go a very little way
toward verifying a conclusion drawn respecting their effect in this
generation and in this country. It thus happens, in most cases, that the
only individual instance really fitted to verify the predictions of theory
is the very instance for which the predictions were made; and the
verification comes too late to be of any avail for practical guidance.

Although, however, direct verification is impossible, there is an indirect
verification, which is scarcely of less value, and which is always
practicable. The conclusion drawn as to the individual case can only be
directly verified in that case; but it is verified indirectly, by the
verification of other conclusions, drawn in other individual cases from
the same laws. The experience which comes too late to verify the
particular proposition to which it refers, is not too late to help toward
verifying the general sufficiency of the theory. The test of the degree in
which the science affords safe ground for predicting (and consequently for
practically dealing with) what has not yet happened, is the degree in
which it would have enabled us to predict what has actually occurred.
Before our theory of the influence of a particular cause, in a given state
of circumstances, can be entirely trusted, we must be able to explain and
account for the existing state of all that portion of the social phenomena
which that cause has a tendency to influence. If, for instance, we would
apply our speculations in political economy to the prediction or guidance
of the phenomena of any country, we must be able to explain all the
mercantile or industrial facts of a general character, appertaining to the
present state of that country; to point out causes sufficient to account
for all of them, and prove, or show good ground for supposing, that these
causes have really existed. If we can not do this, it is a proof either
that the facts which ought to be taken into account are not yet completely
known to us, or that although we know the facts, we are not masters of a
sufficiently perfect theory to enable us to assign their consequences. In
either case we are not, in the present state of our knowledge, fully
competent to draw conclusions, speculative or practical, for that country.
In like manner, if we would attempt to judge of the effect which any
political institution would have, supposing that it could be introduced
into any given country, we must be able to show that the existing state of
the practical government of that country, and of whatever else depends
thereon, together with the particular character and tendencies of the
people, and their state in respect to the various elements of social
well-being, are such as the institutions they have lived under, in
conjunction with the other circumstances of their nature or of their
position, were calculated to produce.

To prove, in short, that our science, and our knowledge of the particular
case, render us competent to predict the future, we must show that they
would have enabled us to predict the present and the past. If there be any
thing which we could not have predicted, this constitutes a residual
phenomenon, requiring further study for the purpose of explanation; and we
must either search among the circumstances of the particular case until we
find one which, on the principles of our existing theory, accounts for the
unexplained phenomenon, or we must turn back, and seek the explanation by
an extension and improvement of the theory itself.



                                Chapter X.


Of The Inverse Deductive, Or Historical, Method.


§ 1. There are two kinds of sociological inquiry. In the first kind, the
question proposed is, what effect will follow from a given cause, a
certain general condition of social circumstances being presupposed. As,
for example, what would be the effect of imposing or of repealing corn
laws, of abolishing monarchy or introducing universal suffrage, in the
present condition of society and civilization in any European country, or
under any other given supposition with regard to the circumstances of
society in general, without reference to the changes which might take
place, or which may already be in progress, in those circumstances. But
there is also a second inquiry, namely, what are the laws which determine
those general circumstances themselves. In this last the question is, not
what will be the effect of a given cause in a certain state of society,
but what are the causes which produce, and the phenomena which
characterize, states of society generally. In the solution of this
question consists the general Science of Society; by which the conclusions
of the other and more special kind of inquiry must be limited and
controlled.

§ 2. In order to conceive correctly the scope of this general science, and
distinguish it from the subordinate departments of sociological
speculation, it is necessary to fix the ideas attached to the phrase, “A
State of Society.” What is called a state of society, is the simultaneous
state of all the greater social facts or phenomena. Such are: the degree
of knowledge, and of intellectual and moral culture, existing in the
community, and in every class of it; the state of industry, of wealth and
its distribution; the habitual occupations of the community; their
division into classes, and the relations of those classes to one another;
the common beliefs which they entertain on all the subjects most important
to mankind, and the degree of assurance with which those beliefs are held;
their tastes, and the character and degree of their æsthetic development;
their form of government, and the more important of their laws and
customs. The condition of all these things, and of many more which will
readily suggest themselves, constitute the state of society, or the state
of civilization, at any given time.

When states of society, and the causes which produce them, are spoken of
as a subject of science, it is implied that there exists a natural
correlation among these different elements; that not every variety of
combination of these general social facts is possible, but only certain
combinations; that, in short, there exist Uniformities of Co-existence
between the states of the various social phenomena. And such is the truth;
as is indeed a necessary consequence of the influence exercised by every
one of those phenomena over every other. It is a fact implied in the
_consensus_ of the various parts of the social body.

States of society are like different constitutions or different ages in
the physical frame; they are conditions not of one or a few organs or
functions, but of the whole organism. Accordingly, the information which
we possess respecting past ages, and respecting the various states of
society now existing in different regions of the earth, does, when duly
analyzed, exhibit uniformities. It is found that when one of the features
of society is in a particular state, a state of many other features, more
or less precisely determinate, always or usually co-exists with it.

But the uniformities of co-existence obtaining among phenomena which are
effects of causes, must (as we have so often observed) be corollaries from
the laws of causation by which these phenomena are really determined. The
mutual correlation between the different elements of each state of
society, is, therefore, a derivative law, resulting from the laws which
regulate the succession between one state of society and another; for the
proximate cause of every state of society is the state of society
immediately preceding it. The fundamental problem, therefore, of the
social science, is to find the laws according to which any state of
society produces the state which succeeds it and takes its place. This
opens the great and vexed question of the progressiveness of man and
society; an idea involved in every just conception of social phenomena as
the subject of a science.

§ 3. It is one of the characters, not absolutely peculiar to the sciences
of human nature and society, but belonging to them in a peculiar degree,
to be conversant with a subject-matter whose properties are changeable. I
do not mean changeable from day to day, but from age to age; so that not
only the qualities of individuals vary, but those of the majority are not
the same in one age as in another.

The principal cause of this peculiarity is the extensive and constant
reaction of the effects upon their causes. The circumstances in which
mankind are placed, operating according to their own laws and to the laws
of human nature, form the characters of the human beings; but the human
beings, in their turn, mould and shape the circumstances for themselves
and for those who come after them. From this reciprocal action there must
necessarily result either a cycle or a progress. In astronomy also, every
fact is at once effect and cause; the successive positions of the various
heavenly bodies produce changes both in the direction and in the intensity
of the forces by which those positions are determined. But in the case of
the solar system, these mutual actions bring around again, after a certain
number of changes, the former state of circumstances; which, of course,
leads to the perpetual recurrence of the same series in an unvarying
order. Those bodies, in short, revolve in orbits: but there are (or,
conformably to the laws of astronomy, there might be) others which,
instead of an orbit, describe a trajectory—a course not returning into
itself. One or other of these must be the type to which human affairs must
conform.

One of the thinkers who earliest conceived the succession of historical
events as subject to fixed laws, and endeavored to discover these laws by
an analytical survey of history, Vico, the celebrated author of the
_Scienza Nuova_, adopted the former of these opinions. He conceived the
phenomena of human society as revolving in an orbit; as going through
periodically the same series of changes. Though there were not wanting
circumstances tending to give some plausibility to this view, it would not
bear a close scrutiny: and those who have succeeded Vico in this kind of
speculations have universally adopted the idea of a trajectory or
progress, in lieu of an orbit or cycle.

The words Progress and Progressiveness are not here to be understood as
synonymous with improvement and tendency to improvement. It is conceivable
that the laws of human nature might determine, and even necessitate, a
certain series of changes in man and society, which might not in every
case, or which might not on the whole, be improvements. It is my belief,
indeed, that the general tendency is, and will continue to be, saving
occasional and temporary exceptions, one of improvement; a tendency toward
a better and happier state. This, however, is not a question of the method
of the social science, but a theorem of the science itself. For our
purpose it is sufficient that there is a progressive change both in the
character of the human race and in their outward circumstances, so far as
moulded by themselves; that in each successive age the principal phenomena
of society are different from what they were in the age preceding, and
still more different from any previous age: the periods which most
distinctly mark these successive changes being intervals of one
generation, during which a new set of human beings have been educated,
have grown up from childhood, and taken possession of society.

The progressiveness of the human race is the foundation on which a method
of philosophizing in the social science has been of late years erected,
far superior to either of the two modes which had previously been
prevalent, the chemical or experimental, and the geometrical modes. This
method, which is now generally adopted by the most advanced thinkers on
the Continent, consists in attempting, by a study and analysis of the
general facts of history, to discover (what these philosophers term) the
law of progress: which law, once ascertained, must according to them
enable us to predict future events, just as after a few terms of an
infinite series in algebra we are able to detect the principle, of
regularity in their formation, and to predict the rest of the series to
any number of terms we please. The principal aim of historical speculation
in France, of late years, has been to ascertain this law. But while I
gladly acknowledge the great services which have been rendered to
historical knowledge by this school, I can not but deem them to be mostly
chargeable with a fundamental misconception of the true method of social
philosophy. The misconception consists in supposing that the order of
succession which we may be able to trace among the different states of
society and civilization which history presents to us, even if that order
were more rigidly uniform than it has yet been proved to be, could ever
amount to a law of nature. It can only be an empirical law. The succession
of states of the human mind and of human society can not have an
independent law of its own; it must depend on the psychological and
ethological laws which govern the action of circumstances on men and of
men on circumstances. It is conceivable that those laws might be such, and
the general circumstances of the human race such, as to determine the
successive transformations of man and society to one given and unvarying
order. But even if the case were so, it can not be the ultimate aim of
science to discover an empirical law. Until that law could be connected
with the psychological and ethological laws on which it must depend, and,
by the consilience of deduction _a priori_ with historical evidence, could
be converted from an empirical law into a scientific one, it could not be
relied on for the prediction of future events, beyond, at most, strictly
adjacent cases. M. Comte alone, among the new historical school, has seen
the necessity of thus connecting all our generalizations from history with
the laws of human nature.

§ 4. But, while it is an imperative rule never to introduce any
generalization from history into the social science unless sufficient
grounds can be pointed out for it in human nature, I do not think any one
will contend that it would have been possible, setting out from the
principles of human nature and from the general circumstances of the
position of our species, to determine _a priori_ the order in which human
development must take place, and to predict, consequently, the general
facts of history up to the present time. After the first few terms of the
series, the influence exercised, over each generation by the generations
which preceded it, becomes, (as is well observed by the writer last
referred to) more and more preponderant over all other influences; until
at length what we now are and do, is in a very small degree the result of
the universal circumstances of the human race, or even of our own
circumstances acting through the original qualities of our species, but
mainly of the qualities produced in us by the whole previous history of
humanity. So long a series of actions and reactions between Circumstances
and Man, each successive term being composed of an ever greater number and
variety of parts, could not possibly be computed by human faculties from
the elementary laws which produce it. The mere length of the series would
be a sufficient obstacle, since a slight error in any one of the terms
would augment in rapid progression at every subsequent step.

If, therefore, the series of the effects themselves did not, when examined
as a whole, manifest any regularity, we should in vain attempt to
construct a general science of society. We must in that case have
contented ourselves with that subordinate order of sociological
speculation formerly noticed, namely, with endeavoring to ascertain what
would be the effect of the introduction of any new cause, in a state of
society supposed to be fixed—a knowledge sufficient for the more common
exigencies of daily political practice, but liable to fail in all cases in
which the progressive movement of society is one of the influencing
elements; and therefore more precarious in proportion as the case is more
important. But since both the natural varieties of mankind, and the
original diversities of local circumstances, are much less considerable
than the points of agreement, there will naturally be a certain degree of
uniformity in the progressive development of the species and of its works.
And this uniformity tends to become greater, not less, as society
advances; since the evolution of each people, which is at first determined
exclusively by the nature and circumstances of that people, is gradually
brought under the influence (which becomes stronger as civilization
advances) of the other nations of the earth, and of the circumstances by
which they have been influenced. History accordingly does, when
judiciously examined, afford Empirical Laws of Society. And the problem of
general sociology is to ascertain these, and connect them with the laws of
human nature, by deductions showing that such were the derivative laws
naturally to be expected as the consequences of those ultimate ones.

It is, indeed, hardly ever possible, even after history has suggested the
derivative law, to demonstrate _a priori_ that such was the only order of
succession or of co-existence in which the effects could, consistently
with the laws of human nature, have been produced. We can at most make out
that there were strong _a priori_ reasons for expecting it, and that no
other order of succession or co-existence would have been so likely to
result from the nature of man and the general circumstances of his
position. Often we can not do even this; we can not even show that what
did take place was probable _a priori_, but only that it was possible.
This, however—which, in the Inverse Deductive Method that we are now
characterizing, is a real process of verification—is as indispensable, as
verification by specific experience has been shown to be, where the
conclusion is originally obtained by the direct way of deduction. The
empirical laws must be the result of but a few instances, since few
nations have ever attained at all, and still fewer by their own
independent development, a high stage of social progress. If, therefore,
even one or two of these few instances be insufficiently known, or
imperfectly analyzed into their elements, and therefore not adequately
compared with other instances, nothing is more probable than that a wrong
empirical law will emerge instead of the right one. Accordingly, the most
erroneous generalizations are continually made from the course of history;
not only in this country, where history can not yet be said to be at all
cultivated as a science, but in other countries where it is so cultivated,
and by persons well versed in it. The only check or corrective is,
constant verification by psychological and ethological laws. We may add to
this, that no one but a person competently skilled in those laws is
capable of preparing the materials for historical generalization, by
analyzing the facts of history, or even by observing the social phenomena
of his own time. No other will be aware of the comparative importance of
different facts, nor consequently know what facts to look for, or to
observe; still less will he be capable of estimating the evidence of facts
which, as is the case with most, can not be ascertained by direct
observation or learned from testimony, but must be inferred from marks.

§ 5. The Empirical Laws of Society are of two kinds; some are uniformities
of co-existence, some of succession. According as the science is occupied
in ascertaining and verifying the former sort of uniformities or the
latter, M. Comte gives it the title of Social Statics, or of Social
Dynamics; conformably to the distinction in mechanics between the
conditions of equilibrium and those of movement; or in biology, between
the laws of organization and those of life. The first branch of the
science ascertains the conditions of stability in the social union; the
second, the laws of progress. Social Dynamics is the theory of Society
considered in a state of progressive movement; while Social Statics is the
theory of the _consensus_ already spoken of as existing among the
different parts of the social organism; in other words, the theory of the
mutual actions and reactions of contemporaneous social phenomena;
making(279) provisionally, as far as possible, abstraction, for scientific
purposes, of the fundamental movement which is at all times gradually
modifying the whole of them.

“In this first point of view, the provisions of sociology will enable us
to infer one from another (subject to ulterior verification by direct
observation) the various characteristic marks of each distinct mode of
social existence, in a manner essentially analogous to what is now
habitually practiced in the anatomy of the physical body. This preliminary
aspect, therefore, of political science, of necessity supposes that
(contrary to the existing habits of philosophers) each of the numerous
elements of the social state, ceasing to be looked at independently and
absolutely, shall be always and exclusively considered relatively to all
the other elements, with the whole of which it is united by mutual
interdependence. It would be superfluous to insist here upon the great and
constant utility of this branch of sociological speculation. It is, in the
first place, the indispensable basis of the theory of social progress. It
may, moreover, be employed, immediately, and of itself, to supply the
place, provisionally at least, of direct observation, which in many cases
is not always practicable for some of the elements of society, the real
condition of which may, however, be sufficiently judged of by means of the
relations which connect them with others previously known. The history of
the sciences may give us some notion of the habitual importance of this
auxiliary resource, by reminding us, for example, how the vulgar errors of
mere erudition concerning the pretended acquirements of the ancient
Egyptians in the higher astronomy were irrevocably dissipated (even before
sentence had been passed on them by a sounder erudition) from the single
consideration of the inevitable connection between the general state of
astronomy and that of abstract geometry, then evidently in its infancy. It
would be easy to cite a multitude of analogous cases, the character of
which could admit of no dispute. In order to avoid exaggeration, however,
it should be remarked, that these necessary relations among the different
aspects of society can not, from their very nature, be so simple and
precise that the results observed could only have arisen from some one
mode of mutual co-ordination. Such a notion, already too narrow in the
science of life, would be completely at variance with the still more
complex nature of sociological speculations. But the exact estimation of
these limits of variation, both in the healthy and in the morbid state,
constitutes, at least as much as in the anatomy of the natural body, an
indispensable complement to every theory of Sociological Statics; without
which the indirect exploration above spoken of would often lead into
error.

“This is not the place for methodically demonstrating the existence of a
necessary relation among all the possible aspects of the same social
organism; a point on which, in principle at least, there is now little
difference of opinion among sound thinkers. From whichever of the social
elements we choose to set out, we may easily recognize that it has always
a connection, more or less immediate, with all the other elements, even
with those which at first sight appear the most independent of it. The
dynamical consideration of the progressive development of civilized
humanity, affords, no doubt, a still more efficacious means of effecting
this interesting verification of the _consensus_ of the social phenomena,
by displaying the manner in which every change in any one part, operates
immediately, or very speedily, upon all the rest. But this indication may
be preceded, or at all events followed, by a confirmation of a purely
statical kind; for, in politics as in mechanics, the communication of
motion from one object to another proves a connection between them.
Without descending to the minute interdependence of the different branches
of any one science or art, is it not evident that among the different
sciences, as well as among most of the arts, there exists such a
connection, that if the state of any one well-marked division of them is
sufficiently known to us, we can with real scientific assurance infer,
from their necessary correlation, the contemporaneous state of every one
of the others? By a further extension of this consideration, we may
conceive the necessary relation which exists between the condition of the
sciences in general and that of the arts in general, except that the
mutual dependence is less intense in proportion as it is more indirect.
The same is the case, when, instead of considering the aggregate of the
social phenomena in some one people, we examine it simultaneously in
different contemporaneous nations; between which the perpetual reciprocity
of influence, especially in modern times, can not be contested, though the
_consensus_ must in this case be ordinarily of a less decided character,
and must decrease gradually with the affinity of the cases and the
multiplicity of the points of contact, so as at last, in some cases, to
disappear almost entirely; as for, example, between Western Europe and
Eastern Asia, of which the various general states of society appear to
have been hitherto almost independent of one another.

These remarks are followed by illustrations of one of the most important,
and until lately, most neglected, of the general principles which, in this
division of the social science, may be considered as established; namely,
the necessary correlation between the form of government existing in any
society and the contemporaneous state of civilization: a natural law which
stamps the endless discussions and innumerable theories respecting forms
of government in the abstract, as fruitless and worthless, for any other
purpose than as a preparatory treatment of materials to be afterward used
for the construction of a better philosophy.

As already remarked, one of the main results of the science of social
statics would be to ascertain the requisites of stable political union.
There are some circumstances which, being found in all societies without
exception, and in the greatest degree where the social union is most
complete, may be considered (when psychological and ethological laws
confirm the indication) as conditions of the existence of the complex
phenomena called a State. For example, no numerous society has ever been
held together without laws, or usages equivalent to them; without
tribunals, and an organized force of some sort to execute their decisions.
There have always been public authorities whom, with more or less
strictness and in cases more or less accurately defined, the rest of the
community obeyed, or according to general opinion were bound to obey. By
following out this course of inquiry we shall find a number of requisites,
which have been present in every society that has maintained a collective
existence, and on the cessation of which it has either merged in some
other society, or reconstructed itself on some new basis, in which the
conditions were conformed to. Although these results, obtained by
comparing different forms and states of society, amount in themselves only
to empirical laws; some of them, when once suggested, are found to follow
with so much probability from general laws of human nature, that the
consilience of the two processes raises the evidence to proof, and the
generalizations to the rank of scientific truths.

This seems to be affirmable (for instance) of the conclusions arrived at
in the following passage, extracted, with some alterations, from a
criticism on the negative philosophy of the eighteenth century,(280) and
which I quote, though (as in some former instances) from myself, because I
have no better way of illustrating the conception I have formed of the
kind of theorems of which sociological statics would consist.

“The very first element of the social union, obedience to a government of
some sort, has not been found so easy a thing to establish in the world.
Among a timid and spiritless race like the inhabitants of the vast plains
of tropical countries, passive obedience may be of natural growth; though
even there we doubt whether it has ever been found among any people with
whom fatalism, or in other words, submission to the pressure of
circumstances as a divine decree, did not prevail as a religious doctrine.
But the difficulty of inducing a brave and warlike race to submit their
individual _arbitrium_ to any common umpire, has always been felt to be so
great, that nothing short of supernatural power has been deemed adequate
to overcome it; and such tribes have always assigned to the first
institution of civil society a divine origin. So differently did those
judge who knew savage men by actual experience, from those who had no
acquaintance with them except in the civilized state. In modern Europe
itself, after the fall of the Roman empire, to subdue the feudal anarchy
and bring the whole people of any European nation into subjection to
government (though Christianity in the most concentrated form of its
influence was co-operating in the work) required thrice as many centuries
as have elapsed since that time.

“Now if these philosophers had known human nature under any other type
than that of their own age, and of the particular classes of society among
whom they lived, it would have occurred to them, that wherever this
habitual submission to law and government has been firmly and durably
established, and yet the vigor and manliness of character which resisted
its establishment have been in any degree preserved, certain requisites
have existed, certain conditions have been fulfilled, of which the
following may be regarded as the principal.

“First: there has existed, for all who were accounted citizens—for all who
were not slaves, kept down by brute force—a system of _education_,
beginning with infancy and continued through life, of which whatever else
it might include, one main and incessant ingredient was _restraining
discipline_. To train the human being in the habit, and thence the power,
of subordinating his personal impulses and aims to what were considered
the ends of society; of adhering, against all temptation, to the course of
conduct which those ends prescribed; of controlling in himself all
feelings which were liable to militate against those ends, and encouraging
all such as tended toward them; this was the purpose, to which every
outward motive that the authority directing the system could command, and
every inward power or principle which its knowledge of human nature
enabled it to evoke, were endeavored to be rendered instrumental. The
entire civil and military policy of the ancient commonwealths was such a
system of training; in modern nations its place has been attempted to be
supplied, principally, by religious teaching. And whenever and in
proportion as the strictness of the restraining discipline was relaxed,
the natural tendency of mankind to anarchy re-asserted itself; the state
became disorganized from within; mutual conflict for selfish ends,
neutralized the energies which were required to keep up the contest
against natural causes of evil; and the nation, after a longer or briefer
interval of progressive decline, became either the slave of a despotism,
or the prey of a foreign invader.

“The second condition of permanent political society has been found to be,
the existence, in some form or other, of the feeling of allegiance or
loyalty. This feeling may vary in its objects, and is not confined to any
particular form of government; but whether in a democracy or in a
monarchy, its essence is always the same; viz., that there be in the
constitution of the state _something_ which is settled, something
permanent, and not to be called in question; something which, by general
agreement, has a right to be where it is, and to be secure against
disturbance, whatever else may change. This feeling may attach itself, as
among the Jews (and in most of the commonwealths of antiquity), to a
common God or gods, the protectors and guardians of their state. Or it may
attach itself to certain persons, who are deemed to be, whether by divine
appointment, by long prescription, or by the general recognition of their
superior capacity and worthiness, the rightful guides and guardians of the
rest. Or it may connect itself with laws; with ancient liberties or
ordinances. Or, finally, (and this is the only shape in which the feeling
is likely to exist hereafter), it may attach itself to the principles of
individual freedom and political and social equality, as realized in
institutions which as yet exist nowhere, or exist only in a rudimentary
state. But in all political societies which have had a durable existence,
there has been some fixed point: something which people agreed in holding
sacred; which, wherever freedom of discussion was a recognized principle,
it was of course lawful to contest in theory, but which no one could
either fear or hope to see shaken in practice; which, in short (except
perhaps during some temporary crisis), was in the common estimation placed
beyond discussion. And the necessity of this may easily be made evident. A
state never is, nor until mankind are vastly improved, can hope to be, for
any long time exempt from internal dissension; for there neither is nor
has ever been any state of society in which collisions did not occur
between the immediate interests and passions of powerful sections of the
people. What, then, enables nations to weather these storms, and pass
through turbulent times without any permanent weakening of the securities
for peaceable existence? Precisely this—that however important the
interests about which men fell out, the conflict did not affect the
fundamental principle of the system of social union which happened to
exist; nor threaten large portions of the community with the subversion of
that on which they had built their calculations, and with which their
hopes and aims had become identified. But when the questioning of these
fundamental principles is (not the occasional disease, or salutary
medicine, but) the habitual condition of the body politic, and when all
the violent animosities are called forth, which spring naturally from such
a situation, the state is virtually in a position of civil war; and can
never long remain free from it in act and fact.

“The third essential condition of stability in political society, is a
strong and active principle of cohesion among the members of the same
community or state. We need scarcely say that we do not mean nationality,
in the vulgar sense of the term; a senseless antipathy to foreigners;
indifference to the general welfare of the human race, or an unjust
preference of the supposed interests of our own country; a cherishing of
bad peculiarities because they are national, or a refusal to adopt what
has been found good by other countries. We mean a principle of sympathy,
not of hostility; of union, not of separation. We mean a feeling of common
interest among those who live under the same government, and are contained
within the same natural or historical boundaries. We mean, that one part
of the community do not consider themselves as foreigners with regard to
another part; that they set a value on their connection—feel that they are
one people, that their lot is cast together, that evil to any of their
fellow-countrymen is evil to themselves, and do not desire selfishly to
free themselves from their share of any common inconvenience by severing
the connection. How strong this feeling was in those ancient commonwealths
which attained any durable greatness, every one knows. How happily Rome,
in spite of all her tyranny, succeeded in establishing the feeling of a
common country among the provinces of her vast and divided empire, will
appear when any one who has given due attention to the subject shall take
the trouble to point it out. In modern times the countries which have had
that feeling in the strongest degree have been the most powerful
countries: England, France, and, in proportion to their territory and
resources, Holland and Switzerland; while England in her connection with
Ireland is one of the most signal examples of the consequences of its
absence. Every Italian knows why Italy is under a foreign yoke; every
German knows what maintains despotism in the Austrian empire;(281) the
evils of Spain flow as much from the absence of nationality among the
Spaniards themselves, as from the presence of it in their relations with
foreigners: while the completest illustration of all is afforded by the
republics of South America, where the parts of one and the same state
adhere so slightly together, that no sooner does any province think itself
aggrieved by the general government than it proclaims itself a separate
nation.”

§ 6. While the derivative laws of social statics are ascertained by
analyzing different states of society, and comparing them with one
another, without regard to the order of their succession, the
consideration of the successive order is, on the contrary, predominant in
the study of social dynamics, of which the aim is to observe and explain
the sequences of social conditions. This branch of the social science
would be as complete as it can be made, if every one of the leading
general circumstances of each generation were traced to its causes in the
generation immediately preceding. But the _consensus_ is so complete
(especially in modern history), that in the filiation of one generation
and another, it is the whole which produces the whole, rather than any
part a part. Little progress, therefore, can be made in establishing the
filiation, directly from laws of human nature, without having first
ascertained the immediate or derivative laws according to which social
states generate one another as society advances; the _axiomata media_ of
General Sociology.

The empirical laws which are most readily obtained by generalization from
history do not amount to this. They are not the "middle principles"
themselves, but only evidence toward the establishment of such principles.
They consist of certain general tendencies which may be perceived in
society; a progressive increase of some social elements, and diminution of
others, or a gradual change in the general character of certain elements.
It is easily seen, for instance, that as society advances, mental tend
more and more to prevail over bodily qualities, and masses over
individuals; that the occupation of all that portion of mankind who are
not under external restraint is at first chiefly military, but society
becomes progressively more and more engrossed with productive pursuits,
and the military spirit gradually gives way to the industrial; to which
many similar truths might be added. And with generalizations of this
description, ordinary inquirers, even of the historical school now
predominant on the Continent, are satisfied. But these and all such
results are still at too great a distance from the elementary laws of
human nature on which they depend—too many links intervene, and the
concurrence of causes at each link is far too complicated—to enable these
propositions to be presented as direct corollaries from those elementary
principles. They have, therefore, in the minds of most inquirers, remained
in the state of empirical laws, applicable only within the bounds of
actual observation; without any means of determining their real limits,
and of judging whether the changes which have hitherto been in progress
are destined to continue indefinitely, or to terminate, or even to be
reversed.

§ 7. In order to obtain better empirical laws, we must not rest satisfied
with noting the progressive changes which manifest themselves in the
separate elements of society, and in which nothing is indicated but the
relation of fragments of the effect to corresponding fragments of the
cause. It is necessary to combine the statical view of social phenomena
with the dynamical, considering not only the progressive changes of the
different elements, but the contemporaneous condition of each; and thus
obtain empirically the law of correspondence not only between the
simultaneous states, but between the simultaneous changes, of those
elements. This law of correspondence it is, which, duly verified _a
priori_, would become the real scientific derivative law of the
development of humanity and human affairs.

In the difficult process of observation and comparison which is here
required, it would evidently be a great assistance if it should happen to
be the fact, that some one element in the complex existence of social man
is pre-eminent over all others as the prime agent of the social movement.
For we could then take the progress of that one element as the central
chain, to each successive link of which, the corresponding links of all
the other progressions being appended, the succession of the facts would
by this alone be presented in a kind of spontaneous order, far more nearly
approaching to the real order of their filiation than could be obtained by
any other merely empirical process.

Now, the evidence of history and that of human nature combine, by a
striking instance of consilience, to show that there really is one social
element which is thus predominant, and almost paramount, among the agents
of the social progression. This is, the state of the speculative faculties
of mankind; including the nature of the beliefs which by any means they
have arrived at, concerning themselves and the world by which they are
surrounded.

It would be a great error, and one very little likely to be committed, to
assert that speculation, intellectual activity, the pursuit of truth, is
among the more powerful propensities of human nature, or holds a
predominating place in the lives of any, save decidedly exceptional,
individuals. But, notwithstanding the relative weakness of this principle
among other sociological agents, its influence is the main determining
cause of the social progress; all the other dispositions of our nature
which contribute to that progress being dependent on it for the means of
accomplishing their share of the work. Thus (to take the most obvious case
first), the impelling force to most of the improvements effected in the
arts of life, is the desire of increased material comfort; but as we can
only act upon external objects in proportion to our knowledge of them, the
state of knowledge at any time is the limit of the industrial improvements
possible at that time; and the progress of industry must follow, and
depend on, the progress of knowledge. The same thing may be shown to be
true, though it is not quite so obvious, of the progress of the fine arts.
Further, as the strongest propensities of uncultivated or half-cultivated
human nature (being the purely selfish ones, and those of a sympathetic
character which partake most of the nature of selfishness) evidently tend
in themselves to disunite mankind, not to unite them—to make them rivals,
not confederates, social existence is only possible by a disciplining of
those more powerful propensities, which consists in subordinating them to
a common system of opinions. The degree of this subordination is the
measure of the completeness of the social union, and the nature of the
common opinions determines its kind. But in order that mankind should
conform their actions to any set of opinions, these opinions must exist,
must be believed by them. And thus, the state of the speculative
faculties, the character of the propositions assented to by the intellect,
essentially determines the moral and political state of the community, as
we have already seen that it determines the physical.

These conclusions, deduced from the laws of human nature, are in entire
accordance with the general facts of history. Every considerable change
historically known to us in the condition of any portion of mankind, when
not brought about by external force, has been preceded by a change, of
proportional extent, in the state of their knowledge, or in their
prevalent beliefs. As between any given state of speculation, and the
correlative state of every thing else, it was almost always the former
which first showed itself; though the effects, no doubt, reacted potently
upon the cause. Every considerable advance in material civilization has
been preceded by an advance in knowledge: and when any great social change
has come to pass, either in the way of gradual development or of sudden
conflict, it has had for its precursor a great change in the opinions and
modes of thinking of society. Polytheism, Judaism, Christianity,
Protestantism, the critical philosophy of modern Europe, and its positive
science—each of these has been a primary agent in making society what it
was at each successive period, while society was but secondarily
instrumental in making _them_, each of them (so far as causes can be
assigned for its existence) being mainly an emanation not from the
practical life of the period, but from the previous state of belief and
thought. The weakness of the speculative propensity in mankind generally
has not, therefore, prevented the progress of speculation from governing
that of society at large; it has only, and too often, prevented progress
altogether, where the intellectual progression has come to an early stand
for want of sufficiently favorable circumstances.

From this accumulated evidence, we are justified in concluding, that the
order of human progression in all respects will mainly depend on the order
of progression in the intellectual convictions of mankind, that is, on the
law of the successive transformations of human opinions. The question
remains, whether this law can be determined; at first from history as an
empirical law, then converted into a scientific theorem by deducing it _a
priori_ from the principles of human nature. As the progress of knowledge
and the changes in the opinions of mankind are very slow, and manifest
themselves in a well-defined manner only at long intervals, it can not be
expected that the general order of sequence should be discoverable from
the examination of less than a very considerable part of the duration of
the social progress. It is necessary to take into consideration the whole
of past time, from the first recorded condition of the human race, to the
memorable phenomena of the last and present generations.

§ 8. The investigation which I have thus endeavored to characterize, has
been systematically attempted, up to the present time, by M. Comte alone.
His work is hitherto the only known example of the study of social
phenomena according to this conception of the Historical Method. Without
discussing here the worth of his conclusions, and especially of his
predictions and recommendations with respect to the Future of society,
which appear to me greatly inferior in value to his appreciation of the
Past, I shall confine myself to mentioning one important generalization,
which M. Comte regards as the fundamental law of the progress of human
knowledge. Speculation he conceives to have, on every subject of human
inquiry, three successive stages; in the first of which it tends to
explain the phenomena by supernatural agencies, in the second by
metaphysical abstractions, and in the third or final state confines itself
to ascertaining their laws of succession and similitude. This
generalization appears to me to have that high degree of scientific
evidence which is derived from the concurrence of the indications of
history with the probabilities derived from the constitution of the human
mind. Nor could it be easily conceived, from the mere enunciation of such
a proposition, what a flood of light it lets in upon the whole course of
history, when its consequences are traced, by connecting with each of the
three states of human intellect which it distinguishes, and with each
successive modification of those three states, the correlative condition
of other social phenomena.(282)

But whatever decision competent judges may pronounce on the results
arrived at by any individual inquirer, the method now characterized is
that by which the derivative laws of social order and of social progress
must be sought. By its aid we may hereafter succeed not only in looking
far forward into the future history of the human race, but in determining
what artificial means may be used, and to what extent, to accelerate the
natural progress in so far as it is beneficial; to compensate for whatever
may be its inherent inconveniences or disadvantages; and to guard against
the dangers or accidents to which our species is exposed from the
necessary incidents of its progression. Such practical instructions,
founded on the highest branch of speculative sociology, will form the
noblest and most beneficial portion of the Political Art.

That of this science and art even the foundations are but beginning to be
laid, is sufficiently evident. But the superior minds are fairly turning
themselves toward that object. It has become the aim of really scientific
thinkers to connect by theories the facts of universal history: it is
acknowledged to be one of the requisites of a general system of social
doctrine, that it should explain, so far as the data exist, the main facts
of history; and a Philosophy of History is generally admitted to be at
once the verification, and the initial form, of the Philosophy of the
Progress of Society.

If the endeavors now making in all the more cultivated nations, and
beginning to be made even in England (usually the last to enter into the
general movement of the European mind) for the construction of a
Philosophy of History, shall be directed and controlled by those views of
the nature of sociological evidence which I have (very briefly and
imperfectly) attempted to characterize; they can not fail to give birth to
a sociological system widely removed from the vague and conjectural
character of all former attempts, and worthy to take its place, at last,
among the sciences. When this time shall come, no important branch of
human affairs will be any longer abandoned to empiricism and unscientific
surmise: the circle of human knowledge will be complete, and it can only
thereafter receive further enlargement by perpetual expansion from within.



                               Chapter XI.


Additional Elucidations Of The Science Of History.


§ 1. The doctrine which the preceding chapters were intended to enforce
and elucidate—that the collective series of social phenomena, in other
words the course of history, is subject to general laws, which philosophy
may possibly detect—has been familiar for generations to the scientific
thinkers of the Continent, and has for the last quarter of a century
passed out of their peculiar domain, into that of newspapers and ordinary
political discussion. In our own country, however, at the time of the
first publication of this Treatise, it was almost a novelty, and the
prevailing habits of thought on historical subjects were the very reverse
of a preparation for it. Since then a great change has taken place, and
has been eminently promoted by the important work of Mr. Buckle; who, with
characteristic energy, flung down this great principle, together with many
striking exemplifications of it, into the arena of popular discussion, to
be fought over by a sort of combatants, in the presence of a sort of
spectators, who would never even have been aware that there existed such a
principle if they had been left to learn its existence from the
speculations of pure science. And hence has arisen a considerable amount
of controversy, tending not only to make the principle rapidly familiar to
the majority of cultivated minds, but also to clear it from the confusions
and misunderstandings by which it was but natural that it should for a
time be clouded, and which impair the worth of the doctrine to those who
accept it, and are the stumbling-block of many who do not.

Among the impediments to the general acknowledgment, by thoughtful minds,
of the subjection of historical facts to scientific laws, the most
fundamental continues to be that which is grounded on the doctrine of Free
Will, or, in other words, on the denial that the law of invariable
Causation holds true of human volitions; for if it does not, the course of
history, being the result of human volitions, can not be a subject of
scientific laws, since the volitions on which it depends can neither be
foreseen, nor reduced to any canon of regularity even after they have
occurred. I have discussed this question, as far as seemed suitable to the
occasion, in a former chapter; and I only think it necessary to repeat,
that the doctrine of the Causation of human actions, improperly called the
doctrine of Necessity, affirms no mysterious _nexus_, or overruling
fatality: it asserts only that men’s actions are the joint result of the
general laws and circumstances of human nature, and of their own
particular characters; those characters again being the consequence of the
natural and artificial circumstances that constituted their education,
among which circumstances must be reckoned their own conscious efforts.
Any one who is willing to take (if the expression may be permitted) the
trouble of thinking himself into the doctrine as thus stated, will find
it, I believe, not only a faithful interpretation of the universal
experience of human conduct, but a correct representation of the mode in
which he himself, in every particular case, spontaneously interprets his
own experience of that conduct.

But if this principle is true of individual man, it must be true of
collective man. If it is the law of human life, the law must be realized
in history. The experience of human affairs when looked at _en masse_,
must be in accordance with it if true, or repugnant to it if false. The
support which this _a posteriori_ verification affords to the law, is the
part of the case which has been most clearly and triumphantly brought out
by Mr. Buckle.

The facts of statistics, since they have been made a subject of careful
recordation and study, have yielded conclusions, some of which have been
very startling to persons not accustomed to regard moral actions as
subject to uniform laws. The very events which in their own nature appear
most capricious and uncertain, and which in any individual case no
attainable degree of knowledge would enable us to foresee, occur, when
considerable numbers are taken into the account, with a degree of
regularity approaching to mathematical. What act is there which all would
consider as more completely dependent on individual character, and on the
exercise of individual free will, than that of slaying a fellow-creature?
Yet in any large country, the number of murders, in proportion to the
population, varies (it has been found) very little from one year to
another, and in its variations never deviates widely from a certain
average. What is still more remarkable, there is a similar approach to
constancy in the proportion of these murders annually committed with every
particular kind of instrument. There is a like approximation to identity,
as between one year and another, in the comparative number of legitimate
and of illegitimate births. The same thing is found true of suicides,
accidents, and all other social phenomena of which the registration is
sufficiently perfect; one of the most curiously illustrative examples
being the fact, ascertained by the registers of the London and Paris
post-offices, that the number of letters posted which the writers have
forgotten to direct, is nearly the same, in proportion to the whole number
of letters posted, in one year as in another. “Year after year,” says Mr.
Buckle, “the same proportion of letter-writers forget this simple act; so
that for each successive period we can actually foretell the number of
persons whose memory will fail them in regard to this trifling, and as it
might appear, accidental occurrence.”(283)

This singular degree of regularity _en masse_, combined with the extreme
of irregularity in the cases composing the mass, is a felicitous
verification _a posteriori_ of the law of causation in its application to
human conduct. Assuming the truth of that law, every human action, every
murder, for instance, is the concurrent result of two sets of causes. On
the one part, the general circumstances of the country and its
inhabitants; the moral, educational, economical, and other influences
operating on the whole people, and constituting what we term the state of
civilization. On the other part, the great variety of influences special
to the individual: his temperament, and other peculiarities of
organization, his parentage, habitual associates, temptations, and so
forth. If we now take the whole of the instances which occur within a
sufficiently large field to exhaust all the combinations of these special
influences, or, in other words, to eliminate chance; and if all these
instances have occurred within such narrow limits of time, that no
material change can have taken place in the general influences
constituting the state of civilization of the country; we may be certain,
that if human actions are governed by invariable laws, the aggregate
result will be something like a constant quantity. The number of murders
committed within that space and time, being the effect partly of general
causes which have not varied, and partly of partial causes the whole round
of whose variations has been included, will be, practically speaking,
invariable.

Literally and mathematically invariable it is not, and could not be
expected to be: because the period of a year is too short to include _all_
the possible combinations of partial causes, while it is, at the same
time, sufficiently long to make it probable that in some years at least,
of every series, there will have been introduced new influences of a more
or less general character; such as a more vigorous or a more relaxed
police; some temporary excitement from political or religious causes; or
some incident generally notorious, of a nature to act morbidly on the
imagination. That in spite of these unavoidable imperfections in the data,
there should be so very trifling a margin of variation in the annual
results, is a brilliant continuation of the general theory.

§ 2. The same considerations which thus strikingly corroborate the
evidence of the doctrine, that historical facts are the invariable effects
of causes, tend equally to clear that doctrine from various
misapprehensions, the existence of which has been put in evidence by the
recent discussions. Some persons, for instance, seemingly imagine the
doctrine to imply, not merely that the total number of murders committed
in a given space and time is entirely the effect of the general
circumstances of society, but that every particular murder is so too—that
the individual murderer is, so to speak, a mere instrument in the hands of
general causes that he himself has no option, or, if he has, and chose to
exercise it, some one else would be necessitated to take his place; that
if any one of the actual murderers had abstained from the crime, some
person who would otherwise have remained innocent, would have committed an
extra murder to make up the average. Such a corollary would certainly
convict any theory which necessarily led to it of absurdity. It is
obvious, however, that each particular murder depends, not on the general
state of society only, but on that combined with causes special to the
case, which are generally much more powerful; and if these special causes,
which have greater influence than the general ones in causing every
particular murder, have no influence on the number of murders in a given
period, it is because the field of observation is so extensive as to
include all possible combinations of the special causes—all varieties of
individual character and individual temptation compatible with the general
state of society. The collective experiment, as it may be termed, exactly
separates the effect of the general from that of the special causes, and
shows the net result of the former; but it declares nothing at all
respecting the amount of influence of the special causes, be it greater or
smaller, since the scale of the experiment extends to the number of cases
within which the effects of the special causes balance one another, and
disappear in that of the general causes.

I will not pretend that all the defenders of the theory have always kept
their language free from this same confusion, and have shown no tendency
to exalt the influence of general causes at the expense of special. I am
of opinion, on the contrary, that they have done so in a very great
degree, and by so doing have encumbered their theory with difficulties,
and laid it open to objections, which do not necessarily affect it. Some,
for example (among whom is Mr. Buckle himself), have inferred, or allowed
it to be supposed that they inferred, from the regularity in the
recurrence of events which depend on moral qualities, that the moral
qualities of mankind are little capable of being improved, or are of
little importance in the general progress of society, compared with
intellectual or economic causes. But to draw this inference is to forget
that the statistical tables, from which the invariable averages are
deduced, were compiled from facts occurring within narrow geographical
limits and in a small number of successive years; that is, from a field
the whole of which was under the operation of the same general causes, and
during too short a time to allow of much change therein. All moral causes
but those common to the country generally, have been eliminated by the
great number of instances taken; and those which are common to the whole
country have not varied considerably, in the short space of time comprised
in the observations. If we admit the supposition that they have varied; if
we compare one age with another, or one country with another, or even one
part of a country with another, differing in position and character as to
the moral elements, the crimes committed within a year give no longer the
same, but a widely different numerical aggregate. And this can not but be
the case: for, inasmuch as every single crime committed by an individual
mainly depends on his moral qualities, the crimes committed by the entire
population of the country must depend in an equal degree on their
collective moral qualities. To render this element inoperative upon the
large scale, it would be necessary to suppose that the general moral
average of mankind does not vary from country to country or from age to
age; which is not true, and, even if it were true, could not possibly be
proved by any existing statistics. I do not on this account the less agree
in the opinion of Mr. Buckle, that the intellectual element in mankind,
including in that expression the nature of their beliefs, the amount of
their knowledge, and the development of their intelligence, is the
predominant circumstance in determining their progress. But I am of this
opinion, not because I regard their moral or economical condition either
as less powerful or less variable agencies, but because these are in a
great degree the consequences of the intellectual condition, and are, in
all cases, limited by it; as was observed in the preceding chapter. The
intellectual changes are the most conspicuous agents in history, not from
their superior force, considered in themselves, but because practically
they work with the united power belonging to all three.(284)

§ 3. There is another distinction often neglected in the discussion of
this subject, which it is extremely important to observe. The theory of
the subjection of social progress to invariable laws, is often held in
conjunction with the doctrine, that social progress can not be materially
influenced by the exertions of individual persons, or by the acts of
governments. But though these opinions are often held by the same persons,
they are two very different opinions, and the confusion between them is
the eternally recurring error of confounding Causation with Fatalism.
Because whatever happens will be the effect of causes, human volitions
among the rest, it does not follow that volitions, even those of peculiar
individuals, are not of great efficacy as causes. If any one in a storm at
sea, because about the same number of persons in every year perish by
shipwreck, should conclude that it was useless for him to attempt to save
his own life, we should call him a Fatalist; and should remind him that
the efforts of shipwrecked persons to save their lives are so far from
being immaterial, that the average amount of those efforts is one of the
causes on which the ascertained annual number of deaths by shipwreck
depend. However universal the laws of social development may be, they can
not be more universal or more rigorous than those of the physical agencies
of nature; yet human will can convert these into instruments of its
designs, and the extent to which it does so makes the chief difference
between savages and the most highly civilized people. Human and social
facts, from their more complicated nature, are not less, but more,
modifiable than mechanical and chemical facts; human agency, therefore,
has still greater power over them. And accordingly, those who maintain
that the evolution of society depends exclusively, or almost exclusively,
on general causes, always include among these the collective knowledge and
intellectual development of the race. But if of the race, why not also of
some powerful monarch or thinker, or of the ruling portion of some
political society, acting through its government? Though the varieties of
character among ordinary individuals neutralize one another on any large
scale, exceptional individuals in important positions do not in any given
age neutralize one another; there was not another Themistocles, or Luther,
or Julius Cæsar, of equal powers and contrary dispositions, who exactly
balanced the given Themistocles, Luther, and Cæsar, and prevented them
from having any permanent effect. Moreover, for aught that appears, the
volitions of exceptional persons, or the opinions and purposes of the
individuals who at some particular time compose a government, may be
indispensable links in the chain of causation by which even the general
causes produce their effects; and I believe this to be the only tenable
form of the theory.

Lord Macaulay, in a celebrated passage of one of his early essays (let me
add that it was one which he did not himself choose to reprint), gives
expression to the doctrine of the absolute inoperativeness of great men,
more unqualified, I should think, than has been given to it by any writer
of equal abilities. He compares them to persons who merely stand on a
loftier height, and thence receive the sun’s rays a little earlier, than
the rest of the human race. “The sun illuminates the hills while it is
still below the horizon, and truth is discovered by the highest minds a
little before it becomes manifest to the multitude. This is the extent of
their superiority. They are the first to catch and reflect a light which,
without their assistance, must in a short time be visible to those who lie
far beneath them.”(285) If this metaphor is to be carried out, it follows
that if there had been no Newton, the world would not only have had the
Newtonian system, but would have had it equally soon; as the sun would
have risen just as early to spectators in the plain if there had been no
mountain at hand to catch still earlier rays. And so it would be, if
truths, like the sun, rose by their own proper motion, without human
effort; but not otherwise. I believe that if Newton had not lived, the
world must have waited for the Newtonian philosophy until there had been
another Newton, or his equivalent. No ordinary man, and no succession of
ordinary men, could have achieved it. I will not go the length of saying
that what Newton did in a single life, might not have been done in
successive steps by some of those who followed him, each singly inferior
to him in genius. But even the least of those steps required a man of
great intellectual superiority. Eminent men do not merely see the coming
light from the hill-top, they mount on the hill-top and evoke it; and if
no one had ever ascended thither, the light, in many cases, might never
have risen upon the plain at all. Philosophy and religion are abundantly
amenable to general causes; yet few will doubt that, had there been no
Socrates, no Plato, and no Aristotle, there would have been no philosophy
for the next two thousand years, nor in all probability then; and that if
there had been no Christ, and no St. Paul, there would have been no
Christianity.

The point in which, above all, the influence of remarkable individuals is
decisive, is in determining the celerity of the movement. In most states
of society it is the existence of great men which decides even whether
there shall be any progress. It is conceivable that Greece, or that
Christian Europe, might have been progressive in certain periods of their
history through general causes only: but if there had been no Mohammed,
would Arabia have produced Avicenna or Averroes, or Caliphs of Bagdad or
of Cordova? In determining, however, in what manner and order the progress
of mankind shall take place if it take place at all, much less depends on
the character of individuals. There is a sort of necessity established in
this respect by the general laws of human nature—by the constitution of
the human mind. Certain truths can not be discovered, nor inventions made,
unless certain others have been made first; certain social improvements,
from the nature of the case, can only follow, and not precede, others. The
order of human progress, therefore, may to a certain extent have definite
laws assigned to it: while as to its celerity, or even as to its taking
place at all, no generalization, extending to the human species generally,
can possibly be made; but only some very precarious approximate
generalizations, confined to the small portion of mankind in whom there
has been any thing like consecutive progress within the historical period,
and deduced from their special position, or collected from their
particular history. Even looking to the _manner_ of progress, the order of
succession of social states, there is need of great flexibility in our
generalizations. The limits of variation in the possible development of
social, as of animal life, are a subject of which little is yet
understood, and are one of the great problems in social science. It is, at
all events, a fact, that different portions of mankind, under the
influence of different circumstances, have developed themselves in a more
or less different manner and into different forms; and among these
determining circumstances, the individual character of their great
speculative thinkers or practical organizers may well have been one. Who
can tell how profoundly the whole subsequent history of China may have
been influenced by the individuality of Confucius? and of Sparta (and
hence of Greece and the world) by that of Lycurgus?

Concerning the nature and extent of what a great man under favorable
circumstances can do for mankind, as well as of what a government can do
for a nation, many different opinions are possible; and every shade of
opinion on these points is consistent with the fullest recognition that
there are invariable laws of historical phenomena. Of course the degree of
influence which has to be assigned to these more special agencies, makes a
great difference in the precision which can be given to the general laws,
and in the confidence with which predictions can be grounded on them.
Whatever depends on the peculiarities of individuals, combined with the
accident of the positions they hold, is necessarily incapable of being
foreseen. Undoubtedly these casual combinations might be eliminated like
any others, by taking a sufficiently large cycle: the peculiarities of a
great historical character make their influence felt in history sometimes
for several thousand years, but it is highly probable that they will make
no difference at all at the end of fifty millions. Since, however, we can
not obtain an average of the vast length of time necessary to exhaust all
the possible combinations of great men and circumstances, as much of the
law of evolution of human affairs as depends upon this average, is and
remains inaccessible to us; and within the next thousand years, which are
of considerably more importance to us than the whole remainder of the
fifty millions, the favorable and unfavorable combinations which will
occur will be to us purely accidental. We can not foresee the advent of
great men. Those who introduce new speculative thoughts or great practical
conceptions into the world, can not have their epoch fixed beforehand.
What science can do, is this. It can trace through past history the
general causes which had brought mankind into that preliminary state
which, when the right sort of great man appeared, rendered them accessible
to his influence. If this state continues, experience renders it tolerably
certain that in a longer or shorter period the great man will be produced;
provided that the general circumstances of the country and people are
(which very often they are not) compatible with his existence; of which
point also, science can in some measure judge. It is in this manner that
the results of progress, except as to the celerity of their production,
can be, to a certain extent, reduced to regularity and law. And the belief
that they can be so, is equally consistent with assigning very great, or
very little efficacy, to the influence of exceptional men, or of the acts
of governments. And the same may be said of all other accidents and
disturbing causes.

§ 4. It would nevertheless be a great error to assign only a trifling
importance to the agency of eminent individuals, or of governments. It
must not be concluded that the influence of either is small, because they
can not bestow what the general circumstances of society, and the course
of its previous history, have not prepared it to receive. Neither thinkers
nor governments effect all that they intend, but in compensation they
often produce important results which they did not in the least foresee.
Great men, and great actions, are seldom wasted; they send forth a
thousand unseen influences, more effective than those which are seen; and
though nine out of every ten things done, with a good purpose, by those
who are in advance of their age, produce no material effect, the tenth
thing produces effects twenty times as great as any one would have dreamed
of predicting from it. Even the men who for want of sufficiently favorable
circumstances left no impress at all upon their own age, have often been
of the greatest value to posterity. Who could appear to have lived more
entirely in vain than some of the early heretics? They were burned or
massacred, their writings extirpated, their memory anathematized, and
their very names and existence left for seven or eight centuries in the
obscurity of musty manuscripts—their history to be gathered, perhaps, only
from the sentences by which they were condemned. Yet the memory of these
men—men who resisted certain pretensions or certain dogmas of the Church
in the very age in which the unanimous assent of Christendom was afterward
claimed as having been given to them, and asserted as the ground of their
authority—broke the chain of tradition, established a series of precedents
for resistance, inspired later Reformers with the courage, and armed them
with the weapons, which they needed when mankind were better prepared to
follow their impulse. To this example from men, let us add another from
governments. The comparatively enlightened rule of which Spain had the
benefit during a considerable part of the eighteenth century, did not
correct the fundamental defects of the Spanish people; and in consequence,
though it did great temporary good, so much of that good perished with it,
that it may plausibly be affirmed to have had no permanent effect. The
case has been cited as a proof how little governments can do in opposition
to the causes which have determined the general character of the nation.
It does show how much there is which they can not do; but not that they
can do nothing. Compare what Spain was at the beginning of that
half-century of liberal government, with what she had become at its close.
That period fairly let in the light of European thought upon the more
educated classes; and it never afterward ceased to go on spreading.
Previous to that time the change was in an inverse direction; culture,
light, intellectual and even material activity, were becoming
extinguished. Was it nothing to arrest this downward and convert it into
an upward course? How much that Charles the Third and Aranda could not do,
has been the ultimate consequence of what they did! To that half-century
Spain owes that she has got rid of the Inquisition, that she has got rid
of the monks, that she now has parliaments and (save in exceptional
intervals) a free press, and the feelings of freedom and citizenship, and
is acquiring railroads and all the other constituents of material and
economical progress. In the Spain which preceded that era, there was not a
single element at work which could have led to these results in any length
of time, if the country had continued to be governed as it was by the last
princes of the Austrian dynasty, or if the Bourbon rulers had been from
the first what, both in Spain and in Naples, they afterward became.

And if a government can do much, even when it seems to have done little,
in causing positive improvement, still greater are the issues dependent on
it in the way of warding off evils, both internal and external, which else
would stop improvement altogether. A good or a bad counselor, in a single
city at a particular crisis, has affected the whole subsequent fate of the
world. It is as certain as any contingent judgment respecting historical
events can be, that if there had been no Themistocles there would have
been no victory of Salamis; and had there not, where would have been all
our civilization? How different, again, would have been the issue if
Epaminondas, or Timoleon, or even Iphicrates, instead of Chares and
Lysicles, had commanded at Chæroneia. As is well said in the second of two
Essays on the Study of History,(286) in my judgment the soundest and most
philosophical productions which the recent controversies on this subject
have called forth, historical science authorizes not absolute, but only
conditional predictions. General causes count for much, but individuals
also “produce great changes in history, and color its whole complexion
long after their death.... No one can doubt that the Roman republic would
have subsided into a military despotism if Julius Cæsar had never lived”
(thus much was rendered practically certain by general causes); “but is it
at all clear that in that case Gaul would ever have formed a province of
the empire? Might not Varus have lost his three legions on the banks of
the Rhone? and might not that river have become the frontier instead of
the Rhine? This might well have happened if Cæsar and Crassus had changed
provinces; and it is surely impossible to say that in such an event the
venue (as lawyers say) of European civilization might not have been
changed. The Norman Conquest in the same way was as much the act of a
single man, as the writing of a newspaper article; and knowing as we do
the history of that man and his family, we can retrospectively predict
with all but infallible certainty, that no other person” (no other in that
age, I presume, is meant) “could have accomplished the enterprise. If it
had not been accomplished, is there any ground to suppose that either our
history or our national character would have been what they are?”

As is most truly remarked by the same writer, the whole stream of Grecian
history, as cleared up by Mr. Grote, is one series of examples how often
events on which the whole destiny of subsequent civilization turned, were
dependent on the personal character for good or evil of some one
individual. It must be said, however, that Greece furnishes the most
extreme example of this nature to be found in history, and is a very
exaggerated specimen of the general tendency. It has happened only that
once, and will probably never happen again, that the fortunes of mankind
depended upon keeping a certain order of things in existence in a single
town, or a country scarcely larger than Yorkshire; capable of being ruined
or saved by a hundred causes, of very slight magnitude in comparison with
the general tendencies of human affairs. Neither ordinary accidents, nor
the characters of individuals, can ever again be so vitally important as
they then were. The longer our species lasts, and the more civilized it
becomes, the more, as Comte remarks, does the influence of past
generations over the present, and of mankind _en masse_ over every
individual in it, predominate over other forces; and though the course of
affairs never ceases to be susceptible of alteration both by accidents and
by personal qualities, the increasing preponderance of the collective
agency of the species over all minor causes, is constantly bringing the
general evolution of the race into something which deviates less from a
certain and preappointed track. Historical science, therefore, is always
becoming more possible; not solely because it is better studied, but
because, in every generation, it becomes better adapted for study.



                               Chapter XII.


Of The Logic Of Practice, Or Art; Including Morality And Policy.


§ 1. In the preceding chapters we have endeavored to characterize the
present state of those among the branches of knowledge called Moral, which
are sciences in the only proper sense of the term, that is, inquiries into
the course of nature. It is customary, however, to include under the term
moral knowledge, and even (though improperly) under that of moral science,
an inquiry the results of which do not express themselves in the
indicative, but in the imperative mood, or in periphrases equivalent to
it; what is called the knowledge of duties; practical ethics, or morality.

Now, the imperative mood is the characteristic of art, as distinguished
from science. Whatever speaks in rules, or precepts, not in assertions
respecting matters of fact, is art; and ethics, or morality, is properly a
portion of the art corresponding to the sciences of human nature and
society.(287)

The Method, therefore, of Ethics, can be no other than that of Art, or
Practice, in general; and the portion yet uncompleted of the task which we
proposed to ourselves in the concluding Book, is to characterize the
general Method of Art, as distinguished from Science.

§ 2. In all branches of practical business there are cases in which
individuals are bound to conform their practice to a pre-established rule,
while there are others in which it is part of their task to find or
construct the rule by which they are to govern their conduct. The first,
for example, is the case of a judge, under a definite written code. The
judge is not called upon to determine what course would be intrinsically
the most advisable in the particular case in hand, but only within what
rule of law it falls; what the legislature has ordained to be done in the
kind of case, and must therefore be presumed to have intended in the
individual case. The method must here be wholly and exclusively one of
ratiocination, or syllogism; and the process is obviously, what in our
analysis of the syllogism we showed that all ratiocination is, namely the
interpretation of a formula.

In order that our illustration of the opposite case may be taken from the
same class of subjects as the former, we will suppose, in contrast with
the situation of the judge, the position of the legislator. As the judge
has laws for his guidance, so the legislator has rules, and maxims of
policy; but it would be a manifest error to suppose that the legislator is
bound by these maxims in the same manner as the judge is bound by the
laws, and that all he has to do is to argue down from them to the
particular case, as the judge does from the laws. The legislator is bound
to take into consideration the reasons or grounds of the maxim; the judge
has nothing to do with those of the law, except so far as a consideration
of them may throw light upon the intention of the law-maker, where his
words have left it doubtful. To the judge, the rule, once positively
ascertained, is final; but the legislator, or other practitioner, who goes
by rules rather than by their reasons, like the old-fashioned German
tacticians who were vanquished by Napoleon, or the physician who preferred
that his patients should die by rule rather than recover contrary to it,
is rightly judged to be a mere pedant, and the slave of his formulas.

Now, the reasons of a maxim of policy, or of any other rule of art, can be
no other than the theorems of the corresponding science.

The relation in which rules of art stand to doctrines of science may be
thus characterized. The art proposes to itself an end to be attained,
defines the end, and hands it over to the science. The science receives
it, considers it as a phenomenon or effect to be studied, and having
investigated its causes and conditions, sends it back to art with a
theorem of the combination of circumstances by which it could be produced.
Art then examines these combinations of circumstances, and according as
any of them are or are not in human power, pronounces the end attainable
or not. The only one of the premises, therefore, which Art supplies, is
the original major premise, which asserts that the attainment of the given
end is desirable. Science then lends to Art the proposition (obtained by a
series of inductions or of deductions) that the performance of certain
actions will attain the end. From these premises Art concludes that the
performance of these actions is desirable, and finding it also
practicable, converts the theorem into a rule or precept.

§ 3. It deserves particular notice, that the theorem or speculative truth
is not ripe for being turned into a precept, until the whole, and not a
part merely, of the operation which belongs to science, has been
performed. Suppose that we have completed the scientific process only up
to a certain point; have discovered that a particular cause will produce
the desired effect, but have not ascertained all the negative conditions
which are necessary, that is, all the circumstances which, if present,
would prevent its production. If, in this imperfect state of the
scientific theory, we attempt to frame a rule of art, we perform that
operation prematurely. Whenever any counteracting cause, overlooked by the
theorem, takes place, the rule will be at fault; we shall employ the means
and the end will not follow. No arguing from or about the rule itself will
then help us through the difficulty; there is nothing for it but to turn
back and finish the scientific process which should have preceded the
formation of the rule. We must re-open the investigation to inquire into
the remainder of the conditions on which the effect depends; and only
after we have ascertained the whole of these are we prepared to transform
the completed law of the effect into a precept, in which those
circumstances or combinations of circumstances which the science exhibits
as conditions are prescribed as means.

It is true that, for the sake of convenience, rules must be formed from
something less than this ideally perfect theory: in the first place,
because the theory can seldom be made ideally perfect; and next, because,
if all the counteracting contingencies, whether of frequent or of rare
occurrence, were included, the rules would be too cumbrous to be
apprehended and remembered by ordinary capacities, on the common occasions
of life. The rules of art do not attempt to comprise more conditions than
require to be attended to in ordinary cases; and are therefore always
imperfect. In the manual arts, where the requisite conditions are not
numerous, and where those which the rules do not specify are generally
either plain to common observation or speedily learned from practice,
rules may often be safely acted on by persons who know nothing more than
the rule. But in the complicated affairs of life, and still more in those
of states and societies, rules can not be relied on, without constantly
referring back to the scientific laws on which they are founded. To know
what are the practical contingencies which require a modification of the
rule, or which are altogether exceptions to it, is to know what
combinations of circumstances would interfere with, or entirely
counteract, the consequences of those laws; and this can only be learned
by a reference to the theoretic grounds of the rule.

By a wise practitioner, therefore, rules of conduct will only be
considered as provisional. Being made for the most numerous cases, or for
those of most ordinary occurrence, they point out the manner in which it
will be least perilous to act, where time or means do not exist for
analyzing the actual circumstances of the case, or where we can not trust
our judgment in estimating them. But they do not at all supersede the
propriety of going through, when circumstances permit, the scientific
process requisite for framing a rule from the data of the particular case
before us. At the same time, the common rule may very properly serve as an
admonition that a certain mode of action has been found by ourselves and
others to be well adapted to the cases of most common occurrence; so that
if it be unsuitable to the case in hand, the reason of its being so will
be likely to arise from some unusual circumstance.

§ 4. The error is therefore apparent of those who would deduce the line of
conduct proper to particular cases from supposed universal practical
maxims, overlooking the necessity of constantly referring back to the
principles of the speculative science, in order to be sure of attaining
even the specific end which the rules have in view. How much greater
still, then, must the error be, of setting up such unbending principles,
not merely as universal rules for attaining a given end, but as rules of
conduct generally, without regard to the possibility, not only that some
modifying cause may prevent the attainment of the given end by the means
which the rule prescribes, but that success itself may conflict with some
other end, which may possibly chance to be more desirable.

This is the habitual error of many of the political speculators whom I
have characterized as the geometrical school; especially in France, where
ratiocination from rules of practice forms the staple commodity of
journalism and political oratory—a misapprehension of the functions of
Deduction which has brought much discredit, in the estimation of other
countries, upon the spirit of generalization so honorably characteristic
of the French mind. The commonplaces of politics in France are large and
sweeping practical maxims, from which, as ultimate premises, men reason
downward to particular applications; and this they call being logical and
consistent. For instance, they are perpetually arguing that such and such
a measure ought to be adopted, because it is a consequence of the
principle on which the form of government is founded; of the principle of
legitimacy, or the principle of the sovereignty of the people. To which it
may be answered, that if these be really practical principles, they must
rest on speculative grounds; the sovereignty of the people, for example,
must be a right foundation for government, because a government thus
constituted tends to produce certain beneficial effects. Inasmuch,
however, as no government produces all possible beneficial effects, but
all are attended with more or fewer inconveniences, and since these can
not usually be combated by means drawn from the very causes which produce
them, it would be often a much stronger recommendation of some practical
arrangement, that it does not follow from what is called the general
principle of the government, than that it does. Under a government of
legitimacy, the presumption is far rather in favor of institutions of
popular origin; and in a democracy, in favor of arrangements tending to
check the impetus of popular will. The line of augmentation so commonly
mistaken in France for political philosophy, tends to the practical
conclusion that we should exert our utmost efforts to aggravate, instead
of alleviating, whatever are the characteristic imperfections of the
system of institutions which we prefer, or under which we happen to live.

§ 5. The grounds, then, of every rule of art, are to be found in the
theorems of science. An art, or a body of art, consists of the rules,
together with as much of the speculative propositions as comprises the
justification of those rules. The complete art of any matter includes a
selection of such a portion from the science as is necessary to show on
what conditions the effects, which the art aims at producing, depend. And
Art in general, consists of the truths of Science, arranged in the most
convenient order for practice, instead of the order which is the most
convenient for thought. Science groups and arranges its truths, so as to
enable us to take in at one view as much as possible of the general order
of the universe. Art, though it must assume the same general laws, follows
them only into such of their detailed consequences as have led to the
formation of rules of conduct; and brings together from parts of the field
of science most remote from one another, the truths relating to the
production of the different and heterogeneous conditions necessary to each
effect which the exigencies of practical life require to be produced.(288)

Science, therefore, following one cause to its various effects, while art
traces one effect to its multiplied and diversified causes and conditions,
there is need of a set of intermediate scientific truths, derived from the
higher generalities of science, and destined to serve as the generalia or
first principles of the various arts. The scientific operation of framing
these intermediate principles, M. Comte characterizes as one of those
results of philosophy which are reserved for futurity. The only complete
example which he points out as actually realized, and which can be held up
as a type to be imitated in more important matters, is the general theory
of the art of Descriptive Geometry, as conceived by M. Monge. It is not,
however, difficult to understand what the nature of these intermediate
principles must generally be. After framing the most comprehensive
possible conception of the end to be aimed at, that is, of the effect to
be produced, and determining in the same comprehensive manner the set of
conditions on which that effect depends, there remains to be taken, a
general survey of the resources which can be commanded for realizing this
set of conditions; and when the result of this survey has been embodied in
the fewest and most extensive propositions possible, those propositions
will express the general relation between the available means and the end,
and will constitute the general scientific theory of the art, from which
its practical methods will follow as corollaries.

§ 6. But though the reasonings which connect the end or purpose of every
art with its means belong to the domain of Science, the definition of the
end itself belongs exclusively to Art, and forms its peculiar province.
Every art has one first principle, or general major premise, not borrowed
from science; that which enunciates the object aimed at, and affirms it to
be a desirable object. The builder’s art assumes that it is desirable to
have buildings; architecture, as one of the fine arts, that it is
desirable to have them beautiful or imposing. The hygienic and medical
arts assume, the one that the preservation of health, the other that the
cure of disease, are fitting and desirable ends. These are not
propositions of science. Propositions of science assert a matter of fact:
an existence, a co-existence, a succession, or a resemblance. The
propositions now spoken of do not assert that any thing is, but enjoin or
recommend that something should be. They are a class by themselves. A
proposition of which the predicate is expressed by the words _ought_ or
_should be_, is generically different from one which is expressed by _is_,
or _will be_. It is true, that in the largest sense of the words, even
these propositions assert something as a matter of fact. The fact affirmed
in them is, that the conduct recommended excites in the speaker’s mind the
feeling of approbation. This, however, does not go to the bottom of the
matter; for the speaker’s approbation is no sufficient reason why other
people should approve; nor ought it to be a conclusive reason even with
himself. For the purposes of practice, every one must be required to
justify his approbation; and for this there is need of general premises,
determining what are the proper objects of approbation, and what the
proper order of precedence among those objects.

These general premises, together with the principal conclusions which may
be deduced from them, form (or rather might form) a body of doctrine,
which is properly the Art of Life, in its three departments, Morality,
Prudence or Policy, and Æsthetics; the Right, the Expedient, and the
Beautiful or Noble, in human conduct and works. To this art (which, in the
main, is unfortunately still to be created), all other arts are
subordinate; since its principles are those which must determine whether
the special aim of any particular art is worthy and desirable, and what is
its place in the scale of desirable things. Every art is thus a joint
result of laws of nature disclosed by science, and of the general
principles of what has been called Teleology, or the Doctrine of
Ends;(289) which, borrowing the language of the German metaphysicians, may
also be termed, not improperly, the principles of Practical Reason.

A scientific observer or reasoner, merely as such, is not an adviser for
practice. His part is only to show that certain consequences follow from
certain causes, and that to obtain certain ends, certain means are the
most effectual. Whether the ends themselves are such as ought to be
pursued, and if so, in what cases and to how great a length, it is no part
of his business as a cultivator of science to decide, and science alone
will never qualify him for the decision. In purely physical science, there
is not much temptation to assume this ulterior office; but those who treat
of human nature and society invariably claim it: they always undertake to
say, not merely what is, but what ought to be. To entitle them to do this,
a complete doctrine of Teleology is indispensable. A scientific theory,
however perfect, of the subject-matter, considered merely as part of the
order of nature, can in no degree serve as a substitute. In this respect
the various subordinate arts afford a misleading analogy. In them there is
seldom any visible necessity for justifying the end, since in general its
desirableness is denied by nobody, and it is only when the question of
precedence is to be decided between that end and some other, that the
general principles of Teleology have to be called in; but a writer on
Morals and Politics requires those principles at every step. The most
elaborate and well-digested exposition of the laws of succession and
co-existence among mental or social phenomena, and of their relation to
one another as causes and effects, will be of no avail toward the art of
Life or of Society, if the ends to be aimed at by that art are left to the
vague suggestions of the _intellectus sibi permissus_, or are taken for
granted without analysis or questioning.

§ 7. There is, then, a _philosophia prima_ peculiar to Art, as there is
one which belongs to Science. There are not only first principles of
Knowledge, but first principles of Conduct. There must be some standard by
which to determine the goodness or badness, absolute and comparative, of
ends, or objects of desire. And whatever that standard is, there can be
but one; for if there were several ultimate principles of conduct, the
same conduct might be approved by one of those principles and condemned by
another; and there would be needed some more general principle, as umpire
between them.

Accordingly, writers on Moral Philosophy have mostly felt the necessity
not only of referring all rules of conduct, and all judgments of praise
and blame, to principles, but of referring them to some one principle;
some rule, or standard, with which all other rules of conduct were
required to be consistent, and from which by ultimate consequence they
could all be deduced. Those who have dispensed with the assumption of such
a universal standard, have only been enabled to do so by supposing that a
moral sense, or instinct, inherent in our constitution, informs us, both
what principles of conduct we are bound to observe, and also in what order
these should be subordinated to one another.

The theory of the foundations of morality is a subject which it would be
out of place, in a work like this, to discuss at large, and which could
not to any useful purpose be treated incidentally. I shall content myself,
therefore, with saying, that the doctrine of intuitive moral principles,
even if true, would provide only for that portion of the field of conduct
which is properly called moral. For the remainder of the practice of life
some general principle, or standard, must still be sought; and if that
principle be rightly chosen, it will be found, I apprehend, to serve quite
as well for the ultimate principle of Morality, as for that of Prudence,
Policy, or Taste.

Without attempting in this place to justify my opinion, or even to define
the kind of justification which it admits of, I merely declare my
conviction, that the general principle to which all rules of practice
ought to conform, and the test by which they should be tried, is that of
conduciveness to the happiness of mankind, or rather, of all sentient
beings; in other words, that the promotion of happiness is the ultimate
principle of Teleology.(290)

I do not mean to assert that the promotion of happiness should be itself
the end of all actions, or even of all rules of action. It is the
justification, and ought to be the controller, of all ends, but it is not
itself the sole end. There are many virtuous actions, and even virtuous
modes of action (though the cases are, I think, less frequent than is
often supposed), by which happiness in the particular instance is
sacrificed, more pain being produced than pleasure. But conduct of which
this can be truly asserted, admits of justification only because it can be
shown that, on the whole, more happiness will exist in the world, if
feelings are cultivated which will make people, in certain cases,
regardless of happiness. I fully admit that this is true; that the
cultivation of an ideal nobleness of will and conduct should be to
individual human beings an end, to which the specific pursuit either of
their own happiness or of that of others (except so far as included in
that idea) should, in any case of conflict, give way. But I hold that the
very question, what constitutes this elevation of character, is itself to
be decided by a reference to happiness as the standard. The character
itself should be, to the individual, a paramount end, simply because the
existence of this ideal nobleness of character, or of a near approach to
it, in any abundance, would go farther than all things else toward making
human life happy, both in the comparatively humble sense of pleasure and
freedom from pain, and in the higher meaning, of rendering life, not what
it now is almost universally, puerile and insignificant, but such as human
beings with highly developed faculties can care to have.

§ 8. With these remarks we must close this summary view of the application
of the general logic of scientific inquiry to the moral and social
departments of science. Notwithstanding the extreme generality of the
principles of method which I have laid down (a generality which, I trust,
is not, in this instance, synonymous with vagueness), I have indulged the
hope that to some of those on whom the task will devolve of bringing those
most important of all sciences into a more satisfactory state, these
observations may be useful, both in removing erroneous, and in clearing up
the true, conceptions of the means by which, on subjects of so high a
degree of complication, truth can be attained. Should this hope be
realized, what is probably destined to be the great intellectual
achievement of the next two or three generations of European thinkers will
have been in some degree forwarded.

THE END.



FOOTNOTES


    1 In the later editions of Archbishop Whately’s “Logic,” he states his
      meaning to be, not that “rules” for the ascertainment of truths by
      inductive investigation can not be laid down, or that they may not
      be “of eminent service,” but that they “must always be comparatively
      vague and general, and incapable of being built up into a regular
      demonstrative theory like that of the Syllogism.” (Book iv., ch.
      iv., § 3.) And he observes, that to devise a system for this
      purpose, capable of being “brought into a scientific form,” would be
      an achievement which “he must be more sanguine than scientific who
      expects.” (Book iv., ch. ii., § 4.) To effect this, however, being
      the express object of the portion of the present work which treats
      of Induction, the words in the text are no overstatement of the
      difference of opinion between Archbishop Whately and me on the
      subject.

    2 Now forming a chapter in his volume on “The Philosophy of
      Discovery.”

    3 Archbishop Whately.

    4 I use these terms indiscriminately, because, for the purpose in
      view, there is no need for making any distinction between them. But
      metaphysicians usually restrict the name Intuition to the direct
      knowledge we are supposed to have of things external to our minds,
      and Consciousness to our knowledge of our own mental phenomena.

    5 This important theory has of late been called in question by a
      writer of deserved reputation, Mr. Samuel Bailey; but I do not
      conceive that the grounds on which it has been admitted as an
      established doctrine for a century past, have been at all shaken by
      that gentleman’s objections. I have elsewhere said what appeared to
      me necessary in reply to his arguments. (_Westminster Review_ for
      October, 1842; reprinted in “Dissertations and Discussions,” vol.
      ii.)

    6 The view taken in the text, of the definition and purpose of Logic,
      stands in marked opposition to that of the school of philosophy
      which, in this country, is represented by the writings of Sir
      William Hamilton and of his numerous pupils. Logic, as this school
      conceives it, is “the Science of the Formal Laws of Thought;” a
      definition framed for the express purpose of excluding, as
      irrelevant to Logic, whatever relates to Belief and Disbelief, or to
      the pursuit of truth as such, and restricting the science to that
      very limited portion of its total province, which has reference to
      the conditions, not of Truth, but of Consistency. What I have
      thought it useful to say in opposition to this limitation of the
      field of Logic, has been said at some length in a separate work,
      first published in 1865, and entitled “An Examination of Sir William
      Hamilton’s Philosophy, and of the Principal Philosophical Questions
      discussed in his Writings.” For the purposes of the present
      Treatise, I am content that the justification of the larger
      extension which I give to the domain of the science, should rest on
      the sequel of the Treatise itself. Some remarks on the relation
      which the Logic of Consistency bears to the Logic of Truth, and on
      the place which that particular part occupies in the whole to which
      it belongs, will be found in the present volume (Book II., chap.
      iii., § 9).

_    7 Computation or Logic_, chap. ii.

    8 In the original “had, _or had not_.” These last words, as involving
      a subtlety foreign to our present purpose, I have forborne to quote.

    9 Vide infra, note at the end of § 3, book ii., chap. ii.

_   10 Notare_, to mark; _con_notare, to mark _along with_; to mark one
      thing _with_ or _in addition to_ another.

   11 Archbishop Whately, who, in the later editions of his _Elements of
      Logic_, aided in reviving the important distinction treated of in
      the text, proposes the term “Attributive” as a substitute for
      “Connotative” (p. 22, 9th edit.). The expression is, in itself,
      appropriate; but as it has not the advantage of being connected with
      any verb, of so markedly distinctive a character as “to connote,” it
      is not, I think, fitted to supply the place of the word Connotative
      in scientific use.

   12 A writer who entitles his book _Philosophy; or, the Science of
      Truth_, charges me in his very first page (referring at the foot of
      it to this passage) with asserting that _general_ names have
      properly no signification. And he repeats this statement many times
      in the course of his volume, with comments, not at all flattering,
      thereon. It is well to be now and then reminded to how great a
      length perverse misquotation (for, strange as it appears, I do not
      believe that the writer is dishonest) can sometimes go. It is a
      warning to readers when they see an author accused, with volume and
      page referred to, and the apparent guarantee of inverted commas, of
      maintaining something more than commonly absurd, not to give
      implicit credence to the assertion without verifying the reference.

   13 “Take the familiar term Stone. It is applied to mineral and rocky
      materials, to the kernels of fruit, to the accumulations in the
      gall-bladder and in the kidney; while it is refused to polished
      minerals (called gems), to rocks that have the cleavage suited for
      roofing (slates), and to baked clay (bricks). It occurs in the
      designation of the magnetic oxide of iron (loadstone), and not in
      speaking of other metallic ores. Such a term is wholly unfit for
      accurate reasoning, unless hedged round on every occasion by other
      phrases; as building stone, precious stone, gall-stone, etc.
      Moreover, the methods of definition are baffled for want of
      sufficient community to ground upon. There is no quality uniformly
      present in the cases where it is applied, and uniformly absent where
      it is not applied; hence the definer would have to employ largely
      the license of striking off existing applications, and taking in new
      ones.”—BAIN, _Logic_, ii., 172.

   14 Before quitting the subject of connotative names, it is proper to
      observe, that the first writer who, in our times, has adopted from
      the schoolmen the word _to connote_, Mr. James Mill, in his
      _Analysis of the Phenomena of the Human Mind_, employs it in a
      signification different from that in which it is here used. He uses
      the word in a sense co-extensive with its etymology, applying it to
      every case in which a name, while pointing directly to one thing
      (which is consequently termed its signification), includes also a
      tacit reference to some other thing. In the case considered in the
      text, that of concrete general names, his language and mine are the
      converse of one another. Considering (very justly) the signification
      of the name to lie in the attribute, he speaks of the word as
      _noting_ the attribute, and _connoting_ the things possessing the
      attribute. And he describes abstract names as being properly
      concrete names with their connotation dropped; whereas, in my view,
      it is the _de_notation which would be said to be dropped, what was
      previously connoted becoming the whole signification.

      In adopting a phraseology at variance with that which so high an
      authority, and one which I am less likely than any other person to
      undervalue, has deliberately sanctioned, I have been influenced by
      the urgent necessity for a term exclusively appropriated to express
      the manner in which a concrete general name serves to mark the
      attributes which are involved in its signification. This necessity
      can scarcely be felt in its full force by any one who has not found
      by experience how vain is the attempt to communicate clear ideas on
      the philosophy of language without such a word. It is hardly an
      exaggeration to say, that some of the most prevalent of the errors
      with which logic has been infected, and a large part of the
      cloudiness and confusion of ideas which have enveloped it, would, in
      all probability, have been avoided, if a term had been in common use
      to express exactly what I have signified by the term to connote. And
      the schoolmen, to whom we are indebted for the greater part of our
      logical language, gave us this also, and in this very sense. For
      though some of their general expressions countenance the use of the
      word in the more extensive and vague acceptation in which it is
      taken by Mr. Mill, yet when they had to define it specifically as a
      technical term, and to fix its meaning as such, with that admirable
      precision which always characterizes their definitions, they clearly
      explained that nothing was said to be connoted except _forms_, which
      word may generally, in their writings, be understood as synonymous
      with _attributes_.

      Now, if the word _to connote_, so well suited to the purpose to
      which they applied it, be diverted from that purpose by being taken
      to fulfill another, for which it does not seem to me to be at all
      required; I am unable to find any expression to replace it, but such
      as are commonly employed in a sense so much more general, that it
      would be useless attempting to associate them peculiarly with this
      precise idea. Such are the words, to involve, to imply, etc. By
      employing these, I should fail of attaining the object for which
      alone the name is needed, namely, to distinguish this particular
      kind of involving and implying from all other kinds, and to assure
      to it the degree of habitual attention which its importance demands.

   15 Professor Bain (_Logic_, i., 56) thinks that negative names are not
      names of all things whatever except those denoted by the correlative
      positive name, but only for all things of some particular class:
      _not-white_, for instance, he deems not to be a name for every thing
      in nature except white things, but only for every _colored_ thing
      other than white. In this case, however, as in all others, the test
      of what a name denotes is what it can be predicated of: and we can
      certainly predicate of a sound, or a smell, that it is not white.
      The affirmation and the negation of the same attribute can not but
      divide the whole field of predication between them.

   16 Or rather, all objects except itself and the percipient mind; for,
      as we shall see hereafter, to ascribe any attribute to an object,
      necessarily implies a mind to perceive it.

      The simple and clear explanation given in the text, of relation and
      relative names, a subject so long the opprobrium of metaphysics, was
      given (as far as I know) for the first time, by Mr. James Mill, in
      his Analysis of the Phenomena of the Human Mind.

   17 On the preceding passage Professor Bain remarks (Logic, i., 265):
      “The Categories do not seem to have been intended as a
      classification of Namable Things, in the sense of ‘an enumeration of
      all kinds of Things which are capable of being made predicates, or
      of having any thing predicated of them.’ They seem to have been
      rather intended as a generalization of predicates; an analysis of
      the final import of predication. Viewed in this light, they are not
      open to the objections offered by Mr. Mill. The proper question to
      ask is not—In what Category are we to place sensations or other
      feelings or states of mind? but, Under what Categories can we
      predicate regarding states of mind? Take, for example, Hope. When we
      say that it is a state of mind, we predicate Substance: we may also
      describe how great it is (Quantity), what is the quality of it,
      pleasurable or painful (Quality), what it has reference to
      (Relation). Aristotle seems to have framed the Categories on the
      plan—Here is an individual; what is the final analysis of all that
      we can predicate about him?”

      This is doubtless a true statement of the leading idea in the
      classification. The Category Οὐσία was certainly understood by
      Aristotle to be a general name for all possible answers to the
      question Quid sit? when asked respecting a concrete individual; as
      the other Categories are names comprehending all possible answers to
      the questions Quantum sit? Quale sit? etc. In Aristotle’s
      conception, therefore, the Categories may not have been a
      classification of Things; but they were soon converted into one by
      his Scholastic followers, who certainly regarded and treated them as
      a classification of Things, and carried them out as such, dividing
      down the Category Substance as a naturalist might do, into the
      different classes of physical or metaphysical objects as
      distinguished from attributes, and the other Categories into the
      principal varieties of quantity, quality, relation, etc. It is,
      therefore, a just subject of complaint against them, that they had
      no Category of Feeling. Feeling is assuredly predicable as a summum
      genus, of every particular kind of feeling, for instance, as in Mr.
      Bain’s example, of Hope: but it can not be brought within any of the
      Categories as interpreted either by Aristotle or by his followers.

_   18 Philosophy of the Inductive Sciences_, vol. i., p. 40.

_   19 Discussions on Philosophy_, etc. Appendix I., pp. 643, 644.

   20 It is to be regretted that Sir William Hamilton, though he often
      strenuously insists on this doctrine, and though, in the passage
      quoted, he states it with a comprehensiveness and force which leave
      nothing to be desired, did not consistently adhere to his own
      doctrine, but maintained along with it opinions with which it is
      utterly irreconcilable. See the third and other chapters of _An
      Examination of Sir William Hamilton’s Philosophy_.

   21 “Nous savons qu’il existe quelque chose hors de nous, parceque nous
      ne pouvons expliquer nos perceptions sans les rattacher à des causes
      distinctes de nous mêmes; nous savons de plus que ces causes, dont
      nous ne connaissons pas d’ailleurs l’essence, produisent les effets
      les plus variables, les plus divers, et même les plus contraires,
      selon qu’elles rencontrent telle nature ou telle disposition du
      sujet. Mais savons-nous quelque chose de plus? et même, vu le
      caractère indéterminé des causes que nous concevons dans les corps,
      y a-t-il quelque chose de plus à savoir? Y a-t-il lieu de nous
      enquérir si nous percevons les choses telles qu’elles sont? Non
      évidemment.... Je ne dis pas que le problème est insoluble, _je dis
      qu’il est absurde et enferme une contradiction_. Nous _ne savons pas
      ce que ces causes sont en elles-mêmes_, et la raison nous défend de
      chercher à le connaître: mais il est bien évident _à priori_,
      qu’_elles ne sont pas en elles-mêmes ce qu’elles sont par rapport à
      nous_, puisque la présence du sujet modifie nécessairement leur
      action. Supprimez tout sujet sentant, il est certain que ces causes
      agiraient encore puisqu’elles continueraient d’exister; mais elles
      agiraient autrement; elles seraient encore des qualités et des
      propriétés, mais qui ne ressembleraient à rien de ce que nous
      connaissons. Le feu ne manifesterait plus aucune des propriétés que
      nous lui connaissons: que serait-il? C’est ce que nous ne saurons
      jamais. _C’est d’ailleurs peut-être un problème qui ne répugne pas
      seulement à la nature de notre esprit, mais à l’essence même des
      choses._ Quand même en effet on supprimerait par le pensée tous les
      sujets sentants, il faudrait encore admettre que nul corps ne
      manifesterait ses propriétés autrement qu’en relation avec un sujet
      quelconque, et dans ce cas _ses propriétés ne seraient encore que
      relatives_: en sorte qu’il me paraît fort raisonnable d’admettre que
      les propriétés déterminées des corps n’existent pas indépendamment
      d’un sujet quelconque, et que quand on demande si les propriétés de
      la matiere sont telles que nous les percevons, il faudrait voir
      auparavant si elles sont en tant que déterminées, et dans quel sens
      il est vrai de dire qu’elles sont.”—_Cours d’Histoire de la
      Philosophie Morale au 18me siècle_, 8me leçon.

   22 An attempt, indeed, has been made by Reid and others, to establish
      that although some of the properties we ascribe to objects exist
      only in our sensations, others exist in the things themselves, being
      such as can not possibly be copies of any impression upon the
      senses; and they ask, from what sensations our notions of extension
      and figure have been derived? The gauntlet thrown down by Reid was
      taken up by Brown, who, applying greater powers of analysis than had
      previously been applied to the notions of extension and figure,
      pointed out that the sensations from which those notions are
      derived, are sensations of touch, combined with sensations of a
      class previously too little adverted to by metaphysicians, those
      which have their seat in our muscular frame. His analysis, which was
      adopted and followed up by James Mill, has been further and greatly
      improved upon in Professor Bain’s profound work, _The Senses and the
      Intellect_, and in the chapters on “Perception” of a work of eminent
      analytic power, Mr. Herbert Spencer’s _Principles of Psychology_.

      On this point M. Cousin may again be cited in favor of the better
      doctrine. M. Cousin recognizes, in opposition to Reid, the essential
      subjectivity of our conceptions of what are called the primary
      qualities of matter, as extension, solidity, etc., equally with
      those of color, heat, and the remainder of the so-called secondary
      qualities.—_Cours_, ut supra, 9me leçon.

   23 This doctrine, which is the most complete form of the philosophical
      theory known as the Relativity of Human Knowledge, has, since the
      recent revival in this country of an active interest in metaphysical
      speculation, been the subject of a greatly increased amount of
      discussion and controversy; and dissentients have manifested
      themselves in considerably greater number than I had any knowledge
      of when the passage in the text was written. The doctrine has been
      attacked from two sides. Some thinkers, among whom are the late
      Professor Ferrier, in his _Institutes of Metaphysic_, and Professor
      John Grote, in his _Exploratio Philosophica_, appear to deny
      altogether the reality of Noumena, or Things in themselves—of an
      unknowable substratum or support for the sensations which we
      experience, and which, according to the theory, constitute all our
      knowledge of an external world. It seems to me, however, that in
      Professor Grote’s case at least, the denial of Noumena is only
      apparent, and that he does not essentially differ from the other
      class of objectors, including Mr. Bailey in his valuable _Letters on
      the Philosophy of the Human Mind_, and (in spite of the striking
      passage quoted in the text) also Sir William Hamilton, who contend
      for a direct knowledge by the human mind of more than the
      sensations—of certain attributes or properties as they exist not in
      us, but in the Things themselves.

      With the first of these opinions, that which denies Noumena, I have,
      as a metaphysician, no quarrel; but, whether it be true or false, it
      is irrelevant to Logic. And since all the forms of language are in
      contradiction to it, nothing but confusion could result from its
      unnecessary introduction into a treatise, every essential doctrine
      of which could stand equally well with the opposite and accredited
      opinion. The other and rival doctrine, that of a direct perception
      or intuitive knowledge of the outward object as it is in itself,
      considered as distinct from the sensations we receive from it, is of
      far greater practical moment. But even this question, depending on
      the nature and laws of Intuitive Knowledge, is not within the
      province of Logic. For the grounds of my own opinion concerning it,
      I must content myself with referring to a work already mentioned—_An
      Examination of Sir William Hamilton’s Philosophy_; several chapters
      of which are devoted to a full discussion of the questions and
      theories relating to the supposed direct perception of external
      objects.

   24 Professor Bain (_Logic_, i., 49) defines attributes as “points of
      community among classes.” This definition expresses well one point
      of view, but is liable to the objection that it applies only to the
      attributes of classes; though an object, unique in its kind, may be
      said to have attributes. Moreover, the definition is not ultimate,
      since the points of community themselves admit of, and require,
      further analysis; and Mr. Bain does analyze them into resemblances
      in the sensations, or other states of consciousness excited by the
      object.

_   25 Analysis of the Human Mind_, i., 126 et seq.

_   26 Logic_, i., 85.

   27 Instead of Universal and Particular as applied to propositions,
      Professor Bain proposes (_Logic_, i., 81) the terms Total and
      Partial; reserving the former pair of terms for their inductive
      meaning, “the contrast between a general proposition and the
      particulars or individuals that we derive it from.” This change in
      nomenclature would be attended with the further advantage, that
      Singular propositions, which in the Syllogism follow the same rules
      as Universal, would be included along with them in the same class,
      that of Total predications. It is not the Subject’s denoting many
      things or only one, that is of importance in reasoning, it is that
      the assertion is made of the whole or a part only of what the
      Subject denotes. The words Universal and Particular, however, are so
      familiar and so well understood in both the senses mentioned by Mr.
      Bain, that the double meaning does not produce any material
      inconvenience.

   28 It may, however, be considered as equivalent to a universal
      proposition with a different predicate, viz.: “All wine is good
      _quâ_ wine,” or “is good in respect of the qualities which
      constitute it wine.”

_   29 Logic_, i., 82.

   30 Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this
      statement, and asks, “Are we to say that a mole can not dig the
      ground, except he has an idea of the ground, and of the snout and
      paws with which he digs it?” I do not know what passes in a mole’s
      mind, nor what amount of mental apprehension may or may not
      accompany his instinctive actions. But a human being does not use a
      spade by instinct; and he certainly could not use it unless he had
      knowledge of a spade, and of the earth which he uses it upon.

   31 Professor Bain remarks, in qualification of the statement in the
      text (_Logic_, i., 50), that the word Class has two meanings; “the
      class definite, and the class indefinite. The class definite is an
      enumeration of actual individuals, as the Peers of the Realm, the
      oceans of the globe, the known planets.... The class indefinite is
      unenumerated. Such classes are stars, planets, gold-bearing rocks,
      men, poets, virtuous.... In this last acceptation of the word, class
      name and general name are identical. The class name denotes an
      indefinite number of individuals, and connotes the points of
      community or likeness.”

      The theory controverted in the text, tacitly supposes all classes to
      be _definite_. I have assumed them to be indefinite; because, for
      the purposes of Logic, definite classes, as such, are almost
      useless; though often serviceable as means of abridged expression.
      (Vide infra, book iii., chap. ii.)

   32 “From hence also this may be deduced, that the first truths were
      arbitrarily made by those that first of all imposed names upon
      things, or received them from the imposition of others. For it is
      true (for example) that _man is a living creature_, but it is for
      this reason, that it pleased men to impose both these names on the
      same thing.”—_Computation or Logic_, chap. iii., sect. 8.

   33 “Men are subject to err not only in affirming and denying, but also
      in perception, and in silent cogitation.... Tacit errors, or the
      errors of sense and cogitation, are made by passing from one
      imagination to the imagination of another different thing; or by
      feigning that to be past, or future, which never was, nor ever shall
      be; as when by seeing the image of the sun in water, we imagine the
      sun itself to be there; or by seeing swords, that there has been, or
      shall be, fighting, because it used to be so for the most part; or
      when from promises we feign the mind of the promiser to be such and
      such; or, lastly, when from any sign we vainly imagine something to
      be signified which is not. And errors of this sort are common to all
      things that have sense.”—_Computation or Logic_, chap. v., sect. 1.

   34 Chap. iii., sect 3.

   35 To the preceding statement it has been objected, that “we naturally
      construe the subject of a proposition in its extension, and the
      predicate (which therefore may be an adjective) in its intension
      (connotation): and that consequently co-existence of attributes does
      not, any more than the opposite theory of equation of groups,
      correspond with the living processes of thought and language.” I
      acknowledge the distinction here drawn, which, indeed, I had myself
      laid down and exemplified a few pages back (p. 77). But though it is
      true that we naturally “construe the subject of a proposition in its
      extension,” this extension, or in other words, the extent of the
      class denoted by the name, is not apprehended or indicated directly.
      It is both apprehended and indicated solely through the attributes.
      In the “living processes of thought and language” the extension,
      though in this case really thought of (which in the case of the
      predicate it is not), is thought of only through the medium of what
      my acute and courteous critic terms the “intension.”

      For further illustrations of this subject, see _Examination of Sir
      William Hamilton’s Philosophy_, chap. xxii.

   36 Professor Bain, in his _Logic_ (i., 256), excludes Existence from
      the list, considering it as a mere name. All propositions, he says,
      which predicate mere existence “are more or less abbreviated, or
      elliptical: when fully expressed they fall under either co-existence
      or succession. When we say there _exists_ a conspiracy for a
      particular purpose, we mean that at the present time a body of men
      have formed themselves into a society for a particular object; which
      is a complex affirmation, resolvable into propositions of
      co-existence and succession (as causation). The assertion that the
      dodo does not exist, points to the fact that this animal, once known
      in a certain place, has disappeared or become extinct; is no longer
      associated with the locality: all which may be better stated without
      the use of the verb ‘exist.’ There is a debated question—Does an
      ether exist? but the concrete form would be this—‘Are heat and light
      and other radiant influences propagated by an ethereal medium
      diffused in space;’ which is a proposition of causation. In like
      manner the question of the Existence of a Deity can not be discussed
      in that form. It is properly a question as to the First _Cause_ of
      the Universe, and as to the continued exertion of that Cause in
      providential superintendence.” (i., 407.)

      Mr. Bain thinks it “fictitious and unmeaning language” to carry up
      the classification of Nature to one _summum genus_, Being, or that
      which Exists; since nothing can be perceived or apprehended but by
      way of contrast with something else (of which important truth, under
      the name of Law of Relativity, he has been in our time the principal
      expounder and champion), and we have no other class to oppose to
      Being, or fact to contrast with Existence.

      I accept fully Mr. Bain’s Law of Relativity, but I do not understand
      by it that to enable us to apprehend or be conscious of any fact, it
      is necessary that we should contrast it with some other positive
      fact. The antithesis necessary to consciousness need not, I
      conceive, be an antithesis between two positives; it may be between
      one positive and its negative. Hobbes was undoubtedly right when he
      said that a single sensation indefinitely prolonged would cease to
      be felt at all; but simple intermission, without other change, would
      restore it to consciousness. In order to be conscious of heat, it is
      not necessary that we should pass to it from cold; it suffices that
      we should pass to it from a state of no sensation, or from a
      sensation of some other kind. The relative opposite of Being,
      considered as a summum genus, is Nonentity, or Nothing; and we have,
      now and then, occasion to consider and discuss things merely in
      contrast with Nonentity.

      I grant that the _decision_ of questions of Existence usually if not
      always depends on a previous question of either Causation or
      Co-existence. But Existence is nevertheless a different thing from
      Causation or Co-existence, and can be predicated apart from them.
      The meaning of the abstract name Existence, and the connotation of
      the concrete name Being, consist, like the meaning of all other
      names, in sensations or states of consciousness: their peculiarity
      is that to exist, is to excite, or be capable of exciting, _any_
      sensations or states of consciousness: no matter what, but it is
      indispensable that there should be some. It was from overlooking
      this that Hegel, finding that Being is an abstraction reached by
      thinking away all particular attributes, arrived at the
      self-contradictory proposition on which he founded all his
      philosophy, that Being is the same as Nothing. It is really the name
      of Something, taken in the most comprehensive sense of the word.

   37 Book iv., chap. vii.

_   38 Logic_, i., 103-105.

   39 The doctrines which prevented the real meaning of Essences from
      being understood, had not assumed so settled a shape in the time of
      Aristotle and his immediate followers, as was afterward given to
      them by the Realists of the Middle Ages. Aristotle himself (in his
      Treatise on the Categories) expressly denies that the δεύτεραι
      οὔσιαι, or Substantiæ Secundæ, inhere in a subject. They are only,
      he says, predicated of it.

   40 The always acute and often profound author of _An Outline of
      Sematology_ (Mr. B. H. Smart) justly says, “Locke will be much more
      intelligible, if, in the majority of places, we substitute ‘the
      knowledge of’ for what he calls ‘the Idea of’ ” (p. 10). Among the
      many criticisms on Locke’s use of the word Idea, this is the one
      which, as it appears to me, most nearly hits the mark; and I quote
      it for the additional reason that it precisely expresses the point
      of difference respecting the import of Propositions, between my view
      and what I have spoken of as the Conceptualist view of them. Where a
      Conceptualist says that a name or a proposition expresses our Idea
      of a thing, I should generally say (instead of our Idea) our
      Knowledge, or Belief, concerning the thing itself.

   41 This distinction corresponds to that which is drawn by Kant and
      other metaphysicians between what they term _analytic_ and
      _synthetic_, judgments; the former being those which can be evolved
      from the meaning of the terms used.

   42 If we allow a differentia to what is not really a species. For the
      distinction of Kinds, in the sense explained by us, not being in any
      way applicable to attributes, it of course follows that although
      attributes may be put into classes, those classes can be admitted to
      be genera or species only by courtesy.

   43 Professor Bain, in his Logic, takes a peculiar view of Definition.
      He holds (i., 71) with the present work, that “the definition in its
      full import, is the sum of all the properties connoted by the name;
      it exhausts the meaning of a word.” But he regards the meaning of a
      general name as including, not indeed all the common properties of
      the class named, but all of them that are ultimate properties, not
      resolvable into one another. “The enumeration of the attributes of
      oxygen, of gold, of man, should be an enumeration of the final (so
      far as can be made out), the underivable, powers or functions of
      each,” and nothing less than this is a complete Definition (i., 75).
      An independent property, not derivable from other properties, even
      if previously unknown, yet as soon as discovered becomes, according
      to him, part of the meaning of the term, and should be included in
      the definition. “When we are told that diamond, which we know to be
      a transparent, glittering, hard, and high-priced substance, is
      composed of carbon, and is combustible, we must put these additional
      properties on the same level as the rest; to us they are henceforth
      connoted by the name” (i., 73). Consequently the propositions that
      diamond is composed of carbon, and that it is combustible, are
      regarded by Mr. Bain as merely verbal propositions. He carries this
      doctrine so far as to say that unless mortality can be shown to be a
      consequence of the ultimate laws of animal organization, mortality
      is connoted by man, and “Man is Mortal” is a merely verbal
      proposition. And one of the peculiarities (I think a disadvantageous
      peculiarity) of his able and valuable treatise, is the large number
      of propositions requiring proof, and learned by experience, which,
      in conformity with this doctrine, he considers as not real, but
      verbal, propositions.

      The objection I have to this language is that it confounds, or at
      least confuses, a much more important distinction than that which it
      draws. The only reason for dividing Propositions into real and
      verbal, is in order to discriminate propositions which convey
      information about facts, from those which do not. A proposition
      which affirms that an object has a given attribute, while
      designating the object by a name which already signifies the
      attribute, adds no information to that which was already possessed
      by all who understood the name. But when this is said, it is implied
      that, by the signification of a name, is meant the signification
      attached to it in the common usage of life. I can not think we ought
      to say that the meaning of a word includes matters of fact which are
      unknown to every person who uses the word unless he has learned them
      by special study of a particular department of Nature; or that
      because a few persons are aware of these matters of fact, the
      affirmation of them is a proposition conveying no information. I
      hold that (special scientific connotation apart) a name means, or
      connotes, only the properties which it is a mark of in the general
      mind; and that in the case of any additional properties, however
      uniformly found to accompany these, it remains possible that a thing
      which did not possess the properties might still be thought entitled
      to the name. Ruminant, according to Mr. Bain’s use of language,
      connotes cloven-hoofed, since the two properties are always found
      together, and no connection has ever been discovered between them:
      but ruminant does not mean cloven-hoofed; and were an animal to be
      discovered which chews the cud, but has its feet undivided, I
      venture to say that it would still be called ruminant.

   44 In the fuller discussion which Archbishop Whately has given to this
      subject in his later editions, he almost ceases to regard the
      definitions of names and those of things as, in any important sense,
      distinct. He seems (9th ed., p. 145) to limit the notion of a Real
      Definition to one which “explains any thing _more_ of the nature of
      the thing than is implied in the name;” (including under the word
      “implied,” not only what the name connotes, but every thing which
      can be deduced by reasoning from the attributes connoted). Even
      this, as he adds, is usually called not a Definition, but a
      Description; and (as it seems to me) rightly so called. A
      Description, I conceive, can only be ranked among Definitions, when
      taken (as in the case of the zoological definition of man) to
      fulfill the true office of a Definition, by declaring the
      connotation given to a word in some special use, as a term of
      science or art: which special connotation of course would not be
      expressed by the proper definition of the word in its ordinary
      employment.

      Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
      understands by a Real Definition one which contains _less_ than the
      Nominal Definition, provided only that what it contains is
      sufficient for distinction. “By _real_ definition I mean such an
      explanation of the word, be it the whole of the meaning or only
      part, as will be sufficient to separate the things contained under
      that word from all others. Thus the following, I believe, is a
      complete definition of an elephant: An animal which naturally drinks
      by drawing the water into its nose, and then spurting it into its
      mouth.”—_Formal Logic_, p. 36. Mr. De Morgan’s general proposition
      and his example are at variance; for the peculiar mode of drinking
      of the elephant certainly forms no part of the meaning of the word
      elephant. It could not be said, because a person happened to be
      ignorant of this property, that he did not know what an elephant
      means.

   45 In the only attempt which, so far as I know, has been made to refute
      the preceding argumentation, it is maintained that in the first form
      of the syllogism,

      A dragon is a thing which breathes flame,
      A dragon is a serpent,
      Therefore some serpent or serpents breathe flame,

      “there is just as much truth in the conclusion as there is in the
      premises, or rather, no more in the latter than in the former. If
      the general name serpent includes both real and imaginary serpents,
      there is no falsity in the conclusion; if not, there is falsity in
      the minor premise.”

      Let us, then, try to set out the syllogism on the hypothesis that
      the name serpent includes imaginary serpents. We shall find that it
      is now necessary to alter the predicates; for it can not be asserted
      that an imaginary creature breathes flame; in predicating of it such
      a fact, we assert by the most positive implication that it is real,
      and not imaginary. The conclusion must run thus, “Some serpent or
      serpents either do or are _imagined_ to breathe flame.” And to prove
      this conclusion by the instance of dragons, the premises must be, A
      dragon is _imagined_ as breathing flame. A dragon is a (real or
      imaginary) serpent: from which it undoubtedly follows, that there
      are serpents which are imagined to breathe flame; but the major
      premise is not a definition, nor part of a definition; which is all
      that I am concerned to prove.

      Let us now examine the other assertion—that if the word serpent
      stands for none but real serpents, the minor premise (a dragon is a
      serpent) is false. This is exactly what I have myself said of the
      premise, considered as a statement of fact: but it is not false as
      part of the definition of a dragon; and since the premises, or one
      of them, must be false (the conclusion being so), the real premise
      can not be the definition, which is true, but the statement of fact,
      which is false.

   46 “Few people” (I have said in another place) “have reflected how
      great a knowledge of Things is required to enable a man to affirm
      that any given argument turns wholly upon words. There is, perhaps,
      not one of the leading terms of philosophy which is not used in
      almost innumerable shades of meaning, to express ideas more or less
      widely different from one another. Between two of these ideas a
      sagacious and penetrating mind will discern, as it were intuitively,
      an unobvious link of connection, upon which, though perhaps unable
      to give a logical account of it, he will found a perfectly valid
      argument, which his critic, not having so keen an insight into the
      Things, will mistake for a fallacy turning on the double meaning of
      a term. And the greater the genius of him who thus safely leaps over
      the chasm, the greater will probably be the crowing and vainglory of
      the mere logician, who, hobbling after him, evinces his own superior
      wisdom by pausing on its brink, and giving up as desperate his
      proper business of bridging it over.”

   47 The different cases of Equipollency, or “Equivalent Propositional
      Forms,” are set forth with some fullness in Professor Bain’s
      _Logic_. One of the commonest of these changes of expression, that
      from affirming a proposition to denying its negative, or _vicè
      versa_, Mr. Bain designates, very happily, by the name Obversion.

   48 As Sir William Hamilton has pointed out, “Some A is not B” may also
      be converted in the following form: “No B is _some_ A.” Some men are
      not negroes; therefore, No negroes are _some_ men (_e.g._,
      Europeans).

   49 Contraries:
      All  A is B
      No   A is B

      Subtraries:
      Some A is B
      Some A is not B

      Contradictories:
      All  A is B
      Some A is not B

      Also contradictories:
      No A is B
      Some A is B

      Respectively subalternate:
      All  A is B and No A is B
      Some A is B and Some A is not B

   50 Professor Bain denies the claim of Singular Propositions to be
      classed, for the purposes of ratiocination, with Universal; though
      they come within the designation which he himself proposes as an
      equivalent for Universal, that of Total. He would even, to use his
      own expression, banish them entirely from the syllogism. He takes as
      an example,

      Socrates is wise,
      Socrates is poor, therefore
      Some poor men are wise,

      or more properly (as he observes) “one poor man is wise.” “Now, if
      wise, poor, and a man, are attributes belonging to the meaning of
      the word Socrates, there is then no march of reasoning at all. We
      have given in Socrates, _inter alia_, the facts wise, poor, and a
      man, and we merely repeat the concurrence which is selected from the
      whole aggregate of properties making up the whole, Socrates. The
      case is one under the head ‘Greater and Less Connotation’ in
      Equivalent Propositional Forms, or Immediate Inference.

      “But the example in this form does not do justice to the syllogism
      of singulars. We must suppose both propositions to be real, the
      predicates being in no way involved in the subject. Thus

      Socrates was the master of Plato,
      Socrates fought at Delium,
      The master of Plato fought at Delium.

      “It may fairly be doubted whether the transitions, in this instance,
      are any thing more than equivalent forms. For the proposition
      ‘Socrates was the master of Plato and fought at Delium,’ compounded
      out of the two premises, is obviously nothing more than a
      grammatical abbreviation. No one can say that there is here any
      change of meaning, or any thing beyond a verbal modification of the
      original form. The next step is, ‘The master of Plato fought at
      Delium,’ which is the previous statement cut down by the omission of
      Socrates. It contents itself with reproducing a part of the meaning,
      or saying less than had been previously said. The full equivalent of
      the affirmation is, ‘The master of Plato fought at Delium, and the
      master of Plato was Socrates:’ the new form omits the last piece of
      information, and gives only the first. Now, we never consider that
      we have made a real inference, a step in advance, when we repeat
      _less_ than we are entitled to say, or drop from a complex statement
      some portion not desired at the moment. Such an operation keeps
      strictly within the domain of equivalence, or Immediate Inference.
      In no way, therefore, can a syllogism with two singular premises be
      viewed as a genuine syllogistic or deductive inference.” (_Logic_,
      i., 159.)

      The first argument, as will have been seen, rests upon the
      supposition that the name Socrates has a meaning; that man, wise,
      and poor, are parts of this meaning; and that by predicating them of
      Socrates we convey no information; a view of the signification of
      names which, for reasons already given (Note to § 4 of the chapter
      on Definition, _supra_, pp. 110, 111.), I can not admit, and which,
      as applied to the class of names which Socrates belongs to, is at
      war with Mr. Bain’s own definition of a Proper Name (i., 148), “a
      single _meaningless_ mark or designation appropriated to the thing.”
      Such names, Mr. Bain proceeded to say, do not necessarily indicate
      even human beings: much less then does the name Socrates include the
      meaning of wise or poor. Otherwise it would follow that if Socrates
      had grown rich, or had lost his mental faculties by illness, he
      would no longer have been called Socrates.

      The second part of Mr. Bain’s argument, in which he contends that
      even when the premises convey real information, the conclusion is
      merely the premises with a part left out, is applicable, if at all,
      as much to universal propositions as to singular. In every syllogism
      the conclusion contains less than is asserted in the two premises
      taken together. Suppose the syllogism to be

      All bees are intelligent,
      All bees are insects, therefore
      Some insects are intelligent:

      one might use the same liberty taken by Mr. Bain, of joining
      together the two premises as if they were one—“All bees are insects
      and intelligent”—and might say that in omitting the middle term
      _bees_ we make no real inference, but merely reproduce part of what
      had been previously said. Mr. Bain’s is really an objection to the
      syllogism itself, or at all events to the third figure: it has no
      special applicability to singular propositions.

   51 His conclusions are, “The first figure is suited to the discovery or
      proof of the properties of a thing; the second to the discovery or
      proof of the distinctions between things; the third to the discovery
      or proof of instances and exceptions; the fourth to the discovery,
      or exclusion, of the different species of a genus.” The reference of
      syllogisms in the last three figures to the _dictum de omni et
      nullo_ is, in Lambert’s opinion, strained and unnatural: to each of
      the three belongs, according to him, a separate axiom, co-ordinate
      and of equal authority with that _dictum_, and to which he gives the
      names of _dictum de diverso_ for the second figure, _dictum de
      exemplo_ for the third, and _dictum de reciproco_ for the fourth.
      See part i., or _Dianoiologie_, chap, iv., § 229 _et seqq._ Mr.
      Bailey (_Theory of Reasoning_, 2d ed., pp. 70-74) takes a similar
      view of the subject.

   52 Since this chapter was written, two treatises have appeared (or
      rather a treatise and a fragment of a treatise), which aim at a
      further improvement in the theory of the forms of ratiocination: Mr.
      De Morgan’s “Formal Logic; or, the Calculus of Inference, Necessary
      and Probable;” and the “New Analytic of Logical Forms,” attached as
      an Appendix to Sir William Hamilton’s _Discussions on Philosophy_,
      and at greater length, to his posthumous _Lectures on Logic_.

      In Mr. De Morgan’s volume—abounding, in its more popular parts, with
      valuable observations felicitously expressed—the principal feature
      of originality is an attempt to bring within strict technical rules
      the cases in which a conclusion can be drawn from premises of a form
      usually classed as particular. Mr. De Morgan observes, very justly,
      that from the premises most Bs are Cs, most Bs are As, it may be
      concluded with certainty that some As are Cs, since two portions of
      the class B, each of them comprising more than half, must
      necessarily in part consist of the same individuals. Following out
      this line of thought, it is equally evident that if we knew exactly
      what proportion the “most” in each of the premises bear to the
      entire class B, we could increase in a corresponding degree the
      definiteness of the conclusion. Thus if 60 per cent. of B are
      included in C, and 70 per cent. in A, 30 per cent. at least must be
      common to both; in other words, the number of As which are Cs, and
      of Cs which are As, must be at least equal to 30 per cent. of the
      class B. Proceeding on this conception of “numerically definite
      propositions,” and extending it to such forms as these:—“45 Xs (or
      more) are each of them one of 70 Ys,” or “45 Xs (or more) are no one
      of them to be found among 70 Ys,” and examining what inferences
      admit of being drawn from the various combinations which may be made
      of premises of this description, Mr. De Morgan establishes universal
      formulæ for such inferences; creating for that purpose not only a
      new technical language, but a formidable array of symbols analogous
      to those of algebra.

      Since it is undeniable that inferences, in the cases examined by Mr.
      De Morgan, can legitimately be drawn, and that the ordinary theory
      takes no account of them, I will not say that it was not worth while
      to show in detail how these also could be reduced to formulæ as
      rigorous as those of Aristotle. What Mr. De Morgan has done was
      worth doing once (perhaps more than once, as a school exercise); but
      I question if its results are worth studying and mastering for any
      practical purpose. The practical use of technical forms of reasoning
      is to bar out fallacies: but the fallacies which require to be
      guarded against in ratiocination properly so called, arise from the
      incautious use of the common forms of language; and the logician
      must track the fallacy into that territory, instead of waiting for
      it on a territory of his own. While he remains among propositions
      which have acquired the numerical precision of the Calculus of
      Probabilities, the enemy is left in possession of the only ground on
      which he can be formidable. And since the propositions (short of
      universal) on which a thinker has to depend, either for purposes of
      speculation or of practice, do not, except in a few peculiar cases,
      admit of any numerical precision; common reasoning can not be
      translated into Mr. De Morgan’s forms, which therefore can not serve
      any purpose as a test of it.

      Sir William Hamilton’s theory of the “quantification of the
      predicate” may be described as follows:

      “Logically” (I quote his words) “we ought to take into account the
      quantity, always understood in thought, but usually, for manifest
      reasons, elided in its expression, not only of the subject, but also
      of the predicate of a judgment.” All A is B, is equivalent to all A
      is _some_ B. No A is B, to No A is _any_ B. Some A is B, is
      tantamount to some A is _some_ B. Some A is not B, to Some A is _not
      any_ B. As in these forms of assertion the predicate is exactly
      co-extensive with the subject, they all admit of simple conversion;
      and by this we obtain two additional forms—Some B is _all_ A, and No
      B is _some_ A. We may also make the assertion All A is all B, which
      will be true if the classes A and B are exactly co-extensive. The
      last three forms, though conveying real assertions, have no place in
      the ordinary classification of Propositions. All propositions, then,
      being supposed to be translated into this language, and written each
      in that one of the preceding forms which answers to its
      signification, there emerges a new set of syllogistic rules,
      materially different from the common ones. A general view of the
      points of difference may be given in the words of Sir W. Hamilton
      (_Discussions_, 2d ed., p. 651):

      “The revocation of the two terms of a Proposition to their true
      relation; a proposition being always an _equation_ of its subject
      and its predicate.

      “The consequent reduction of the Conversion of Propositions from
      three species to one—that of Simple Conversion.

      “The reduction of all the _General Laws_ of Categorical Syllogisms
      to a single Canon.

      “The evolution from that one canon of all the Species and varieties
      of Syllogisms.

      “The abrogation of all the _Special Laws_ of Syllogism.

      “A demonstration of the exclusive possibility of Three Syllogistic
      Figures; and (on new grounds) the scientific and final abolition of
      the Fourth.

      “A manifestation that Figure is an unessential variation in
      syllogistic form; and the consequent absurdity of Reducing the
      syllogisms of the other figures to the first.

      “An enouncement of _one Organic Principle_ for each Figure.

      “A determination of the true number of the Legitimate Moods; with

      “Their amplification in number (thirty-six);

      “Their numerical equality under all the figures; and

      “Their relative equivalence, or virtual identity, throughout every
      schematic difference.

      “That, in the second and third figures, the extremes holding both
      the same relation to the middle term, there is not, as in the first,
      an opposition and subordination between a term major and a term
      minor, mutually containing and contained, in the counter wholes of
      Extension and Comprehension.

      “Consequently, in the second and third figures, there is no
      determinate major and minor premises, and there are two indifferent
      conclusions: whereas in the first the premises are determinate, and
      there is a single proximate conclusion.”

      This doctrine, like that of Mr. De Morgan previously noticed, is a
      real addition to the syllogistic theory; and has moreover this
      advantage over Mr. De Morgan’s “numerically definite Syllogism,”
      that the forms it supplies are really available as a test of the
      correctness of ratiocination; since propositions in the common form
      may always have their predicates quantified, and so be made amenable
      to Sir W. Hamilton’s rules. Considered, however, as a contribution
      to the _Science_ of Logic, that is, to the analysis of the mental
      processes concerned in reasoning, the new doctrine appears to me, I
      confess, not merely superfluous, but erroneous; since the form in
      which it clothes propositions does not, like the ordinary form,
      express what is in the mind of the speaker when he enunciates the
      proposition. I can not think Sir William Hamilton right in
      maintaining that the quantity of the predicate is “always understood
      in thought.” It is implied, but is not present to the mind of the
      person who asserts the proposition. The quantification of the
      predicate, instead of being a means of bringing out more clearly the
      meaning of the proposition, actually leads the mind out of the
      proposition, into another order of ideas. For when we say, All men
      are mortal, we simply mean to affirm the attribute mortality of all
      men; without thinking at all of the _class_ mortal in the concrete,
      or troubling ourselves about whether it contains any other beings or
      not. It is only for some artificial purpose that we ever look at the
      proposition in the aspect in which the predicate also is thought of
      as a class-name, either including the subject only, or the subject
      and something more. (See above, p. 77, 78.)

      For a fuller discussion of this subject, see the twenty-second
      chapter of a work already referred to, “An Examination of Sir
      William Hamilton’s Philosophy.”

   53 Mr. Herbert Spencer (_Principles of Psychology_, pp. 125-7), though
      his theory of the syllogism coincides with all that is essential of
      mine, thinks it a logical fallacy to present the two axioms in the
      text, as the regulating principles of syllogism. He charges me with
      falling into the error pointed out by Archbishop Whately and myself,
      of confounding exact likeness with literal identity; and maintains,
      that we ought not to say that Socrates possesses _the same_
      attributes which are connoted by the word Man, but only that he
      possesses attributes _exactly like_ them: according to which
      phraseology, Socrates, and the attribute mortality, are not two
      things co-existing with the same thing, as the axiom asserts, but
      two things coexisting with two different things.

      The question between Mr. Spencer and me is merely one of language;
      for neither of us (if I understand Mr. Spencer’s opinions rightly)
      believes an attribute to be a real thing, possessed of objective
      existence; we believe it to be a particular mode of naming our
      sensations, or our expectations of sensation, when looked at in
      their relation to an external object which excites them. The
      question raised by Mr. Spencer does not, therefore, concern the
      properties of any really existing thing, but the comparative
      appropriateness, for philosophical purposes, of two different modes
      of using a name. Considered in this point of view, the phraseology I
      have employed, which is that commonly used by philosophers, seems to
      me to be the best. Mr. Spencer is of opinion that because Socrates
      and Alcibiades are not the same man, the attribute which constitutes
      them men should not be called the same attribute; that because the
      humanity of one man and that of another express themselves to our
      senses not by the same individual sensations but by sensations
      exactly alike, humanity ought to be regarded as a different
      attribute in every different man. But on this showing, the humanity
      even of any one man should be considered as different attributes now
      and half an hour hence; for the sensations by which it will then
      manifest itself to my organs will not be a continuation of my
      present sensations, but a repetition of them; fresh sensations, not
      identical with, but only exactly like the present. If every general
      conception, instead of being “the One in the Many,” were considered
      to be as many different conceptions as there are things to which it
      is applicable, there would be no such thing as general language. A
      name would have no general meaning if _man_ connoted one thing when
      predicated of John, and another, though closely resembling, thing
      when predicated of William. Accordingly a recent pamphlet asserts
      the impossibility of general knowledge on this precise ground.

      The meaning of any general name is some outward or inward
      phenomenon, consisting, in the last resort, of feelings; and these
      feelings, if their continuity is for an instant broken, are no
      longer the same feelings, in the sense of individual identity. What,
      then, is the common something which gives a meaning to the general
      name? Mr. Spencer can only say, it is the similarity of the
      feelings; and I rejoin, the attribute is precisely that similarity.
      The names of attributes are in their ultimate analysis names for the
      resemblances of our sensations (or other feelings). Every general
      name, whether abstract or concrete, denotes or connotes one or more
      of those resemblances. It will not, probably, be denied, that if a
      hundred sensations are undistinguishably alike, their resemblance
      ought to be spoken of as one resemblance, and not a hundred
      resemblances which merely _resemble_ one another. The things
      compared are many, but the something common to all of them must be
      conceived as one, just as the name is conceived as one, though
      corresponding to numerically different sensations of sound each time
      it is pronounced. The general term _man_ does not connote the
      sensations derived once from one man, which, once gone, can no more
      occur again than the same flash of lightning. It connotes the
      general type of the sensations derived always from all men, and the
      power (always thought of as one) of producing sensations of that
      type. And the axiom might be thus worded: Two _types of sensation_
      each of which co-exists with a third type, co-exist with another; or
      Two _powers_ each of which co-exists with a third power co-exist
      with one another.

      Mr. Spencer has misunderstood me in another particular. He supposes
      that the co-existence spoken of in the axiom, of two things with the
      same third thing, means simultaneousness in time. The co-existence
      meant is that of being jointly attributes of the same subject. The
      attribute of being born without teeth, and the attribute of having
      thirty-two teeth in mature age, are in this sense co-existent, both
      being attributes of man, though _ex vi termini_ never of the same
      man at the same time.

   54 Supra, p. 93.

   55 Professor Bain (_Logic_, i., 157) considers the axiom (or rather
      axioms) here proposed as a substitute for the _dictum de omni_, to
      possess certain advantages, but to be “unworkable as a basis of the
      syllogism. The fatal defect consists in this, that it is ill-adapted
      to bring out the difference between total and partial coincidence of
      terms, the observation of which is the essential precaution in
      syllogizing correctly. If all the terms were co-extensive, the axiom
      would flow on admirably; A carries B, all B and none but B; B
      carries C in the same manner; at once A carries C, without
      limitation or reserve. But in point of fact, we know that while A
      carries B, other things carry B also; whence a process of limitation
      is required, in transferring A to C through B. A (in common with
      other things) carries B; B (in common with other things) carries C;
      whence A (in common with other things) carries C. The axiom provides
      no means of making this limitation; if we were to follow A
      literally, we should be led to suppose A and C co-extensive: for
      such is the only obvious meaning of ‘the attribute A coincides with
      the attribute C.’ ”

      It is certainly possible that a careless learner here and there may
      suppose that if A carries B, it follows that B carries A. But if any
      one is so incautious as to commit this mistake, the very earliest
      lesson in the logic of inference, the Conversion of propositions,
      will correct it. The first of the two forms in which I have stated
      the axiom, is in some degree open to Mr. Bain’s criticism: when B is
      said to co-exist with A (it must be by a _lapsus calami_ that Mr.
      Bain uses the word _coincide_), it is possible, in the absence of
      warning, to suppose the meaning to be that the two things are only
      found together. But this misinterpretation is excluded by the other,
      or practical, form of the maxim; _Nota notœ est nota rei ipsius._ No
      one would be in any danger of inferring that because _a_ is a mark
      of _b, b_ can never exist without _a_; that because being in a
      confirmed consumption is a mark of being about to die, no one dies
      who is not in a consumption; that because being coal is a mark of
      having come out of the earth, nothing can come out of the earth
      except coal. Ordinary knowledge of English seems a sufficient
      protection against these mistakes, since in speaking of a mark of
      any thing we are never understood as implying reciprocity.

      A more fundamental objection is stated by Mr. Bain in a subsequent
      passage (p. 158). “The axiom does not accommodate itself to the type
      of Deductive Reasoning as contrasted with Induction—the application
      of a general principle to a special case. Any thing that fails to
      make prominent this circumstance is not adapted as a foundation for
      the syllogism.” But though it may be proper to limit the term
      Deduction to the application of a general principle to a special
      case, it has never been held that Ratiocination or Syllogism is
      subject to the same limitation; and the adoption of it would exclude
      a great amount of valid and conclusive syllogistic reasoning.
      Moreover, if the _dictum de omni_ makes prominent the fact of the
      application of a general principle to a particular case, the axiom I
      propose makes prominent the condition which alone makes that
      application a real inference.

      I conclude, therefore, that both forms have their value, and their
      place in Logic. The _dictum de omni_ should be retained as the
      fundamental axiom of the logic of mere consistency, often called
      Formal Logic; nor have I ever quarreled with the use of it in that
      character, nor proposed to banish it from treatises on Formal Logic.
      But the other is the proper axiom for the logic of the pursuit of
      truth by way of Deduction; and the recognition of it can alone show
      how it is possible that deductive reasoning can be a road to truth.

_   56 Logic_, p. 239 (9th ed.).

   57 It is hardly necessary to say, that I am not contending for any such
      absurdity as that we _actually_ “ought to have known” and considered
      the case of every individual man, past, present, and future, before
      affirming that all men are mortal: although this interpretation has
      been, strangely enough, put upon the preceding observations. There
      is no difference between me and Archbishop Whately, or any other
      defender of the syllogism, on the practical part of the matter; I am
      only pointing out an inconsistency in the logical theory of it, as
      conceived by almost all writers. I do not say that a person who
      affirmed, before the Duke of Wellington was born, that all men are
      mortal, _knew_ that the Duke of Wellington was mortal; but I do say
      that he _asserted_ it; and I ask for an explanation of the apparent
      logical fallacy, of adducing in proof of the Duke of Wellington’s
      mortality, a general statement which presupposes it. Finding no
      sufficient resolution of this difficulty in any of the writers on
      Logic, I have attempted to supply one.

   58 The language of ratiocination would, I think, be brought into closer
      agreement with the real nature of the process, if the general
      propositions employed in reasoning, instead of being in the form All
      men are mortal, or Every man is mortal, were expressed in the form
      Any man is mortal. This mode of expression, exhibiting as the type
      of all reasoning from experience “The men A, B, C, etc., are so and
      so, therefore _any_ man is so and so,” would much better manifest
      the true idea—that inductive reasoning is always, at bottom,
      inference from particulars to particulars, and that the whole
      function of general propositions in reasoning, is to vouch for the
      legitimacy of such inferences.

   59 Review of Quetelet on Probabilities, _Essays_, p. 367.

_   60 Philosophy of Discovery_, p. 289.

_   61 Theory of Reasoning_, chap. iv., to which I may refer for an able
      statement and enforcement of the grounds of the doctrine.

   62 On a recent careful reperusal of Berkeley’s whole works, I have been
      unable to find this doctrine in them. Sir John Herschel probably
      meant that it is implied in Berkeley’s argument against abstract
      ideas. But I can not find that Berkeley saw the implication, or had
      ever asked himself what bearing his argument had on the theory of
      the syllogism. Still less can I admit that the doctrine is (as has
      been affirmed by one of my ablest and most candid critics) “among
      the standing marks of what is called the empirical philosophy.”

_   63 Logic_, book iv., chap. i., sect. 1.

   64 See the important chapter on Belief, in Professor Bain’s great
      treatise, _The Emotions and the Will_, pp. 581-4.

   65 A writer in the “British Quarterly Review” (August, 1846), in a
      review of this treatise, endeavors to show that there is no _petitio
      principii_ in the syllogism, by denying that the proposition, All
      men are mortal, asserts or assumes that Socrates is mortal. In
      support of this denial, he argues that we may, and in fact do, admit
      the general proposition that all men are mortal, without having
      particularly examined the case of Socrates, and even without knowing
      whether the individual so named is a man or something else. But this
      of course was never denied. That we can and do draw conclusions
      concerning cases specifically unknown to us, is the datum from which
      all who discuss this subject must set out. The question is, in what
      terms the evidence, or ground, on which we draw these conclusions,
      may best be designated—whether it is most correct to say, that the
      unknown case is proved by known cases, or that it is proved by a
      general proposition including both sets of cases, the unknown and
      the known? I contend for the former mode of expression. I hold it an
      abuse of language to say, that the proof that Socrates is mortal, is
      that all men are mortal. Turn it in what way we will, this seems to
      me to be asserting that a thing is the proof of itself. Whoever
      pronounces the words, All men are mortal, has affirmed that Socrates
      is mortal, though he may never have heard of Socrates; for since
      Socrates, whether known to be so or not, really is a man, he is
      included in the words, All men, and in every assertion of which they
      are the subject. If the reviewer does not see that there is a
      difficulty here, I can only advise him to reconsider the subject
      until he does: after which he will be a better judge of the success
      or failure of an attempt to remove the difficulty. That he had
      reflected very little on the point when he wrote his remarks, is
      shown by his oversight respecting the _dictum de omni et nullo_. He
      acknowledges that this maxim as commonly expressed—“Whatever is true
      of a class, is true of every thing included in the class,” is a mere
      identical proposition, since the class _is_ nothing but the things
      included in it. But he thinks this defect would be cured by wording
      the maxim thus—“Whatever is true of a class, is true of every thing
      which _can be shown_ to be a member of the class:” as if a thing
      could “be shown” to be a member of the class without being one. If a
      class means the sum of all the things included in the class, the
      things which can “be shown” to be included in it are part of the
      sum, and the _dictum_ is as much an identical proposition with
      respect to them as to the rest. One would almost imagine that, in
      the reviewer’s opinion, things are not members of a class until they
      are called up publicly to take their place in it—that so long, in
      fact, as Socrates is not known to be a man, he _is not_ a man, and
      any assertion which can be made concerning men does not at all
      regard him, nor is affected as to its truth or falsity by any thing
      in which he is concerned.

      The difference between the reviewer’s theory and mine may be thus
      stated. Both admit that when we say, All men are mortal, we make an
      assertion reaching beyond the sphere of our knowledge of individual
      cases; and that when a new individual, Socrates, is brought within
      the field of our knowledge by means of the minor premise, we learn
      that we have already made an assertion respecting Socrates without
      knowing it: our own general formula being, to that extent, for the
      first time _interpreted_ to us. But according to the reviewer’s
      theory, the smaller assertion is proved by the larger: while I
      contend, that both assertions are proved together, by the same
      evidence, namely, the grounds of experience on which the general
      assertion was made, and by which it must be justified.

      The reviewer says, that if the major premise included the
      conclusion, “we should be able to affirm the conclusion without the
      intervention of the minor premise; but every one sees that that is
      impossible.” A similar argument is urged by Mr. De Morgan (_Formal
      Logic_, p. 259): “The whole objection tacitly assumes the
      superfluity of the minor; that is, tacitly assumes we know Socrates
      (Mr. De Morgan says ‘Plato,’ but to prevent confusion I have kept to
      my own _exemplum_.) to be a man as soon as we know him to be
      Socrates.” The objection would be well grounded if the assertion
      that the major premise includes the conclusion, meant that it
      individually specifies all it includes. As, however, the only
      indication it gives is a description by marks, we have still to
      compare any new individual with the marks; and to show that this
      comparison has been made, is the office of the minor. But since, by
      supposition, the new individual has the marks, whether we have
      ascertained him to have them or not; if we have affirmed the major
      premise, we have asserted him to be mortal. Now my position is that
      this assertion can not be a necessary part of the argument. It can
      not be a necessary condition of reasoning that we should begin by
      making an assertion, which is afterward to be employed in proving a
      part of itself. I can conceive only one way out of this difficulty,
      viz., that what really forms the proof is _the other_ part of the
      assertion: the portion of it, the truth of which has been
      ascertained previously: and that the unproved part is bound up in
      one formula with the proved part in mere anticipation, and as a
      memorandum of the nature of the conclusions which we are prepared to
      prove.

      With respect to the minor premise in its formal shape, the minor as
      it stands in the syllogism, predicating of Socrates a definite class
      name, I readily admit that it is no more a necessary part of
      reasoning than the major. When there is a major, doing its work by
      means of a class name, minors are needed to interpret it: but
      reasoning can be carried on without either the one or the other.
      They are not the conditions of reasoning, but a precaution against
      erroneous reasoning. The only minor premise necessary to reasoning
      in the example under consideration, is, Socrates is _like_ A, B, C,
      and the other individuals who are known to have died. And this is
      the only universal type of that step in the reasoning process which
      is represented by the minor. Experience, however, of the uncertainty
      of this loose mode of inference, teaches the expediency of
      determining beforehand what _kind_ of likeness to the cases
      observed, is necessary to bring an unobserved case within the same
      predicate; and the answer to this question is the major. The minor
      then identifies the precise kind of likeness possessed by Socrates,
      as being the kind required by the formula. Thus the syllogistic
      major and the syllogistic minor start into existence together, and
      are called forth by the same exigency. When we conclude from
      personal experience without referring to any record—to any general
      theorems, either written, or traditional, or mentally registered by
      ourselves as conclusions of our own drawing—we do not use, in our
      thoughts, either a major or a minor, such as the syllogism puts into
      words. When, however, we revise this rough inference from
      particulars to particulars, and substitute a careful one, the
      revision consists in selecting two syllogistic premises. But this
      neither alters nor adds to the evidence we had before; it only puts
      us in a better position for judging whether our inference from
      particulars to particulars is well grounded.

   66 Infra, book iii., chap. ii.

   67 Infra, book iii., ch. iv., § 3, and elsewhere.

   68 It is justly remarked by Professor Bain (_Logic_, ii., 134) that the
      word Hypothesis is here used in a somewhat peculiar sense. An
      hypothesis, in science, usually means a supposition not proved to be
      true, but surmised to be so, because if true it would account for
      certain known facts; and the final result of the speculation may be
      to prove its truth. The hypotheses spoken of in the text are of a
      different character; they are known not to be literally true, while
      as much of them as is true is not hypothetical, but certain. The two
      cases, however, resemble in the circumstance that in both we reason,
      not from a truth, but from an assumption, and the truth therefore of
      the conclusions is conditional, not categorical. This suffices to
      justify, in point of logical propriety, Stewart’s use of the term.
      It is of course needful to bear in mind that the hypothetical
      element in the definitions of geometry is the assumption that what
      is very nearly true is exactly so. This unreal exactitude might be
      called a fiction, as properly as an hypothesis; but that
      appellation, still more than the other, would fail to point out the
      close relation which exists between the fictitious point or line and
      the points and lines of which we have experience.

_   69 Mechanical Euclid_, pp. 149 _et seqq._

   70 We might, it is true, insert this property into the definition of
      parallel lines, framing the definition so as to require, both that
      when produced indefinitely they shall never meet, and also that any
      straight line which intersects one of them shall, if prolonged, meet
      the other. But by doing this we by no means get rid of the
      assumption; we are still obliged to take for granted the geometrical
      truth, that all straight lines in the same plane, which have the
      former of these properties, have also the latter. For if it were
      possible that they should not, that is, if any straight lines in the
      same plane, other than those which are parallel according to the
      definition, had the property of never meeting although indefinitely
      produced, the demonstrations of the subsequent portions of the
      theory of parallels could not be maintained.

   71 Some persons find themselves prevented from believing that the
      axiom, Two straight lines can not inclose a space, could ever become
      known to us through experience, by a difficulty which may be stated
      as follows: If the straight lines spoken of are those contemplated
      in the definition—lines absolutely without breadth and absolutely
      straight—that such are incapable of inclosing a space is not proved
      by experience, for lines such as these do not present themselves in
      our experience. If, on the other hand, the lines meant are such
      straight lines as we do meet with in experience, lines straight
      enough for practical purposes, but in reality slightly zigzag, and
      with some, however trifling, breadth; as applied to these lines the
      axiom is not true, for two of them may, and sometimes do, inclose a
      small portion of space. In neither case, therefore, does experience
      prove the axiom.

      Those who employ this argument to show that geometrical axioms can
      not be proved by induction, show themselves unfamiliar with a common
      and perfectly valid mode of inductive proof; proof by approximation.
      Though experience furnishes us with no lines so unimpeachably
      straight that two of them are incapable of inclosing the smallest
      space, it presents us with gradations of lines possessing less and
      less either of breadth or of flexure, of which series the straight
      line of the definition is the ideal limit. And observation shows
      that just as much, and as nearly, as the straight lines of
      experience approximate to having no breadth or flexure, so much and
      so nearly does the space-inclosing power of any two of them approach
      to zero. The inference that if they had no breadth or flexure at
      all, they would inclose no space at all, is a correct inductive
      inference from these facts, conformable to one of the four Inductive
      Methods hereinafter characterized, the Method of Concomitant
      Variations; of which the mathematical Doctrine of Limits presents
      the extreme case.

   72 Whewell’s _History of Scientific Ideas_, i., 140.

   73 Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it
      unreasonable to contend that we know by experience, that our idea of
      a line exactly resembles a real line. “It does not appear,” he says,
      “how we can compare our ideas with the realities, since we know the
      realities only by our ideas.” We know the realities by our
      sensations. Dr. Whewell surely does not hold the “doctrine of
      perception by means of ideas,” which Reid gave himself so much
      trouble to refute. If Dr. Whewell doubts whether we compare our
      ideas with the corresponding sensations, and assume that they
      resemble, let me ask on what evidence do we judge that a portrait of
      a person not present is like the original. Surely because it is like
      our idea, or mental image of the person, and because our idea is
      like the man himself.

      Dr. Whewell also says, that it does not appear why this resemblance
      of ideas to the sensations of which they are copies, should be
      spoken of as if it were a peculiarity of one class of ideas, those
      of space. My reply is, that I do not so speak of it. The peculiarity
      I contend for is only one of degree. All our ideas of sensation of
      course resemble the corresponding sensations, but they do so with
      very different degrees of exactness and of reliability. No one, I
      presume, can recall in imagination a color or an odor with the same
      distinctness and accuracy with which almost every one can mentally
      reproduce an image of a straight line or a triangle. To the extent,
      however, of their capabilities of accuracy, our recollections of
      colors or of odors may serve as subjects of experimentation, as well
      as those of lines and spaces, and may yield conclusions which will
      be true of their external prototypes. A person in whom, either from
      natural gift or from cultivation, the impressions of color were
      peculiarly vivid and distinct, if asked which of two blue flowers
      was of the darkest tinge, though he might never have compared the
      two, or even looked at them together, might be able to give a
      confident answer on the faith of his distinct recollection of the
      colors; that is, he might examine his mental pictures, and find
      there a property of the outward objects. But in hardly any case
      except that of simple geometrical forms, could this be done by
      mankind generally, with a degree of assurance equal to that which is
      given by a contemplation of the objects themselves. Persons differ
      most widely in the precision of their recollection, even of forms:
      one person, when he has looked any one in the face for half a
      minute, can draw an accurate likeness of him from memory; another
      may have seen him every day for six months, and hardly know whether
      his nose is long or short. But every body has a perfectly distinct
      mental image of a straight line, a circle, or a rectangle. And every
      one concludes confidently from these mental images to the
      corresponding outward things. The truth is, that we may, and
      continually do, study nature in our recollections, when the objects
      themselves are absent; and in the case of geometrical forms we can
      perfectly, but in most other cases only imperfectly, trust our
      recollections.

_   74 Logic_, i., 222.

   75 Ibid., 226.

_   76 History of Scientific Ideas_, i., 65-67.

   77 Ibid., i., 60.

   78 Ibid., 58, 59.

   79 “If all mankind had spoken one language, we can not doubt that there
      would have been a powerful, perhaps a universal, school of
      philosophers, who would have believed in the inherent connection
      between names and things, who would have taken the sound _man_ to be
      the mode of agitating the air which is essentially communicative of
      the ideas of reason, cookery, bipedality, etc.”—De Morgan, _Formal
      Logic_, p. 246.

   80 It would be difficult to name a man more remarkable at once for the
      greatness and the wide range of his mental accomplishments, than
      Leibnitz. Yet this eminent man gave as a reason for rejecting
      Newton’s scheme of the solar system, that God _could not_ make a
      body revolve round a distant centre, unless either by some impelling
      mechanism, or by miracle: “Tout ce qui n’est pas explicable,” says
      he in a letter to the Abbé Conti, “par la nature des créatures, est
      miraculeux. Il ne suffit pas de dire: Dieu a fait une telle loi de
      nature; donc la chose est naturelle. Il faut que la loi soit
      exécutable par les natures des créatures. Si Dien donnait cette loi,
      par exemple, à un corps libre, de tourner à l’entour d’un certain
      centre, _il faudrait ou qu’il y joignît d’autres corps qui par leur
      impulsion l’obligeassent de rester toujours dans son orbite
      circulaire, ou qu’il mît un ange à ses trousses, ou enfin il
      faudrait qu’il y concourût extraordinairement_; car naturellement il
      s’écartera par la tangente.”—_Works of Leibnitz_, ed. Dutens, iii.,
      446.

_   81 Novum Organum Renovatum_, pp. 32, 33.

_   82 History of Scientific Ideas_, i., 264.

   83 Ibid., i., 263.

   84 Ibid., 240.

_   85 Hist. Scientific Ideas_, ii., 25, 26.

_   86 Phil. of Disc._, p. 339.

_   87 Phil. of Disc._, p. 338.

   88 Ibid., p. 463.

_   89 Phil. of Disc._, pp. 472, 473.

   90 The _Quarterly Review_ for June, 1841, contained an article of great
      ability on Dr. Whewell’s two great works (since acknowledged and
      reprinted in Sir John Herschel’s Essays) which maintains, on the
      subject of axioms, the doctrine advanced in the text, that they are
      generalizations from experience, and supports that opinion by a line
      of argument strikingly coinciding with mine. When I state that the
      whole of the present chapter (except the last four pages, added in
      the fifth edition) was written before I had seen the article (the
      greater part, indeed, before it was published), it is not my object
      to occupy the reader’s attention with a matter so unimportant as the
      degree of originality which may or may not belong to any portion of
      my own speculations, but to obtain for an opinion which is opposed
      to reigning doctrines, the recommendation derived from a striking
      concurrence of sentiment between two inquirers entirely independent
      of one another. I embrace the opportunity of citing from a writer of
      the extensive acquirements in physical and metaphysical knowledge
      and the capacity of systematic thought which the article evinces,
      passages so remarkably in unison with my own views as the following:

      “The truths of geometry are summed up and embodied in its
      definitions and axioms.... Let us turn to the axioms, and what do we
      find? A string of propositions concerning magnitude in the abstract,
      which are equally true of space, time, force, number, and every
      other magnitude susceptible of aggregation and subdivision. Such
      propositions, where they are not mere definitions, as some of them
      are, carry their inductive origin on the face of their
      enunciation.... Those which declare that two straight lines can not
      inclose a space, and that two straight lines which cut one another
      can not both be parallel to a third, are in reality the only ones
      which express characteristic properties of space, and these it will
      be worth while to consider more nearly. Now the only clear notion we
      can form of straightness is uniformity of direction, for space in
      its ultimate analysis is nothing but an assemblage of distances and
      directions. And (not to dwell on the notion of continued
      contemplation, _i.e._, mental experience, as included in the very
      idea of uniformity; nor on that of transfer of the contemplating
      being from point to point, and of experience, during such transfer,
      of the homogeneity of the interval passed over) we can not even
      propose the proposition in an intelligible form to any one whose
      experience ever since he was born has not assured him of the fact.
      The unity of direction, or that we can not march from a given point
      by more than one path direct to the same object, is matter of
      practical experience long before it can by possibility become matter
      of abstract thought. _We can not attempt mentally to exemplify the
      conditions of the assertion in an imaginary case opposed to it,
      without violating our habitual recollection of this experience, and
      defacing our mental picture of space as grounded on it._ What but
      experience, we may ask, can possibly assure us of the homogeneity of
      the parts of distance, time, force, and measurable aggregates in
      general, on which the truth of the other axioms depends? As regards
      the latter axiom, after what has been said it must be clear that the
      very same course of remarks equally applies to its case, and that
      its truth is quite as much forced on the mind as that of the former
      by daily and hourly experience, ... _including always, be it
      observed, in our notion of experience, that which is gained by
      contemplation of the inward picture which the mind forms to itself
      in any proposed case, or which it arbitrarily selects as an
      example—such picture, in virtue of the extreme simplicity of these
      primary relations, being called up by the imagination with as much
      vividness and clearness as could be done by any external impression,
      which is the only meaning we can attach to the word intuition, as
      applied to such relations_.”

      And again, of the axioms of mechanics: “As we admit no such
      propositions, other than as truths inductively collected from
      observation, even in geometry itself, it can hardly be expected
      that, in a science of obviously contingent relations, we should
      acquiesce in a contrary view. Let us take one of these axioms and
      examine its evidence: for instance, that equal forces
      perpendicularly applied at the opposite ends of equal arms of a
      straight lever will balance each other. What but experience, we may
      ask, in the first place, can possibly inform us that a force so
      applied will have any tendency to turn the lever on its centre at
      all? or that force can be so transmitted along a rigid line
      perpendicular to its direction, as to act elsewhere in space than
      along its own line of action? Surely this is so far from being
      self-evident that it has even a paradoxical appearance, which is
      only to be removed by giving our lever thickness, material
      composition, and molecular powers. Again, we conclude, that the two
      forces, being equal and applied under precisely similar
      circumstances, must, if they exert any effort at all to turn the
      lever, exert equal and opposite efforts: but what _a priori_
      reasoning can possibly assure us that they _do_ act under precisely
      similar circumstances? that points which differ in place _are_
      similarly circumstanced as regards the exertion of force? that
      universal space may not have relations to universal force—or, at all
      events, that the organization of the material universe may not be
      such as to place that portion of space occupied by it in such
      relations to the forces exerted in it, as may invalidate the
      absolute similarity of circumstances assumed? Or we may argue, what
      have we to do with the notion of angular movement in the lever at
      all? The case is one of rest, and of quiescent destruction of force
      by force. Now how is this destruction effected? Assuredly by the
      counter-pressure which supports the fulcrum. But would not this
      destruction equally arise, and by the same amount of counteracting
      force, if each force simply pressed its own half of the lever
      against the fulcrum? And what can assure us that it is not so,
      except removal of one or other force, and consequent tilting of the
      lever? The other fundamental axiom of statics, that the pressure on
      the point of support is the sum of the weights ... is merely a
      scientific transformation and more refined mode of stating a coarse
      and obvious result of universal experience, viz., that the weight of
      a rigid body is the same, handle it or suspend it in what position
      or by what point we will, and that whatever sustains it sustains its
      total weight. Assuredly, as Mr. Whewell justly remarks, ‘No one
      probably ever made a trial for the purpose of showing that the
      pressure on the support is equal to the sum of the weights.’ ... But
      it is precisely because in every action of his life from earliest
      infancy he has been continually making the trial, and seeing it made
      by every other living being about him, that he never dreams of
      staking its result on one additional attempt made with scientific
      accuracy. This would be as if a man should resolve to decide by
      experiment whether his eyes were useful for the purpose of seeing,
      by hermetically sealing himself up for half an hour in a metal
      case.”

      On the “paradox of universal propositions obtained by experience,”
      the same writer says: “If there be necessary and universal truths
      expressible in propositions of axiomatic simplicity and obviousness,
      and having for their subject-matter the elements of all our
      experience and all our knowledge, surely these are the truths which,
      if experience suggest to us any truths at all, it ought to suggest
      most readily, clearly, and unceasingly. If it were a truth,
      universal and necessary, that a net is spread over the whole surface
      of every planetary globe, we should not travel far on our own
      without getting entangled in its meshes, and making the necessity of
      some means of extrication an axiom of locomotion.... There is,
      therefore, nothing paradoxical, but the reverse, in our being led by
      observation to a recognition of such truths, as _general_
      propositions, co-extensive at least with all human experience. That
      they pervade all the objects of experience, must insure their
      continual suggestion _by_ experience; that they are true, must
      insure that consistency of suggestion, that iteration of
      uncontradicted assertion, which commands implicit assent, and
      removes all occasion of exception; that they are simple, and admit
      of no misunderstanding, must secure their admission by every mind.”

      “A truth, necessary and universal, relative to any object of our
      knowledge, must verify itself in every instance where that object is
      before our contemplation, and if at the same time it be simple and
      intelligible, its verification must be obvious. _The sentiment of
      such a truth can not, therefore, but be present to our minds
      whenever that object is contemplated, and must therefore make a part
      of the mental picture or idea of that object which we may on any
      occasion summon before our imagination.... All propositions,
      therefore, become not only untrue but inconceivable_, if ... axioms
      be violated in their enunciation.”

      Another eminent mathematician had previously sanctioned by his
      authority the doctrine of the origin of geometrical axioms in
      experience. “Geometry is thus founded likewise on observation; but
      of a kind so familiar and obvious, that the primary notions which it
      furnishes might seem intuitive.”—_Sir John Leslie_, quoted by Sir
      William Hamilton, _Discourses_, etc., p. 272.

   91 Principles of Psychology.

   92 Mr. Spencer is mistaken in supposing me to claim any peculiar
      “necessity” for this axiom as compared with others. I have corrected
      the expressions which led him into that misapprehension of my
      meaning.

   93 Mr. Spencer, in recently returning to the subject (Principles of
      Psychology, new edition, chap. xii.: “The Test of Relative
      Validity”), makes two answers to the preceding remarks. One is:

      “Were an argument formed by repeating the same proposition over and
      over again, it would be true that any intrinsic fallibility of the
      postulate would not make the conclusion more untrustworthy than the
      first step. But an argument consists of unlike propositions. Now,
      since Mr. Mill’s criticism on the Universal Postulate is that in
      some cases, which he names, it has proved to be an untrustworthy
      test; it follows that in any argument consisting of heterogeneous
      propositions, there is a risk, increasing as the number of
      propositions increases, that some one of them belongs to this class
      of cases, and is wrongly accepted because of the inconceivableness
      of its negation.”

      No doubt: but this supposes new _premises_ to be taken in. The point
      we are discussing is the fallibility not of the premises, but of the
      reasoning, as distinguished from the premises. Now the validity of
      the reasoning depends always upon the same axiom, repeated (in
      thought) “over and over again,” viz., that whatever has a mark, has
      what it is a mark of. Even, therefore, on the assumption that this
      axiom rests ultimately on the Universal Postulate, and that, the
      Postulate not being wholly trustworthy, the axiom may be one of the
      cases of its failure; all the risk there is of this is incurred at
      the very first step of the reasoning, and is not added to, however
      long may be the series of subsequent steps.

      I am here arguing, of course, from Mr. Spencer’s point of view. From
      my own the case is still clearer; for, in my view, the truth that
      whatever has a mark has what it is a mark of, is wholly trustworthy,
      and derives none of its evidence from so very untrustworthy a test
      as the inconceivability of the negative.

      Mr. Spencer’s second answer is valid up to a certain point; it is,
      that every prolongation of the process involves additional chances
      of casual error, from carelessness in the reasoning operation. This
      is an important consideration in the private speculations of an
      individual reasoner; and even with respect to mankind at large, it
      must be admitted that, though mere oversights in the syllogistic
      process, like errors of addition in an account, are special to the
      individual, and seldom escape detection, confusion of thought
      produced (for example) by ambiguous terms has led whole nations or
      ages to accept fallacious reasoning as valid. But this very fact
      points to causes of error so much more dangerous than the mere
      length of the process, as quite to vitiate the doctrine that the
      “test of the relative validities of conflicting conclusions” is the
      number of times the fundamental postulate is involved. On the
      contrary, the subjects on which the trains of reasoning are longest,
      and the assumption, therefore, oftenest repeated, are in general
      those which are best fortified against the really formidable causes
      of fallacy; as in the example already given of mathematics.

   94 Mr. Spencer makes a distinction between conceiving myself looking
      into darkness, and conceiving _that I am_ then and there looking
      into darkness. To me it seems that this change of the expression to
      the form _I am_, just marks the transition from conception to
      belief, and that the phrase “to conceive that _I am_,” or “that any
      thing _is_,” is not consistent with using the word conceive in its
      rigorous sense.

   95 I have myself accepted the contest, and fought it out on this
      battle-ground, in the eleventh chapter of _An Examination of Sir
      William Hamilton’s Philosophy._

   96 Chap. xi.

   97 In one of the three cases, Mr. Spencer, to my no small surprise,
      thinks that the belief of mankind “can not be rightly said to have
      undergone” the change I allege. Mr. Spencer himself still thinks we
      are unable to conceive gravitation acting through empty space. “If
      an astronomer avowed that he could conceive gravitative force as
      exercised through space absolutely void, my private opinion would be
      that he mistook the nature of conception. Conception implies
      representation. Here the elements of the representation are the two
      bodies and an agency by which either affects the other. To conceive
      this agency is to represent it in some terms derived from our
      experiences—that is, from our sensations. As this agency gives us no
      sensations, we are obliged (if we try to conceive it) to use symbols
      idealized from our sensations—imponderable units forming a medium.”

      If Mr. Spencer means that the action of gravitation gives us no
      sensations, the assertion is one than which I have not seen, in the
      writings of philosophers, many more startling. What other sensation
      do we need than the sensation of one body moving toward another?
      “The elements of the representation” are not two bodies and an
      “agency,” but two bodies and an effect; viz., the fact of their
      approaching one another. If we are able to conceive a vacuum, is
      there any difficulty in conceiving a body falling to the earth
      through it?

_   98 Discussions_, etc., 2d ed., p. 624.

   99 Professor Bain (_Logic_, i., 16) identifies the Principle of
      Contradiction with his Law of Relativity, viz., that “every thing
      that can be thought of, every affirmation that can be made, has an
      opposite or counter notion or affirmation;” a proposition which is
      one of the general results of the whole body of human experience.
      For further considerations respecting the axioms of Contradiction
      and Excluded Middle, see the twenty-first chapter of _An Examination
      of Sir William Hamilton’s Philosophy_.

  100 Dr. Whewell thinks it improper to apply the term Induction to any
      operation not terminating in the establishment of a general truth.
      Induction, he says (_Philosophy of Discovery_, p. 245), “is not the
      same thing as experience and observation. Induction is experience or
      observation _consciously_ looked at in a _general_ form. This
      consciousness and generality are necessary parts of that knowledge
      which is science.” And he objects (p. 241) to the mode in which the
      word Induction is employed in this work, as an undue extension of
      that term “not only to the cases in which the general induction is
      consciously applied to a particular instance, but to the cases in
      which the particular instance is dealt with by means of experience
      in that rude sense in which experience can be asserted of brutes,
      and in which of course we can in no way imagine that the law is
      possessed or understood as a general proposition.” This use of the
      term he deems a “confusion of knowledge with practical tendencies.”

      I disclaim, as strongly as Dr. Whewell can do, the application of
      such terms as induction, inference, or reasoning, to operations
      performed by mere instinct, that is, from an animal impulse, without
      the exertion of any intelligence. But I perceive no ground for
      confining the use of those terms to cases in which the inference is
      drawn in the forms and with the precautions required by scientific
      propriety. To the idea of Science, an express recognition and
      distinct apprehension of general laws as such, is essential: but
      nine-tenths of the conclusions drawn from experience in the course
      of practical life, are drawn without any such recognition: they are
      direct inferences from known cases, to a case supposed to be
      similar. I have endeavored to show that this is not only as
      legitimate an operation, but substantially the same operation, as
      that of ascending from known cases to a general proposition; except
      that the latter process has one great security for correctness which
      the former does not possess. In science, the inference must
      necessarily pass through the intermediate stage of a general
      proposition, because Science wants its conclusions for record, and
      not for instantaneous use. But the inferences drawn for the guidance
      of practical affairs, by persons who would often be quite incapable
      of expressing in unexceptionable terms the corresponding
      generalizations, may and frequently do exhibit intellectual powers
      quite equal to any which have ever been displayed in science; and if
      these inferences are not inductive, what are they? The limitation
      imposed on the term by Dr. Whewell seems perfectly arbitrary;
      neither justified by any fundamental distinction between what he
      includes and what he desires to exclude, nor sanctioned by usage, at
      least from the time of Reid and Stewart, the principal legislators
      (as far as the English language is concerned) of modern metaphysical
      terminology.

  101 Supra, p. 145.

_  102 Novum Organum Renovatum_, pp. 72, 73.

_  103 Novum Organum Renovatum_, p. 32.

_  104 Cours de Philosophie Positive_, vol. ii., p. 202.

  105 Dr. Whewell, in his reply, contests the distinction here drawn, and
      maintains, that not only different descriptions, but different
      explanations of a phenomenon, may all be true. Of the three theories
      respecting the motions of the heavenly bodies, he says (_Philosophy
      of Discovery_, p. 231): “Undoubtedly all these explanations may be
      true and consistent with each other, and would be so if each had
      been followed out so as to show in what manner it could be made
      consistent with the facts. And this was, in reality, in a great
      measure done. The doctrine that the heavenly bodies were moved by
      vortices was successfully modified, so that it came to coincide in
      its results with the doctrine of an inverse-quadratic centripetal
      force.... When this point was reached, the vortex was merely a
      machinery, well or ill devised, for producing such a centripetal
      force, and therefore did not contradict the doctrine of a
      centripetal force. Newton himself does not appear to have been
      averse to explaining gravity by impulse. So little is it true that
      if one theory be true the other must be false. The attempt to
      explain gravity by the impulse of streams of particles flowing
      through the universe in all directions, which I have mentioned in
      the _Philosophy_, is so far from being inconsistent with the
      Newtonian theory, that it is founded entirely upon it. And even with
      regard to the doctrine, that the heavenly bodies move by an inherent
      virtue; if this doctrine had been maintained in any such way that it
      was brought to agree with the facts, the inherent virtue must have
      had its laws determined; and then it would have been found that the
      virtue had a reference to the central body; and so, the ‘inherent
      virtue’ must have coincided in its effect with the Newtonian force;
      and then, the two explanations would agree, except so far as the
      word ‘inherent’ was concerned. And if such a part of an earlier
      theory as this word _inherent_ indicates, is found to be untenable,
      it is of course rejected in the transition to later and more exact
      theories, in Inductions of this kind, as well as in what Mr. Mill
      calls Descriptions. There is, therefore, still no validity
      discoverable in the distinction which Mr. Mill attempts to draw
      between descriptions like Kepler’s law of elliptical orbits, and
      other examples of induction.”

      If the doctrine of vortices had meant, not that vortices existed,
      but only that the planets moved _in the same manner_ as if they had
      been whirled by vortices; if the hypothesis had been merely a mode
      of representing the facts, not an attempt to account for them; if,
      in short, it had been only a Description; it would, no doubt, have
      been reconcilable with the Newtonian theory. The vortices, however,
      were not a mere aid to conceiving the motions of the planets, but a
      supposed physical agent, actively impelling them; a material fact,
      which might be true or not true, but could not be both true and not
      true. According to Descartes’s theory it was true, according to
      Newton’s it was not true. Dr. Whewell probably means that since the
      phrases, centripetal and projectile force, do not declare the nature
      but only the direction of the forces, the Newtonian theory does not
      absolutely contradict any hypothesis which may be framed respecting
      the mode of their production. The Newtonian theory, regarded as a
      mere _description_ of the planetary motions, does not; but the
      Newtonian theory as an _explanation_ of them does. For in what does
      the explanation consist? In ascribing those motions to a general law
      which obtains between all particles of matter, and in identifying
      this with the law by which bodies fall to the ground. If the planets
      are kept in their orbits by a force which draws the particles
      composing them toward every other particle of matter in the solar
      system, they are not kept in those orbits by the impulsive force of
      certain streams of matter which whirl them round. The one
      explanation absolutely excludes the other. Either the planets are
      not moved by vortices, or they do not move by a law common to all
      matter. It is impossible that both opinions can be true. As well
      might it be said that there is no contradiction between the
      assertions, that a man died because somebody killed him, and that he
      died a natural death.

      So, again, the theory that the planets move by a virtue inherent in
      their celestial nature, is incompatible with either of the two
      others: either that of their being moved by vortices, or that which
      regards them as moving by a property which they have in common with
      the earth and all terrestrial bodies. Dr. Whewell says that the
      theory of an inherent virtue agrees with Newton’s when the word
      inherent is left out, which of course it would be (he says) if
      “found to be untenable.” But leave that out, and where is the
      theory? The word inherent _is_ the theory. When that is omitted,
      there remains nothing except that the heavenly bodies move “by a
      virtue,” _i.e._, by a power of some sort; or by virtue of their
      celestial nature, which directly contradicts the doctrine that
      terrestrial bodies fall by the same law.

      If Dr. Whewell is not yet satisfied, any other subject will serve
      equally well to test his doctrine. He will hardly say that there is
      no contradiction between the emission theory and the undulatory
      theory of light; or that there can be both one and two
      electricities; or that the hypothesis of the production of the
      higher organic forms by development from the lower, and the
      supposition of separate and successive acts of creation, are quite
      reconcilable; or that the theory that volcanoes are fed from a
      central fire, and the doctrines which ascribe them to chemical
      action at a comparatively small depth below the earth’s surface, are
      consistent with one another, and all true as far as they go.

      If different explanations of the same fact can not both be true,
      still less, surely, can different predictions. Dr. Whewell quarrels
      (on what ground it is not necessary here to consider) with the
      example I had chosen on this point, and thinks an objection to an
      illustration a sufficient answer to a theory. Examples not liable to
      his objection are easily found, if the proposition that conflicting
      predictions can not both be true, can be made clearer by many
      examples. Suppose the phenomenon to be a newly-discovered comet, and
      that one astronomer predicts its return once in every 300
      years—another once in every 400: can they both be right? When
      Columbus predicted that by sailing constantly westward he should in
      time return to the point from which he set out, while others
      asserted that he could never do so except by turning back, were both
      he and his opponents true prophets? Were the predictions which
      foretold the wonders of railways and steamships, and those which
      averred that the Atlantic could never be crossed by steam
      navigation, nor a railway train propelled ten miles an hour, both
      (in Dr. Whewell’s words) “true, and consistent with one another?”

      Dr. Whewell sees no distinction between holding contradictory
      opinions on a question of fact, and merely employing different
      analogies to facilitate the conception of the same fact. The case of
      different Inductions belongs to the former class, that of different
      Descriptions to the latter.

_  106 Phil. of Discov._, p. 256.

_  107 Essays on the Pursuit of Truth._

  108 In the first edition a note was appended at this place, containing
      some criticism on Archbishop Whately’s mode of conceiving the
      relation between Syllogism and Induction. In a subsequent issue of
      his _Logic_, the Archbishop made a reply to the criticism, which
      induced me to cancel part of the note, incorporating the remainder
      in the text. In a still later edition, the Archbishop observes in a
      tone of something like disapprobation, that the objections,
      “doubtless from their being fully answered and found untenable, were
      silently suppressed,” and that hence he might appear to some of his
      readers to be combating a shadow. On this latter point, the
      Archbishop need give himself no uneasiness. His readers, I make bold
      to say, will fully credit his mere affirmation that the objections
      have actually been made.

      But as he seems to think that what he terms the suppression of the
      objections ought not to have been made “silently,” I now break that
      silence, and state exactly what it is that I suppressed, and why. I
      suppressed that alone which might be regarded as personal criticism
      on the Archbishop. I had imputed to him the having omitted to ask
      himself a particular question. I found that he had asked himself the
      question, and could give it an answer consistent with his own
      theory. I had also, within the compass of a parenthesis, hazarded
      some remarks on certain general characteristics of Archbishop
      Whately as a philosopher. These remarks, though their tone, I hope,
      was neither disrespectful nor arrogant, I felt, on reconsideration,
      that I was hardly entitled to make; least of all, when the instance
      which I had regarded as an illustration of them, failed, as I now
      saw, to bear them out. The real matter at the bottom of the whole
      dispute, the different view we take of the function of the major
      premise, remains exactly where it was; and so far was I from
      thinking that my opinion had been fully “answered” and was
      “untenable,” that in the same edition in which I canceled the note,
      I not only enforced the opinion by further arguments, but answered
      (though without naming him) those of the Archbishop.

      For not having made this statement before, I do not think it needful
      to apologize. It would be attaching very great importance to one’s
      smallest sayings, to think a formal retractation requisite every
      time that one falls into an error. Nor is Archbishop Whately’s
      well-earned fame of so tender a quality as to require that in
      withdrawing a slight criticism on him I should have been bound to
      offer a public _amende_ for having made it.

  109 But though it is a condition of the validity of every induction that
      there be uniformity in the course of nature, it is not a necessary
      condition that the uniformity should pervade all nature. It is
      enough that it pervades the particular class of phenomena to which
      the induction relates. An induction concerning the motions of the
      planets, or the properties of the magnet, would not be vitiated
      though we were to suppose that wind and weather are the sport of
      chance, provided it be assumed that astronomical and magnetic
      phenomena are under the dominion of general laws. Otherwise the
      early experience of mankind would have rested on a very weak
      foundation; for in the infancy of science it could not be known that
      _all_ phenomena are regular in their course.

      Neither would it be correct to say that every induction by which we
      infer any truth, implies the general fact of uniformity _as
      foreknown_, even in reference to the kind of phenomena concerned. It
      implies, _either_ that this general fact is already known, _or_ that
      we may now know it: as the conclusion, the Duke of Wellington is
      mortal, drawn from the instances A, B, and C, implies either that we
      have already concluded all men to be mortal, or that we are now
      entitled to do so from the same evidence. A vast amount of confusion
      and paralogism respecting the grounds of Induction would be
      dispelled by keeping in view these simple considerations.

  110 Infra, chap. xxi.

  111 Infra, chap. xxi., xxii.

  112 In strictness, wherever the present constitution of space exists;
      which we have ample reason to believe that it does in the region of
      the fixed stars.

  113 Dr. Whewell (_Phil. of Discov._, p. 246) will not allow these and
      similar erroneous judgments to be called inductions; inasmuch as
      such superstitious fancies “were not collected from the facts by
      seeking a law of their occurrence, but were suggested by an
      imagination of the anger of superior powers, shown by such
      deviations from the ordinary course of nature.” I conceive the
      question to be, not in what manner these notions were at first
      suggested, but by what evidence they have, from time to time, been
      supposed to be substantiated. If the believers in these erroneous
      opinions had been put on their defense, they would have referred to
      experience: to the comet which preceded the assassination of Julius
      Cæsar, or to oracles and other prophecies known to have been
      fulfilled. It is by such appeals to facts that all analogous
      superstitions, even in our day, attempt to justify themselves; the
      supposed evidence of experience is necessary to their hold on the
      mind. I quite admit that the influence of such coincidences would
      not be what it is, if strength were not lent to it by an antecedent
      presumption; but this is not peculiar to such cases; preconceived
      notions of probability form part of the explanation of many other
      cases of belief on insufficient evidence. The _a priori_ prejudice
      does not prevent the erroneous opinion from being sincerely regarded
      as a legitimate conclusion from experience; though it improperly
      predisposes the mind to that interpretation of experience.

      Thus much in defense of the sort of examples objected to. But it
      would be easy to produce instances, equally adapted to the purpose,
      and in which no antecedent prejudice is at all concerned. “For many
      ages,” says Archbishop Whately, “all farmers and gardeners were
      firmly convinced—and convinced of their knowing it by
      experience—that the crops would never turn out good unless the seed
      were sown during the increase of the moon.” This was induction, but
      bad induction; just as a vicious syllogism is reasoning, but bad
      reasoning.

  114 The assertion, that any and every one of the conditions of a
      phenomenon may be and is, on some occasions and for some purposes,
      spoken of as the cause, has been disputed by an intelligent reviewer
      of this work in the _Prospective Review_ (the predecessor of the
      justly esteemed _National Review_), who maintains that “we always
      apply the word cause rather to that element in the antecedents which
      exercises _force_, and which would _tend_ at all times to produce
      the same or a similar effect to that which, under certain
      conditions, it would actually produce.” And he says, that “every one
      would feel” the expression, that the cause of a surprise was the
      sentinel’s being off his post, to be incorrect; but that the
      “allurement or force which _drew_ him off his post, might be so
      called, because in doing so it removed a resisting power which would
      have prevented the surprise.” I can not think that it would be wrong
      to say, that the event took place because the sentinel was absent,
      and yet right to say that it took place because he was bribed to be
      absent. Since the only direct effect of the bribe was his absence,
      the bribe could be called the remote cause of the surprise, only on
      the supposition that the absence was the proximate cause; nor does
      it seem to me that any one (who had not a theory to support) would
      use the one expression and reject the other.

      The reviewer observes, that when a person dies of poison, his
      possession of bodily organs is a necessary condition, but that no
      one would ever speak of it as the cause. I admit the fact; but I
      believe the reason to be, that the occasion could never arise for so
      speaking of it; for when in the inaccuracy of common discourse we
      are led to speak of some one condition of a phenomenon as its cause,
      the condition so spoken of is always one which it is at least
      possible that the hearer may require to be informed of. The
      possession of bodily organs is a known condition, and to give that
      as the answer, when asked the cause of a person’s death, would not
      supply the information sought. Once conceive that a doubt could
      exist as to his having bodily organs, or that he were to be compared
      with some being who had them not, and cases may be imagined in which
      it might be said that his possession of them was the cause of his
      death. If Faust and Mephistopheles together took poison, it might be
      said that Faust died because he was a human being, and had a body,
      while Mephistopheles survived because he was a spirit.

      It is for the same reason that no one (as the reviewer remarks)
      “calls the cause of a leap, the muscles or sinews of the body,
      though they are necessary conditions; nor the cause of a
      self-sacrifice, the knowledge which was necessary for it; nor the
      cause of writing a book, that a man has time for it, which is a
      necessary condition.” These conditions (besides that they are
      antecedent _states_, and not proximate antecedent _events_, and are
      therefore never the conditions in closest apparent proximity to the
      effect) are all of them so obviously implied, that it is hardly
      possible there should exist that necessity for insisting on them,
      which alone gives occasion for speaking of a single condition as if
      it were the cause. Wherever this necessity exists in regard to some
      one condition, and does not exist in regard to any other, I conceive
      that it is consistent with usage, when scientific accuracy is not
      aimed at, to apply the name cause to that one condition. If the only
      condition which can be supposed to be unknown is a negative
      condition, the negative condition may be spoken of as the cause. It
      might be said that a person died for want of medical advice: though
      this would not be likely to be said, unless the person was already
      understood to be ill, and in order to indicate that this negative
      circumstance was what made the illness fatal, and not the weakness
      of his constitution, or the original virulence of the disease. It
      might be said that a person was drowned because he could not swim;
      the positive condition, namely, that he fell into the water, being
      already implied in the word drowned. And here let me remark, that
      his falling into the water is in this case the only positive
      condition: all the conditions not expressly or virtually included in
      this (as that he could not swim, that nobody helped him, and so
      forth) are negative. Yet, if it were simply said that the cause of a
      man’s death was falling into the water, there would be quite as
      great a sense of impropriety in the expression, as there would be if
      it were said that the cause was his inability to swim; because,
      though the one condition is positive and the other negative, it
      would be felt that neither of them was sufficient, without the
      other, to produce death.

      With regard to the assertion that nothing is termed the cause,
      except the element which exerts active force; I waive the question
      as to the meaning of active force, and accepting the phrase in its
      popular sense, I revert to a former example, and I ask, would it be
      more agreeable to custom to say that a man fell because his foot
      slipped in climbing a ladder, or that he fell because of his weight?
      for his weight, and not the motion of his foot, was the active force
      which determined his fall. If a person walking out in a frosty day,
      stumbled and fell, it might be said that he stumbled because the
      ground was slippery, or because he was not sufficiently careful: but
      few people, I suppose, would say, that he stumbled because he
      walked. Yet the only active force concerned was that which he
      exerted in walking: the others were mere negative conditions; but
      they happened to be the only ones which there could be any necessity
      to state; for he walked, most likely, in exactly his usual manner,
      and the negative conditions made all the difference. Again, if a
      person were asked why the army of Xerxes defeated that of Leonidas,
      he would probably say, because they were a thousand times the
      number; but I do not think he would say, it was because they fought,
      though that was the element of active force. To borrow another
      example, used by Mr. Grove and by Mr. Baden Powell, the opening of
      flood-gates is said to be the cause of the flow of water; yet the
      active force is exerted by the water itself, and opening the
      flood-gates merely supplies a negative condition. The reviewer adds,
      “There are some conditions absolutely passive, and yet absolutely
      necessary to physical phenomena, viz., the relations of space and
      time; and to these no one ever applies the word cause without being
      immediately arrested by those who hear him.” Even from this
      statement I am compelled to dissent. Few persons would feel it
      incongruous to say (for example) that a secret became known because
      it was spoken of when A. B. was within hearing; which is a condition
      of space: or that the cause why one of two particular trees is
      taller than the other, is that it has been longer planted; which is
      a condition of time.

  115 There are a few exceptions; for there are some properties of objects
      which seem to be purely preventive; as the property of opaque
      bodies, by which they intercept the passage of light. This, as far
      as we are able to understand it, appears an instance not of one
      cause counteracting another by the same law whereby it produces its
      own effects, but of an agency which manifests itself in no other way
      than in defeating the effects of another agency. If we knew on what
      other relations to light, or on what peculiarities of structure,
      opacity depends, we might find that this is only an apparent, not a
      real, exception to the general proposition in the text. In any case
      it needs not affect the practical application. The formula which
      includes all the negative conditions of an effect in the single one
      of the absence of counteracting causes, is not violated by such
      cases as this; though, if all counteracting agencies were of this
      description, there would be no purpose served by employing the
      formula.

  116 I mean by this expression, the ultimate laws of nature (whatever
      they may be) as distinguished from the derivative laws and from the
      collocations. The diurnal revolution of the earth (for example) is
      not a part of the constitution of things, because nothing can be so
      called which might possibly be terminated or altered by natural
      causes.

  117 I use the words “straight line” for brevity and simplicity. In
      reality the line in question is not exactly straight, for, from the
      effect of refraction, we actually see the sun for a short interval
      during which the opaque mass of the earth is interposed in a direct
      line between the sun and our eyes; thus realizing, though but to a
      limited extent, the coveted desideratum of seeing round a corner.

_  118 Second Burnett Prize Essay_, by Principal Tulloch, p. 25.

_  119 Letters on the Philosophy of the Human Mind_, First Series, p. 219.

_  120 Essays_, pp. 206-208.

  121 To the universality which mankind are agreed in ascribing to the Law
      of Causation, there is one claim of exception, one disputed case,
      that of the Human Will; the determinations of which, a large class
      of metaphysicians are not willing to regard as following the causes
      called motives, according to as strict laws as those which they
      suppose to exist in the world of mere matter. This controverted
      point will undergo a special examination when we come to treat
      particularly of the Logic of the Moral Sciences (Book vi., chap. 2).
      In the mean time, I may remark that these metaphysicians, who, it
      must be observed, ground the main part of their objection on the
      supposed repugnance of the doctrine in question to our
      consciousness, seem to me to mistake the fact which consciousness
      testifies against. What is really in contradiction to consciousness,
      they would, I think, on strict self-examination, find to be, the
      application to human actions and volitions of the ideas involved in
      the common use of the term Necessity; which I agree with them in
      objecting to. But if they would consider that by saying that a
      person’s actions _necessarily_ follow from his character, all that
      is really meant (for no more is meant in any case whatever of
      causation) is that he invariably _does_ act in conformity to his
      character, and that any one who thoroughly knew his character could
      certainly predict how he would act in any supposable case; they
      probably would not find this doctrine either contrary to their
      experience or revolting to their feelings. And no more than this is
      contended for by any one but an Asiatic fatalist.

  122 I believe, however, the accredited authorities do suppose that
      molecular motion, equivalent in amount to that which will be
      manifested in the combustion of the coal, is actually taking place
      during the whole of the long interval, if not in the coal, yet in
      the oxygen which will then combine with it. But how purely
      hypothetical this supposition is, need hardly be remarked; I venture
      to say, unnecessarily and extravagantly hypothetical.

_  123 Lectures on Metaphysics_, vol. ii., Lect. xxxix., pp. 391-2.

      I regret that I can not invoke the authority of Sir William Hamilton
      in favor of my own opinions on Causation, as I can against the
      particular theory which I am now combating. But that acute thinker
      has a theory of Causation peculiar to himself, which has never yet,
      as far as I know, been analytically examined, but which, I venture
      to think, admits of as complete refutation as any one of the false
      or insufficient psychological theories which strew the ground in
      such numbers under his potent metaphysical scythe. (Since examined
      and controverted in the sixteenth chapter of _An Examination of Sir
      William Hamilton’s Philosophy_.)

  124 Unless we are to consider as such the following statement, by one of
      the writers quoted in the text: “In the case of mental exertion, the
      result to be accomplished is _preconsidered_ or meditated, and is
      therefore known _a priori_, or before experience.”—(Bowen’s _Lowell
      Lectures on the Application of Metaphysical and Ethical Science to
      the Evidence of Religion_. Boston, 1849.) This is merely saying that
      when we will a thing we have an idea of it. But to have an idea of
      what we wish to happen, does not imply a prophetic knowledge that it
      will happen. Perhaps it will be said that the _first time_ we
      exerted our will, when we had of course no experience of any of the
      powers residing in us, we nevertheless must already have known that
      we possessed them, since we can not will that which we do not
      believe to be in our power. But the impossibility is perhaps in the
      words only, and not in the facts; for we may _desire_ what we do not
      know to be in our power; and finding by experience that our bodies
      move according to our _desire_, we may then, and only then, pass
      into the more complicated mental state which is termed will.

      After all, even if we had an instinctive knowledge that our actions
      would follow our will, this, as Brown remarks, would prove nothing
      as to the nature of Causation. Our knowing, previous to experience,
      that an antecedent will be followed by a certain consequent, would
      not prove the relation between them to be any thing more than
      antecedence and consequence.

  125 Reid’s _Essays on the Active Powers_, Essay iv., chap. 3.

_  126 Prospective Review_ for February, 1850.

  127 Vide supra, p. 178, note.

_  128 Westminster Review_ for October, 1855.

  129 See the whole doctrine in Aristotle _de Ánimâ_, where the θρεπτικὴ
      ψυχὴ is treated as exactly equivalent to θρεπτικὴ δύναμις.

  130 It deserves notice that the parts of nature which Aristotle regards
      as representing evidence of design, are the Uniformities: the
      phenomena in so far as reducible to law. Τύχη and τὸ αὐτομάτον
      satisfy him as explanations of the variable element in phenomena,
      but their occurring according to a fixed rule can only, to his
      conceptions, be accounted for by an Intelligent Will. The common, or
      what may be called the instinctive, religious interpretation of
      nature, is the reverse of this. The events in which men
      spontaneously see the hand of a supernatural being, are those which
      can not, as they think, be reduced to a physical law. What they can
      distinctly connect with physical causes, and especially what they
      can predict, though of course ascribed to an Author of Nature, if
      they already recognize such an author, might be conceived, they
      think, to arise from a blind fatality, and in any case do not appear
      to them to bear so obviously the mark of a divine will. And this
      distinction has been countenanced by eminent writers on Natural
      Theology, in particular by Dr. Chalmers, who thinks that though
      design is present everywhere, the irresistible evidence of it is to
      be found not in the _laws_ of nature but in the collocations,
      _i.e._, in the part of nature in which it is impossible to trace any
      law. A few properties of dead matter might, he thinks, conceivably
      account for the regular and invariable succession of effects and
      causes; but that the different kinds of matter have been so placed
      as to promote beneficent ends, is what he regards as the proof of a
      Divine Providence. Mr. Baden Powell, in his Essay entitled
      “Philosophy of Creation,” has returned to the point of view of
      Aristotle and the ancients, and vigorously re-asserts the doctrine
      that the indication of design in the universe is not special
      adaptations, but Uniformity and Law, these being the evidences of
      mind, and not what appears to us to be a provision for our uses.
      While I decline to express any opinion here on this _vexata
      quæstio_, I ought not to mention Mr. Powell’s volume without the
      acknowledgment due to the philosophic spirit which pervades
      generally the three Essays composing it, forming in the case of one
      of them (the “Unity of Worlds”) an honorable contrast with the other
      dissertations, so far as they have come under my notice, which have
      appeared on either side of that controversy.

  131 In the words of Fontenelle, another celebrated Cartesian, “les
      philosophes aussi bien que le peuple avaient cru que l’âme et le
      corps agissaient réellement et physiquement l’un sur l’autre.
      Descartes vint, qui prouva que leur nature ne permettait point cette
      sorte de communication véritable, et qu’ils n’en pouvaient avoir
      qu’une apparente, dont Dieu était le Médiateur.”—(_Œuvres de
      Fontenelle_, ed. 1767, tom. v., p. 534.)

  132 I omit, for simplicity, to take into account the effect, in this
      latter case, of the diminution of pressure, in diminishing the flow
      of water through the drain; which evidently in no way affects the
      truth or applicability of the principle, since when the two causes
      act simultaneously the conditions of that diminution of pressure do
      not arise.

  133 Professor Bain adds several other well-established chemical
      generalizations: “The laws that simple substances exhibit the
      strongest affinities; that compounds are more fusible than their
      elements; that combination tends to a lower state of matter from gas
      down to solid;” and some general propositions concerning the
      circumstances which facilitate or resist chemical combination.
      (Logic, ii., 254.)

  134 Professor Bain (Logic, ii., 39) points out a class of cases, other
      than that spoken of in the text, which he thinks must be regarded as
      an exception to the Composition of Causes. “Causes that merely make
      good the collocation for bringing a prime mover into action, or that
      release a potential force, do not follow any such rule. One man may
      direct a gun upon a fort as well as three: two sparks are not more
      effectual than one in exploding a barrel of gunpowder. In medicine
      there is a certain dose that answers the end; and adding to it does
      no more good.”

      I am not sure that these cases are really exceptions. The law of
      Composition of Causes, I think, is really fulfilled, and the
      appearance to the contrary is produced by attending to the remote
      instead of the immediate effect of the causes. In the cases
      mentioned, the immediate effect of the causes in action is a
      collocation, and the duplication of the cause does double the
      quantity of collocation. Two men could raise the gun to the required
      angle twice as quickly as one, though one is enough. Two sparks put
      two sets of particles of the gunpowder into the state of intestine
      motion which makes them explode, though one is sufficient. It is the
      collocation itself that does not, by being doubled, always double
      the effect; because in many cases a certain collocation, once
      obtained, is all that is required for the production of the whole
      amount of effect which can be produced at all at the given time and
      place. Doubling the collocation with difference of time and place,
      as by pointing two guns, or exploding a second barrel after the
      first, does double the effect. This remark applies still more to Mr.
      Bain’s third example, that of a double dose of medicine; for a
      double dose of an aperient does purge more violently, and a double
      dose of laudanum does produce longer and sounder sleep. But a double
      purging, or a double amount of narcotism, may have remote effects
      different in kind from the effect of the smaller amount, reducing
      the case to that of heteropathic laws, discussed in the text.

  135 Unless, indeed, the consequent was generated, not by the antecedent,
      but by the means employed to produce the antecedent. As, however,
      these means are under our power, there is so far a probability that
      they are also sufficiently within our knowledge to enable us to
      judge whether that could be the case or not.

_  136 Discourse on the Study of Natural Philosophy_, p. 179.

  137 For this speculation, as for many other of my scientific
      illustrations, I am indebted to Professor Bain, whose subsequent
      treatise on Logic abounds with apt illustrations of all the
      inductive methods.

  138 This view of the necessary co-existence of opposite excitements
      involves a great extension of the original doctrine of two
      electricities. The early theorists assumed that, when amber was
      rubbed, the amber was made positive and the rubber negative to the
      same degree; but it never occurred to them to suppose that the
      existence of the amber charge was dependent on an opposite charge in
      the bodies with which the amber was contiguous, while the existence
      of the negative charge on the rubber was equally dependent on a
      contrary state of the surfaces that might accidentally be confronted
      with it; that, in fact, in a case of electrical excitement by
      friction, four charges were the minimum that could exist. But this
      double electrical action is essentially implied in the explanation
      now universally adopted in regard to the phenomena of the common
      electric machine.

  139 Pp. 110, 111.

  140 Infra, book iv., chap. ii., On Abstraction.

  141 I must, however, remark, that this example, which seems to militate
      against the assertion we made of the comparative inapplicability of
      the Method of Difference to cases of pure observation, is really one
      of those exceptions which, according to a proverbial expression,
      prove the general rule. For in this case, in which Nature, in her
      experiment, seems to have imitated the type of the experiments made
      by man, she has only succeeded in producing the likeness of man’s
      most imperfect experiments; namely, those in which, though he
      succeeds in producing the phenomenon, he does so by employing
      complex means, which he is unable perfectly to analyze, and can
      form, therefore, no sufficient judgment what portion of the effects
      may be due, not to the supposed cause, but to some unknown agency of
      the means by which that cause was produced. In the natural
      experiment which we are speaking of, the means used was the clearing
      off a canopy of clouds; and we certainly do not know sufficiently in
      what this process consists, or on what it depends, to be certain _a
      priori_ that it might not operate upon the deposition of dew
      independently of any thermometric effect at the earth’s surface.
      Even, therefore, in a case so favorable as this to Nature’s
      experimental talents, her experiment is of little value except in
      corroboration of a conclusion already attained through other means.

  142 In his subsequent work, _Outlines of Astronomy_ (§ 570), Sir John
      Herschel suggests another possible explanation of the acceleration
      of the revolution of a comet.

  143 Discourse, pp. 156-8, and 171.

  144 Outlines of Astronomy, § 856.

_  145 Philosophy of Discovery_, pp. 263, 264.

  146 See, on this point, the second chapter of the present book.

  147 Ante, chap. vii., § 1.

  148 It seems hardly necessary to say that the word _impinge_, as a
      general term to express collision of forces, is here used by a
      figure of speech, and not as expressive of any theory respecting the
      nature of force.

_  149 Essays on some Unsettled Questions of Political Economy_, Essay V.

  150 It is justly remarked by Professor Bain, that though the Methods of
      Agreement and Difference are not applicable to these cases, they are
      not wholly inaccessible to the Method of Concomitant Variations. “If
      a cause happens to vary alone, the effect will also vary alone: a
      cause and effect may be thus singled out under the greatest
      complications. Thus, when the appetite for food increases with the
      cold, we have a strong evidence of connection between these two
      facts, although other circumstances may operate in the same
      direction. The assigning of the respective parts of the sun and moon
      in the action of the tides may be effected, to a certain degree of
      exactness, by the variations of the amount according to the
      positions of the two attractive bodies. By a series of experiments
      of Concomitant Variations, directed to ascertain the elimination of
      nitrogen from the human body under varieties of muscular exercise,
      Dr. Parkes obtained the remarkable conclusion, that a muscle grows
      during exercise, and loses bulk during the subsequent rest.”
      (_Logic_, ii., 83.)

      It is, no doubt, often possible to single out the influencing causes
      from among a great number of mere concomitants, by noting what are
      the antecedents, a variation in which is followed by a variation in
      the effect. But when there are many influencing causes, no one of
      them greatly predominating over the rest, and especially when some
      of these are continually changing, it is scarcely ever possible to
      trace such a relation between the variations of the effect and those
      of any one cause as would enable us to assign to that cause its real
      share in the production of the effect.

  151 Bain’s _Logic_, ii., 360.

  152 What is said in the text on the applicability of the experimental
      methods to resolve particular questions of medical treatment, does
      not detract from their efficacy in ascertaining the general laws of
      the animal or human system. The functions, for example, of the
      different classes of nerves have been discovered, and probably could
      only have been discovered, by experiments on living animals.
      Observation and experiment are the ultimate basis of all knowledge:
      from them we obtain the elementary laws of life, as we obtain all
      other elementary truths. It is in dealing with the complex
      combinations that the experimental methods are for the most part
      illusory, and the deductive mode of investigation must be invoked to
      disentangle the complexity.

  153 Professor Bain, though concurring generally in the views expressed
      in this chapter, seems to estimate more highly than I do the scope
      for specific experimental evidence in politics. (_Logic_, ii.,
      333-337.) There are, it is true, as he remarks (p. 336), some cases
      “when an agent suddenly introduced is almost instantaneously
      followed by some other changes, as when the announcement of a
      diplomatic rupture between two nations is followed the same day by a
      derangement of the money-market.” But this experiment would be quite
      inconclusive merely as an experiment. It can only serve, as any
      experiment may, to verify the conclusion of a deduction. Unless we
      already knew by our knowledge of the motives which act on business
      men, that the prospect of war _tends_ to derange the money-market,
      we should never have been able to prove a connection between the two
      facts, unless after having ascertained historically that the one
      followed the other in too great a number of instances to be
      consistent with their having been recorded with due precautions.
      Whoever has carefully examined any of the attempts continually made
      to prove economic doctrines by such a recital of instances, knows
      well how futile they are. It always turns out that the circumstances
      of scarcely any of the cases have been fully stated; and that cases,
      in equal or greater numbers, have been omitted which would have
      tended to an opposite conclusion.

  154 Vide Memoir by Thomas Graham, F.R.S., Master of the Mint, “On Liquid
      Diffusion applied to Analysis,” in the _Philosophical Transactions_
      for 1862, reprinted in the _Journal of the Chemical Society_, and
      also separately as a pamphlet.

  155 It was an old generalization in surgery, that tight bandaging had a
      tendency to prevent or dissipate local inflammation. This sequence,
      being, in the progress of physiological knowledge, resolved into
      more general laws, led to the important surgical invention made by
      Dr. Arnott, the treatment of local inflammation and tumors by means
      of an equable pressure, produced by a bladder partially filled with
      air. The pressure, by keeping back the blood from the part, prevents
      the inflammation, or the tumor, from being nourished: in the case of
      inflammation, it removes the stimulus, which the organ is unfit to
      receive; in the case of tumors, by keeping back the nutritive fluid,
      it causes the absorption of matter to exceed the supply, and the
      diseased mass is gradually absorbed and disappears.

  156 Since acknowledged and reprinted in Mr. Martineau’s _Miscellanies_.

_  157 Dissertations and Discussions_, vol. i., fourth paper.

  158 Written before the rise of the new views respecting the relation of
      heat to mechanical force; but confirmed rather than contradicted by
      them.

  159 As is well remarked by Professor Bain, in the very valuable chapter
      of his Logic which treats of this subject (ii., 121), “scientific
      explanation and inductive generalization being the same thing, the
      limits of Explanation are the limits of Induction,” and “the limits
      to inductive generalization are the limits to the agreement or
      community of facts. Induction supposes similarity among phenomena;
      and when such similarity is discovered, it reduces the phenomena
      under a common statement. The similarity of terrestrial gravity to
      celestial attraction enables the two to be expressed as one
      phenomenon. The similarity between capillary attraction, solution,
      the operation of cements, etc., leads to their being regarded not as
      a plurality, but as a unity, a single causative link, the operation
      of a single agency.... If it be asked whether we can merge gravity
      itself in some still higher law, the answer must depend upon the
      facts. Are there any other forces, at present held distinct from
      gravity, that we may hope to make fraternize with it, so as to join
      in constituting a higher unity? Gravity is an attractive force; and
      another great attractive force is cohesion, or the force that binds
      together the atoms of solid matter. Might we, then, join these two
      in a still higher unity, expressed under a more comprehensive law?
      Certainly we might, but not to any advantage. The two kinds of force
      agree in the one point, attraction, but they agree in no other;
      indeed, in the manner of the attraction, they differ widely; so
      widely that we should have to state totally distinct laws for each.
      Gravity is common to all matter, and equal in amount in equal masses
      of matter, whatever be the kind; it follows the law of the diffusion
      of space from a point (the inverse square of the distance); it
      extends to distances unlimited; it is indestructible and invariable.
      Cohesion is special for each separate substance; it decreases
      according to distance much more rapidly than the inverse square,
      vanishing entirely at very small distances. Two such forces have not
      sufficient kindred to be generalized into one force; the
      generalization is only illusory; the statement of the difference
      would still make two forces; while the consideration of one would
      not in any way simplify the phenomena of the other, as happened in
      the generalization of gravity itself.”

      To the impassable limit of the explanation of laws of nature, set
      forth in the text, must therefore be added a further limitation.
      Although, when the phenomena to be explained are not, in their own
      nature, generically distinct, the attempt to refer them to the same
      cause is scientifically legitimate; yet to the success of the
      attempt it is indispensable that the cause should be shown to be
      capable of producing them according to the same law. Otherwise the
      unity of cause is a mere guess, and the generalization only a
      nominal one, which, even if admitted, would not diminish the number
      of ultimate laws of nature.

_  160 Cours de Philosophie Positive_, ii., 656.

  161 Vide supra, book iii., chap. xi.

_  162 Philosophy of Discovery_, p. 185 et seq.

  163 Comte, _Philosophie Positive_, ii., 434-437.

  164 As an example of legitimate hypothesis according to the test here
      laid down, has been justly cited that of Broussais, who, proceeding
      on the very rational principle that every disease must originate in
      some definite part or other of the organism, boldly assumed that
      certain fevers, which not being known to be local were called
      constitutional, had their origin in the mucous membrane of the
      alimentary canal. The supposition was, indeed, as is now generally
      admitted, erroneous; but he was justified in making it, since by
      deducing the consequences of the supposition, and comparing them
      with the facts of those maladies, he might be certain of disproving
      his hypothesis if it was ill founded, and might expect that the
      comparison would materially aid him in framing another more
      conformable to the phenomena.

      The doctrine now universally received that the earth is a natural
      magnet, was originally an hypothesis of the celebrated Gilbert.

      Another hypothesis, to the legitimacy of which no objection can lie,
      and which is well calculated to light the path of scientific
      inquiry, is that suggested by several recent writers, that the brain
      is a voltaic pile, and that each of its pulsations is a discharge of
      electricity through the system. It has been remarked that the
      sensation felt by the hand from the beating of a brain, bears a
      strong resemblance to a voltaic shock. And the hypothesis, if
      followed to its consequences, might afford a plausible explanation
      of many physiological facts, while there is nothing to discourage
      the hope that we may in time sufficiently understand the conditions
      of voltaic phenomena to render the truth of the hypothesis amenable
      to observation and experiment.

      The attempt to localize, in different regions of the brain, the
      physical organs of our different mental faculties and propensities,
      was, on the part of its original author, a legitimate example of a
      scientific hypothesis; and we ought not, therefore, to blame him for
      the extremely slight grounds on which he often proceeded, in an
      operation which could only be tentative, though we may regret that
      materials barely sufficient for a first rude hypothesis should have
      been hastily worked up into the vain semblance of a science. If
      there be really a connection between the scale of mental endowments
      and the various degrees of complication in the cerebral system, the
      nature of that connection was in no other way so likely to be
      brought to light as by framing, in the first instance, an hypothesis
      similar to that of Gall. But the verification of any such hypothesis
      is attended, from the peculiar nature of the phenomena, with
      difficulties which phrenologists have not shown themselves even
      competent to appreciate, much less to overcome.

      Mr. Darwin’s remarkable speculation on the Origin of Species is
      another unimpeachable example of a legitimate hypothesis. What he
      terms “natural selection” is not only a _vera causa_, but one proved
      to be capable of producing effects of the same kind with those which
      the hypothesis ascribes to it; the question of possibility is
      entirely one of degree. It is unreasonable to accuse Mr. Darwin (as
      has been done) of violating the rules of Induction. The rules of
      Induction are concerned with the conditions of Proof. Mr. Darwin has
      never pretended that his doctrine was proved. He was not bound by
      the rules of Induction, but by those of Hypothesis. And these last
      have seldom been more completely fulfilled. He has opened a path of
      inquiry full of promise, the results of which none can foresee. And
      is it not a wonderful feat of scientific knowledge and ingenuity to
      have rendered so bold a suggestion, which the first impulse of every
      one was to reject at once, admissible and discussible, even as a
      conjecture?

  165 Whewell’s _Phil. of Discovery_, pp. 275, 276.

  166 What has most contributed to accredit the hypothesis of a physical
      medium for the conveyance of light, is the certain fact that light
      _travels_ (which can not be proved of gravitation); that its
      communication is not instantaneous, but requires time; and that it
      is intercepted (which gravitation is not) by intervening objects.
      These are analogies between its phenomena and those of the
      mechanical motion of a solid or fluid substance. But we are not
      entitled to assume that mechanical motion is the only power in
      nature capable of exhibiting those attributes.

_  167 Phil. of Discovery_, p. 274.

  168 P. 271.

  169 P. 251 and the whole of Appendix G.

  170 In Dr. Whewell’s latest version of his theory (_Philosophy of
      Discovery_, p. 331) he makes a concession respecting the medium of
      the transmission of light, which, taken in conjunction with the rest
      of his doctrine on the subject, is not, I confess, very intelligible
      to me, but which goes far toward removing, if it does not actually
      remove, the whole of the difference between us. He is contending,
      against Sir William Hamilton, that all matter has weight. Sir
      William, in proof of the contrary, cited the luminiferous ether, and
      the calorific and electric fluids, “which,” he said, “we can neither
      denude of their character of substance, nor clothe with the
      attribute of weight.” “To which,” continues Dr. Whewell, “my reply
      is, that precisely because I can not clothe these agents with the
      attribute of Weight, I _do_ denude them of the character of
      Substance. They are not substances, but agencies. These Imponderable
      Agents are not properly called Imponderable Fluids. This I conceive
      that I have proved.” Nothing can be more philosophical. But if the
      luminiferous ether is not matter, and fluid matter, too, what is the
      meaning of its undulations? Can an agency undulate? Can there be
      alternate motion forward and backward of the particles of an agency?
      And does not the whole mathematical theory of the undulations imply
      them to be material? Is it not a series of deductions from the known
      properties of elastic fluids? _This_ opinion of Dr. Whewell reduces
      the undulations to a figure of speech, and the undulatory theory to
      the proposition which all must admit, that the transmission of light
      takes place according to laws which present a very striking and
      remarkable agreement with those of undulations. If Dr. Whewell is
      prepared to stand by this doctrine, I have no difference with him on
      the subject.

  171 Thus water, of which eight-ninths in weight are oxygen, dissolves
      most bodies which contain a high proportion of oxygen, such as all
      the nitrates (which have more oxygen than any others of the common
      salts), most of the sulphates, many of the carbonates, etc. Again,
      bodies largely composed of combustible elements, like hydrogen and
      carbon, are soluble in bodies of similar composition; resin, for
      instance, will dissolve in alcohol, tar in oil of turpentine. This
      empirical generalization is far from being universally true; no
      doubt because it is a remote, and therefore easily defeated, result
      of general laws too deep for us at present to penetrate; but it will
      probably in time suggest processes of inquiry, leading to the
      discovery of those laws.

  172 Or, according to Laplace’s theory, the sun and the sun’s rotation.

  173 Supra, book iii., chap. v., § 7.

  174 Supra, book iii., chap. x., § 2

  175 In the preceding discussion, the _mean_ is spoken of as if it were
      exactly the same thing with the _average_. But the mean, for
      purposes of inductive inquiry, is not the average, or arithmetical
      mean, though in a familiar illustration of the theory the difference
      may be disregarded. If the deviations on one side of the average are
      much more numerous than those on the other (these last being fewer
      but greater), the effect due to the invariable cause, as distinct
      from the variable ones, will not coincide with the average, but will
      be either below or above the average, the deviation being toward the
      side on which the greatest number of the instances are found. This
      follows from a truth, ascertained both inductively and deductively,
      that small deviations from the true central point are greatly more
      frequent than large ones. The mathematical law is, “that the most
      probable determination of one or more invariable elements from
      observation is that in which the _sum of the squares_ of the
      individual aberrations,” or deviations, “_shall be the least
      possible_.” See this principle stated, and its grounds popularly
      explained, by Sir John Herschel, in his review of Quetelet on
      Probabilities, _Essays_, p. 395 _et seq._

_  176 Essai Philosophique sur les Probabilités_, fifth Paris edition, p.
      7.

  177 It even appears to me that the calculation of chances, where there
      are no data grounded either on special experience or on special
      inference, must, in an immense majority of cases, break down, from
      sheer impossibility of assigning any principle by which to be guided
      in setting out the list of possibilities. In the case of the colored
      balls we have no difficulty in making the enumeration, because we
      ourselves determine what the possibilities shall be. But suppose a
      case more analogous to those which occur in nature: instead of three
      colors, let there be in the box all possible colors, we being
      supposed ignorant of the comparative frequency with which different
      colors occur in nature, or in the productions of art. How is the
      list of cases to be made out? Is every distinct shade to count as a
      color? If so, is the test to be a common eye, or an educated eye—a
      painter’s, for instance? On the answer to these questions would
      depend whether the chances against some particular color would be
      estimated at ten, twenty, or perhaps five hundred to one. While if
      we knew from experience that the particular color occurs on an
      average a certain number of times in every hundred or thousand, we
      should not require to know any thing either of the frequency or of
      the number of the other possibilities.

_  178 Prospective Review_ for February, 1850.

  179 “If this be not so, why do we feel so much more probability added by
      the first instance than by any single subsequent instance? Why,
      except that the first instance gives us its possibility (a cause
      _adequate_ to it), while every other only gives us the frequency of
      its conditions? If no reference to a cause be supposed, possibility
      would have no meaning; yet it is clear that, antecedent to its
      happening, we might have supposed the event impossible, _i.e._, have
      believed that there was no physical energy really existing in the
      world equal to producing it.... After the first time of happening,
      which is, then, more important to the whole probability than any
      other single instance (because proving the possibility), the
      _number_ of times becomes important as an index to the intensity or
      extent of the cause, and its independence of any particular time. If
      we took the case of a tremendous leap, for instance, and wished to
      form an estimate of the probability of its succeeding a certain
      number of times; the first instance, by showing its possibility
      (before doubtful) is of the most importance; but every succeeding
      leap shows the power to be more perfectly under control, greater and
      more invariable, and so increases the probability; and no one would
      think of reasoning in this case straight from one instance to the
      next, without referring to the physical energy which each leap
      indicated. Is it not, then, clear that we do not ever” (let us
      rather say, that we do not in an advanced state of our knowledge)
      “conclude directly from the happening of an event to the probability
      of its happening again; but that we refer to the cause, regarding
      the past cases as an index to the cause, and the cause as our guide
      to the future?”—_Ibid._

  180 The writer last quoted says that the valuation of chances by
      comparing the number of cases in which the event occurs with the
      number in which it does not occur, “would generally be wholly
      erroneous,” and “is not the true theory of probability.” It is at
      least that which forms the foundation of insurance, and of all those
      calculations of chances in the business of life which experience so
      abundantly verifies. The reason which the reviewer gives for
      rejecting the theory is, that it “would regard an event as certain
      which had hitherto never failed; which is exceedingly far from the
      truth, even for a very large number of constant successes.” This is
      not a defect in a particular theory, but in any theory of chances.
      No principle of evaluation can provide for such a case as that which
      the reviewer supposes. If an event has never once failed, in a
      number of trials sufficient to eliminate chance, it really has all
      the certainty which can be given by an empirical law; it _is_
      certain during the continuance of the same collocation of causes
      which existed during the observations. If it ever fails, it is in
      consequence of some change in that collocation. Now, no theory of
      chances will enable us to infer the future probability of an event
      from the past, if the causes in operation, capable of influencing
      the event, have intermediately undergone a change.

  181 Pp. 18, 19. The theorem is not stated by Laplace in the exact terms
      in which I have stated it; but the identity of import of the two
      modes of expression is easily demonstrable.

  182 For a fuller treatment of the many interesting questions raised by
      the theory of probabilities, I may now refer to a recent work by Mr.
      Venn, Fellow of Caius College, Cambridge, “The Logic of Chance;” one
      of the most thoughtful and philosophical treatises on any subject
      connected with Logic and Evidence which have been produced, to my
      knowledge, for many years. Some criticisms contained in it have been
      very useful to me in revising the corresponding chapters of the
      present work. In several of Mr. Venn’s opinions, however, I do not
      agree. What these are will be obvious to any reader of Mr. Venn’s
      work who is also a reader of this.

  183 Hartley’s _Observations on Man_, vol. i., p. 16. The passage is not
      in Priestley’s curtailed edition.

  184 I am happy to be able to quote the following excellent passage from
      Mr. Baden Powell’s _Essay on the Inductive Philosophy_, in
      confirmation, both in regard to history and to doctrine, of the
      statement made in the text. Speaking of the “conviction of the
      universal and permanent uniformity of nature,” Mr. Powell says (pp.
      98-100):

      “We may remark that this idea, in its proper extent, is by no means
      one of popular acceptance or natural growth. Just so far as the
      daily experience of every one goes, so far indeed he comes to
      embrace a certain persuasion of this kind, but merely to this
      limited extent, that what is going on around him at present, in his
      own narrow sphere of observation, will go on in like manner in
      future. The peasant believes that the sun which rose to-day will
      rise again to-morrow; that the seed put into the ground will be
      followed in due time by the harvest this year as it was last year,
      and the like; but has no notion of such inferences in subjects
      beyond his immediate observation. And it should be observed that
      each class of persons, in admitting this belief within the limited
      range of his own experience, though he doubt or deny it in every
      thing beyond, is, in fact, bearing unconscious testimony to its
      universal truth. Nor, again, is it only among the _most_ ignorant
      that this limitation is put upon the truth. There is a very general
      propensity to believe that every thing beyond common experience, or
      especially ascertained laws of nature, is left to the dominion of
      chance or fate or arbitrary intervention; and even to object to any
      attempted explanation by physical causes, if conjecturally thrown
      out for an apparently unaccountable phenomenon.

      “The precise doctrine of the _generalization_ of this idea of the
      uniformity of nature, so far from being obvious, natural, or
      intuitive, is utterly beyond the attainment of the many. In all the
      extent of its universality it is characteristic of the philosopher.
      It is clearly the result of philosophic cultivation and training,
      and by no means the spontaneous offspring of any primary principle
      naturally inherent in the mind, as some seem to believe. It is no
      mere vague persuasion taken up without examination, as a common
      prepossession to which we are always accustomed; on the contrary,
      all common prejudices and associations are against it. It is
      pre-eminently _an acquired idea_. It is not attained without deep
      study and reflection. The best informed philosopher is the man who
      most firmly believes it, even in opposition to received notions; its
      acceptance depends on the extent and profoundness of his inductive
      studies.”

  185 Supra, book iii., chap. iii., § 1

  186 It deserves remark, that these early generalizations did not, like
      scientific inductions, presuppose causation. What they did
      presuppose, was _uniformity_ in physical facts. But the observers
      were as ready to presume uniformity in the co-existence of facts as
      in the sequences. On the other hand, they never thought of assuming
      that this uniformity was a principle pervading all nature: their
      generalizations did not imply that there was uniformity in every
      thing, but only that as much uniformity as existed within their
      observation, existed also beyond it. The induction, fire burns, does
      not require for its validity that all nature should observe uniform
      laws, but only that there should be uniformity in one particular
      class of natural phenomena; the effects of fire on the senses and on
      combustible substances. And uniformity to this extent was not
      assumed, anterior to the experience, but proved by the experience.
      The same observed instances which proved the narrower truth, proved
      as much of the wider one as corresponded to it. It is from losing
      sight of this fact, and considering the law of causation in its full
      extent as necessarily presupposed in the very earliest
      generalizations, that persons have been led into the belief that the
      law of causation is known _a priori_, and is not itself a conclusion
      from experience.

  187 Book ii., chap. iii.

  188 One of the most rising thinkers of the new generation in France, M.
      Taine (who has given, in the _Revue des Deux Mondes_, the most
      masterly analysis, at least in one point of view, ever made of the
      present work), though he rejects, on this and similar points of
      psychology, the intuition theory in its ordinary form, nevertheless
      assigns to the law of causation, and to some other of the most
      universal laws, that certainty beyond the bounds of human
      experience, which I have not been able to accord to them. He does
      this on the faith of our faculty of abstraction, in which he seems
      to recognize an independent source of evidence, not indeed
      disclosing truths not contained in our experience, but affording an
      assurance which experience can not give, of the universality of
      those which it does contain. By abstraction M. Taine seems to think
      that we are able, not merely to analyze that part of nature which we
      see, and exhibit apart the elements which pervade it, but to
      distinguish such of them as are elements of the system of nature
      considered as a whole, not incidents belonging to our limited
      terrestrial experience. I am not sure that I fully enter into M.
      Taine’s meaning; but I confess I do not see how any mere abstract
      conception, elicited by our minds from our experience, can be
      evidence of an objective fact in universal Nature, beyond what the
      experience itself bears witness of; or how, in the process of
      interpreting in general language the testimony of experience, the
      limitations of the testimony itself can be cast off.

      Dr. Ward, in an able article in the _Dublin Review_ for October,
      1871, contends that the uniformity of nature can not be proved from
      experience, but from “transcendental considerations” only, and that,
      consequently, all physical science would be deprived of its basis,
      if such transcendental proof were impossible.

      When physical science is said to depend on the assumption that the
      course of nature is invariable, all that is meant is that the
      conclusions of physical science are not known as _absolute_ truths:
      the truth of them is _conditional_ on the uniformity of the course
      of nature; and all that the most conclusive observations and
      experiments can prove, is that the result arrived at will be true
      if, and as long as, the present laws of nature are valid. But this
      is all the assurance we require for the guidance of our conduct. Dr.
      Ward himself does not think that his transcendental proofs make it
      practically greater; for he believes, as a Catholic, that the course
      of nature not only has been, but frequently and even daily is,
      suspended by supernatural intervention.

      But though this conditional conclusiveness of the evidence of
      experience, which is sufficient for the purposes of life, is all
      that I was necessarily concerned to prove, I have given reasons for
      thinking that the uniformity, as itself a part of experience, is
      sufficiently proved to justify undoubting reliance on it. This Dr.
      Ward contests, for the following reasons:

      First (p. 315), supposing it true that there has hitherto been no
      well authenticated case of a breach in the uniformity of nature;
      “the number of natural agents constantly at work is incalculably
      large; and the observed cases of uniformity in their action must be
      immeasurably fewer than one thousandth of the whole. Scientific men,
      we assume for the moment, have discovered that in a certain
      proportion of instances—immeasurably fewer than one thousandth of
      the whole—a certain fact has prevailed; the fact of uniformity; and
      they have not found a single instance in which that fact does _not_
      prevail. Are they justified, we ask, in inferring from these
      premises that the fact is universal? Surely the question answers
      itself. Let us make a very grotesque supposition, in which, however,
      the conclusion would really be tried according to the arguments
      adduced. In some desert of Africa there is an enormous connected
      edifice, surrounding some vast space, in which dwell certain
      reasonable beings, who are unable to leave the inclosure. In this
      edifice are more than a thousand chambers, which some years ago were
      entirely locked up, and the keys no one knew where. By constant
      diligence twenty-five keys have been found, out of the whole number;
      and the corresponding chambers, situated promiscuously throughout
      the edifice, have been opened. Each chamber, when examined, is found
      to be in the precise shape of a dodecahedron. Are the inhabitants
      justified on that account in holding with certitude that the
      remaining 975 chambers are built on the same plan?”

      Not with perfect certitude, but (if the chambers to which the keys
      have been found are really “situated promiscuously”) with so high a
      degree of probability that they would be justified in acting upon
      the presumption until an exception appeared.

      Dr. Ward’s argument, however, does not touch mine as it stands in
      the text. My argument is grounded on the fact that the uniformity of
      the course of nature as a whole, is constituted by the uniform
      sequences of special effects from special natural agencies; that the
      number of these natural agencies in the part of the universe known
      to us is not incalculable, nor even extremely great; that we have
      now reason to think that at least the far greater number of them, if
      not separately, at least in some of the combinations into which they
      enter, have been made sufficiently amenable to observation, to have
      enabled us actually to ascertain some of their fixed laws; and that
      this amount of experience justifies the same degree of assurance
      that the course of nature is uniform throughout, which we previously
      had of the uniformity of sequence among the phenomena best known to
      us. This view of the subject, if correct, destroys the force of Dr.
      Ward’s first argument.

      His second argument is, that many or most persons, both scientific
      and unscientific, believe that there _are_ well authenticated cases
      of breach in the uniformity of nature, namely, miracles. Neither
      does this consideration touch what I have said in the text. I admit
      no other uniformity in the events of nature than the law of
      Causation; and (as I have explained in the chapter of this volume
      which treats of the Grounds of Disbelief) a miracle is no exception
      to that law. In every case of alleged miracle, a _new antecedent_ is
      affirmed to exist; a _counteracting cause_, namely, the volition of
      a supernatural being. To all, therefore, to whom beings with
      superhuman power over nature are a _vera causa_, a miracle is a
      _case_ of the Law of Universal Causation, not a deviation from it.

      Dr. Ward’s last, and as he says, strongest argument, is the familiar
      one of Reid, Stewart, and their followers—that whatever knowledge
      experience gives us of the past and present, it gives us none of the
      future. I confess that I see no force whatever in this argument.
      Wherein does a future fact differ from a present or a past fact,
      except in their merely momentary relation to the human beings at
      present in existence? The answer made by Priestley, in his
      _Examination of Reid_, seems to me sufficient, viz., that though we
      have had no experience of what _is_ future, we have had abundant
      experience of what _was_ future. The “leap in the dark” (as
      Professor Bain calls it) from the past to the future, is exactly as
      much in the dark and no more, as the leap from a past which we have
      personally observed, to a past which we have not. I agree with Mr.
      Bain in the opinion that the resemblance of what we have not
      experienced to what we have, is, by a law of our nature, presumed
      through the mere energy of the idea, before experience has proved
      it. This _psychological_ truth, however, is not, as Dr. Ward when
      criticising Mr. Bain appears to think, inconsistent with the
      _logical_ truth that experience does prove it. The proof comes after
      the presumption, and consists in its invariable _verification_ by
      experience when the experience arrives. The fact which while it was
      future could not be observed, having as yet no existence, is always,
      when it becomes present and _can_ be observed, found conformable to
      the past.

      Dr. M’Cosh maintains (_Examination of Mr. J. S. Mill’s Philosophy_,
      p. 257) that the uniformity of the course of nature is a different
      thing from the law of causation; and while he allows that the former
      is only proved by a long continuance of experience, and that it is
      not inconceivable nor necessarily incredible that there may be
      worlds in which it does not prevail, he considers the law of
      causation to be known intuitively. There is, however, no other
      uniformity in the events of nature than that which arises from the
      law of causation: so long therefore as there remained any doubt that
      the course of nature was uniform throughout, at least when not
      modified by the intervention of a new (supernatural) cause, a doubt
      was necessarily implied, not indeed of the reality of causation, but
      of its universality. If the uniformity of the course of nature has
      any exceptions—if any events succeed one another without fixed
      laws—to that extent the law of causation fails; there are events
      which do not depend on causes.

  189 Book i., chap. vii.

  190 In some cases, a Kind is sufficiently identified by some one
      remarkable property: but most commonly several are required; each
      property considered singly, being a joint property of that and of
      other Kinds. The color and brightness of the diamond are common to
      it with the paste from which false diamonds are made; its octohedral
      form is common to it with alum, and magnetic iron ore; but the color
      and brightness and the form together, identify its Kind: that is,
      are a mark to us that it is combustible; that when burned it
      produces carbonic acid; that it can not be cut with any known
      substance; together with many other ascertained properties, and the
      fact that there exist an indefinite number still unascertained.

  191 This doctrine of course assumes that the allotropic forms of what is
      chemically the same substance are so many different Kinds; and such,
      in the sense in which the word Kind is used in this treatise, they
      really are.

  192 Professor Bain (Logic, ii., 13) mentions two empirical laws, which
      he considers to be, with the exception of the law connecting Gravity
      with Resistance to motion, “the two most widely operating laws as
      yet discovered whereby two distinct properties are conjoined
      throughout substances generally.” The first is, “a law connecting
      Atomic Weight and Specific Heat by an inverse proportion. For equal
      weights of the simple bodies, the atomic weight multiplied by a
      number expressing the specific heat, gives a nearly uniform product.
      The products, for all the elements, are near the constant number 6.”
      The other is a law which obtains “between the specific gravity of
      substances in the gaseous state, and the atomic weights. The
      relationship of the two numbers is in some instances equality; in
      other instances the one is a multiple of the other.”

      Neither of these generalizations has the smallest appearance of
      being an ultimate law. They point unmistakably to higher laws. Since
      the heat necessary to raise to a given temperature the same weight
      of different substances (called their specific heat) is inversely as
      their atomic weight, that is, directly as the number of atoms in a
      given weight of the substance, it follows that a single atom of
      every substance requires the same amount of heat to raise it to a
      given temperature; a most interesting and important law, but a law
      of causation. The other law mentioned by Mr. Bain points to the
      conclusion, that in the gaseous state all substances contain, in the
      same space, the same number of atoms; which, as the gaseous state
      suspends all cohesive force, might naturally be expected, though it
      could not have been positively assumed. This law may also be a
      result of the mode of action of causes, namely, of molecular
      motions. The cases in which one of the numbers is not identical with
      the other, but a multiple of it, may be explained on the nowise
      unlikely supposition, that in our present estimate of the atomic
      weights of some substances, we mistake two, or three, atoms for one,
      or one for several.

  193 Dr. M’Cosh (p. 324 of his book) considers the laws of the chemical
      composition of bodies as not coming under the principle of
      Causation; and thinks it an omission in this work not to have
      provided special canons for their investigation and proof. But every
      case of chemical composition is, as I have explained, a case of
      causation. When it is said that water is composed of hydrogen and
      oxygen, the affirmation is that hydrogen and oxygen, by the action
      on one another which they exert under certain conditions, _generate_
      the properties of water. The Canons of Induction, therefore, as laid
      down in this treatise, are applicable to the case. Such special
      adaptations as the Inductive methods may require in their
      application to chemistry, or any other science, are a proper subject
      for any one who treats of the logic of the special sciences, as
      Professor Bain has done in the latter part of his work; but they do
      not appertain to General Logic.

      Dr. M’Cosh also complains (p. 325) that I have given no canons for
      those sciences in which “the end sought is not the discovery of
      Causes or of Composition, but of Classes; that is, Natural Classes.”
      Such canons could be no other than the principles and rules of
      Natural Classification, which I certainly thought that I had
      expounded at considerable length. But this is far from the only
      instance in which Dr. M’Cosh does not appear to be aware of the
      contents of the books he is criticising.

  194 Mr. De Morgan, in his _Formal Logic_, makes the just remark, that
      from two such premises as Most A are B, and Most A are C, we may
      infer with certainty that some B are C. But this is the utmost limit
      of the conclusions which can be drawn from two approximate
      generalizations, when the precise degree of their approximation to
      universality is unknown or undefined.

_  195 Rationale of Judicial Evidence_, vol. iii., p. 224.

  196 The evaluation of the chances in this statement has been objected to
      by a mathematical friend. The correct mode, in his opinion, of
      setting out the possibilities is as follows. If the thing (let us
      call it T) which is both an A and a C, is a B, something is true
      which is only true twice in every thrice, and something else which
      is only true thrice in every four times. The first fact being true
      eight times in twelve, and the second being true six times in every
      eight, and consequently six times in those eight; both facts will be
      true only six times in twelve. On the other hand, if T, although it
      is both an A and a C, is not a B, something is true which is only
      true once in every thrice, and something else which is only true
      once in every four times. The former being true four times out of
      twelve, and the latter once in every four, and therefore once in
      those four; both are only true in one case out of twelve. So that T
      is a B six times in twelve, and T is not a B, only once: making the
      comparative probabilities, not eleven to one, as I had previously
      made them, but six to one.

      In the last edition I accepted this reasoning as conclusive. More
      attentive consideration, however, has convinced me that it contains
      a fallacy.

      The objector argues, that the fact of A’s being a B is true eight
      times in twelve, and the fact of C’s being a B six times in eight,
      and consequently six times in those eight; both facts, therefore,
      are true only six times in every twelve. That is, he concludes that
      because among As taken indiscriminately only eight out of twelve are
      Bs and the remaining four are not, it must equally hold that four
      out of twelve are not Bs when the twelve are taken from the select
      portion of As which are also Cs. And by this assumption he arrives
      at the strange result, that there are fewer Bs among things which
      are both As and Cs than there are among either As or Cs taken
      indiscriminately; so that a thing which has both chances of being a
      B, is less likely to be so than if it had only the one chance or
      only the other.

      The objector (as has been acutely remarked by another correspondent)
      applies to the problem under consideration, a mode of calculation
      only suited to the reverse problem. Had the question been—If two of
      every three Bs are As and three out of every four Bs are Cs, how
      many Bs will be both As and Cs, his reasoning would have been
      correct. For the Bs that are both As and Cs must be fewer than
      either the Bs that are As or the Bs that are Cs, and to find their
      number we must abate either of these numbers in the ratio due to the
      other. But when the problem is to find, not how many Bs are both As
      and Cs, but how many things that are both As and Cs are Bs, it is
      evident that among these the proportion of Bs must be not less, but
      greater, than among things which are only A, or among things which
      are only B.

      The true theory of the chances is best found by going back to the
      scientific grounds on which the proportions rest. The degree of
      frequency of a coincidence depends on, and is a measure of, the
      frequency, combined with the efficacy, of the causes in operation
      that are favorable to it. If out of every twelve As taken
      indiscriminately eight are Bs and four are not, it is implied that
      there are causes operating on A which tend to make it a B, and that
      these causes are sufficiently constant and sufficiently powerful to
      succeed in eight out of twelve cases, but fail in the remaining
      four. So if of twelve Cs, nine are Bs and three are not, there must
      be causes of the same tendency operating on C, which succeed in nine
      cases and fail in three. Now suppose twelve cases which are both As
      and Cs. The whole twelve are now under the operation of both sets of
      causes. One set is sufficient to prevail in eight of the twelve
      cases, the other in nine. The analysis of the cases shows that six
      of the twelve will be Bs through the operation of both sets of
      causes; two more in virtue of the causes operating on A; and three
      more through those operating on C, and that there will be only one
      case in which all the causes will be inoperative. The total number,
      therefore, which are Bs will be eleven in twelve, and the evaluation
      in the text is correct.

  197 Supra, book i., chap. v.

  198 Supra, book i., chap. v., § 1, and book ii., chap, v., § 5.

  199 The axiom, “Equals subtracted from equals leave equal differences,”
      may be demonstrated from the two axioms in the text. If A = _a_ and
      B = _b_, A-B = _a-b_. For if not, let A-B = _a-b+c_. Then since B =
      _b_, adding equals to equals, A = _a+c_. But A = _a_. Therefore _a =
      a+c_, which is impossible.

      This proposition having been demonstrated, we may, by means of it,
      demonstrate the following: “If equals be added to unequals, the sums
      are unequal.” If A = _a_ and B not = _b_, A+B is not = _a+b_. For
      suppose it to be so. Then, since A = _a_ and A+B = _a+b_,
      subtracting equals from equals, B = _b_; which is contrary to the
      hypothesis.

      So again, it may be proved that two things, one of which is equal
      and the other unequal to a third thing, are unequal to one another.
      If A = _a_ and A not = B, neither is _a_ = B. For suppose it to be
      equal. Then since A = _a_ and _a_ = B, and since things equal to the
      same thing are equal to one another A = B; which is contrary to the
      hypothesis.

  200 Geometers have usually preferred to define parallel lines by the
      property of being in the same plane and never meeting. This,
      however, has rendered it necessary for them to assume, as an
      additional axiom, some other property of parallel lines; and the
      unsatisfactory manner in which properties for that purpose have been
      selected by Euclid and others has always been deemed the opprobrium
      of elementary geometry. Even as a verbal definition, equidistance is
      a fitter property to characterize parallels by, since it is the
      attribute really involved in the signification of the name. If to be
      in the same plane and never to meet were all that is meant by being
      parallel, we should feel no incongruity in speaking of a curve as
      parallel to its asymptote. The meaning of parallel lines is, lines
      which pursue exactly the same direction, and which, therefore,
      neither draw nearer nor go farther from one another; a conception
      suggested at once by the contemplation of nature. That the lines
      will never meet is of course included in the more comprehensive
      proposition that they are everywhere equally distant. And that any
      straight lines which are in the same plane and not equidistant will
      certainly meet, may be demonstrated in the most rigorous manner from
      the fundamental property of straight lines assumed in the text,
      viz., that if they set out from the same point, they diverge more
      and more without limit.

_  201 Philosophie Positive_, iii., 414-416.

  202 See the two remarkable notes (A) and (F), appended to his _Inquiry
      into the Relation of Cause and Effect_.

  203 Supra, p. 413.

  204 A writer to whom I have several times referred, gives as the
      definition of an impossibility, that which there exists in the world
      no cause adequate to produce. This definition does not take in such
      impossibilities as these—that two and two should make five; that two
      straight lines should inclose a space; or that any thing should
      begin to exist without a cause. I can think of no definition of
      impossibility comprehensive enough to include all its varieties,
      except the one which I have given: viz., An impossibility is that,
      the truth of which would conflict with a complete induction, that
      is, with the most conclusive evidence which we possess of universal
      truth.

      As to the reputed impossibilities which rest on no other grounds
      than our ignorance of any cause capable of producing the supposed
      effects; very few of them are certainly impossible, or permanently
      incredible. The facts of traveling seventy miles an hour, painless
      surgical operations, and conversing by instantaneous signals between
      London and New York, held a high place, not many years ago, among
      such impossibilities.

  205 Not, however, as might at first sight appear, 999 times as much. A
      complete analysis of the cases shows that (always assuming the
      veracity of the witness to be 9/10) in 10,000 drawings, the drawing
      of No. 79 will occur nine times, and be announced incorrectly once;
      the credibility, therefore, of the announcement of No. 79 is 9/10;
      while the drawing of a white ball will occur nine times, and be
      announced incorrectly 999 times. The credibility, therefore, of the
      announcement of white is 9/1008, and the ratio of the two 1008:10;
      the one announcement being thus only about a hundred times more
      credible than the other, instead of 999 times.

  206 Supra, book iii., chap. ii., § 3, 4, 5.

  207 Mr. Bailey has given the best statement of this theory. “The general
      name,” he says, “raises up the image sometimes of one individual of
      the class formerly seen, sometimes of another, not unfrequently of
      many individuals in succession; and it sometimes suggests an image
      made up of elements from several different objects, by a latent
      process of which I am not conscious.” (Letters on the Philosophy of
      the Human Mind, 1st series, letter 22.) But Mr. Bailey must allow
      that we carry on inductions and ratiocinations respecting the class,
      by means of this idea or conception of some one individual in it.
      This is all I require. The name of a class calls up some idea,
      through which we can, to all intents and purposes, think of the
      class as such, and not solely of an individual member of it.

  208 I have entered rather fully into this question in chap. xvii. of _An
      Examination of Sir William Hamilton’s Philosophy_, headed “The
      Doctrine of Concepts or General Notions,” which contains my last
      views on the subject.

  209 Other examples of inappropriate conceptions are given by Dr. Whewell
      (_Phil. Ind. Sc._ ii., 185) as follows: “Aristotle and his followers
      endeavored in vain to account for the mechanical relation of forces
      in the lever, by applying the _inappropriate_ geometrical
      conceptions of the properties of the circle: they failed in
      explaining the _form_ of the luminous spot made by the sun shining
      through a hole, because they applied the _inappropriate_ conception
      of a circular _quality_ in the sun’s light: they speculated to no
      purpose about the elementary composition of bodies, because they
      assumed the _inappropriate_ conception of _likeness_ between the
      elements and the compound, instead of the genuine notion of elements
      merely _determining_ the qualities of the compound.” But in these
      cases there is more than an inappropriate conception; there is a
      false conception; one which has no prototype in nature, nothing
      corresponding to it in facts. This is evident in the last two
      examples, and is equally true in the first; the “properties of the
      circle” which were referred to, being purely fantastical. There is,
      therefore, an error beyond the wrong choice of a principle of
      generalization; there is a false assumption of matters of fact. The
      attempt is made to resolve certain laws of nature into a more
      general law, that law not being one which, though real, is
      inappropriate, but one wholly imaginary.

  210 Professor Bain.

  211 This sentence having been erroneously understood as if I had meant
      to assert that belief is nothing but an irresistible association, I
      think it necessary to observe that I express no theory respecting
      the ultimate analysis either of reasoning or of belief, two of the
      most obscure points in analytical psychology. I am speaking not of
      the powers themselves, but of the previous conditions necessary to
      enable those powers to exert themselves: of which conditions I am
      contending that language is not one, senses and association being
      sufficient without it. The irresistible association theory of
      belief, and the difficulties connected with the subject, have been
      discussed at length in the notes to the new edition of Mr. James
      Mill’s _Analysis of the Phenomena of the Human Mind_.

  212 Mr. Bailey agrees with me in thinking that whenever “from something
      actually present to my senses, conjoined with past experience, I
      feel satisfied that something has happened, or will happen, or is
      happening, beyond the sphere of my personal observation,” I may with
      strict propriety be said to reason: and of course to reason
      inductively, for demonstrative reasoning is excluded by the
      circumstances of the case. (_The Theory of Reasoning_, 2d ed., p.
      27.)

_  213 Novum Organum Renovatum_, pp. 35-37.

_  214 Novum Organum Renovatum_, pp. 39, 40.

  215 P. 217, 4to edition.

  216 “E, ex, extra, extraneus, étranger, stranger.”

      Another etymological example sometimes cited is the derivation of
      the English _uncle_ from the Latin _avus_. It is scarcely possible
      for two words to bear fewer outward marks of relationship, yet there
      is but one step between them, _avus_, _avunculus_, _uncle_. So
      _pilgrim_, from _ager_: _per agrum_, _peragrinus_, _peregrinus_,
      _pellegrino_, _pilgrim_. Professor Bain gives some apt examples of
      these transitions of meaning. “The word ‘damp’ primarily signified
      moist, humid, wet. But the property is often accompanied with the
      feeling of cold or chilliness, and hence the idea of cold is
      strongly suggested by the word. This is not all. Proceeding upon the
      superadded meaning, we speak of damping a man’s ardor, a metaphor
      where the cooling is the only circumstance concerned; we go on still
      further to designate the iron slide that shuts off the draft of a
      stove, ‘the damper,’ the primary meaning being now entirely dropped.
      ‘Dry,’ in like manner, through signifying the absence of moisture,
      water, or liquidity, is applied to sulphuric acid containing water,
      although not thereby ceasing to be a moist, wet, or liquid
      substance.” So in the phrases, dry sherry, or Champagne.

      “ ‘Street,’ originally a paved way, with or without houses, has been
      extended to roads lined with houses, whether paved or unpaved.
      ‘Impertinent’ signified at first irrelevant, alien to the purpose in
      hand: through which it has come to mean, meddling, intrusive,
      unmannerly, insolent.” (_Logic_, ii., 173, 174.)

  217 Pp. 226, 227.

_  218 Essays_, p. 214.

_  219 Essays_, p. 215.

  220 Though no such evil consequences as take place in these instances
      are likely to arise from the modern freak of writing _sanatory_
      instead of sanitary, it deserves notice as a charming specimen of
      pedantry ingrafted upon ignorance. Those who thus undertake to
      correct the spelling of the classical English writers, are not aware
      that the meaning of _sanatory_, if there were such a word in the
      language, would have reference not to the preservation of health,
      but to the cure of disease.

_  221 Historical Introduction_, vol. i., pp. 66-68.

_  222 History of Scientific Ideas_, ii., 110, 111.

_  223 History of Scientific Ideas_, ii., 111-113.

_  224 Nov. Org. Renov._, pp. 286, 287.

_  225 History of Scientific Ideas_, ii., 120-122.

_  226 Nov. Org. Renov._, p. 274.

_  227 Hist. Sc. Id._, i. 133.

  228 Dr. Whewell, in his reply (_Philosophy of Discovery_, p. 270) says
      that he “stopped short of, or rather passed by, the doctrine of a
      series of organized beings,” because he “thought it bad and narrow
      philosophy.” If he did, it was evidently without understanding this
      form of the doctrine; for he proceeds to quote a passage from his
      “History,” in which the doctrine he condemns is designated as that
      of “a mere linear progression in nature, which would place each
      genus in contact only with the preceding and succeeding ones.” Now
      the series treated of in the text agrees with this linear
      progression in nothing whatever but in being a progression.

  229 Supra, p. 137.

_  230 Vulgar Errors_, book v., chap. 21.

_  231 Pharmacologia_, Historical Introduction, p. 16.

  232 The author of one of the Bridgewater Treatises has fallen, as it
      seems to me, into a similar fallacy when, after arguing in rather a
      curious way to prove that matter may exist without any of the known
      properties of matter, and may therefore be changeable, he concludes
      that it can not be eternal, because “eternal (passive) existence
      necessarily involves incapability of change.” I believe it would be
      difficult to point out any other connection between the facts of
      eternity and unchangeableness, than a strong association between the
      two ideas. Most of the _a priori_ arguments, both religious and
      anti-religious, on the origin of things, are fallacies drawn from
      the same source.

  233 Supra, book ii., chap. v., § 6, and chap. vii., § 1, 2, 3, 4. See
      also _Examination of Sir William Hamilton’s Philosophy_, chap. vi.
      and elsewhere.

  234 It seems that this doctrine was, before the time I have mentioned,
      disputed by some thinkers. Dr. Ward mentions Scotus, Vasquez, Biel,
      Francis Lugo, and Valentia.

  235 I quote this passage from Playfair’s celebrated _Dissertation on the
      Progress of Mathematical and Physical Science_.

  236 This statement I must now correct, as too unqualified. The maxim in
      question was maintained with full conviction by no less an authority
      than Sir William Hamilton. See my _Examination_, chap. xxiv.

_  237 Nouveaux Essais sur l’Entendement Humain—Avant-propos._ (Œuvres,
      Paris ed., 1842, vol. i., p. 19.)

  238 This doctrine also was accepted as true, and conclusions were
      grounded on it, by Sir William Hamilton. See _Examination_, chap.
      xxiv.

  239 Not that of Leibnitz, but the principle commonly appealed to under
      that name by mathematicians.

_  240 Dissertation_, p. 27.

_  241 Hist. Ind. Sc._, Book i., chap. i.

_  242 Novum Organum_, Aph. 75.

  243 Supra, book iii., chap. vii., § 4.

  244 It is hardly needful to remark that nothing is here intended to be
      said against the possibility at some future period of making gold—by
      first discovering it to be a compound, and putting together its
      different elements or ingredients. But this is a totally different
      idea from that of the seekers of the grand arcanum.

_  245 Pharmacologia_, pp. 43-45.

  246 Vol. i., chap. 8.

_  247 Nov. Org._, Aph. 46.

  248 Playfair’s _Dissertation_, sect. 4.

_  249 Nov. Org. Renov._, p. 61.

_  250 Pharmacologia_, p. 21.

_  251 Pharmacologia_, pp. 23, 24.

  252 Ibid., p. 28.

  253 Ibid., p. 62.

  254 Ibid., pp. 61, 62.

_  255 Supra_, p. 450.

_  256 Elements of the Philosophy of the Mind_, vol. ii., chap. 4, sect.
      5.

  257 “Thus Fourcroy,” says Dr. Paris, “explained the operation of mercury
      by its specific gravity, and the advocates of this doctrine favored
      the general introduction of the preparations of iron, especially in
      scirrhus of the spleen or liver, upon the same hypothetical
      principle; for, say they, whatever is most forcible in removing the
      obstruction must be the most proper instrument of cure: such is
      steel, which, besides the attenuating power with which it is
      furnished, has still a greater force in this case from the gravity
      of its particles, which, being seven times specifically heavier than
      any vegetable, acts in proportion with a stronger impulse, and
      therefore is a more powerful deobstruent. This may be taken as a
      specimen of the style in which these mechanical physicians reasoned
      and practiced.”—_Pharmacologia_, pp. 38, 39.

_  258 Pharmacologia_, pp. 39, 40.

  259 I quote from Dr. Whewell’s _Hist. Ind. Sc._, 3d ed., i., 129.

_  260 Hist. Ind. Sc._, i., 52.

_  261 Nov. Org._, Aph. 60.

  262 “An advocate,” says Mr. De Morgan (_Formal Logic_, p. 270), “is
      sometimes guilty of the argument _à dicto secundum quid ad dictum
      simpliciter_: it is his business to do for his client all that his
      client might _honestly_ do for himself. Is not the word in italics
      frequently omitted? _Might_ any man honestly try to do for himself
      all that counsel frequently try to do for him? We are often reminded
      of the two men who stole the leg of mutton; one could swear he had
      not got it, the other that he had not taken it. The counsel is doing
      his duty by his client, the client has left the matter to his
      counsel. Between the unexecuted intention of the client, and the
      unintended execution of the counsel, there may be a wrong done, and,
      if we are to believe the usual maxims, no wrong-doer.”

      The same writer justly remarks (p. 251) that there is a converse
      fallacy, _à dicto simpliciter ad dictum secundum quid_, called by
      the scholastic logicians _fallacia accidentis_; and another which
      may be called _à dicto secundum quid ad dictum secundum alterum
      quid_ (p. 265). For apt instances of both, I must refer the reader
      to Mr. De Morgan’s able chapter on Fallacies.

  263 An example of this fallacy is the popular error that _strong_ drink
      must be a cause of _strength_. There is here fallacy within fallacy;
      for granting that the words “strong” and “strength” were not (as
      they are) applied in a totally different sense to fermented liquors
      and to the human body, there would still be involved the error of
      supposing that an effect must be like its cause; that the conditions
      of a phenomenon are likely to resemble the phenomenon itself; which
      we have already treated of as an _a priori_ fallacy of the first
      rank. As well might it be supposed that a strong poison will make
      the person who takes it strong.

  264 In his later editions, Archbishop Whately confines the name of
      Petitio Principii “to those cases in which one of the premises
      either is manifestly the same in sense with the conclusion, or is
      actually proved from it, or is such as the persons you are
      addressing are not likely to know, or to admit, except as an
      inference from the conclusion; as, _e.g._, if any one should infer
      the authenticity of a certain history, from its recording such and
      such facts, the reality of which rests on the evidence of that
      history.”

  265 No longer even a probable hypothesis, since the establishment of the
      atomic theory; it being now certain that the integral particles of
      different substances gravitate unequally. It is true that these
      particles, though real _minima_ for the purposes of chemical
      combination, may not be the ultimate particles of the substance; and
      this doubt alone renders the hypothesis admissible, even as an
      hypothesis.

_  266 Hist. Ind. Sc._, i., 34.

  267 “And coxcombs vanquish Berkeley with a grin.”

  268 Some arguments and explanations, supplementary to those in the text,
      will be found in _An Examination of Sir William Hamilton’s
      Philosophy_, chap. xxvi.

_  269 Supra_, p. 424.

  270 When this chapter was written, Professor Bain had not yet published
      even the first part (“The Senses and the Intellect”) of his profound
      Treatise on the Mind. In this the laws of association have been more
      comprehensively stated and more largely exemplified than by any
      previous writer; and the work, having been completed by the
      publication of “The Emotions and the Will,” may now be referred to
      as incomparably the most complete analytical exposition of the
      mental phenomena, on the basis of a legitimate Induction, which has
      yet been produced. More recently still, Mr. Bain has joined with me
      in appending to a new edition of the “Analysis,” notes intended to
      bring up the analytic science of Mind to its latest improvements.

      Many striking applications of the laws of association to the
      explanation of complex mental phenomena are also to be found in Mr.
      Herbert Spencer’s “Principles of Psychology.”

  271 In the case of the moral sentiments the place of direct experiment
      is to a considerable extent supplied by historical experience, and
      we are able to trace with a tolerable approach to certainty the
      particular associations by which those sentiments are engendered.
      This has been attempted, so far as respects the sentiment of
      justice, in a little work by the present author, entitled
      _Utilitarianism_.

  272 The most favorable cases for making such approximate generalizations
      are what may be termed collective instances; where we are
      fortunately enabled to see the whole class respecting which we are
      inquiring in action at once, and, from the qualities displayed by
      the collective body, are able to judge what must be the qualities of
      the majority of the individuals composing it. Thus the character of
      a nation is shown in its acts as a nation; not so much in the acts
      of its government, for those are much influenced by other causes;
      but in the current popular maxims, and other marks of the general
      direction of public opinion; in the character of the persons or
      writings that are held in permanent esteem or admiration; in laws
      and institutions, so far as they are the work of the nation itself,
      or are acknowledged and supported by it; and so forth. But even here
      there is a large margin of doubt and uncertainty. These things are
      liable to be influenced by many circumstances; they are partially
      determined by the distinctive qualities of that nation or body of
      persons, but partly also by external causes which would influence
      any other body of persons in the same manner. In order, therefore,
      to make the experiment really complete, we ought to be able to try
      it without variation upon other nations: to try how Englishmen would
      act or feel if placed in the same circumstances in which we have
      supposed Frenchmen to be placed; to apply, in short, the Method of
      Differences as well as that of Agreement. Now these experiments we
      can not try, nor even approximate to.

  273 “To which,” says Dr. Whewell, “we may add, that it is certain, from
      the history of the subject, that in that case the hypothesis would
      never have been framed at all.”

      Dr. Whewell (_Philosophy of Discovery_, pp. 277-282) defends Bacon’s
      rule against the preceding strictures. But his defense consists only
      in asserting and exemplifying a proposition which I had myself
      stated, viz., that though the largest generalizations may be the
      earliest made, they are not at first seen in their entire
      generality, but acquire it by degrees, as they are found to explain
      one class after another of phenomena. The laws of motion, for
      example, were not known to extend to the celestial regions, until
      the motions of the celestial bodies had been deduced from them.
      This, however, does not in any way affect the fact, that the middle
      principles of astronomy, the central force, for example, and the law
      of the inverse square, could not have been discovered, if the laws
      of motion, which are so much more universal, had not been known
      first. On Bacon’s system of step-by-step generalization, it would be
      impossible in any science to ascend higher than the empirical laws;
      a remark which Dr. Whewell’s own Inductive Tables, referred to by
      him in support of his argument, amply bear out.

_  274 Supra_, page 317 to the end of the chapter.

_  275 Biographia Literaria_, i., 214.

_  276 Supra_, p. 321.

_  277 Essays on some Unsettled Questions of Political Economy_, pp.
      137-140.

  278 The quotations in this paragraph are from a paper written by the
      author, and published in a periodical in 1834.

_  279 Cours de Philosophie Positive_, iv., 325-29.

  280 Since reprinted entire in _Dissertations and Discussions_, as the
      concluding paper of the first volume.

  281 Written and first published in 1840.

  282 This great generalization is often unfavorably criticised (as by Dr.
      Whewell, for instance) under a misapprehension of its real import.
      The doctrine, that the theological explanation of phenomena belongs
      only to the infancy of our knowledge of them, ought not to be
      construed as if it was equivalent to the assertion, that mankind, as
      their knowledge advances, will necessarily cease to believe in any
      kind of theology. This was M. Comte’s opinion; but it is by no means
      implied in his fundamental theorem. All that is implied is, that in
      an advanced state of human knowledge, no other Ruler of the World
      will be acknowledged than one who rules by universal laws, and does
      not at all, or does not unless in very peculiar cases, produce
      events by special interpositions. Originally all natural events were
      ascribed to such interpositions. At present every educated person
      rejects this explanation in regard to all classes of phenomena of
      which the laws have been fully ascertained; though some have not yet
      reached the point of referring all phenomena to the idea of Law, but
      believe that rain and sunshine, famine and pestilence, victory and
      defeat, death and life, are issues which the Creator does not leave
      to the operation of his general laws, but reserves to be decided by
      express acts of volition. M. Comte’s theory is the negation of this
      doctrine.

      Dr. Whewell equally misunderstands M. Comte’s doctrine respecting
      the second or metaphysical stage of speculation. M. Comte did not
      mean that “discussions concerning ideas” are limited to an early
      stage of inquiry, and cease when science enters into the positive
      stage. (_Philosophy of Discovery_, pp. 226 et seq.) In all M.
      Comte’s speculations as much stress is laid on the process of
      clearing up our conceptions as on the ascertainment of facts. When
      M. Comte speaks of the metaphysical stage of speculation, he means
      the stage in which men speak of “Nature” and other abstractions as
      if they were active forces, producing effects; when Nature is said
      to do this, or forbid that; when Nature’s horror of a vacuum,
      Nature’s non-admission of a break, Nature’s _vis medicatrix_, were
      offered as explanations of phenomena; when the qualities of things
      were mistaken for real entities dwelling in the things; when the
      phenomena of living bodies were thought to be accounted for by being
      referred to a “vital force;” when, in short, the abstract names of
      phenomena were mistaken for the causes of their existence. In this
      sense of the word it can not be reasonably denied that the
      metaphysical explanation of phenomena, equally with the theological,
      gives way before the advance of real science.

      That the final, or positive stage, as conceived by M. Comte, has
      been equally misunderstood, and that, notwithstanding some
      expressions open to just criticism, M. Comte never dreamed of
      denying the legitimacy of inquiry into all causes which are
      accessible to human investigation, I have pointed out in a former
      place.

  283 Buckle’s _History of Civilization_, i., 30.

  284 I have been assured by an intimate friend of Mr. Buckle that he
      would not have withheld his assent from these remarks, and that he
      never intended to affirm or imply that mankind are not progressive
      in their moral as well as in their intellectual qualities. “In
      dealing with his problem, he availed himself of the artifice
      resorted to by the Political Economist, who leaves out of
      consideration the generous and benevolent sentiments, and founds his
      science on the proposition that mankind are actuated by acquisitive
      propensities alone,” not because such is the fact, but because it is
      necessary to begin by treating the principal influence as if it was
      the sole one, and make the due corrections afterward. “He desired to
      make abstraction of the intellect as the determining and dynamical
      element of the progression, eliminating the more dependent set of
      conditions, and treating the more active one as if it were an
      entirely independent variable.”

      The same friend of Mr. Buckle states that when he used expressions
      which seemed to exaggerate the influence of general at the expense
      of special causes, and especially at the expense of the influence of
      individual minds, Mr. Buckle really intended no more than to affirm
      emphatically that the greatest men can not effect great changes in
      human affairs unless the general mind has been in some considerable
      degree prepared for them by the general circumstances of the age; a
      truth which, of course, no one thinks of denying. And there
      certainly are passages in Mr. Buckle’s writings which speak of the
      influence exercised by great individual intellects in as strong
      terms as could be desired.

  285 Essay on Dryden, in Miscellaneous Writings, i., 186.

  286 In the _Cornhill Magazine_ for June and July, 1861.

  287 It is almost superfluous to observe, that there is another meaning
      of the word Art, in which it may be said to denote the poetical
      department or aspect of things in general, in contradistinction to
      the scientific. In the text, the word is used in its older, and I
      hope, not yet obsolete sense.

  288 Professor Bain and others call the selection from the truths of
      science made for the purposes of an art, a Practical Science, and
      confine the name Art to the actual rules.

  289 The word Teleology is also, but inconveniently and improperly,
      employed by some writers as a name for the attempt to explain the
      phenomena of the universe from final causes.

  290 For an express discussion and vindication of this principle, see the
      little volume entitled “Utilitarianism.”





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