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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