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Title: A System of Logic: Ratiocinative and Inductive - 7th Edition, Vol. I
Author: Mill, John Stuart, 1806-1873
Language: English
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*** Start of this LibraryBlog Digital Book "A System of Logic: Ratiocinative and Inductive - 7th Edition, Vol. I" ***















This book makes no pretence 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 defence
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 endeavoured to combat their
theory in the manner in which Diogenes confuted the sceptical reasonings
against the possibility of motion; remembering that Diogenes' 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 endeavoured 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 towards 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.


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 cancelled 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 favourable 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 defence.

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. In the present (seventh) edition, a few further corrections
have been made, but no material additions.


[1] In the later editions of Archbishop Whately's _Logic_, he states his
meaning to be, not that "rules" for the ascertainment of truths by
inductive investigation cannot be laid down, or that they may not be "of
eminent service," but that they "must always be comparatively vague and
general, and incapable of being built up into a regular demonstrative
theory like that of the Syllogism." (Book IV. ch. iv. § 3.) And he
observes, that to devise a system for this purpose, capable of being
"brought into a scientific form," would be an achievement which "he must
be more sanguine than scientific who expects." (Book IV. ch. ii. § 4.)
To effect this, however, being the express object of the portion of the
present work which treats of Induction, the words in the text are no
overstatement of the difference of opinion between Archbishop Whately
and me on the subject.

[2] Now forming a chapter in his volume on _The Philosophy of



  § 1. A definition at the commencement of a subject must be
       provisional                                                    1

    2. Is logic the art and science of reasoning?                     2

    3. Or the art and science of the pursuit of truth?                3

    4. Logic is concerned with inferences, not with intuitive truths  5

    5. Relation of logic to the other sciences                        8

    6. Its utility, how shown                                        10

    7. Definition of logic stated and illustrated                    11



  CHAPTER I. _Of the Necessity of commencing with an
  Analysis of Language._

  § 1. Theory of names, why a necessary part of logic                17

    2. First step in the analysis of Propositions                    18

    3. Names must be studied before Things                           21

  CHAPTER II. _Of Names._

  § 1. Names are names of things, not of our ideas                   23

    2. Words which are not names, but parts of names                 24

    3. General and Singular names                                    26

    4. Concrete and Abstract                                         29

    5. Connotative and Non-connotative                               31

    6. Positive and Negative                                         42

    7. Relative and Absolute                                         44

    8. Univocal and Æquivocal                                        47

  CHAPTER III. _Of the Things denoted by Names._

  § 1. Necessity of an enumeration of Nameable Things. The
       Categories of Aristotle                                       49

    2. Ambiguity of the most general names                           51

    3. Feelings, or states of consciousness                          54

    4. Feelings must be distinguished from their physical
       antecedents. Perceptions, what                                56

    5. Volitions, and Actions, what                                  58

    6. Substance and Attribute                                       59

    7. Body                                                          61

    8. Mind                                                          67

    9. Qualities                                                     69

   10. Relations                                                     72

   11. Resemblance                                                   74

   12. Quantity                                                      78

   13. All attributes of bodies are grounded on states of
       consciousness                                                 79

   14. So also all attributes of mind                                80

   15. Recapitulation                                                81

  CHAPTER IV. _Of Propositions._

  § 1. Nature and office of the copula                               85

    2. Affirmative and Negative propositions                         87

    3. Simple and Complex                                            89

    4. Universal, Particular, and Singular                           93

  CHAPTER V. _Of the Import of Propositions._

  § 1. Doctrine that a proposition is the expression of a relation
       between two ideas                                             96

    2. Doctrine that it is the expression of a relation between the
       meanings of two names                                         99

    3. Doctrine that it consists in referring something to, or
       excluding something from, a class                            103

    4. What it really is                                            107

    5. It asserts (or denies) a sequence, a coexistence, a simple
       existence, a causation                                       110

    6. --or a resemblance                                           112

    7. Propositions of which the terms are abstract                 115

  CHAPTER VI. _Of Propositions merely Verbal._

  § 1. Essential and Accidental propositions                        119

    2. All essential propositions are identical propositions        120

    3. Individuals have no essences                                 124

    4. Real propositions, how distinguished from verbal             126

    5. Two modes of representing the import of a Real proposition   127

  CHAPTER VII. _Of the Nature of Classification, and
  the Five Predicables._

  § 1. Classification, how connected with Naming                    129

    2. The Predicables, what                                        131

    3. Genus and Species                                            131

    4. Kinds have a real existence in nature                        134

    5. Differentia                                                  139

    6. Differentiæ for general purposes, and differentiæ for
       special or technical purposes                                141

    7. Proprium                                                     144

    8. Accidens                                                     146

  CHAPTER VIII. _Of Definition._

  § 1. A definition, what                                           148

    2. Every name can be defined, whose meaning is susceptible
       of analysis                                                  150

    3. Complete, how distinguished from incomplete definitions      152

    4. --and from descriptions                                      154

    5. What are called definitions of Things, are definitions of
       Names with an implied assumption of the existence of
       Things corresponding to them                                 157

    6. --even when such things do not in reality exist              165

    7. Definitions, though of names only, must be grounded on
       knowledge of the corresponding Things                        167



  CHAPTER I. _Of Inference, or Reasoning, in general._

  § 1. Retrospect of the preceding book                             175

    2. Inferences improperly so called                              177

    3. Inferences proper, distinguished into inductions and
       ratiocinations                                               181

  CHAPTER II. _Of Ratiocination, or Syllogism._

  § 1. Analysis of the Syllogism                                    184

    2. The _dictum de omni_ not the foundation of reasoning,
       but a mere identical proposition                             191

    3. What is the really fundamental axiom of Ratiocination        196

    4. The other form of the axiom                                  199

  CHAPTER III. _Of the Functions, and Logical Value, of the

  § 1. Is the syllogism a _petitio principii_?                      202

    2. Insufficiency of the common theory                           203

    3. All inference is from particulars to particulars             205

    4. General propositions are a record of such inferences, and
       the rules of the syllogism are rules for the interpretation
       of the record                                                214

    5. The syllogism not the type of reasoning, but a test of it    218

    6. The true type, what                                          222

    7. Relation between Induction and Deduction                     226

    8. Objections answered                                          227

    9. Of Formal Logic, and its relation to the Logic of Truth      231

  CHAPTER IV. _Of Trains of Reasoning, and Deductive

  § 1. For what purpose trains of reasoning exist                   234

    2. A train of reasoning is a series of inductive inferences     234

    3. --from particulars to particulars through marks of marks     237

    4. Why there are deductive sciences                             240

    5. Why other sciences still remain experimental                 244

    6. Experimental sciences may become deductive by the progress
       of experiment                                                246

    7. In what manner this usually takes place                      247

  CHAPTER V. _Of Demonstration, and Necessary Truths._

  § 1. The Theorems of geometry are necessary truths only in
       the sense of necessarily following from hypotheses           251

    2. Those hypotheses are real facts with some of their
       circumstances exaggerated or omitted                         255

    3. Some of the first principles of geometry are axioms, and
       these are not hypothetical                                   256

    4. --but are experimental truths                                258

    5. An objection answered                                        261

    6. Dr. Whewell's opinions on axioms examined                    264

  CHAPTER VI. _The same Subject continued._

  § 1. All deductive sciences are inductive                         281

    2. The propositions of the science of number are not verbal,
       but generalizations from experience                          284

    3. In what sense hypothetical                                   289

    4. The characteristic property of demonstrative science is to
       be hypothetical                                              290

    5. Definition of demonstrative evidence                         292

  CHAPTER VII. _Examination of some Opinions opposed to
  the preceding doctrines._

  § 1. Doctrine of the Universal Postulate                          294

    2. The test of inconceivability does not represent the
       aggregate of past experience                                 296

    3. --nor is implied in every process of thought                 299

    4. Sir W. Hamilton's opinion on the Principles of
       Contradiction and Excluded Middle                            306



  CHAPTER I. _Preliminary Observations on Induction in general._

  § 1. Importance of an Inductive Logic                             313

    2. The logic of science is also that of business and life       314

  CHAPTER II. _Of Inductions improperly so called._

  § 1. Inductions distinguished from verbal transformations         319

    2. --from inductions, falsely so called, in mathematics         321

    3. --and from descriptions                                      323

    4. Examination of Dr. Whewell's theory of Induction             326

    5. Further illustration of the preceding remarks                336

  CHAPTER III. _On the Ground of Induction._

  § 1. Axiom of the uniformity of the course of nature              341

    2. Not true in every sense. Induction _per enumerationem
       simplicem_                                                   346

    3. The question of Inductive Logic stated                       348

  CHAPTER IV. _Of Laws of Nature._

  § 1. The general regularity in nature is a tissue of partial
       regularities, called laws                                    351

    2. Scientific induction must be grounded on previous
       spontaneous inductions                                       355

    3. Are there any inductions fitted to be a test of all others?  357

  CHAPTER V. _Of the Law of Universal Causation._

  § 1. The universal law of successive phenomena is the Law of
       Causation                                                    360

    2. --_i.e._ the law that every consequent has an invariable
       antecedent                                                   363

    3. The cause of a phenomenon is the assemblage of its
       conditions                                                   365

    4. The distinction of agent and patient illusory                373

    5. The cause is not the invariable antecedent, but the
       _unconditional_ invariable antecedent                        375

    6. Can a cause be simultaneous with its effect?                 380

    7. Idea of a Permanent Cause, or original natural agent         383

    8. Uniformities of coexistence between effects of different
       permanent causes, are not laws                               386

    9. Doctrine that volition is an efficient cause, examined       387

  CHAPTER VI. _Of the Composition of Causes._

  § 1. Two modes of the conjunct action of causes, the mechanical
       and the chemical                                             405

    2. The composition of causes the general rule; the other case
       exceptional                                                  408

    3. Are effects proportional to their causes?                    412

  CHAPTER VII. _Of Observation and Experiment._

  § 1. The first step of inductive inquiry is a mental analysis of
       complex phenomena into their elements                        414

    2. The next is an actual separation of those elements           416

    3. Advantages of experiment over observation                    417

    4. Advantages of observation over experiment                    420

  CHAPTER VIII. _Of the Four Methods of Experimental

  § 1. Method of Agreement                                          425

    2. Method of Difference                                         428

    3. Mutual relation of these two methods                         429

    4. Joint Method of Agreement and Difference                     433

    5. Method of Residues                                           436

    6. Method of Concomitant Variations                             437

    7. Limitations of this last method                              443

  CHAPTER IX. _Miscellaneous Examples of the Four Methods._

  § 1. Liebig's theory of metallic poisons                          449

    2. Theory of induced electricity                                453

    3. Dr. Wells' theory of dew                                     457

    4. Dr. Brown-Séquard's theory of cadaveric rigidity             465

    5. Examples of the Method of Residues                           471

    6. Dr. Whewell's objections to the Four Methods                 475

  CHAPTER X. _Of Plurality of Causes; and of the Intermixture
  of Effects._

  § 1. One effect may have several causes                           482

    2. --which is the source of a characteristic imperfection of
       the Method of Agreement                                      483

    3. Plurality of Causes, how ascertained                         487

    4. Concurrence of Causes which do not compound their effects    489

    5. Difficulties of the investigation, when causes compound
       their effects                                                494

    6. Three modes of investigating the laws of complex effects     499

    7. The method of simple observation inapplicable                500

    8. The purely experimental method inapplicable                  501

  CHAPTER XI. _Of the Deductive Method._

  § 1. First stage; ascertainment of the laws of the separate
       causes by direct induction                                   507

    2. Second stage; ratiocination from the simple laws of the
       complex cases                                                512

    3. Third stage; verification by specific experience             514

  CHAPTER XII. _Of the Explanation of Laws of Nature._

  § 1. Explanation defined                                          518

    2. First mode of explanation, by resolving the law of a complex
       effect into the laws of the concurrent causes and
       the fact of their coexistence                                518

    3. Second mode; by the detection of an intermediate link in
       the sequence                                                 519

    4. Laws are always resolved into laws more general than
       themselves                                                   520

    5. Third mode; the subsumption of less general laws under
       a more general one                                           524

    6. What the explanation of a law of nature amounts to           526

  CHAPTER XIII. _Miscellaneous Examples of the Explanation of
  Laws of Nature._

  § 1. The general theories of the sciences                         529

    2. Examples from chemical speculations                          531

    3. Example from Dr. Brown-Séquard's researches on the
       nervous system                                               533

    4. Examples of following newly-discovered laws into their
       complex manifestations                                       534

    5. Examples of empirical generalizations, afterwards confirmed
       and explained deductively                                    536

    6. Example from mental science                                  538

    7. Tendency of all the sciences to become deductive             539


§ 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 favour.

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 anything, 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 anything 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 cannot 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 these volumes.

§ 2. Logic has often been called the Art of Reasoning. A writer[1] 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 connexion 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;[2] 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

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 cannot
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 coloured surface; that when we fancy we see distance,
all we really see is certain variations of apparent size, and degrees of
faintness of colour; 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
colour of the object as they appear at the time, and the size and colour
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

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
anything 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
analysing 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
_à 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 afterwards 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 coextensive 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 fulfils
these conditions, or whether facts can be found which fulfil 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 Bacon so expressively called it,
_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 everything 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 farther 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 marshalling
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 connexion 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
towards 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 analyse 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, analyse 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 analyse 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 connexion 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 cannot, 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 favourable to the adoption of some one
opinion, on these controverted subjects, rather than another. For
metaphysics, in endeavouring 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.[4]


[1] Archbishop Whately.

[2] I use these terms indiscriminately, because, for the purpose in
view, there is no need for making any distinction between them. But
metaphysicians usually restrict the name Intuition to the direct
knowledge we are supposed to have of things external to our minds, and
Consciousness to our knowledge of our own mental phenomena.

[3] This important theory has of late been called in question by a
writer of deserved reputation, Mr. Samuel Bailey; but I do not conceive
that the grounds on which it has been admitted as an established
doctrine for a century past, have been at all shaken by that gentleman's
objections. I have elsewhere said what appeared to me necessary in reply
to his arguments. (_Westminster Review_ for October 1842; reprinted in
_Dissertations and Discussions_, vol. ii.)

[4] The view taken in the text, of the definition and purpose of Logic,
stands in marked opposition to that of the school of philosophy which,
in this country, is represented by the writings of Sir William Hamilton
and of his numerous pupils. Logic, as this school conceives it, is "the
Science of the Formal Laws of Thought;" a definition framed for the
express purpose of excluding, as irrelevant to Logic, whatever relates
to Belief and Disbelief, or to the pursuit of truth as such, and
restricting the science to that very limited portion of its total
province, which has reference to the conditions, not of Truth, but of
Consistency. What I have thought it useful to say in opposition to this
limitation of the field of Logic, has been said at some length in a
separate work, first published in 1865, and entitled _An Examination of
Sir William Hamilton's Philosophy, and of the Principal Philosophical
Questions discussed in his Writings_. For the purposes of the present
Treatise, I am content that the justification of the larger extension
which I give to the domain of the science, should rest on the sequel of
the Treatise itself. Some remarks on the relation which the Logic of
Consistency bears to the Logic of Truth, and on the place which that
particular part occupies in the whole to which it belongs, will be found
in the present volume (Book II. chap. iii. § 9).



'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_.



§ 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 practise 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 cannot 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 apprize
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

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 towards 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 _nameable 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 cannot 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 analyse 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

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 labours 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 recognised 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 recognised, 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
recognising 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.



§ 1. "A name," says Hobbes,[1] "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[2] 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,
cannot 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 cannot be denied. Nevertheless, there seems good reason for
adhering to the common usage, and calling 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 anything can be affirmed or denied. We cannot 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 cannot 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 colour. 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 colour,
instead of, A white colour, or, The colour 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 cannot, generally speaking,
be done. We may say, The earth is round; but we cannot 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, cannot 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 anything which belongs to them in
common; and cannot 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 cannot 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 cannot 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 cannot be predicated of them
severally. We may say, Jones is a soldier, and Thompson is a soldier,
and Smith is a soldier, but we cannot 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 unrivalled 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, 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 _colour_, which is a name common to whiteness, redness,
&c. 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; milkwhiteness; 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.[3] 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 colour 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 colour. We mean that they are things
having the colour. The reverse is the case with the word whiteness; what
we affirm to _be_ whiteness is not snow, but the colour of snow.
Whiteness, therefore, is the name of the colour exclusively: white is a
name of all things whatever having the colour; 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 anything 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, &c., and implies, or as it
was termed by the schoolmen, _connotes_[4], the attribute _whiteness_.
The word white is not predicated of the attribute, but of the subjects,
snow, &c.; but when we predicate it of them, we imply, or connote, 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 anything 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.[5]

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 place 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 anything 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 connexion with some
determinate event, and the connexion 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 afterwards 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.[6]

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 anything 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

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 anything 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 hearer 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 anything 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 recognised 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

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
recognised 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. 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 analyse, 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 recognised
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.[7]

§ 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.

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

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

§ 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 cannot, 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 cannot, 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

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 cannot be explained but by mentioning another. Or we may
state it thus--when the name cannot 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;[8] 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.



§ 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 everything 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 anything 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 intended by him and his followers as 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 nameable 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.
  Κεῖσθαι,     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 anything 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
counted among realities, but they cannot be reckoned either among
substances or attributes.

§ 2. Before recommencing, under better auspices, the attempt made with
such imperfect success by the great founder of the science of logic, 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 endeavour 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 applied 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, colour,
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 enclosed 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 long 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
endeavour 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
licence 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 nameable things; the term
Feeling being of course understood in its most enlarged sense.


§ 3. A Feeling and a State of Consciousness are, in the language of
philosophy, equivalent expressions: everything is a feeling of which the
mind is conscious; everything 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 colour 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 anything 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 an 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, _colour_ stands for the sensations of white, red, &c., but also
for the quality in the coloured object. We talk of the colours 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 colour blue, is a feeling of blue
colour, 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 anything 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 hyper-physical objects is

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[9]) 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 nameable things, viz. Feelings or
States of Consciousness, we began by recognising 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.
Without seeking to prejudge the metaphysical question whether any mental
state or phenomenon can be found which is not included in one or other
of these four species, it appears to me that the amount of illustration
bestowed upon these may, so far as we are concerned, suffice for the
whole genus. We shall, therefore, proceed to the two remaining classes
of nameable things; all things which are external to the mind being
considered as belonging either to the class of Substances or to that of


Logicians have endeavoured 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; colour, for example, must be the colour _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_
anything; the moon is not the moon _of_ anything, 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
anything 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 colour, 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
colour, 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 colour 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 connexion, 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 connexion
presents itself to our imagination; a mode of, as it were, realizing the
idea. If there be such a substratum, suppose it 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
anything 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 connexion, 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 cannot 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 an 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,[10] "be they external, be
they internal, we know nothing, or know them only as incognisable; 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
cannot think as unconditioned, irrelative, existent in and of
themselves. All that we know is therefore phænomenal,--phænomenal of the
unknown."[11] 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.[12]

There is not the slightest reason for believing that what we call the
sensible qualities of the object are a type of anything 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?[13] Or
on what principle are we authorized to deduce from the effects, anything
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

§ 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 sceptical
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 Mr. 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, &c.; a something
which I conceive to be not the thoughts, but the being that has the
thoughts, and which I can conceive as existing for ever 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 anything new concerning my
own nature, I cannot with my present faculties conceive this new
information to be anything 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 anything; and if anything, 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 Nameable


§ 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 cannot know,
anything 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 colour 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_ cannot be put indiscriminately one for the
other, it is supposed that they cannot 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 anything in fact but a
lingering remnant of the scholastic 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 "l'opium endormit," by the
maxim "parcequ'il a une vertu soporifique."

It is evident that when the physician stated that opium had "une vertu
soporifique," he did not account for, but merely asserted over again,
the fact that it _endormit_. 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 cannot 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 cannot 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.


§ 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 analyse the matter any farther.

§ 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 colours be a third state of consciousness, which
I have _after_ having the two sensations of colour, 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 analyse 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

But, though likeness or unlikeness cannot be resolved into anything
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 cannot 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

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.


§ 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 the province of Logic to analyse 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.
Everybody 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.


§ 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 recognise 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 cannot, 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.


§ 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.
If there be any other kind of mental state not included under these
subdivisions, we did not think it necessary or proper in this place to
discuss its existence, or the rank which ought to be assigned to it.

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

The only remaining class of Nameable 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
anything 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

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

1st. Feelings, or States of Consciousness.

2nd. The Minds which experience those feelings.

3rd. The Bodies, or external objects, which excite certain of those
feelings, together with the powers or properties whereby they excite
them; these last being included rather in compliance with common
opinion, and because their existence is taken for granted in the common
language from which I cannot 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
abortive Classification of Existences, termed the Categories of
Aristotle. 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
Nameable 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.



§ 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
cannot 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

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 cannot 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 labour 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[15] 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 recognise 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 anything 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

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 cannot 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 anything 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. A
simple proposition is that in which one predicate is affirmed or denied
of one subject. A complex 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 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_.

An 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, Mahomet is the
prophet of God, we do not intend to affirm either that the Koran does
come from God, or that Mahomet 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
"Mahomet:" for nothing is affirmed or denied either of the Koran or of
Mahomet. The real subject of the predication is the entire proposition,
"Mahomet 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 an 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 an 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

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

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 an 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 an 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.

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 an 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.[16]

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 an universal and a particular proposition.
An 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.



§ 1. An inquiry into the nature of propositions must have one of two
objects: to analyse the state of mind called Belief, or to analyse what
is believed. All language recognises 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 downwards, 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 analyse 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 Mahomet was an apostle
of God, we must put the idea of Mahomet 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
everything else that I do. I cannot 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.[17] 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 cannot 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
anything 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 everything of which _man_
is a name. All men are six feet high, is not true, because _six feet
high_ is not a name of everything (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-coloured, 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-coloured. 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 farther; 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 much more.

The only propositions of which Hobbes' 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
analysing 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'
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 dreamt 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 analysed, 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' theory of Predication has not, in the terms in
which he stated it, met with a very favourable 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 anything
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 everything 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 cannot 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.

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' theory of Predication, according to the
well-known remark of Leibnitz, and the avowal of Hobbes himself,[18]
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
cannot be made in stronger terms than it is by Hobbes himself;[19]
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 anything
works upon our senses, but by most men they are called _accidents_."[20]
It is strange that having gone so far, he should not have gone one step
farther, 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 farther 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, &c., 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.[21]

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 one, we have assurance of the existence of the other. 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 farther
than to the occurrence of the phenomenon at some time or other, leaving
the precise 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 anything 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 honour. Who would expect to recognise 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 honour admits of a similar analysis. Honour, as here
used, means a state of approving and admiring emotion, followed on
occasion by corresponding outward acts. "Worthy of honour" connotes all
this, together with our approval of the act of showing honour. All these
are phenomena; states of internal consciousness, accompanied or followed
by physical facts. When we say, A generous person is worthy of honour,
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, honour, 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: their
_conjunction_, in short, so that where the one is found, we may
calculate on finding both.

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 cotemporary 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 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
Coexistence, there are some which assert simple Existence; 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 analyse; 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 colour
is like that colour;--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 colours is _followed_ by a specific feeling
termed the feeling of resemblance. But there would be nothing gained by
encumbering ourselves, especially in this place, with a generalization
which may be looked upon as strained. Logic does not undertake to
analyse 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,
everything 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

But we remarked some time ago (and the reasons of the remark will be
more fully entered into in a subsequent Book[22]) 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 recognised; 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 unanalysable 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
colour I saw yesterday was a white colour, or, The sensation I feel is
one of tightness, in both cases the attribute I affirm of the colour 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, Coexistence, 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. Instead of Coexistence and Sequence, we shall
sometimes say, for greater particularity, Order in Place, and Order in
Time: Order in Place being the specific mode of coexistence, not
necessary to be more particularly analysed here; while the mere fact of
coexistence, or simultaneousness, 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 analyse 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 analysed 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 anything 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 anything 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, Coexistence, Causation, Sequence, or Resemblance. An
attribute, therefore, is necessarily either an existence, a coexistence,
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 anything 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 Coexistence, or of Causation, or of Sequence, or of Resemblance.

It is impossible to imagine any proposition expressed in abstract terms,
which cannot 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 colour;" or "The
colour 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 colour,--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 honour," thus, "All
courageous persons are deserving of honour _in so far_ as they are
courageous:" which is equivalent to this--"All courageous persons
deserve an addition to the honour, 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 analyse
the antecedent. Prudence is an attribute; and, in connexion 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 an 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, Coexistence, 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 coexist 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 coexistence 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.



§ 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 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

If all propositions respecting the signification of words were as simple
and unimportant as those which served us for examples when examining
Hobbes' 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 connexion 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_ cannot be conceived without rationality. But
though _man_ cannot, 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 cannot 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 certain general substance, called gold in general, which substance,
together with all the properties that belonged to it, _inhered_ in every
individual piece of gold.[23] 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 an
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 anything
wanting to render the third book of Locke's Essay a nearly
unexceptionable 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.[24]
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.[25]

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.



§ 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 connexion 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_, &c., 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, cannot 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 cannot 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 five-fold 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_             (_εἶδος_).
  A _differentia_         (_διαφορὰ_).
  A _proprium_            (_ἴδιόν_).
  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, &c. 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,
&c. _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, &c. are species. _Virtue_ is a genus;
justice, prudence, courage, fortitude, generosity, &c. 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, &c., 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

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 connexion 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 colour, 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 recognise 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

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, Sir 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

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, &c., 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 afterwards 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, &c. 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 could possibly 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, specially 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, cannot 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, &c., 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 anything
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

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 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

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 colours, and desire to justify, or even merely to
point out, the particular place assigned to whiteness in our
arrangement, we may define it "the colour 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

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

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 connexion 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 connexion.

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 connexion 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 connexion
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, an
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 colour of an 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. _À 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.



§ 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 cannot 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, cannot 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 cannot 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
anything, signifies the possession of such and such attributes by that
thing." Or thus: Man is everything which possesses such and such
attributes: Man is everything 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
may 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 an 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 coexistent or in succession. To obtain a
definition of the attribute, we must analyse 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 ascribed 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 analyse, 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 recal 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 cannot 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

§ 3. Having stated what seems to be the true idea of a Definition, we
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.
Anything, therefore, is to them a sufficient definition of a term, which
will serve as a correct index to what the term denotes; 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
anything 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 everything
of which it is predicable, and of nothing of which it is not predicable;
though the attributes specified may have no connexion with those which
mankind had in view when they formed or recognised 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 cannot 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, &c. 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 cannot 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 cannot 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.

§ 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 work, Archbishop Whately's _Logic_.[27] 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

"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, cannot,
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, cannot 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,' &c., the sense would remain unchanged: in the second, 'A
triangle means,' &c., 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 afterwards, 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
anything 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
analysed, 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 cannot be true. But the premises,
considered as parts of a definition, are true. Therefore, the premises
considered as parts of a definition cannot 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
  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.[28]

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 will 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 endeavour 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
cannot form any such notion; it cannot 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 cannot 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 nameable 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 cannot 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 demeanour,
_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 recognise, 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 in 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
connexions 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

Whenever the inquiry into the definition of the name of any real object
consists of anything 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 endeavour 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.


[1] _Computation or Logic_, chap. ii.

[2] In the original "had, _or had not_." These last words, as involving
a subtlety foreign to our present purpose, I have forborne to quote.

[3] Vide infra, note at the end of § 3, book ii. ch. ii.

[4] _Notare_, to mark; _con_notare, to mark _along with_; to mark one
thing _with_ or _in addition to_ another.

[5] Archbishop Whately, who, in the later editions of his _Elements of
Logic_, aided in reviving the important distinction treated of in the
text, proposes the term "Attributive" as a substitute for "Connotative"
(p. 22, 9th ed.) The expression is, in itself, appropriate; but as it
has not the advantage of being connected with any verb, of so markedly
distinctive a character as "to connote," it is not, I think, fitted to
supply the place of the word Connotative in scientific use.

[6] A writer who entitles his book _Philosophy; or, the Science of
Truth_, charges me in his very first page (referring at the foot of it
to this passage) with asserting that _general_ names have properly no
signification. And he repeats this statement many times in the course of
his volume, with comments, not at all flattering, thereon. It is well to
be now and then reminded to how great a length perverse misquotation
(for, strange as it appears, I do not believe that the writer is
dishonest) can sometimes go. It is a warning to readers, when they see
an author accused, with volume and page referred to, and the apparent
guarantee of inverted commas, of maintaining something more than
commonly absurd, not to give implicit credence to the assertion without
verifying the reference.

[7] Before quitting the subject of connotative names, it is proper to
observe, that the first writer who, in our times, has adopted from the
schoolmen the word _to connote_, Mr. James Mill, in his _Analysis of the
Phenomena of the Human Mind_, employs it in a signification different
from that in which it is here used. He uses the word in a sense
coextensive with its etymology, applying it to every case in which a
name, while pointing directly to one thing, (which is consequently
termed its signification,) includes also a tacit reference to some other
thing. In the case considered in the text, that of concrete general
names, his language and mine are the converse of one another.
Considering (very justly) the signification of the name to lie in the
attribute, he speaks of the word as _noting_ the attribute, and
_connoting_ the things possessing the attribute. And he describes
abstract names as being properly concrete names with their connotation
dropped: whereas, in my view, it is the _de_notation which would be said
to be dropped, what was previously connoted becoming the whole

In adopting a phraseology at variance with that which so high an
authority, and one which I am less likely than any other person to
undervalue, has deliberately sanctioned, I have been influenced by the
urgent necessity for a term exclusively appropriated to express the
manner in which a concrete general name serves to mark the attributes
which are involved in its signification. This necessity can scarcely be
felt in its full force by any one who has not found by experience how
vain is the attempt to communicate clear ideas on the philosophy of
language without such a word. It is hardly an exaggeration to say, that
some of the most prevalent of the errors with which logic has been
infected, and a large part of the cloudiness and confusion of ideas
which have enveloped it, would, in all probability, have been avoided,
if a term had been in common use to express exactly what I have
signified by the term to connote. And the schoolmen, to whom we are
indebted for the greater part of our logical language, gave us this
also, and in this very sense. For though some of their general
expressions countenance the use of the word in the more extensive and
vague acceptation in which it is taken by Mr. Mill, yet when they had to
define it specifically as a technical term, and to fix its meaning as
such, with that admirable precision which always characterizes their
definitions, they clearly explained that nothing was said to be connoted
except _forms_, which word may generally, in their writings, be
understood as synonymous with _attributes_.

Now, if the word _to connote_, so well suited to the purpose to which
they applied it, be diverted from that purpose by being taken to fulfil
another, for which it does not seem to me to be at all required; I am
unable to find any expression to replace it, but such as are commonly
employed in a sense so much more general, that it would be useless
attempting to associate them peculiarly with this precise idea. Such are
the words, to involve, to imply, &c. By employing these, I should fail
of attaining the object for which alone the name is needed, namely, to
distinguish this particular kind of involving and implying from all
other kinds, and to assure to it the degree of habitual attention which
its importance demands.

[8] Or rather, all objects except itself and the percipient mind; for,
as we shall see hereafter, to ascribe any attribute to an object,
necessarily implies a mind to perceive it.

The simple and clear explanation given in the text, of relation and
relative names, a subject so long the opprobrium of metaphysics, was
given (as far as I know) for the first time, by Mr. James Mill, in his
Analysis of the Phenomena of the Human Mind.

[9] _Philosophy of the Inductive Sciences_, vol. i. p. 40.

[10] _Discussions on Philosophy_, &c. Appendix I. pp. 643-4.

[11] It is to be regretted that Sir William Hamilton, though he often
strenuously insists on this doctrine, and though, in the passage quoted,
he states it with a comprehensiveness and force which leave nothing to
be desired, did not consistently adhere to his own doctrine, but
maintained along with it opinions with which it is utterly
irreconcileable. See the third and other chapters of _An Examination of
Sir William Hamilton's Philosophy_.

[12] "Nous savons qu'il existe quelque chose hors de nous, parceque nous
ne pouvons expliquer nos perceptions sans les rattacher à des causes
distinctes de nous-mêmes; nous savons de plus que ces causes, dont nous
ne connaissons pas d'ailleurs l'essence, produisent les effets les plus
variables, les plus divers, et même les plus contraires, selon qu'elles
rencontrent telle nature ou telle disposition du sujet. Mais savons-nous
quelque chose de plus? et même, vu le caractère indéterminé des causes
que nous concevons dans les corps, y a-t-il quelque chose de plus à
savoir? Y a-t-il lieu de nous enquérir si nous percevons les choses
telles qu'elles sont? Non évidemment.... Je ne dis pas que le problème
est insoluble, _je dis qu'il est absurde et enferme une contradiction_.
Nous _ne savons pas ce que ces causes sont en elles-mêmes_, et la raison
nous défend de chercher à le connaître: mais il est bien évident _à
priori_, qu'_elles ne sont pas en elles-mêmes ce qu'elles sont par
rapport à nous_, puisque la présence du sujet modifie nécessairement
leur action. Supprimez tout sujet sentant, il est certain que ces causes
agiraient encore puisqu'elles continueraient d'exister; mais elles
agiraient autrement; elles seraient encore des qualités et des
propriétés, mais qui ne ressembleraient à rien de ce que nous
connaissons. Le feu ne manifesterait plus aucune des propriétés que nous
lui connaissons: que serait-il? C'est ce que nous ne saurons jamais.
_C'est d'ailleurs peut-être un problème qui ne répugne pas seulement à
la nature de notre esprit, mais à l'essence même des choses._ Quand même
en effet on supprimerait par la pensée tous les sujets sentants, il
faudrait encore admettre que nul corps ne manifesterait ses propriétés
autrement qu'en relation avec un sujet quelconque, et dans ce cas _ses
propriétés ne seraient encore que relatives_: en sorte qu'il me paraît
fort raisonnable d'admettre que les propriétés déterminées des corps
n'existent pas indépendamment d'un sujet quelconque, et que quand on
demande si les propriétés de la matière sont telles que nous les
percevons, il faudrait voir auparavant si elles sont en tant que
déterminées, et dans quel sens il est vrai de dire qu'elles
sont."--_Cours d'Histoire de la Philosophie Morale au 18me siècle_, 8me

[13] An attempt, indeed, has been made by Reid and others, to establish
that although some of the properties we ascribe to objects exist only in
our sensations, others exist in the things themselves, being such as
cannot possibly be copies of any impression upon the senses; and they
ask, from what sensations our notions of extension and figure have been
derived? The gauntlet thrown down by Reid was taken up by Brown, who,
applying greater powers of analysis than had previously been applied to
the notions of extension and figure, pointed out that the sensations
from which those notions are derived, are sensations of touch, combined
with sensations of a class previously too little adverted to by
metaphysicians, those which have their seat in our muscular frame. His
analysis, which was adopted and followed up by James Mill, has been
further and greatly improved upon in Professor Bain's profound work,
_The Senses and the Intellect_, and in the chapters on "Perception" of a
work of eminent analytic power, Mr. Herbert Spencer's _Principles of

On this point M. Cousin may again be cited in favour of the better
doctrine. M. Cousin recognises, in opposition to Reid, the essential
subjectivity of our conceptions of what are called the primary qualities
of matter, as extension, solidity, &c., equally with those of colour,
heat, and the remainder of the so-called secondary qualities.--_Cours_,
ut supra, 9me leçon.

[14] This doctrine, which is the most complete form of the philosophical
theory known as the Relativity of Human Knowledge, has, since the recent
revival in this country of an active interest in metaphysical
speculation, been the subject of a greatly increased amount of
discussion and controversy; and dissentients have manifested themselves
in considerably greater number than I had any knowledge of when the
passage in the text was written. The doctrine has been attacked from two
sides. Some thinkers, among whom are the late Professor Ferrier, in his
_Institutes of Metaphysic_, and Professor John Grote in his _Exploratio
Philosophica_, appear to deny altogether the reality of Noumena, or
Things in themselves--of an unknowable substratum or support for the
sensations which we experience, and which, according to the theory,
constitute all our knowledge of an external world. It seems to me,
however, that in Professor Grote's case at least, the denial of Noumena
is only apparent, and that he does not essentially differ from the other
class of objectors, including Mr. Bailey in his valuable _Letters on the
Philosophy of the Human Mind_, and (in spite of the striking passage
quoted in the text) also Sir William Hamilton, who contend for a direct
knowledge by the human mind of more than the sensations--of certain
attributes or properties as they exist not in us, but in the Things

With the first of these opinions, that which denies Noumena, I have, as
a metaphysician, no quarrel; but, whether it be true or false, it is
irrelevant to Logic. And since all the forms of language are in
contradiction to it, nothing but confusion could result from its
unnecessary introduction into a treatise, every essential doctrine of
which could stand equally well with the opposite and accredited opinion.
The other and rival doctrine, that of a direct perception or intuitive
knowledge of the outward object as it is in itself, considered as
distinct from the sensations we receive from it, is of far greater
practical moment. But even this question, depending on the nature and
laws of Intuitive Knowledge, is not within the province of Logic. For
the grounds of my own opinion concerning it, I must content myself with
referring to a work already mentioned--_An Examination of Sir William
Hamilton's Philosophy_; several chapters of which are devoted to a full
discussion of the questions and theories relating to the supposed direct
perception of external objects.

[15] _Analysis of the Human Mind_, i. 126 et seq.

[16] It may, however, be considered as equivalent to an universal
proposition with a different predicate, viz. "All wine is good _quâ_
wine," or "is good in respect of the qualities which constitute it

[17] Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this
statement, and asks, "Are we to say that a mole cannot dig the ground,
except he has an idea of the ground, and of the snout and paws with
which he digs it?" I do not know what passes in a mole's mind, nor what
amount of mental apprehension may or may not accompany his instinctive
actions. But a human being does not use a spade by instinct; and he
certainly could not use it unless he had knowledge of a spade, and of
the earth which he uses it upon.

[18] "From hence also this may be deduced, that the first truths were
arbitrarily made by those that first of all imposed names upon things,
or received them from the imposition of others. For it is true (for
example) that _man is a living creature_, but it is for this reason,
that it pleased men to impose both these names on the same
thing."--_Computation or Logic_, ch. iii. sect. 8.

[19] "Men are subject to err not only in affirming and denying, but also
in perception, and in silent cogitation.... Tacit errors, or the errors
of sense and cogitation, are made by passing from one imagination to the
imagination of another different thing; or by feigning that to be past,
or future, which never was, nor ever shall be; as when by seeing the
image of the sun in water, we imagine the sun itself to be there; or by
seeing swords, that there has been, or shall be, fighting, because it
uses to be so for the most part; or when from promises we feign the mind
of the promiser to be such and such; or, lastly, when from any sign we
vainly imagine something to be signified which is not. And errors of
this sort are common to all things that have sense."--_Computation or
Logic_, ch. v. sect. 1.

[20] Ch. iii. sect. 3.

[21] To the preceding statement it has been objected, that "we naturally
construe the subject of a proposition in its extension, and the
predicate (which therefore may be an adjective) in its intension,
(connotation): and that consequently coexistence of attributes does not,
any more than the opposite theory of equation of groups, correspond with
the living processes of thought and language." I acknowledge the
distinction here drawn, which, indeed, I had myself laid down and
exemplified a few pages back (p. 104). But though it is true that we
naturally "construe the subject of a proposition in its extension," this
extension, or in other words, the extent of the class denoted by the
name, is not apprehended or indicated directly. It is both apprehended
and indicated solely through the attributes. In the "living processes of
thought and language" the extension, though in this case really thought
of (which in the case of the predicate it is not), is thought of only
through the medium of what my acute and courteous critic terms the

For further illustrations of this subject, see _Examination of Sir
William Hamilton's Philosophy_, ch. xxii.

[22] Book iv. ch. vii.

[23] The doctrines which prevented the real meaning of Essences from
being understood, had not assumed so settled a shape in the time of
Aristotle and his immediate followers, as was afterwards given to them
by the Realists of the middle ages. Aristotle himself (in his Treatise
on the Categories) expressly denies that the _δεύτεραι οὔσιαι_, or
Substantiæ Secundæ, inhere in a subject. They are only, he says,
predicated of it.

[24] The always acute and often profound author of _An Outline of
Sematology_ (Mr. B. H. Smart) justly says, "Locke will be much more
intelligible if, in the majority of places, we substitute 'the knowledge
of' for what he calls 'the Idea of'" (p. 10). Among the many criticisms
on Locke's use of the word Idea, this is the one which, as it appears to
me, most nearly hits the mark; and I quote it for the additional reason
that it precisely expresses the point of difference respecting the
import of Propositions, between my view and what I have spoken of as the
Conceptualist view of them. Where a Conceptualist says that a name or a
proposition expresses our Idea of a thing, I should generally say
(instead of our Idea) our Knowledge, or Belief, concerning the thing

[25] This distinction corresponds to that which is drawn by Kant and
other metaphysicians between what they term _analytic_, and _synthetic_,
judgments; the former being those which can be evolved from the meaning
of the terms used.

[26] If we allow a differentia to what is not really a species. For the
distinction of Kinds, in the sense explained by us, not being in any way
applicable to attributes, it of course follows that although attributes
may be put into classes, those classes can be admitted to be genera or
species only by courtesy.

[27] In the fuller discussion which Archbishop Whately has given to this
subject in his later editions, he almost ceases to regard the
definitions of names and those of things as, in any important sense,
distinct. He seems (9th ed. p. 145) to limit the notion of a Real
Definition to one which "explains anything _more_ of the nature of the
thing than is implied in the name;" (including under the word "implied,"
not only what the name connotes, but everything which can be deduced by
reasoning from the attributes connoted). Even this, as he adds, is
usually called, not a Definition, but a Description; and (as it seems to
me) rightly so called. A Description, I conceive, can only be ranked
among Definitions, when taken (as in the case of the zoological
definition of man) to fulfil the true office of a Definition, by
declaring the connotation given to a word in some special use, as a term
of science or art: which special connotation of course would not be
expressed by the proper definition of the word in its ordinary

Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
understands by a Real Definition one which contains _less_ than the
Nominal Definition, provided only that what it contains is sufficient
for distinction. "By _real_ definition I mean such an explanation of the
word, be it the whole of the meaning or only part, as will be sufficient
to separate the things contained under that word from all others. Thus
the following, I believe, is a complete definition of an elephant: An
animal which naturally drinks by drawing the water into its nose, and
then spurting it into its mouth."--_Formal Logic_, p. 36. Mr. De
Morgan's general proposition and his example are at variance; for the
peculiar mode of drinking of the elephant certainly forms no part of the
meaning of the word elephant. It could not be said, because a person
happened to be ignorant of this property, that he did not know what an
elephant means.

[28] In the only attempt which, so far as I know, has been made to
refute the preceding argumentation, it is maintained that in the first
form of the syllogism,

  A dragon is a thing which breathes flame,
  A dragon is a serpent,
  Therefore some serpent or serpents breathe flame,

"there is just as much truth in the conclusion as there is in the
premises, or rather, no more in the latter than in the former. If the
general name serpent includes both real and imaginary serpents, there is
no falsity in the conclusion; if not, there is falsity in the minor

Let us, then, try to set out the syllogism on the hypothesis that the
name serpent includes imaginary serpents. We shall find that it is now
necessary to alter the predicates; for it cannot be asserted that an
imaginary creature breathes flame: in predicating of it such a fact, we
assert by the most positive implication that it is real and not
imaginary. The conclusion must run thus, "Some serpent or serpents
either do or are _imagined_ to breathe flame." And to prove this
conclusion by the instance of dragons, the premises must be, A dragon is
_imagined_ as breathing flame, A dragon is a (real or imaginary)
serpent: from which it undoubtedly follows, that there are serpents
which are imagined to breathe flame; but the major premise is not a
definition, nor part of a definition; which is all that I am concerned
to prove.

Let us now examine the other assertion--that if the word serpent stands
for none but real serpents, the minor premise (a dragon is a serpent) is
false. This is exactly what I have myself said of the premise,
considered as a statement of fact: but it is not false as part of the
definition of a dragon; and since the premises, or one of them, must be
false, (the conclusion being so,) the real premise cannot be the
definition, which is true, but the statement of fact, which is false.

[29] "Few people" (I have said in another place) "have reflected how
great a knowledge of Things is required to enable a man to affirm that
any given argument turns wholly upon words. There is, perhaps, not one
of the leading terms of philosophy which is not used in almost
innumerable shades of meaning, to express ideas more or less widely
different from one another. Between two of these ideas a sagacious and
penetrating mind will discern, as it were intuitively, an unobvious link
of connexion, upon which, though perhaps unable to give a logical
account of it, he will found a perfectly valid argument, which his
critic, not having so keen an insight into the Things, will mistake for
a fallacy turning on the double meaning of a term. And the greater the
genius of him who thus safely leaps over the chasm, the greater will
probably be the crowing and vain-glory of the mere logician, who,
hobbling after him, evinces his own superior wisdom by pausing on its
brink, and giving up as desperate his proper business of bridging it



Διωρισμένων δε τούτων λέγωμεν ἤδη, διὰ τίνων, καὶ πότε, καὶ πῶς γίνεται
πᾶς συλλογισμός ὕστερον δὲ λεκτέον περὶ ἀποδείξεως. Πρότερον γὰρ περὶ
συλλογισμοῦ λεκτέον, ἢ περὶ ἀποδείξεως, διὰ τὸ καθόλου μᾶλλον εἰναὶ τὸν
συλλογισμόν. Ἡ μὲν γὰρ ἀπόδειξις, συλλογισμός τις; ὁ συλλογισμός δὲ οὐ
πᾶς, ἀπόδειξις.

                    ARIST. _Analyt. Prior._ l. i. cap. 4.



§ 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 analysed 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 recognises 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 analysed 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 æquipollency 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 an 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,

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 cannot 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 an universal proposition into a particular,
is termed conversion _per accidens_. From the proposition, Some A is not
B, we cannot 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 recognised 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
æquipollent 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.[1]

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 coexist 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 coexist 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 coexist, 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 cannot be inferred. In order
to reassert, 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 æquipollency of propositions. For, though
that cannot be called reasoning or inference which is a mere reassertion
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 cannot both be true; that subcontrary propositions
may both be true, but cannot 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 _vice versâ_;[2] 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

§ 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.



§ 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 afterwards 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 middleterm, 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 middleterm which is in them both. The
premise which contains the middleterm and the major term is called the
major premise; that which contains the middleterm 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 middleterm, 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 middleterm is the subject of the major premise and the
predicate of the minor. This is reckoned as the first figure. When the
middleterm 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 middleterm 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 middleterm.


  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


  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


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


  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 not C  Some A is C  Some A is not C  Some A is 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.

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
  No A is C,

may be reduced as follows. The proposition, No C is B, being an
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
  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

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

Or if more significant symbols are preferred:--

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

  All animals are mortal;
  All men   }
  Some men  }  are animals;
  Socrates  }
  All men   }
  Some men  }  are mortal.
  Socrates  }

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;
  All negroes   }
  Some negroes  }  are capable of self-control;
  Mr. A's negro }
  No negroes are        }
  Some negroes are not  }  necessarily vicious.
  Mr. A's negro is not  }

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,
  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,
  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.[3] 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 everything 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,
cannot possibly happen with the only class of arguments which are of
first-rate scientific importance, those in which the conclusion is an
universal affirmative, such conclusions being susceptible of proof in
the first figure alone.[4]

§ 2. On examining, then, these two general formulæ, we find that in
both of them, one premise, the major, is an 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
everything included in the class. This axiom, supposed to be the basis
of the syllogistic theory, is termed by logicians the _dictum de omni et

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 everything
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, an 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,

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
Kantians, 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 anything,
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 cannot 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 anything 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) coexist.
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 recognise this
import of propositions, cannot, 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,
  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,
  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 analyse 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 anything 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 coexist with the same thing, coexist
with one another. The second is the principle of negative syllogisms,
and is to this effect: that a thing which coexists with another thing,
with which other a third thing does not coexist, is not coexistent 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

§ 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[6] 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,
  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

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



§ 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

Logicians have been remarkably unanimous in their mode of answering this
question. It is universally allowed that a syllogism is vicious if there
be anything 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,
  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 cannot 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, cannot 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 anything: since from a general principle
we cannot 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 _bonâ fide_ a new truth? Is it not matter of
daily experience that truths previously unthought of, facts which have
not been, and cannot 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,
  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 anything 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[7] that the
object of reasoning is "merely to expand and unfold the assertions wrapt
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 "wrapt up" in a few definitions and axioms. Nor does this
defence 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 everything which it fairly
includes? And if not, is not the syllogistic art _primâ facie_ what its
assailants affirm it to be, a contrivance for catching you in a trap,
and holding you fast in it?[8]

§ 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 afterwards is merely
decyphering 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 cannot help thinking that
the vulgar notion is, in this case, the more correct. If, from our
experience of John, Thomas, &c., 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 company 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, cannot 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 cannot 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 burnt 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 burnt, and on this evidence believes, when he sees a candle,
that if he puts his finger into the flame of it, he will be burnt 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
burnt child, but the burnt 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 neighbour'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
practising the habit of stating to oneself 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 skilful 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, &c., 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 colours, 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 connexion in his
mind between fine effects of colour, 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 court 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 stopt 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 others 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
unpractised 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 ensure 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 favourable 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 travelling 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_
anything, 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 anything, 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 cotemporary
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 for ever. 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

§ 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

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
inferrible 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

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.[9]

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 afterwards 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

§ 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 anything 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 analysing 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 recognising 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 cannot 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 recognised 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 an
universal idea, the common property of all rational creatures, cannot
involve anything 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

§ 7. We have thus obtained what we were seeking, an 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 _bonâ 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 recognise 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 anything 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,[10] Dr. Whewell[11] and Mr. Bailey;[12] Sir
John Herschel considering the doctrine, though not strictly "a
discovery,"[13] 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 cannot be better or more succinctly stated than by
borrowing a sentence from Archbishop Whately.[14] "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 cannot 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 everything
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 already
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.[15] We review our syllogistic as well as our inductive
processes, and recognise 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 recognises
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 towards me because I see him, and not because
I recognise 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 anything 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 skilfully 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
recognised,--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,
cannot 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.[16]

§ 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[17]), 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 cannot 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 anything
else, though the reasons assigned for the practice are in general very
far from philosophical, admits of a philosophical justification.



§ 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 cannot directly observe what is to be proved, but cannot
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 hypochlorite 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

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 vapour 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 vapour had this
smell, &c., 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 the 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 _à 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 cannot 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

§ 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 cannot, we determine once
for all what are the distinguishing marks by which such cases may be
recognised. 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 recognise 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
recognised 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
recognised 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; 2nd, that surface parabolic; 3rd, 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," &c.

§ 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 reconcileable 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
cannot 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 endeavour 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 cannot 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 recognising 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

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 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 being applied to one another

AC, AB, are within this formula by supposition; AD, AE, have been
brought within it by the preceding step. Both these pairs of straight
lines have the property of equality; which, according to the second
formula, is a mark that, if applied to each other, they will coincide.
Coinciding altogether means coinciding in every part, and of course at
their extremities, D, E, and B, C.

THIRD FORMULA. _Straight lines, having their extremities coincident,

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

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[18] that there are weighty scientific
reasons for giving to every science as much of the character of a
Deductive Science as possible; for endeavouring 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 cannot 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 anything 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 colour 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_, &c. 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 inferrible. 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 connexion 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 colouring matters which are reddened by acids
(as well as, reciprocally, all red colouring matters which are rendered
blue by alkalies) contain nitrogen: and it is quite possible that this
circumstance may one day furnish a bond of connexion between the two
propositions in question, by showing that the antagonistic action of
acids and alkalies in producing or destroying the colour 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
coexistence which obtained between phenomena of the more known class,
obtained also between the phenomena which corresponded to them in the
other class. Every sound, being a mark of a particular oscillatory
motion, became a mark of everything which, by the laws of dynamics, was
known to be inferrible from that motion; and everything 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

But the grand agent for transforming experimental into deductive
sciences, is the science of number. The properties of numbers, alone
among all known phenomena, are, in the most rigorous sense, properties
of all things whatever. All things are not coloured, 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 fulfil 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
cannot 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 _vice versâ_, 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.



§ 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 false:
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 _à 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 cannot _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 cannot be supposed to be conversant about non-entities;
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.

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 endeavoured
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."[19] 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 non-entities,)
it follows that any hypothesis we make respecting an object, to
facilitate our study of it, must not involve anything 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 cannot 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
cannot both of them be parallel to a third straight line."[20]

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 cannot 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 unfavourable 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 further 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 cannot 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 _à 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

They cannot, however, but allow that the truth of the axiom, Two
straight lines cannot 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 cannot 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 _à 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.[21]

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, cannot 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 _à priori_ theory are obliged to have recourse to other
arguments. These are reducible to two, which I shall endeavour 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 cannot 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 recognise that two such lines cannot inclose
a space. Intuition is "imaginary looking;"[22] 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 cannot 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 _cannot_
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
cannot 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 cannot 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 practised 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 cannot 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
learnt 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 learnt 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."[23]

§ 6. The first of the two arguments in support of the theory that
axioms are _à 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 cannot 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 cannot 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 cannot 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 cannot offer the
smallest ground for the necessity of a proposition. She can observe and
record what has happened; but she cannot 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 cannot 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 cannot 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."[24] 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."[25]

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 cannot, even by an effort of
imagination, or in a supposition, conceive the reverse of that which is
asserted. That there are such truths cannot be doubted. We may take, for
example, all relations of number. Three and Two added together make
Five. We cannot conceive it to be otherwise. We cannot, by any freak of
thought, imagine Three and Two to make Seven."[26]

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
anything more.

This, therefore, is the principle asserted: that propositions, the
negation of which is inconceivable, or in other words, which we cannot
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 cannot 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 anything 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 practised 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.[27] 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 everybody 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 upwards instead of downwards.
The Cartesians long rejected the Newtonian doctrine of the
gravitation of all bodies towards one another, on the faith of
a general proposition, the reverse of which seemed to them to be
inconceivable--the proposition that a body cannot 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.[28] And they no
doubt found it as impossible to conceive that a body should act upon the
earth at 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. It would
seem that even now the majority of scientific men have not completely
got over this very difficulty; for though they have at last learnt to
conceive the sun _attracting_ the earth without any intervening fluid,
they cannot yet conceive the sun _illuminating_ the earth without some
such medium.

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 afterwards 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 cannot 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 cannot 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 cannot 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 anything 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
recognising 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 recognised 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
coloured 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 cannot 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._"[29]

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 cannot have been learnt 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 cannot intend to
justify this mode of thought: he cannot 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."[30] 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
for ever 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,"[31] 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."[32] 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
sceptic 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:[33] "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 cannot conceive a world in which this should not be the case_, it
would appear that we cannot 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 cannot 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."[34] 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 cannot 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."[35] Necessary truths,
therefore, are not those of which we cannot conceive, but "those of
which we cannot _distinctly_ conceive, the contrary."[36] 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
learnt from experience, we cannot, 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 anything in the theories themselves,
intrinsically and _à 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 cannot 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 cannot 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."[37] 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 favour 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 an
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 an
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.[38]



§ 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
favour 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 _à 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 _à 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 are 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 reconcileable 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 anything 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 anything. 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) = 2a + 2b_, 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 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 are 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 are 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 sum 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,

  o o

may be separated into two parts, thus,

  o o     o.

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, &c., 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 maybe 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 a few such
cases; 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 cannot 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 anything, 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.



§ 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 defence 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,[39] 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
anything, 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 oneself 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 anything 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 cannot 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 cannot, 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 cannot 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 whilst many of these facts, impressing themselves
upon us, are occasional; whilst 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; whilst 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: 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 favour, 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 favour 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 an 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 an 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 cannot 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 farther 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 recognises. 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. It is needless to dwell farther
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 cannot 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 whole 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 recognised as valid except
because we cannot conceive the conclusion not to follow from the

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 cannot 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;[40] 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

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 endeavour 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 cannot 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 cannot, 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 endeavours to use the word inconceivable in this, its proper,
sense: but it may yet be questioned whether his endeavour 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 cannot conceive that I am not feeling
cold, this expression cannot be translated into, "I cannot 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 cannot conceive that he is looking into
darkness, he should have said that a man cannot _believe_ that he is
doing so. For it is surely possible, in broad daylight, to _imagine_
oneself looking into darkness.[41] 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 cannot believe otherwise. And in this case every one
will admit that the necessity 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 cannot 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 cannot
_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 cannot 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 disbelieved them at first), 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 cannot get rid of the idea;
though while looking at a solid object they cannot 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 everybody 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.[42] The amount of their
success in meeting it will probably determine the ultimate verdict of
philosophers on the question.

§ 4. 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."[43] Sir William Hamilton is however a firm believer in the
_à 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 schoolmen, the Principle of
Contradiction, and the Principle of Excluded Middle: the first, that two
contradictory propositions cannot both be true; the second, that they
cannot 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 for ever precluded from discovering which. To take his favourite
example, we cannot conceive the infinite divisibility of matter, and we
cannot 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 cannot 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
cannot at the same time be false and true. But I can go no farther with
the Nominalists; for I cannot 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
outwards, 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 cannot 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 cannot 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 non-entity must be either infinitely or finitely
divisible.[44] 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

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, about a page back, but in
Mr. Spencer it is not an undeveloped thought, but a philosophical

"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 colourless, we think of its having colour,
the change consists in the addition to the concept of an element that
was before absent from it--the object cannot 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 cannot occur without excluding a correlative negative
mode; and that the negative mode cannot 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

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.


[1] As Sir William Hamilton has pointed out, "Some A is not B" may also
be converted in the following form: "No B is _some_ A." Some men are not
negroes; therefore, No negroes are _some_ men (_e.g._ Europeans).

  All A is B } contraries.
  No  A is B }

  Some A is B     } subcontraries.
  Some A is not B }

  All  A is B     } contradictories.
  Some A is not B }

  No   A is B } also contradictories.
  Some A is B }

  All  A is B } and  No   A is B     } respectively subalternate.
  Some A is B }      Some A is not B }

[3] His conclusions are, "The first figure is suited to the discovery or
proof of the properties of a thing; the second to the discovery or proof
of the distinctions between things; the third to the discovery or proof
of instances and exceptions; the fourth to the discovery, or exclusion,
of the different species of a genus." The reference of syllogisms in the
last three figures to the _dictum de omni et nullo_ is, in Lambert's
opinion, strained and unnatural: to each of the three belongs, according
to him, a separate axiom, co-ordinate and of equal authority with that
_dictum_, and to which he gives the names of _dictum de diverso_ for the
second figure, _dictum de exemplo_ for the third, and _dictum de
reciproco_ for the fourth. See part i. or _Dianoiologie_, chap. iv. §
229 _et seqq._ Mr. Bailey, (_Theory of Reasoning_, 2nd ed. pp. 70-74)
takes a similar view of the subject.

[4] Since this chapter was written, two treatises have appeared (or
rather a treatise and a fragment of a treatise), which aim at a further
improvement in the theory of the forms of ratiocination: Mr. De Morgan's
"Formal Logic; or, the Calculus of Inference, Necessary and Probable;"
and the "New Analytic of Logical Forms," attached as an Appendix to Sir
William Hamilton's _Discussions on Philosophy_, and at greater length,
to his posthumous _Lectures on Logic_.

In Mr. De Morgan's volume--abounding, in its more popular parts, with
valuable observations felicitously expressed--the principal feature of
originality is an attempt to bring within strict technical rules the
cases in which a conclusion can be drawn from premises of a form usually
classed as particular. Mr. De Morgan observes, very justly, that from
the premises Most Bs are Cs, most Bs are As, it may be concluded with
certainty that some As are Cs, since two portions of the class B, each
of them comprising more than half, must necessarily in part consist of
the same individuals. Following out this line of thought, it is equally
evident that if we knew exactly what proportion the "most" in each of
the premises bear to the entire class B, we could increase in a
corresponding degree the definiteness of the conclusion. Thus if 60 per
cent of B are included in C, and 70 per cent in A, 30 per cent at least
must be common to both; in other words, the number of As which are Cs,
and of Cs which are As, must be at least equal to 30 per cent of the
class B. Proceeding on this conception of "numerically definite
propositions," and extending it to such forms as these:--"45 Xs (or
more) are each of them one of 70 Ys," or "45 Xs (or more) are no one of
them to be found among 70 Ys," and examining what inferences admit of
being drawn from the various combinations which may be made of premises
of this description, Mr. De Morgan establishes universal formulæ for
such inferences; creating for that purpose not only a new technical
language, but a formidable array of symbols analogous to those of

Since it is undeniable that inferences, in the cases examined by Mr. De
Morgan, can legitimately be drawn, and that the ordinary theory takes no
account of them, I will not say that it was not worth while to show in
detail how these also could be reduced to formulæ as rigorous as those
of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps
more than once, as a school exercise); but I question if its results are
worth studying and mastering for any practical purpose. The practical
use of technical forms of reasoning is to bar out fallacies: but the
fallacies which require to be guarded against in ratiocination properly
so called, arise from the incautious use of the common forms of
language; and the logician must track the fallacy into that territory,
instead of waiting for it on a territory of his own. While he remains
among propositions which have acquired the numerical precision of the
Calculus of Probabilities, the enemy is left in possession of the only
ground on which he can be formidable. And since the propositions (short
of universal) on which a thinker has to depend, either for purposes of
speculation or of practice, do not, except in a few peculiar cases,
admit of any numerical precision; common reasoning cannot be translated
into Mr. De Morgan's forms, which therefore cannot serve any purpose as
a test of it.

Sir William Hamilton's theory of the "quantification of the predicate"
(concerning the originality of which in his case there can be no doubt,
however Mr. De Morgan may have also, and independently, originated an
equivalent doctrine) may be briefly described as follows:--

"Logically" (I quote his own words) "we ought to take into account the
quantity, always understood in thought, but usually, for manifest
reasons, elided in its expression, not only of the subject, but also of
the predicate of a judgment." All A is B, is equivalent to all A is
_some_ B. No A is B, to No A is _any_ B. Some A is B, is tantamount to
some A is _some_ B. Some A is not B, to Some A is _not any_ B. As in
these forms of assertion the predicate is exactly coextensive with the
subject, they all admit of simple conversion; and by this we obtain two
additional forms--Some B is _all_ A, and No B is _some_ A. We may also
make the assertion All A is all B, which will be true if the classes A
and B are exactly coextensive. The last three forms, though conveying
real assertions, have no place in the ordinary classification of
Propositions. All propositions, then, being supposed to be translated
into this language, and written each in that one of the preceding forms
which answers to its signification, there emerges a new set of
syllogistic rules, materially different from the common ones. A general
view of the points of difference may be given in the words of Sir W.
Hamilton (_Discussions_, 2nd ed. p. 651):--

"The revocation of the two terms of a Proposition to their true
relation; a proposition being always an _equation_ of its subject and
its predicate.

"The consequent reduction of the Conversion of Propositions from three
species to one--that of Simple Conversion.

"The reduction of all the _General Laws_ of Categorical Syllogisms to a
single Canon.

"The evolution from that one canon of all the Species and varieties of

"The abrogation of all the _Special Laws_ of Syllogism.

"A demonstration of the exclusive possibility of Three syllogistic
Figures; and (on new grounds) the scientific and final abolition of the

"A manifestation that Figure is an unessential variation in syllogistic
form; and the consequent absurdity of Reducing the syllogisms of the
other figures to the first.

"An enouncement of _one Organic Principle_ for each Figure.

"A determination of the true number of the Legitimate Moods; with

"Their amplification in number (thirty-six);

"Their numerical equality under all the figures; and

"Their relative equivalence, or virtual identity, throughout every
schematic difference.

"That, in the second and third figures, the extremes holding both the
same relation to the middle term, there is not, as in the first, an
opposition and subordination between a term major and a term minor,
mutually containing and contained, in the counter wholes of Extension
and Comprehension.

"Consequently, in the second and third figures, there is no determinate
major and minor premise, and there are two indifferent conclusions:
whereas in the first the premises are determinate, and there is a single
proximate conclusion."

This doctrine, like that of Mr. De Morgan previously noticed, is a real
addition to the syllogistic theory; and has moreover this advantage over
Mr. De Morgan's "numerically definite Syllogism," that the forms it
supplies are really available as a test of the correctness of
ratiocination; since propositions in the common form may always have
their predicates quantified, and so be made amenable to Sir W.
Hamilton's rules. Considered however as a contribution to the _Science_
of Logic, that is, to the analysis of the mental processes concerned in
reasoning, the new doctrine appears to me, I confess, not merely
superfluous, but erroneous; since the form in which it clothes
propositions does not, like the ordinary form, express what is in the
mind of the speaker when he enunciates the proposition. I cannot think
Sir William Hamilton right in maintaining that the quantity of the
predicate is "always understood in thought." It is implied, but is not
present to the mind of the person who asserts the proposition. The
quantification of the predicate, instead of being a means of bringing
out more clearly the meaning of the proposition, actually leads the mind
out of the proposition, into another order of ideas. For when we say,
All men are mortal, we simply mean to affirm the attribute mortality of
all men; without thinking at all of the _class_ mortal in the concrete,
or troubling ourselves about whether it contains any other beings or
not. It is only for some artificial purpose that we ever look at the
proposition in the aspect in which the predicate also is thought of as a
class-name, either including the subject only, or the subject and
something more. (See above, p. 104.)

For a fuller discussion of this subject, see the twenty-second chapter
of a work already referred to, "An Examination of Sir William Hamilton's

[5] Mr. Herbert Spencer (_Principles of Psychology_, pp. 125-7), though
his theory of the syllogism coincides with all that is essential of
mine, thinks it a logical fallacy to present the two axioms in the text,
as the regulating principles of syllogism. He charges me with falling
into the error pointed out by Archbishop Whately and myself, of
confounding exact likeness with literal identity; and maintains, that we
ought not to say that Socrates possesses _the same_ attributes which are
connoted by the word Man, but only that he possesses attributes _exactly
like_ them: according to which phraseology, Socrates, and the attribute
mortality, are not two things coexisting with the same thing, as the
axiom asserts, but two things coexisting with two different things.

The question between Mr. Spencer and me is merely one of language; for
neither of us (if I understand Mr. Spencer's opinions rightly) believes
an attribute to be a real thing, possessed of objective existence; we
believe it to be a particular mode of naming our sensations, or our
expectations of sensation, when looked at in their relation to an
external object which excites them. The question raised by Mr. Spencer
does not, therefore, concern the properties of any really existing
thing, but the comparative appropriateness, for philosophical purposes,
of two different modes of using a name. Considered in this point of
view, the phraseology I have employed, which is that commonly used by
philosophers, seems to me to be the best. Mr. Spencer is of opinion that
because Socrates and Alcibiades are not the same man, the attribute
which constitutes them men should not be called the same attribute; that
because the humanity of one man and that of another express themselves
to our senses not by the same individual sensations but by sensations
exactly alike, humanity ought to be regarded as a different attribute in
every different man. But on this showing, the humanity even of any one
man should be considered as different attributes now and half-an-hour
hence; for the sensations by which it will then manifest itself to my
organs will not be a continuation of my present sensations, but a
repetition of them; fresh sensations, not identical with, but only
exactly like the present. If every general conception, instead of being
"the One in the Many," were considered to be as many different
conceptions as there are things to which it is applicable, there would
be no such thing as general language. A name would have no general
meaning if _man_ connoted one thing when predicated of John, and
another, though closely resembling, thing when predicated of William.
Accordingly a recent pamphlet asserts the impossibility of general
knowledge on this precise ground.

The meaning of any general name is some outward or inward phenomenon,
consisting, in the last resort, of feelings; and these feelings, if
their continuity is for an instant broken, are no longer the same
feelings, in the sense of individual identity. What, then, is the common
something which gives a meaning to the general name? Mr. Spencer can
only say, it is the similarity of the feelings; and I rejoin, the
attribute is precisely that similarity. The names of attributes are in
their ultimate analysis names for the resemblances of our sensations (or
other feelings). Every general name, whether abstract or concrete,
denotes or connotes one or more of those resemblances. It will not,
probably, be denied, that if a hundred sensations are undistinguishably
alike, their resemblance ought to be spoken of as one resemblance, and
not a hundred resemblances which merely _resemble_ one another. The
things compared are many, but the something common to all of them must
be conceived as one, just as the name is conceived as one, though
corresponding to numerically different sensations of sound each time it
is pronounced. The general term _man_ does not connote the sensations
derived once from one man, which, once gone, can no more occur again
than the same flash of lightning. It connotes the general type of the
sensations derived always from all men, and the power (always thought of
as one) of producing sensations of that type. And the axiom might be
thus worded: Two _types of sensation_ each of which coexists with a
third type, coexist with another; or Two _powers_ each of which coexists
with a third power coexist with one another.

Mr. Spencer has misunderstood me in another particular. He supposes that
the coexistence spoken of in the axiom, of two things with the same
third thing, means simultaneousness in time. The coexistence meant is
that of being jointly attributes of the same subject. The attribute of
being born without teeth, and the attribute of having thirty-two teeth
in mature age, are in this sense coexistent, both being attributes of
man, though _ex vi termini_ never of the same man at the same time.

[6] Supra, p. 128.

[7] _Logic_, p. 239 (9th ed.).

[8] It is hardly necessary to say, that I am not contending for any such
absurdity as that we _actually_ "ought to have known" and considered the
case of every individual man, past, present, and future, before
affirming that all men are mortal: although this interpretation has
been, strangely enough, put upon the preceding observations. There is no
difference between me and Archbishop Whately, or any other defender of
the syllogism, on the practical part of the matter; I am only pointing
out an inconsistency in the logical theory of it, as conceived by almost
all writers. I do not say that a person who affirmed, before the Duke of
Wellington was born, that all men are mortal, _knew_ that the Duke of
Wellington was mortal; but I do say that he _asserted_ it; and I ask for
an explanation of the apparent logical fallacy, of adducing in proof of
the Duke of Wellington's mortality, a general statement which
presupposes it. Finding no sufficient resolution of this difficulty in
any of the writers on Logic, I have attempted to supply one.

[9] The language of ratiocination would, I think, be brought into closer
agreement with the real nature of the process, if the general
propositions employed in reasoning, instead of being in the form All men
are mortal, or Every man is mortal, were expressed in the form Any man
is mortal. This mode of expression, exhibiting as the type of all
reasoning from experience "The men A, B, C, &c. are so and so, therefore
_any_ man is so and so," would much better manifest the true idea--that
inductive reasoning is always, at bottom, inference from particulars to
particulars, and that the whole function of general propositions in
reasoning, is to vouch for the legitimacy of such inferences.

[10] Review of Quetelet on Probabilities, _Essays_, p. 367.

[11] _Philosophy of Discovery_, p. 289.

[12] _Theory of Reasoning_, ch. iv. to which I may refer for an able
statement and enforcement of the grounds of the doctrine.

[13] It is very probable that the doctrine is not new, and that it was,
as Sir John Herschel thinks, substantially anticipated by Berkeley. But
I certainly am not aware that it is (as has been affirmed by one of my
ablest and most candid critics) "among the standing marks of what is
called the empirical philosophy."

[14] _Logic_, book iv. ch. i. sect. 1.

[15] See the important chapter on Belief, in Professor Bain's great
treatise, _The Emotions and the Will_, pp. 581-4.

[16] A writer in the "British Quarterly Review" (August 1846), in a
review of this treatise, endeavours to show that there is no _petitio
principii_ in the syllogism, by denying that the proposition, All men
are mortal, asserts or assumes that Socrates is mortal. In support of
this denial, he argues that we may, and in fact do, admit the general
proposition that all men are mortal, without having particularly
examined the case of Socrates, and even without knowing whether the
individual so named is a man or something else. But this of course was
never denied. That we can and do draw conclusions concerning cases
specifically unknown to us, is the datum from which all who discuss this
subject must set out. The question is, in what terms the evidence, or
ground, on which we draw these conclusions, may best be
designated--whether it is most correct to say, that the unknown case is
proved by known cases, or that it is proved by a general proposition
including both sets of cases, the unknown and the known? I contend for
the former mode of expression. I hold it an abuse of language to say,
that the proof that Socrates is mortal, is that all men are mortal. Turn
it in what way we will, this seems to me to be asserting that a thing is
the proof of itself. Whoever pronounces the words, All men are mortal,
has affirmed that Socrates is mortal, though he may never have heard of
Socrates; for since Socrates, whether known to be so or not, really is a
man, he is included in the words, All men, and in every assertion of
which they are the subject. If the reviewer does not see that there is a
difficulty here, I can only advise him to reconsider the subject until
he does: after which he will be a better judge of the success or failure
of an attempt to remove the difficulty. That he had reflected very
little on the point when he wrote his remarks, is shown by his oversight
respecting the _dictum de omni et nullo_. He acknowledges that this
maxim as commonly expressed,--"Whatever is true of a class, is true of
everything included in the class," is a mere identical proposition,
since the class _is_ nothing but the things included in it. But he
thinks this defect would be cured by wording the maxim thus,--"Whatever
is true of a class, is true of everything which _can be shown_ to be a
member of the class:" as if a thing could "be shown" to be a member of
the class without being one. If a class means the sum of all the things
included in the class, the things which can "be shown" to be included in
it are part of the sum, and the _dictum_ is as much an identical
proposition with respect to them as to the rest. One would almost
imagine that, in the reviewer's opinion, things are not members of a
class until they are called up publicly to take their place in it--that
so long, in fact, as Socrates is not known to be a man, he _is not_ a
man, and any assertion which can be made concerning men does not at all
regard him, nor is affected as to its truth or falsity by anything in
which he is concerned.

The difference between the reviewer's theory and mine may be thus
stated. Both admit that when we say, All men are mortal, we make an
assertion reaching beyond the sphere of our knowledge of individual
cases; and that when a new individual, Socrates, is brought within the
field of our knowledge by means of the minor premise, we learn that we
have already made an assertion respecting Socrates without knowing it:
our own general formula being, to that extent, for the first time
_interpreted_ to us. But according to the reviewer's theory, the smaller
assertion is proved by the larger: while I contend, that both assertions
are proved together, by the same evidence, namely, the grounds of
experience on which the general assertion was made, and by which it must
be justified.

The reviewer says, that if the major premise included the conclusion,
"we should be able to affirm the conclusion without the intervention of
the minor premise; but every one sees that that is impossible." A
similar argument is urged by Mr. De Morgan (_Formal Logic_, p. 259):
"The whole objection tacitly assumes the superfluity of the minor; that
is, tacitly assumes we know Socrates[46] to be a man as soon as we know
him to be Socrates." The objection would be well grounded if the
assertion that the major premise includes the conclusion, meant that it
individually specifies all it includes. As however the only indication
it gives is a description by marks, we have still to compare any new
individual with the marks; and to show that this comparison has been
made, is the office of the minor. But since, by supposition, the new
individual has the marks, whether we have ascertained him to have them
or not; if we have affirmed the major premise, we have asserted him to
be mortal. Now my position is that this assertion cannot be a necessary
part of the argument. It cannot be a necessary condition of reasoning
that we should begin by making an assertion, which is afterwards to be
employed in proving a part of itself. I can conceive only one way out of
this difficulty, viz. that what really forms the proof is _the other_
part of the assertion; the portion of it, the truth of which has been
ascertained previously: and that the unproved part is bound up in one
formula with the proved part in mere anticipation, and as a memorandum
of the nature of the conclusions which we are prepared to prove.

With respect to the minor premise in its formal shape, the minor as it
stands in the syllogism, predicating of Socrates a definite class name,
I readily admit that it is no more a necessary part of reasoning than
the major. When there is a major, doing its work by means of a class
name, minors are needed to interpret it: but reasoning can be carried on
without either the one or the other. They are not the conditions of
reasoning, but a precaution against erroneous reasoning. The only minor
premise necessary to reasoning in the example under consideration, is,
Socrates is _like_ A, B, C, and the other individuals who are known to
have died. And this is the only universal type of that step in the
reasoning process which is represented by the minor. Experience,
however, of the uncertainty of this loose mode of inference, teaches the
expediency of determining beforehand what _kind_ of likeness to the
cases observed, is necessary to bring an unobserved case within the same
predicate; and the answer to this question is the major. Thus the
syllogistic major and the syllogistic minor start into existence
together, and are called forth by the same exigency. When we conclude
from personal experience without referring to any record--to any general
theorems, either written, or traditional, or mentally registered by
ourselves as conclusions of our own drawing, we do not use, in our
thoughts, either a major or a minor, such as the syllogism puts into
words. When, however, we revise this rough inference from particulars to
particulars, and substitute a careful one, the revision consists in
selecting two syllogistic premises. But this neither alters nor adds to
the evidence we had before; it only puts us in a better position for
judging whether our inference from particulars to particulars is well

[17] Infra, book iii. ch. ii.

[18] Infra, book iii. ch. iv. § 3, and elsewhere.

[19] _Mechanical Euclid_, pp. 149 _et seqq._

[20] We might, it is true, insert this property into the definition of
parallel lines, framing the definition so as to require, both that when
produced indefinitely they shall never meet, and also that any straight
line which intersects one of them shall, if prolonged, meet the other.
But by doing this we by no means get rid of the assumption; we are still
obliged to take for granted the geometrical truth, that all straight
lines in the same plane, which have the former of these properties, have
also the latter. For if it were possible that they should not, that is,
if any straight lines other than those which are parallel according to
the definition, had the property of never meeting although indefinitely
produced, the demonstrations of the subsequent portions of the theory of
parallels could not be maintained.

[21] Some persons find themselves prevented from believing that the
axiom, Two straight lines cannot inclose a space, could ever become
known to us through experience, by a difficulty which may be stated as
follows. If the straight lines spoken of are those contemplated in the
definition--lines absolutely without breadth and absolutely
straight;--that such are incapable of inclosing a space is not proved by
experience, for lines such as these do not present themselves in our
experience. If, on the other hand, the lines meant are such straight
lines as we do meet with in experience, lines straight enough for
practical purposes, but in reality slightly zigzag, and with some,
however trifling, breadth; as applied to these lines the axiom is not
true, for two of them may, and sometimes do, inclose a small portion of
space. In neither case, therefore, does experience prove the axiom.

Those who employ this argument to show that geometrical axioms cannot be
proved by induction, show themselves unfamiliar with a common and
perfectly valid mode of inductive proof; proof by approximation. Though
experience furnishes us with no lines so unimpeachably straight that two
of them are incapable of inclosing the smallest space, it presents us
with gradations of lines possessing less and less either of breadth or
of flexure, of which series the straight line of the definition is the
ideal limit. And observation shows that just as much, and as nearly, as
the straight lines of experience approximate to having no breadth or
flexure, so much and so nearly does the space-inclosing power of any two
of them approach to zero. The inference that if they had no breadth or
flexure at all, they would inclose no space at all, is a correct
inductive inference from these facts, conformable to one of the four
Inductive Methods hereinafter characterized, the Method of Concomitant
Variations; of which the mathematical Doctrine of Limits presents the
extreme case.

[22] Whewell's _History of Scientific Ideas_, i. 140.

[23] Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it
unreasonable to contend that we know by experience, that our idea of a
line exactly resembles a real line. "It does not appear," he says, "how
we can compare our ideas with the realities, since we know the realities
only by our ideas." We know the realities (I conceive) by our senses.
Dr. Whewell surely does not hold the "doctrine of perception by means of
ideas," which Reid gave himself so much trouble to refute.

If Dr. Whewell doubts whether we compare our ideas with the
corresponding sensations, and assume that they resemble, let me ask on
what evidence do we judge that a portrait of a person not present is
like the original. Surely because it is like our idea, or mental image
of the person, and because our idea is like the man himself.

Dr. Whewell also says, that it does not appear why this resemblance of
ideas to the sensations of which they are copies, should be spoken of as
if it were a peculiarity of one class of ideas, those of space. My reply
is, that I do not so speak of it. The peculiarity I contend for is only
one of degree. All our ideas of sensation of course resemble the
corresponding sensations, but they do so with very different degrees of
exactness and of reliability. No one, I presume, can recal in
imagination a colour or an odour with the same distinctness and accuracy
with which almost every one can mentally reproduce an image of a
straight line or a triangle. To the extent, however, of their
capabilities of accuracy, our recollections of colours or of odours may
serve as subjects of experimentation, as well as those of lines and
spaces, and may yield conclusions which will be true of their external
prototypes. A person in whom, either from natural gift or from
cultivation, the impressions of colour were peculiarly vivid and
distinct, if asked which of two blue flowers was of the darkest tinge,
though he might never have compared the two, or even looked at them
together, might be able to give a confident answer on the faith of his
distinct recollection of the colours; that is, he might examine his
mental pictures, and find there a property of the outward objects. But
in hardly any case except that of simple geometrical forms, could this
be done by mankind generally, with a degree of assurance equal to that
which is given by a contemplation of the objects themselves. Persons
differ most widely in the precision of their recollection, even of
forms: one person, when he has looked any one in the face for half a
minute, can draw an accurate likeness of him from memory; another may
have seen him every day for six months, and hardly know whether his nose
is long or short. But everybody has a perfectly distinct mental image of
a straight line, a circle, or a rectangle. And every one concludes
confidently from these mental images to the corresponding outward
things. The truth is, that we may, and continually do, study nature in
our recollections, when the objects themselves are absent; and in the
case of geometrical forms we can perfectly, but in most other cases only
imperfectly, trust our recollections.

[24] _History of Scientific Ideas_, i. 65-67.

[25] Ibid. 60.

[26] _History of Scientific Ideas_, i. 58, 59.

[27] "If all mankind had spoken one language, we cannot doubt that there
would have been a powerful, perhaps a universal, school of philosophers,
who would have believed in the inherent connexion between names and
things, who would have taken the sound _man_ to be the mode of agitating
the air which is essentially communicative of the ideas of reason,
cookery, bipedality, &c."--De Morgan, _Formal Logic_, p. 246.

[28] It would be difficult to name a man more remarkable at once for the
greatness and the wide range of his mental accomplishments, than
Leibnitz. Yet this eminent man gave as a reason for rejecting Newton's
scheme of the solar system, that God _could not_ make a body revolve
round a distant centre, unless either by some impelling mechanism, or by
miracle:--"Tout ce qui n'est pas explicable" says he in a letter to the
Abbé Conti, "par la nature des créatures, est miraculeux. Il ne suffit
pas de dire: Dieu a fait une telle loi de nature; donc la chose est
naturelle. Il faut que la loi soit exécutable par les natures des
créatures. Si Dieu donnait cette loi, par exemple, à un corps libre, de
tourner à l'entour d'un certain centre, _il faudrait ou qu'il y joignît
d'autres corps qui par leur impulsion l'obligeassent de rester toujours
dans son orbite circulaire, ou qu'il mît un ange à ses trousses, ou
enfin il faudrait qu'il y concourût extraordinairement_; car
naturellement il s'écartera par la tangente."--_Works of Leibnitz_, ed.
Dutens, iii. 446.

[29] _Novum Organum Renovatum_, pp. 32, 33.

[30] _History of Scientific Ideas_, i. 264.

[31] _Hist. Sc. Id._, i. 263.

[32] Ibid. 240.

[33] _Hist. Sc. Id._, ii. 25, 26.

[34] _Phil. of Disc._, p. 339.

[35] _Phil. of Disc._, p. 338.

[36] Ib. p. 463.

[37] _Phil. of Disc._, pp. 472, 473.

[38] The _Quarterly Review_ for June 1841, contained an article of great
ability on Dr. Whewell's two great works (since acknowledged and
reprinted in Sir John Herschel's Essays) which maintains, on the subject
of axioms, the doctrine advanced in the text, that they are
generalizations from experience, and supports that opinion by a line of
argument strikingly coinciding with mine. When I state that the whole of
the present chapter (except the last four pages, added in the fifth
edition) was written before I had seen the article, (the greater part,
indeed, before it was published,) it is not my object to occupy the
reader's attention with a matter so unimportant as the degree of
originality which may or may not belong to any portion of my own
speculations, but to obtain for an opinion which is opposed to reigning
doctrines, the recommendation derived from a striking concurrence of
sentiment between two inquirers entirely independent of one another. I
embrace the opportunity of citing from a writer of the extensive
acquirements in physical and metaphysical knowledge and the capacity of
systematic thought which the article evinces, passages so remarkably in
unison with my own views as the following:--

"The truths of geometry are summed up and embodied in its definitions
and axioms.... Let us turn to the axioms, and what do we find? A string
of propositions concerning magnitude in the abstract, which are equally
true of space, time, force, number, and every other magnitude
susceptible of aggregation and subdivision. Such propositions, where
they are not mere definitions, as some of them are, carry their
inductive origin on the face of their enunciation.... Those which
declare that two straight lines cannot inclose a space, and that two
straight lines which cut one another cannot both be parallel to a third,
are in reality the only ones which express characteristic properties of
space, and these it will be worth while to consider more nearly. Now the
only clear notion we can form of straightness is uniformity of
direction, for space in its ultimate analysis is nothing but an
assemblage of distances and directions. And (not to dwell on the notion
of continued contemplation, _i.e._, mental experience, as included in
the very idea of uniformity; nor on that of transfer of the
contemplating being from point to point, and of experience, during such
transfer, of the homogeneity of the interval passed over) we cannot even
propose the proposition in an intelligible form to any one whose
experience ever since he was born has not assured him of the fact. The
unity of direction, or that we cannot march from a given point by more
than one path direct to the same object, is matter of practical
experience long before it can by possibility become matter of abstract
thought. _We cannot attempt mentally to exemplify the conditions of the
assertion in an imaginary case opposed to it, without violating our
habitual recollection of this experience, and defacing our mental
picture of space as grounded on it._ What but experience, we may ask,
can possibly assure us of the homogeneity of the parts of distance,
time, force, and measurable aggregates in general, on which the truth of
the other axioms depends? As regards the latter axiom, after what has
been said it must be clear that the very same course of remarks equally
applies to its case, and that its truth is quite as much forced on the
mind as that of the former by daily and hourly experience, ...
_including always, be it observed, in our notion of experience, that
which is gained by contemplation of the inward picture which the mind
forms to itself in any proposed case, or which it arbitrarily selects as
an example--such picture, in virtue of the extreme simplicity of these
primary relations, being called up by the imagination with as much
vividness and clearness as could be done by any external impression,
which is the only meaning we can attach to the word intuition, as
applied to such relations_."

And again, of the axioms of mechanics:--"As we admit no such
propositions, other than as truths inductively collected from
observation, even in geometry itself, it can hardly be expected that, in
a science of obviously contingent relations, we should acquiesce in a
contrary view. Let us take one of these axioms and examine its evidence:
for instance, that equal forces perpendicularly applied at the opposite
ends of equal arms of a straight lever will balance each other. What but
experience, we may ask, in the first place, can possibly inform us that
a force so applied will have any tendency to turn the lever on its
centre at all? or that force can be so transmitted along a rigid line
perpendicular to its direction, as to act elsewhere in space than along
its own line of action? Surely this is so far from being self-evident
that it has even a paradoxical appearance, which is only to be removed
by giving our lever thickness, material composition, and molecular
powers. Again, we conclude, that the two forces, being equal and applied
under precisely similar circumstances, must, if they exert any effort at
all to turn the lever, exert equal and opposite efforts: but what _à
priori_ reasoning can possibly assure us that they _do_ act under
precisely similar circumstances? that points which differ in place _are_
similarly circumstanced as regards the exertion of force? that universal
space may not have relations to universal force--or, at all events, that
the organization of the material universe may not be such as to place
that portion of space occupied by it in such relations to the forces
exerted in it, as may invalidate the absolute similarity of
circumstances assumed? Or we may argue, what have we to do with the
notion of angular movement in the lever at all? The case is one of rest,
and of quiescent destruction of force by force. Now how is this
destruction effected? Assuredly by the counter-pressure which supports
the fulcrum. But would not this destruction equally arise, and by the
same amount of counter-acting force, if each force simply pressed its
own half of the lever against the fulcrum? And what can assure us that
it is not so, except removal of one or other force, and consequent
tilting of the lever? The other fundamental axiom of statics, that the
pressure on the point of support is the sum of the weights ... is merely
a scientific transformation and more refined mode of stating a coarse
and obvious result of universal experience, viz. that the weight of a
rigid body is the same, handle it or suspend it in what position or by
what point we will, and that whatever sustains it sustains its total
weight. Assuredly, as Mr. Whewell justly remarks, 'No one probably ever
made a trial for the purpose of showing that the pressure on the support
is equal to the sum of the weights.' ... But it is precisely because in
every action of his life from earliest infancy he has been continually
making the trial, and seeing it made by every other living being about
him, that he never dreams of staking its result on one additional
attempt made with scientific accuracy. This would be as if a man should
resolve to decide by experiment whether his eyes were useful for the
purpose of seeing, by hermetically sealing himself up for half an hour
in a metal case."

On the "paradox of universal propositions obtained by experience," the
same writer says: "If there be necessary and universal truths
expressible in propositions of axiomatic simplicity and obviousness, and
having for their subject-matter the elements of all our experience and
all our knowledge, surely these are the truths which, if experience
suggest to us any truths at all, it ought to suggest most readily,
clearly, and unceasingly. If it were a truth, universal and necessary,
that a net is spread over the whole surface of every planetary globe, we
should not travel far on our own without getting entangled in its
meshes, and making the necessity of some means of extrication an axiom
of locomotion.... There is, therefore, nothing paradoxical, but the
reverse, in our being led by observation to a recognition of such
truths, as _general_ propositions, coextensive at least with all human
experience. That they pervade all the objects of experience, must ensure
their continual suggestion _by_ experience; that they are true, must
ensure that consistency of suggestion, that iteration of uncontradicted
assertion, which commands implicit assent, and removes all occasion of
exception; that they are simple, and admit of no misunderstanding, must
secure their admission by every mind."

"A truth, necessary and universal, relative to any object of our
knowledge, must verify itself in every instance where that object is
before our contemplation, and if at the same time it be simple and
intelligible, its verification must be obvious. _The sentiment of such a
truth cannot, therefore, but be present to our minds whenever that
object is contemplated, and must therefore make a part of the mental
picture or idea of that object which we may on any occasion summon
before our imagination.... All propositions, therefore, become not only
untrue but inconceivable_, if ... axioms be violated in their

Another eminent mathematician had previously sanctioned by his authority
the doctrine of the origin of geometrical axioms in experience.
"Geometry is thus founded likewise on observation; but of a kind so
familiar and obvious, that the primary notions which it furnishes might
seem intuitive."--_Sir John Leslie_, quoted by Sir William Hamilton,
_Discourses_, &c. p. 272.

[39] _Principles of Psychology._

[40] Mr. Spencer is mistaken in supposing me to claim any peculiar
"necessity" for this axiom as compared with others. I have corrected the
expressions which led him into that misapprehension of my meaning.

[41] Mr. Spencer makes a distinction between conceiving myself looking
into darkness, and conceiving _that I am_ then and there looking into
darkness. To me it seems that this change of the expression to the form
_I am_, just marks the transition from conception to belief, and that
the phrase "to conceive that _I am_," or "that anything _is_," is not
consistent with using the word conceive in its rigorous sense.

[42] I have myself accepted the contest, and fought it out on this
battleground, in the eleventh chapter of _An Examination of Sir William
Hamilton's Philosophy_.

[43] _Discussions_, &c., 2nd ed. p. 624.

[44] If it be said that the _existence_ of matter is among the things
proved by the principle of Excluded Middle, that principle must prove
also the existence of dragons and hippogriffs, because they must be
either scaly or not scaly, creeping or not creeping, and so forth.

[45] For further considerations respecting the axioms of Contradiction
and Excluded Middle, see the twenty-first chapter of _An Examination of
Sir William Hamilton's Philosophy_.

[46] Mr. De Morgan says "Plato," but to prevent confusion I have kept to
my own _exemplum_.



"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.



§ 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, cannot 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
endeavouring 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, cannot 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 we take in a new
induction, represented, in the aggregate of its results, by a general

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.[1]

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.



§ 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 anything 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 reassertion 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, cannot 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
cannot 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 an 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 cannot 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[2]) 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 an 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
cannot 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 _à 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 _à 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, cannot but perceive that in raising a binomial to a
power, the coefficients must depend on the laws of permutation and
combination: and as soon as this is recognised, 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

§ 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 cannot 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 anything of the nature of an induction in this process? Did he
infer anything 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 anything to the power of prediction already

§ 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,[3] "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 connexion. 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 endeavouring
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 recognised 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 cannot 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
cannot 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 anything 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 cannot 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 afterwards 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."[4] 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 skilful 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, and facts were disclosed which were not
reconcileable 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 excentrics 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 afterwards 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."[5]

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

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.[6]

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, towards 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 connexion for those facts; a new principle for their

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, re-stating his opinions, but without (as far as I can
perceive) adding anything 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_.[7] 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, cannot 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 connexion 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 everything 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.



§ 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,[8]
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 cannot be found a true major premise.[9]

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, &c. 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, &c. 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, &c. 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.[10]

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.[11] 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,
everybody 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 an uniformity of the course of nature where no such uniformity really

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
cannot 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.[12] 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, cannot 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 colour,
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. 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; an 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 grey.

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 towards
establishing an 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.



§ 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 coexistence 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 connexion between parts of the great whole which we
term nature, a general tissue of connexion 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
three first, therefore, according to the stricter acceptation, are
called laws of nature; the remainder not; because they are in truth mere
_cases_ of the three first; 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 towards 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 towards 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
anything 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 unravelling 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 learnt, 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 connexion 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 afterwards 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

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 colours 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 sort 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

§ 3. The necessity of such a survey is confirmed by the consideration,
that the stronger inductions are the touchstone to which we always
endeavour 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 practised, 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:[13] 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 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.



§ 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 an uniform manner, to some phenomena that coexist 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, coexist; and the
unvarying laws which are the subject of the science of geometry, are an
expression of the mode of their coexistence.

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. If
all the objects in the universe were unchangeably fixed, and had
remained in that condition from eternity, the propositions of geometry
would still be true of those objects. 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 recognise 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
endeavoured 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 cannot 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 towards 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 phenomena, 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 endeavour 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

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 recognise a law which
is universal also in another sense; it is coextensive 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 coextensive with human

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 everything."
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 phenomena 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
anything. 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
cannot, 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
consideration respecting the ultimate mode of production of phenomena,
and of every other question regarding the nature of "Things in

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 connexion 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 connexion
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 fulfilment 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. The production of the consequent required that
they should all _exist_ immediately previous, though not that they
should all _begin_ to exist immediately previous. The statement of the
cause is incomplete, unless in some shape or other we introduce all the
conditions. 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 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 analysing 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 towards 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

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 anything 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.[14]

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,[15] 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, some 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 towards 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 licence 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 colour, 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. 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 anything (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[16] 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[17] 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

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 recognising 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,"[18] 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 coexistence 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 coexist, 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 coexist, 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 coexist 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
coexistence, which, like the earth's motions, or the succession of day
and night, depend on the existence or on the coexistence 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. Comte,
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.
Comte 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. Comte'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,[19]
"who, like M. Comte, 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. Comte 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. Comte's great powers.

§ 6. 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 coexist; 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 a 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
ploughshare once made, remains a ploughshare, 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 these 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,[20]) 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
cannot 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 coexistent phenomena, which is cause
and which effect, we rightly deem the question solved if we can
ascertain which of them preceded the other.

§ 7. 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
grey colour, 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 colour, 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 connexion
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 cannot 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
coexistence, therefore, of Primeval Causes, ranks, to us, among merely
casual concurrences: and all those sequences or coexistences among the
effects of several such causes, which, though invariable while those
causes coexist, would, if the coexistence 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 coexistences 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
towards 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 an 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 coexist.
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.[21] 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 _à 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.

§ 8. Since everything which occurs is determined by laws of causation
and collocations of the original causes, it follows that the
coexistences which are observable among effects cannot be themselves the
subject of any similar set of laws, distinct from laws of causation.
Uniformities there are, as well of coexistence as of succession, among
effects; but these must in all cases be a mere result either of the
identity or of the coexistence of their causes: if the causes did not
coexist, 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
coexistences of phenomena can in no case be universal, unless the
coexistences of the primeval causes to which the effects are ultimately
traceable, can be reduced to an universal law: but we have seen that
they cannot. There are, accordingly, no original and independent, in
other words no unconditional, uniformities of coexistence, between
effects of different causes; if they coexist, it is only because the
causes have casually coexisted. The only independent and unconditional
coexistences 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.

§ 9. 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

According to the theory in question, Mind, or, to speak more 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 _à 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 cannot 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
connexion between them is a subject of experience. I cannot admit that
our consciousness of the volition contains in itself any _à priori_
knowledge that the muscular motion will follow. If our nerves of motion
were paralysed, 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
anything 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 cognisant, and the
internal act of mental determination of which we are also cognisant,
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 connexion 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
fulfil 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

Those against whom I am contending have never produced, and do not
pretend to produce, any positive evidence[23] 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 cannot
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 favour, 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."[24]

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 connexion,
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."[25] 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
connexion "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 connexion between
physical antecedents and their consequents, he demanded some naturally
and _per se_ efficient physical antecedent as the bond of connexion
between Volition itself and its effects. He distinctly refused to admit
the will of God as a sufficient explanation of anything except miracles;
and insisted upon finding something that would account _better_ for the
phenomena of nature than a mere reference to divine volition.[26]

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 connexion, no relation _à 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 afterwards 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 cannot, 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

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 experience 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

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 anything
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 everything 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 everything, 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.


     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:[27] "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 counterstatement as to the first of these
     cases the author shows--what we believe now hardly admits of
     doubt--that the Greek philosophers distinctly recognised 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

     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 Ritter, vol. i.
     p. 211, 2nd 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.[28] 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 cotemporaries,
     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 recognised only the second kind of Cause, the
     Matter of a thing, _τὰς ἐν ὕλης εἴδει μόνας ᾠήθησαν ἀρχὰς εἶναι
     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 material,
     since the material cannot originate its own changes: _οὐ γὰρ δὴ
     τό γε ὑποκείμενον αὐτὸ ποιεῖ μεταβάλλειν ἑαῦτο; λέγω δ' οἶον
     οὔτε τὸ ξύλον οὔτε ὅ χαλκὸς αἴτιος τοῦ μεταβάλλειν έκάτερον
     αὐτῶν, οὐδὲ ποιεῖ τὸ μἑν ξύλον κλίνην ὅ δέ χαλκὸς ἀνδριάντα,
     ἀλλ' ἑτερον τι τῆς μεταβολῆς αἴτιον_, viz., the other kind of
     cause, _ὅθεν 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, _οἶον 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: _οὐδὲν ἐδυσχεράναν
     ἐν ἑαυτοῖς_. It is surely unnecessary to say more in proof of
     the matter of fact which Dr. Tulloch and his reviewer deny.

     Having pointed out what he thinks the error of these early
     speculators in not recognising 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' αὖ τῷ αὐτομάτῳ καὶ τῇ τύχῃ τοσοῦτον
     ἐπιτρέψαι πρᾶγμα καλῶς εἶχεν_: but he does not reject them as
     incapable of producing any effect, but only as incapable of
     producing _that_ effect. He himself recognises _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
     recognised 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.[29]

     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
     Preestablished 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 _à 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 Preestablished Harmony, according to which there is no more
     connexion 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 2, chap. 3, of his Sixth Book,
     having first said that matter cannot 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 veut raisonner selon ses lumières, qu'il n'y a
     aucun esprit créé qui puisse remuer quelque corps que ce soit
     comme cause véritable ou 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

     A doctrine more precisely the reverse of the Volitional theory
     of causation cannot 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 cannot 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 recognise our
     volitions as efficient causes, and then find other thinkers
     maintaining that we know that they are not, and cannot be such
     causes, and cannot 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. 45-7) 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
     anything 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.



§ 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 _à priori_, at a correct prediction of what will
arise from their conjunct agency. To enable us to do this, 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
afterwards 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 entirely different from
those of either of the two substances separately, or 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 colour of blue vitriol a mixture of the
colours 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 all 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 observed 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 conformed 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

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, fibrin, 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 fibrin
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 towards 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,[31] and the stream had flowed in for as long
afterwards. Each agent produced 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 operation 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 affects the one
affects 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 coexist 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 analysed 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.
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 incumbered 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 cannot 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.

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 coexistence, 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.



§ 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 somewhere among the 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 endeavour 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 farther 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 recognised.

§ 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 (_à 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

Thus far the advantage of experimentation over simple observation is
universally recognised: 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 everything 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 connexion 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 practised at a disadvantage in most cases equivalent to
impracticability: from which it follows that the methods of those
sciences, in order to accomplish anything 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 recognised 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
cannot 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 cannot, 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

But though this is certainly the most favourable 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.[32] 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
coexistences, but cannot 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 coexistence, 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 cannot 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.



§ 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_ cannot 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 cannot 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, cannot 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

In this example we may go farther, 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 cannot 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 analyse 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

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 principle the following


_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 endeavoured 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 gun-shot which killed him: for he was in the fulness of life
immediately before, all circumstances being the same, except the wound.

The axioms implied in this method are evidently the following. Whatever
antecedent cannot 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


_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 cannot 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 coexistent 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. Comte
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 anything, 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 anything,
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
cannot 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 cannot 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 connexion 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 connexion between A and _a_. In order to convert this evidence of
connexion 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 connexion 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

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:--


_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

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 cannot 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:--


_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 cannot be
prevented from coexisting. In respect, indeed, to most of the permanent
causes, no such difficulty exists; since though we cannot eliminate
them as coexisting 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 everything
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 cannot be removed from the influence of the earth: we
cannot 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 coexistent 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
cannot effect such a variation of circumstances as the foregoing three
methods require; we cannot 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 cannot 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
_vice versâ_, 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 cannot 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 cannot 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 towards 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 towards the west, as the moon, followed by the nearer
of the tide waves, advances towards 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 towards 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


_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 endeavouring 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 cannot ourselves produce the variations, we must
endeavour, 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 endeavour 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 _towards_ 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
connexion 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 anything 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

§ 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 relation to the variations of A. In that case, when A
diminishes, _a_ will be seen to approach not towards zero, but towards
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 cannot, 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 cannot 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, &c., 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 towards 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 an 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,[33] "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
connexion 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, cannot
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 connexion 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 _à
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.



§ 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 afterwards 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 afterwards 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

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 _à 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 cannot 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,
cannot 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 suboxide, 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 neighbouring 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 rigour 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 hindrance
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
cannot be ascertained to agree in any other property whatsoever. We have
thus, in favour 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[34] 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 neighbourhood 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 cannot 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 cannot 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 neighbouring 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 cannot 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 neighbouring 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 neighbouring 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 neighbouring 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 neighbouring
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 neighbouring 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.[35]

§ 3. Our third example shall be extracted from Sir John Herschel's
_Discourse 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
recognised, 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

"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.[37]

"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 connexion 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 upwards,
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 cannot 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
recognise, 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
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, &c., as unfavourable, but those of a loose one, as
cloth, velvet, wool, eider-down, cotton, &c., as eminently favourable 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 cause 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 coexistence 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 connexion
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 vapour 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 vapour 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 vapour suspended as the air will contain at its
existing temperature, any lowering of that temperature will cause a
portion of the vapour 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 coexistence; 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 vapour,
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 vapour 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.[38]

The accumulated proof of which the Theory of Dew has been found
susceptible, is a striking instance of the fulness 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

§ 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

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 variation. 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. Paralysed muscles have greater irritability than healthy muscles.
Now, paralysed 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 paralysed muscles have
greater irritability than healthy muscles--he ascertained in various
ways, but most decisively by "comparing the duration of irritability in
a paralysed 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 paralysed 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

In the same manner in which Dr. Brown-Séquard proved that paralysed
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 paralysed 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
paralysed 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.

2ndly. 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.

3rdly. 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 connexion 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.

4thly. 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 connexion is therefore inductively proved between the
degree of the nutrition, and the slowness and prolongation of the

5thly. 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.

6thly. 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; 2ndly, hemorrhage in or
around the brain, or in the lungs, the pericardium, &c.; 3rdly,
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 cannot
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 cannot
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 maybe 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 over-exertion, 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 connexion 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 cannot 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
fulfils 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 cannot, therefore, depend upon the causes of
irritability, nor up