Chapter I.

A SYSTEM OF LOGIC,

RATIOCINATIVE AND INDUCTIVE,

BEING A CONNECTED VIEW OF THE

PRINCIPLES OF EVIDENCE,

AND THE

METHODS OF SCIENTIFIC INVESTIGATION.

by

JOHN STUART MILL.

Eighth Edition.

New York:

Harper & Brothers, Publishers,

Franklin Square.

1882.

CONTENTS

Preface To The First Edition.

Preface To The Third And Fourth Editions.

Introduction.

Book I. Of Names And Propositions.

Chapter I. Of The Necessity Of Commencing With An Analysis Of Language.

Chapter II. Of Names.

Chapter III. Of The Things Denoted By Names.

Chapter IV. Of Propositions.

Chapter V. Of The Import Of Propositions.

Chapter VI. Of Propositions Merely Verbal.

Chapter VII. Of The Nature Of Classification, And The Five Predicables.

Chapter VIII. Of Definition.

Book II. On Reasoning.

Chapter I. Of Inference, Or Reasoning, In General.

Chapter II. Of Ratiocination, Or Syllogism.

Chapter III. Of The Functions And Logical Value Of The Syllogism.

Chapter IV. Of Trains Of Reasoning, And Deductive Sciences.

Chapter V. Of Demonstration, And Necessary Truths.

Chapter VI. The Same Subject Continued.

Chapter VII. Examination Of Some Opinions Opposed To The Preceding

Doctrines.

Book III. Of Induction.

Chapter I. Preliminary Observations On Induction In General.

Chapter II. Of Inductions Improperly So Called.

Chapter III. Of The Ground Of Induction.

Chapter IV. Of Laws Of Nature.

Chapter V. Of The Law Of Universal Causation.

Chapter VI. On The Composition Of Causes.

Chapter VII. On Observation And Experiment.

Chapter VIII. Of The Four Methods Of Experimental Inquiry.

Chapter IX. Miscellaneous Examples Of The Four Methods.

Chapter X. Of Plurality Of Causes, And Of The Intermixture Of Effects.

Chapter XI. Of The Deductive Method.

Chapter XII. Of The Explanation Of Laws Of Nature.

Chapter XIII. Miscellaneous Examples Of The Explanation Of Laws Of

Nature.

Chapter XIV. Of The Limits To The Explanation Of Laws Of Nature; And Of

Hypotheses.

Chapter XV. Of Progressive Effects; And Of The Continued Action Of

Causes.

Chapter XVI. Of Empirical Laws.

Chapter XVII. Of Chance And Its Elimination.

Chapter XVIII. Of The Calculation Of Chances.

Chapter XIX. Of The Extension Of Derivative Laws To Adjacent Cases.

Chapter XX. Of Analogy.

Chapter XXI. Of The Evidence Of The Law Of Universal Causation.

Chapter XXII. Of Uniformities Of Co-Existence Not Dependent On

Causation.

Chapter XXIII. Of Approximate Generalizations, And Probable Evidence.

Chapter XXIV. Of The Remaining Laws Of Nature.

Chapter XXV. Of The Grounds Of Disbelief.

Book IV. Of Operations Subsidiary To Induction.

Chapter I. Of Observation And Description.

Chapter II. Of Abstraction, Or The Formation Of Conceptions.

Chapter III. Of Naming, As Subsidiary To Induction.

Chapter IV. Of The Requisites Of A Philosophical Language, And The

Principles Of Definition.

Chapter V. On The Natural History Of The Variations In The Meaning Of

Terms.

Chapter VI. The Principles Of A Philosophical Language Further

Considered.

Chapter VII. Of Classification, As Subsidiary To Induction.

Chapter VIII. Of Classification By Series.

Book V. On Fallacies.

Chapter I. Of Fallacies In General.

Chapter II. Classification Of Fallacies.

Chapter III. Fallacies Of Simple Inspection; Or A Priori Fallacies.

Chapter IV. Fallacies Of Observation.

Chapter V. Fallacies Of Generalization.

Chapter VI. Fallacies Of Ratiocination.

Chapter VII. Fallacies Of Confusion.

Book VI. On The Logic Of The Moral Sciences.

Chapter I. Introductory Remarks.

Chapter II. Of Liberty And Necessity.

Chapter III. That There Is, Or May Be, A Science Of Human Nature.

Chapter IV. Of The Laws Of Mind.

Chapter V. Of Ethology, Or The Science Of The Formation Of Character.

Chapter VI. General Considerations On The Social Science.

Chapter VII. Of The Chemical, Or Experimental, Method In The Social

Science.

Chapter VIII. Of The Geometrical, Or Abstract, Method.

Chapter IX. Of The Physical, Or Concrete Deductive, Method.

Chapter X. Of The Inverse Deductive, Or Historical, Method.

Chapter XI. Additional Elucidations Of The Science Of History.

Chapter XII. Of The Logic Of Practice, Or Art; Including Morality And

Policy.

Footnotes

PREFACE TO THE FIRST EDITION.

This book makes no pretense of giving to the world a new theory of the

intellectual operations. Its claim to attention, if it possess any, is

grounded on the fact that it is an attempt, not to supersede, but to

embody and systematize, the best ideas which have been either promulgated

on its subject by speculative writers, or conformed to by accurate

thinkers in their scientific inquiries.

To cement together the detached fragments of a subject, never yet treated

as a whole; to harmonize the true portions of discordant theories, by

supplying the links of thought necessary to connect them, and by

disentangling them from the errors with which they are always more or less

interwoven, must necessarily require a considerable amount of original

speculation. To other originality than this, the present work lays no

claim. In the existing state of the cultivation of the sciences, there

would be a very strong presumption against any one who should imagine that

he had effected a revolution in the theory of the investigation of truth,

or added any fundamentally new process to the practice of it. The

improvement which remains to be effected in the methods of philosophizing

(and the author believes that they have much need of improvement) can only

consist in performing more systematically and accurately operations with

which, at least in their elementary form, the human intellect, in some one

or other of its employments, is already familiar.

In the portion of the work which treats of Ratiocination, the author has

not deemed it necessary to enter into technical details which may be

obtained in so perfect a shape from the existing treatises on what is

termed the Logic of the Schools. In the contempt entertained by many

modern philosophers for the syllogistic art, it will be seen that he by no

means participates; though the scientific theory on which its defense is

usually rested appears to him erroneous: and the view which he has

suggested of the nature and functions of the Syllogism may, perhaps,

afford the means of conciliating the principles of the art with as much as

is well grounded in the doctrines and objections of its assailants.

The same abstinence from details could not be observed in the First Book,

on Names and Propositions; because many useful principles and distinctions

which were contained in the old Logic have been gradually omitted from the

writings of its later teachers; and it appeared desirable both to revive

these, and to reform and rationalize the philosophical foundation on which

they stood. The earlier chapters of this preliminary Book will

consequently appear, to some readers, needlessly elementary and

scholastic. But those who know in what darkness the nature of our

knowledge, and of the processes by which it is obtained, is often involved

by a confused apprehension of the import of the different classes of Words

and Assertions, will not regard these discussions as either frivolous, or

irrelevant to the topics considered in the later Books.

On the subject of Induction, the task to be performed was that of

generalizing the modes of investigating truth and estimating evidence, by

which so many important and recondite laws of nature have, in the various

sciences, been aggregated to the stock of human knowledge. That this is

not a task free from difficulty may be presumed from the fact that even at

a very recent period, eminent writers (among whom it is sufficient to name

Archbishop Whately, and the author of a celebrated article on Bacon in the

_Edinburgh Review_) have not scrupled to pronounce it impossible.(1) The

author has endeavored to combat their theory in the manner in which

Diogenes confuted the skeptical reasonings against the possibility of

motion; remembering that Diogenes’s argument would have been equally

conclusive, though his individual perambulations might not have extended

beyond the circuit of his own tub.

Whatever may be the value of what the author has succeeded in effecting on

this branch of his subject, it is a duty to acknowledge that for much of

it he has been indebted to several important treatises, partly historical

and partly philosophical, on the generalities and processes of physical

science, which have been published within the last few years. To these

treatises, and to their authors, he has endeavored to do justice in the

body of the work. But as with one of these writers, Dr. Whewell, he has

occasion frequently to express differences of opinion, it is more

particularly incumbent on him in this place to declare, that without the

aid derived from the facts and ideas contained in that gentleman’s

“History of the Inductive Sciences,” the corresponding portion of this

work would probably not have been written.

The concluding Book is an attempt to contribute toward the solution of a

question which the decay of old opinions, and the agitation that disturbs

European society to its inmost depths, render as important in the present

day to the practical interests of human life, as it must at all times be

to the completeness of our speculative knowledge—viz.: Whether moral and

social phenomena are really exceptions to the general certainty and

uniformity of the course of nature; and how far the methods by which so

many of the laws of the physical world have been numbered among truths

irrevocably acquired and universally assented to, can be made instrumental

to the formation of a similar body of received doctrine in moral and

political science.

PREFACE TO THE THIRD AND FOURTH EDITIONS.

Several criticisms, of a more or less controversial character, on this

work, have appeared since the publication of the second edition; and Dr.

Whewell has lately published a reply to those parts of it in which some of

his opinions were controverted.(2)

I have carefully reconsidered all the points on which my conclusions have

been assailed. But I have not to announce a change of opinion on any

matter of importance. Such minor oversights as have been detected, either

by myself or by my critics, I have, in general silently, corrected: but it

is not to be inferred that I agree with the objections which have been

made to a passage, in every instance in which I have altered or canceled

it. I have often done so, merely that it might not remain a

stumbling-block, when the amount of discussion necessary to place the

matter in its true light would have exceeded what was suitable to the

occasion.

To several of the arguments which have been urged against me, I have

thought it useful to reply with some degree of minuteness; not from any

taste for controversy, but because the opportunity was favorable for

placing my own conclusions, and the grounds of them, more clearly and

completely before the reader. Truth on these subjects is militant, and can

only establish itself by means of conflict. The most opposite opinions can

make a plausible show of evidence while each has the statement of its own

case; and it is only possible to ascertain which of them is in the right,

after hearing and comparing what each can say against the other, and what

the other can urge in its defense.

Even the criticisms from which I most dissent have been of great service

to me, by showing in what places the exposition most needed to be

improved, or the argument strengthened. And I should have been well

pleased if the book had undergone a much greater amount of attack; as in

that case I should probably have been enabled to improve it still more

than I believe I have now done.

——————————————————

In the subsequent editions, the attempt to improve the work by additions

and corrections, suggested by criticism or by thought, has been continued.

The additions and corrections in the present (eighth) edition, which are

not very considerable, are chiefly such as have been suggested by

Professor Bain’s “Logic,” a book of great merit and value. Mr. Bain’s view

of the science is essentially the same with that taken in the present

treatise, the differences of opinion being few and unimportant compared

with the agreements; and he has not only enriched the exposition by many

applications and illustrative details, but has appended to it a minute and

very valuable discussion of the logical principles specially applicable to

each of the sciences—a task for which the encyclopedical character of his

knowledge peculiarly qualified him. I have in several instances made use

of his exposition to improve my own, by adopting, and occasionally by

controverting, matter contained in his treatise.

The longest of the additions belongs to the chapter on Causation, and is a

discussion of the question how far, if at all, the ordinary mode of

stating the law of Cause and Effect requires modification to adapt it to

the new doctrine of the Conservation of Force—a point still more fully and

elaborately treated in Mr. Bain’s work.

INTRODUCTION.

§ 1. There is as great diversity among authors in the modes which they

have adopted of defining logic, as in their treatment of the details of

it. This is what might naturally be expected on any subject on which

writers have availed themselves of the same language as a means of

delivering different ideas. Ethics and jurisprudence are liable to the

remark in common with logic. Almost every writer having taken a different

view of some of the particulars which these branches of knowledge are

usually understood to include; each has so framed his definition as to

indicate beforehand his own peculiar tenets, and sometimes to beg the

question in their favor.

This diversity is not so much an evil to be complained of, as an

inevitable and in some degree a proper result of the imperfect state of

those sciences. It is not to be expected that there should be agreement

about the definition of any thing, until there is agreement about the

thing itself. To define, is to select from among all the properties of a

thing, those which shall be understood to be designated and declared by

its name; and the properties must be well known to us before we can be

competent to determine which of them are fittest to be chosen for this

purpose. Accordingly, in the case of so complex an aggregation of

particulars as are comprehended in any thing which can be called a

science, the definition we set out with is seldom that which a more

extensive knowledge of the subject shows to be the most appropriate. Until

we know the particulars themselves, we can not fix upon the most correct

and compact mode of circumscribing them by a general description. It was

not until after an extensive and accurate acquaintance with the details of

chemical phenomena, that it was found possible to frame a rational

definition of chemistry; and the definition of the science of life and

organization is still a matter of dispute. So long as the sciences are

imperfect, the definitions must partake of their imperfection; and if the

former are progressive, the latter ought to be so too. As much, therefore,

as is to be expected from a definition placed at the commencement of a

subject, is that it should define the scope of our inquiries: and the

definition which I am about to offer of the science of logic, pretends to

nothing more than to be a statement of the question which I have put to

myself, and which this book is an attempt to resolve. The reader is at

liberty to object to it as a definition of logic; but it is at all events

a correct definition of the subject of this volume.

§ 2. Logic has often been called the Art of Reasoning. A writer(3) who has

done more than any other person to restore this study to the rank from

which it had fallen in the estimation of the cultivated class in our own

country, has adopted the above definition with an amendment; he has

defined Logic to be the Science, as well as the Art, of reasoning; meaning

by the former term, the analysis of the mental process which takes place

whenever we reason, and by the latter, the rules, grounded on that

analysis, for conducting the process correctly. There can be no doubt as

to the propriety of the emendation. A right understanding of the mental

process itself, of the conditions it depends on, and the steps of which it

consists, is the only basis on which a system of rules, fitted for the

direction of the process, can possibly be founded. Art necessarily

presupposes knowledge; art, in any but its infant state, presupposes

scientific knowledge: and if every art does not bear the name of a

science, it is only because several sciences are often necessary to form

the groundwork of a single art. So complicated are the conditions which

govern our practical agency, that to enable one thing to be _done_, it is

often requisite to _know_ the nature and properties of many things.

Logic, then, comprises the science of reasoning, as well as an art,

founded on that science. But the word Reasoning, again, like most other

scientific terms in popular use, abounds in ambiguities. In one of its

acceptations, it means syllogizing; or the mode of inference which may be

called (with sufficient accuracy for the present purpose) concluding from

generals to particulars. In another of its senses, to reason is simply to

infer any assertion, from assertions already admitted: and in this sense

induction is as much entitled to be called reasoning as the demonstrations

of geometry.

Writers on logic have generally preferred the former acceptation of the

term: the latter, and more extensive signification is that in which I mean

to use it. I do this by virtue of the right I claim for every author, to

give whatever provisional definition he pleases of his own subject. But

sufficient reasons will, I believe, unfold themselves as we advance, why

this should be not only the provisional but the final definition. It

involves, at all events, no arbitrary change in the meaning of the word;

for, with the general usage of the English language, the wider

signification, I believe, accords better than the more restricted one.

§ 3. But reasoning, even in the widest sense of which the word is

susceptible, does not seem to comprehend all that is included, either in

the best, or even in the most current, conception of the scope and

province of our science. The employment of the word Logic to denote the

theory of Argumentation, is derived from the Aristotelian, or, as they are

commonly termed, the scholastic, logicians. Yet even with them, in their

systematic treatises, Argumentation was the subject only of the third

part: the two former treated of Terms, and of Propositions; under one or

other of which heads were also included Definition and Division. By some,

indeed, these previous topics were professedly introduced only on account

of their connection with reasoning, and as a preparation for the doctrine

and rules of the syllogism. Yet they were treated with greater minuteness,

and dwelt on at greater length, than was required for that purpose alone.

More recent writers on logic have generally understood the term as it was

employed by the able author of the Port Royal Logic; viz., as equivalent

to the Art of Thinking. Nor is this acceptation confined to books, and

scientific inquiries. Even in ordinary conversation, the ideas connected

with the word Logic include at least precision of language, and accuracy

of classification: and we perhaps oftener hear persons speak of a logical

arrangement, or of expressions logically defined, than of conclusions

logically deduced from premises. Again, a man is often called a great

logician, or a man of powerful logic, not for the accuracy of his

deductions, but for the extent of his command over premises; because the

general propositions required for explaining a difficulty or refuting a

sophism, copiously and promptly occur to him: because, in short, his

knowledge, besides being ample, is well under his command for

argumentative use. Whether, therefore, we conform to the practice of those

who have made the subject their particular study, or to that of popular

writers and common discourse, the province of logic will include several

operations of the intellect not usually considered to fall within the

meaning of the terms Reasoning and Argumentation.

These various operations might be brought within the compass of the

science, and the additional advantage be obtained of a very simple

definition, if, by an extension of the term, sanctioned by high

authorities, we were to define logic as the science which treats of the

operations of the human understanding in the pursuit of truth. For to this

ultimate end, naming, classification, definition, and all other operations

over which logic has ever claimed jurisdiction, are essentially

subsidiary. They may all be regarded as contrivances for enabling a person

to know the truths which are needful to him, and to know them at the

precise moment at which they are needful. Other purposes, indeed, are also

served by these operations; for instance, that of imparting our knowledge

to others. But, viewed with regard to this purpose, they have never been

considered as within the province of the logician. The sole object of

Logic is the guidance of one’s own thoughts: the communication of those

thoughts to others falls under the consideration of Rhetoric, in the large

sense in which that art was conceived by the ancients; or of the still

more extensive art of Education. Logic takes cognizance of our

intellectual operations only as they conduce to our own knowledge, and to

our command over that knowledge for our own uses. If there were but one

rational being in the universe, that being might be a perfect logician;

and the science and art of logic would be the same for that one person as

for the whole human race.

§ 4. But, if the definition which we formerly examined included too

little, that which is now suggested has the opposite fault of including

too much.

Truths are known to us in two ways: some are known directly, and of

themselves; some through the medium of other truths. The former are the

subject of Intuition, or Consciousness;(4) the latter, of Inference. The

truths known by intuition are the original premises from which all others

are inferred. Our assent to the conclusion being grounded on the truth of

the premises, we never could arrive at any knowledge by reasoning, unless

something could be known antecedently to all reasoning.

Examples of truths known to us by immediate consciousness, are our own

bodily sensations and mental feelings. I know directly, and of my own

knowledge, that I was vexed yesterday, or that I am hungry to-day.

Examples of truths which we know only by way of inference, are occurrences

which took place while we were absent, the events recorded in history, or

the theorems of mathematics. The two former we infer from the testimony

adduced, or from the traces of those past occurrences which still exist;

the latter, from the premises laid down in books of geometry, under the

title of definitions and axioms. Whatever we are capable of knowing must

belong to the one class or to the other; must be in the number of the

primitive data, or of the conclusions which can be drawn from these.

With the original data, or ultimate premises of our knowledge; with their

number or nature, the mode in which they are obtained, or the tests by

which they may be distinguished; logic, in a direct way at least, has, in

the sense in which I conceive the science, nothing to do. These questions

are partly not a subject of science at all, partly that of a very

different science.

Whatever is known to us by consciousness is known beyond possibility of

question. What one sees or feels, whether bodily or mentally, one can not

but be sure that one sees or feels. No science is required for the purpose

of establishing such truths; no rules of art can render our knowledge of

them more certain than it is in itself. There is no logic for this portion

of our knowledge.

But we may fancy that we see or feel what we in reality infer. A truth, or

supposed truth, which is really the result of a very rapid inference, may

seem to be apprehended intuitively. It has long been agreed by thinkers of

the most opposite schools, that this mistake is actually made in so

familiar an instance as that of the eyesight. There is nothing of which we

appear to ourselves to be more directly conscious than the distance of an

object from us. Yet it has long been ascertained, that what is perceived

by the eye, is at most nothing more than a variously colored surface; that

when we fancy we see distance, all we really see is certain variations of

apparent size, and degrees of faintness of color; that our estimate of the

object’s distance from us is the result partly of a rapid inference from

the muscular sensations accompanying the adjustment of the focal distance

of the eye to objects unequally remote from us, and partly of a comparison

(made with so much rapidity that we are unconscious of making it) between

the size and color of the object as they appear at the time, and the size

and color of the same or of similar objects as they appeared when close at

hand, or when their degree of remoteness was known by other evidence. The

perception of distance by the eye, which seems so like intuition, is thus,

in reality, an inference grounded on experience; an inference, too, which

we learn to make; and which we make with more and more correctness as our

experience increases; though in familiar cases it takes place so rapidly

as to appear exactly on a par with those perceptions of sight which are

really intuitive, our perceptions of color.(5)

Of the science, therefore, which expounds the operations of the human

understanding in the pursuit of truth, one essential part is the inquiry:

What are the facts which are the objects of intuition or consciousness,

and what are those which we merely infer? But this inquiry has never been

considered a portion of logic. Its place is in another and a perfectly

distinct department of science, to which the name metaphysics more

particularly belongs: that portion of mental philosophy which attempts to

determine what part of the furniture of the mind belongs to it originally,

and what part is constructed out of materials furnished to it from

without. To this science appertain the great and much debated questions of

the existence of matter; the existence of spirit, and of a distinction

between it and matter; the reality of time and space, as things without

the mind, and distinguishable from the objects which are said to exist in

them. For in the present state of the discussion on these topics, it is

almost universally allowed that the existence of matter or of spirit, of

space or of time, is in its nature unsusceptible of being proved; and that

if any thing is known of them, it must be by immediate intuition. To the

same science belong the inquiries into the nature of Conception,

Perception, Memory, and Belief; all of which are operations of the

understanding in the pursuit of truth; but with which, as phenomena of the

mind, or with the possibility which may or may not exist of analyzing any

of them into simpler phenomena, the logician as such has no concern. To

this science must also be referred the following, and all analogous

questions: To what extent our intellectual faculties and our emotions are

innate—to what extent the result of association: Whether God and duty are

realities, the existence of which is manifest to us _a priori_ by the

constitution of our rational faculty; or whether our ideas of them are

acquired notions, the origin of which we are able to trace and explain;

and the reality of the objects themselves a question not of consciousness

or intuition, but of evidence and reasoning.

The province of logic must be restricted to that portion of our knowledge

which consists of inferences from truths previously known; whether those

antecedent data be general propositions, or particular observations and

perceptions. Logic is not the science of Belief, but the science of Proof,

or Evidence. In so far as belief professes to be founded on proof, the

office of logic is to supply a test for ascertaining whether or not the

belief is well grounded. With the claims which any proposition has to

belief on the evidence of consciousness—that is, without evidence in the

proper sense of the word—logic has nothing to do.

§ 5. By far the greatest portion of our knowledge, whether of general

truths or of particular facts, being avowedly matter of inference, nearly

the whole, not only of science, but of human conduct, is amenable to the

authority of logic. To draw inferences has been said to be the great

business of life. Every one has daily, hourly, and momentary need of

ascertaining facts which he has not directly observed; not from any

general purpose of adding to his stock of knowledge, but because the facts

themselves are of importance to his interests or to his occupations. The

business of the magistrate, of the military commander, of the navigator,

of the physician, of the agriculturist, is merely to judge of evidence,

and to act accordingly. They all have to ascertain certain facts, in order

that they may afterward apply certain rules, either devised by themselves

or prescribed for their guidance by others; and as they do this well or

ill, so they discharge well or ill the duties of their several callings.

It is the only occupation in which the mind never ceases to be engaged;

and is the subject, not of logic, but of knowledge in general.

Logic, however, is not the same thing with knowledge, though the field of

logic is co-extensive with the field of knowledge. Logic is the common

judge and arbiter of all particular investigations. It does not undertake

to find evidence, but to determine whether it has been found. Logic

neither observes, nor invents, nor discovers; but judges. It is no part of

the business of logic to inform the surgeon what appearances are found to

accompany a violent death. This he must learn from his own experience and

observation, or from that of others, his predecessors in his peculiar

pursuit. But logic sits in judgment on the sufficiency of that observation

and experience to justify his rules, and on the sufficiency of his rules

to justify his conduct. It does not give him proofs, but teaches him what

makes them proofs, and how he is to judge of them. It does not teach that

any particular fact proves any other, but points out to what conditions

all facts must conform, in order that they may prove other facts. To

decide whether any given fact fulfills these conditions, or whether facts

can be found which fulfill them in a given case, belongs exclusively to

the particular art or science, or to our knowledge of the particular

subject.

It is in this sense that logic is, what it was so expressively called by

the schoolmen and by Bacon, _ars artium_; the science of science itself.

All science consists of data and conclusions from those data, of proofs

and what they prove: now logic points out what relations must subsist

between data and whatever can be concluded from them, between proof and

every thing which it can prove. If there be any such indispensable

relations, and if these can be precisely determined, every particular

branch of science, as well as every individual in the guidance of his

conduct, is bound to conform to those relations, under the penalty of

making false inferences—of drawing conclusions which are not grounded in

the realities of things. Whatever has at any time been concluded justly,

whatever knowledge has been acquired otherwise than by immediate

intuition, depended on the observance of the laws which it is the province

of logic to investigate. If the conclusions are just, and the knowledge

real, those laws, whether known or not, have been observed.

§ 6. We need not, therefore, seek any further for a solution of the

question, so often agitated, respecting the utility of logic. If a science

of logic exists, or is capable of existing, it must be useful. If there be

rules to which every mind consciously or unconsciously conforms in every

instance in which it infers rightly, there seems little necessity for

discussing whether a person is more likely to observe those rules, when he

knows the rules, than when he is unacquainted with them.

A science may undoubtedly be brought to a certain, not inconsiderable,

stage of advancement, without the application of any other logic to it

than what all persons, who are said to have a sound understanding, acquire

empirically in the course of their studies. Mankind judged of evidence,

and often correctly, before logic was a science, or they never could have

made it one. And they executed great mechanical works before they

understood the laws of mechanics. But there are limits both to what

mechanicians can do without principles of mechanics, and to what thinkers

can do without principles of logic. A few individuals, by extraordinary

genius, or by the accidental acquisition of a good set of intellectual

habits, may work without principles in the same way, or nearly the same

way, in which they would have worked if they had been in possession of

principles. But the bulk of mankind require either to understand the

theory of what they are doing, or to have rules laid down for them by

those who have understood the theory. In the progress of science from its

easiest to its more difficult problems, each great step in advance has

usually had either as its precursor, or as its accompaniment and necessary

condition, a corresponding improvement in the notions and principles of

logic received among the most advanced thinkers. And if several of the

more difficult sciences are still in so defective a state; if not only so

little is proved, but disputation has not terminated even about the little

which seemed to be so; the reason perhaps is, that men’s logical notions

have not yet acquired the degree of extension, or of accuracy, requisite

for the estimation of the evidence proper to those particular departments

of knowledge.

§ 7. Logic, then, is the science of the operations of the understanding

which are subservient to the estimation of evidence: both the process

itself of advancing from known truths to unknown, and all other

intellectual operations in so far as auxiliary to this. It includes,

therefore, the operation of Naming; for language is an instrument of

thought, as well as a means of communicating our thoughts. It includes,

also, Definition, and Classification. For, the use of these operations

(putting all other minds than one’s own out of consideration) is to serve

not only for keeping our evidences and the conclusions from them permanent

and readily accessible in the memory, but for so marshaling the facts

which we may at any time be engaged in investigating, as to enable us to

perceive more clearly what evidence there is, and to judge with fewer

chances of error whether it be sufficient. These, therefore, are

operations specially instrumental to the estimation of evidence, and, as

such, are within the province of Logic. There are other more elementary

processes, concerned in all thinking, such as Conception, Memory, and the

like; but of these it is not necessary that Logic should take any peculiar

cognizance, since they have no special connection with the problem of

Evidence, further than that, like all other problems addressed to the

understanding, it presupposes them.

Our object, then, will be, to attempt a correct analysis of the

intellectual process called Reasoning or Inference, and of such other

mental operations as are intended to facilitate this: as well as, on the

foundation of this analysis, and _pari passu_ with it, to bring together

or frame a set of rules or canons for testing the sufficiency of any given

evidence to prove any given proposition.

With respect to the first part of this undertaking, I do not attempt to

decompose the mental operations in question into their ultimate elements.

It is enough if the analysis as far as it goes is correct, and if it goes

far enough for the practical purposes of logic considered as an art. The

separation of a complicated phenomenon into its component parts is not

like a connected and interdependent chain of proof. If one link of an

argument breaks, the whole drops to the ground; but one step toward an

analysis holds good and has an independent value, though we should never

be able to make a second. The results which have been obtained by

analytical chemistry are not the less valuable, though it should be

discovered that all which we now call simple substances are really

compounds. All other things are at any rate compounded of those elements:

whether the elements themselves admit of decomposition, is an important

inquiry, but does not affect the certainty of the science up to that

point.

I shall, accordingly, attempt to analyze the process of inference, and the

processes subordinate to inference, so far only as may be requisite for

ascertaining the difference between a correct and an incorrect performance

of those processes. The reason for thus limiting our design, is evident.

It has been said by objectors to logic, that we do not learn to use our

muscles by studying their anatomy. The fact is not quite fairly stated;

for if the action of any of our muscles were vitiated by local weakness,

or other physical defect, a knowledge of their anatomy might be very

necessary for effecting a cure. But we should be justly liable to the

criticism involved in this objection, were we, in a treatise on logic, to

carry the analysis of the reasoning process beyond the point at which any

inaccuracy which may have crept into it must become visible. In learning

bodily exercises (to carry on the same illustration) we do, and must,

analyze the bodily motions so far as is necessary for distinguishing those

which ought to be performed from those which ought not. To a similar

extent, and no further, it is necessary that the logician should analyze

the mental processes with which Logic is concerned. Logic has no interest

in carrying the analysis beyond the point at which it becomes apparent

whether the operations have in any individual case been rightly or wrongly

performed: in the same manner as the science of music teaches us to

discriminate between musical notes, and to know the combinations of which

they are susceptible, but not what number of vibrations in a second

correspond to each; which, though useful to be known, is useful for

totally different purposes. The extension of Logic as a Science is

determined by its necessities as an Art: whatever it does not need for its

practical ends, it leaves to the larger science which may be said to

correspond, not to any particular art, but to art in general; the science

which deals with the constitution of the human faculties; and to which, in

the part of our mental nature which concerns Logic, as well as in all

other parts, it belongs to decide what are ultimate facts, and what are

resolvable into other facts. And I believe it will be found that most of

the conclusions arrived at in this work have no necessary connection with

any particular views respecting the ulterior analysis. Logic is common

ground on which the partisans of Hartley and of Reid, of Locke and of

Kant, may meet and join hands. Particular and detached opinions of all

these thinkers will no doubt occasionally be controverted, since all of

them were logicians as well as metaphysicians; but the field on which

their principal battles have been fought, lies beyond the boundaries of

our science.

It can not, indeed, be pretended that logical principles can be altogether

irrelevant to those more abstruse discussions; nor is it possible but that

the view we are led to take of the problem which logic proposes, must have

a tendency favorable to the adoption of some one opinion, on these

controverted subjects, rather than another. For metaphysics, in

endeavoring to solve its own peculiar problem, must employ means, the

validity of which falls under the cognizance of logic. It proceeds, no

doubt, as far as possible, merely by a closer and more attentive

interrogation of our consciousness, or more properly speaking, of our

memory; and so far is not amenable to logic. But wherever this method is

insufficient to attain the end of its inquiries, it must proceed, like

other sciences, by means of evidence. Now, the moment this science begins

to draw inferences from evidence, logic becomes the sovereign judge

whether its inferences are well grounded, or what other inferences would

be so.

This, however, constitutes no nearer or other relation between logic and

metaphysics, than that which exists between logic and every other science.

And I can conscientiously affirm that no one proposition laid down in this

work has been adopted for the sake of establishing, or with any reference

to its fitness for being employed in establishing, preconceived opinions

in any department of knowledge or of inquiry on which the speculative

world is still undecided.(6)

Book I.

OF NAMES AND PROPOSITIONS.

“La scolastique, qui produisit dans la logique, comme dans la morale, et

dans une partie de la métaphysique, une subtilité, une précision d’idées,

dont l’habitude inconnue aux anciens, a contribué plus qu’on ne croit au

progrès de la bonne philosophie.”—CONDORCET, _Vie de Turgot_.

“To the schoolmen the vulgar languages are principally indebted for what

precision and analytic subtlety they possess.”—SIR W. HAMILTON,

_Discussions in Philosophy_.

Chapter I.

Of The Necessity Of Commencing With An Analysis Of Language.

§ 1. It is so much the established practice of writers on logic to

commence their treatises by a few general observations (in most cases, it

is true, rather meagre) on Terms and their varieties, that it will,

perhaps, scarcely be required from me, in merely following the common

usage, to be as particular in assigning my reasons, as it is usually

expected that those should be who deviate from it.

The practice, indeed, is recommended by considerations far too obvious to

require a formal justification. Logic is a portion of the Art of Thinking:

Language is evidently, and by the admission of all philosophers, one of

the principal instruments or helps of thought; and any imperfection in the

instrument, or in the mode of employing it, is confessedly liable, still

more than in almost any other art, to confuse and impede the process, and

destroy all ground of confidence in the result. For a mind not previously

versed in the meaning and right use of the various kinds of words, to

attempt the study of methods of philosophizing, would be as if some one

should attempt to become an astronomical observer, having never learned to

adjust the focal distance of his optical instruments so as to see

distinctly.

Since Reasoning, or Inference, the principal subject of logic, is an

operation which usually takes place by means of words, and in complicated

cases can take place in no other way; those who have not a thorough

insight into the signification and purposes of words, will be under

chances, amounting almost to certainty, of reasoning or inferring

incorrectly. And logicians have generally felt that unless, in the very

first stage, they removed this source of error; unless they taught their

pupil to put away the glasses which distort the object, and to use those

which are adapted to his purpose in such a manner as to assist, not

perplex, his vision; he would not be in a condition to practice the

remaining part of their discipline with any prospect of advantage.

Therefore it is that an inquiry into language, so far as is needful to

guard against the errors to which it gives rise, has at all times been

deemed a necessary preliminary to the study of logic.

But there is another reason, of a still more fundamental nature, why the

import of words should be the earliest subject of the logician’s

consideration: because without it he can not examine into the import of

Propositions. Now this is a subject which stands on the very threshold of

the science of logic.

The object of logic, as defined in the Introductory Chapter, is to

ascertain how we come by that portion of our knowledge (much the greatest

portion) which is not intuitive: and by what criterion we can, in matters

not self-evident, distinguish between things proved and things not proved,

between what is worthy and what is unworthy of belief. Of the various

questions which present themselves to our inquiring faculties, some

receive an answer from direct consciousness, others, if resolved at all,

can only be resolved by means of evidence. Logic is concerned with these

last. But before inquiring into the mode of resolving questions, it is

necessary to inquire what are those which offer themselves; what questions

are conceivable; what inquiries are there, to which mankind have either

obtained, or been able to imagine it possible that they should obtain, an

answer. This point is best ascertained by a survey and analysis of

Propositions.

§ 2. The answer to every question which it is possible to frame, must be

contained in a Proposition, or Assertion. Whatever can be an object of

belief, or even of disbelief, must, when put into words, assume the form

of a proposition. All truth and all error lie in propositions. What, by a

convenient misapplication of an abstract term, we call a Truth, means

simply a True Proposition; and errors are false propositions. To know the

import of all possible propositions would be to know all questions which

can be raised, all matters which are susceptible of being either believed

or disbelieved. How many kinds of inquiries can be propounded; how many

kinds of judgments can be made; and how many kinds of propositions it is

possible to frame with a meaning, are but different forms of one and the

same question. Since, then, the objects of all Belief and of all Inquiry

express themselves in propositions, a sufficient scrutiny of Propositions

and of their varieties will apprise us what questions mankind have

actually asked of themselves, and what, in the nature of answers to those

questions, they have actually thought they had grounds to believe.

Now the first glance at a proposition shows that it is formed by putting

together two names. A proposition, according to the common simple

definition, which is sufficient for our purpose is, _discourse, in which

something is affirmed or denied of something_. Thus, in the proposition,

Gold is yellow, the quality yellow is affirmed of the substance _gold_. In

the proposition, Franklin was not born in England, the fact expressed by

the words _born in England_ is denied of the man Franklin.

Every proposition consists of three parts: the Subject, the Predicate, and

the Copula. The predicate is the name denoting that which is affirmed or

denied. The subject is the name denoting the person or thing which

something is affirmed or denied of. The copula is the sign denoting that

there is an affirmation or denial, and thereby enabling the hearer or

reader to distinguish a proposition from any other kind of discourse.

Thus, in the proposition, The earth is round, the Predicate is the word

_round_, which denotes the quality affirmed, or (as the phrase is)

predicated: _the earth_, words denoting the object which that quality is

affirmed of, compose the Subject; the word _is_, which serves as the

connecting mark between the subject and predicate, to show that one of

them is affirmed of the other, is called the Copula.

Dismissing, for the present, the copula, of which more will be said

hereafter, every proposition, then, consists of at least two names—brings

together two names, in a particular manner. This is already a first step

toward what we are in quest of. It appears from this, that for an act of

belief, _one_ object is not sufficient; the simplest act of belief

supposes, and has something to do with, _two_ objects—two names, to say

the least; and (since the names must be names of something) two _namable

things_. A large class of thinkers would cut the matter short by saying,

two _ideas_. They would say, that the subject and predicate are both of

them names of ideas; the idea of gold, for instance, and the idea of

yellow; and that what takes place (or part of what takes place) in the act

of belief consists in bringing (as it is often expressed) one of these

ideas under the other. But this we are not yet in a condition to say:

whether such be the correct mode of describing the phenomenon, is an after

consideration. The result with which for the present we must be contented,

is, that in every act of belief _two_ objects are in some manner taken

cognizance of; that there can be no belief claimed, or question

propounded, which does not embrace two distinct (either material or

intellectual) subjects of thought; each of them capable, or not, of being

conceived by itself, but incapable of being believed by itself.

I may say, for instance, “the sun.” The word has a meaning, and suggests

that meaning to the mind of any one who is listening to me. But suppose I

ask him, Whether it is true: whether he believes it? He can give no

answer. There is as yet nothing to believe, or to disbelieve. Now,

however, let me make, of all possible assertions respecting the sun, the

one which involves the least of reference to any object besides itself;

let me say, “the sun exists.” Here, at once, is something which a person

can say he believes. But here, instead of only one, we find two distinct

objects of conception: the sun is one object; existence is another. Let it

not be said that this second conception, existence, is involved in the

first; for the sun may be conceived as no longer existing. “The sun” does

not convey all the meaning that is conveyed by “the sun exists:” “my

father” does not include all the meaning of “my father exists,” for he may

be dead; “a round square” does not include the meaning of “a round square

exists,” for it does not and can not exist. When I say “the sun,” “my

father,” or a “round square,” I do not call upon the hearer for any belief

or disbelief, nor can either the one or the other be afforded me; but if I

say, “the sun exists,” “my father exists,” or “a round square exists,” I

call for belief; and should, in the first of the three instances, meet

with it; in the second, with belief or disbelief, as the case might be; in

the third, with disbelief.

§ 3. This first step in the analysis of the object of belief, which,

though so obvious, will be found to be not unimportant, is the only one

which we shall find it practicable to make without a preliminary survey of

language. If we attempt to proceed further in the same path, that is, to

analyze any further the import of Propositions; we find forced upon us, as

a subject of previous consideration, the import of Names. For every

proposition consists of two names; and every proposition affirms or denies

one of these names, of the other. Now what we do, what passes in our mind,

when we affirm or deny two names of one another, must depend on what they

are names of; since it is with reference to that, and not to the mere

names themselves, that we make the affirmation or denial. Here, therefore,

we find a new reason why the signification of names, and the relation

generally between names and the things signified by them, must occupy the

preliminary stage of the inquiry we are engaged in.

It may be objected that the meaning of names can guide us at most only to

the opinions, possibly the foolish and groundless opinions, which mankind

have formed concerning things, and that as the object of philosophy is

truth, not opinion, the philosopher should dismiss words and look into

things themselves, to ascertain what questions can be asked and answered

in regard to them. This advice (which no one has it in his power to

follow) is in reality an exhortation to discard the whole fruits of the

labors of his predecessors, and conduct himself as if he were the first

person who had ever turned an inquiring eye upon nature. What does any

one’s personal knowledge of Things amount to, after subtracting all which

he has acquired by means of the words of other people? Even after he has

learned as much as people usually do learn from others, will the notions

of things contained in his individual mind afford as sufficient a basis

for a _catalogue raisonné_ as the notions which are in the minds of all

mankind?

In any enumeration and classification of Things, which does not set out

from their names, no varieties of things will of course be comprehended

but those recognized by the particular inquirer; and it will still remain

to be established, by a subsequent examination of names, that the

enumeration has omitted nothing which ought to have been included. But if

we begin with names, and use them as our clue to the things, we bring at

once before us all the distinctions which have been recognized, not by a

single inquirer, but by all inquirers taken together. It doubtless may,

and I believe it will, be found, that mankind have multiplied the

varieties unnecessarily, and have imagined distinctions among things,

where there were only distinctions in the manner of naming them. But we

are not entitled to assume this in the commencement. We must begin by

recognizing the distinctions made by ordinary language. If some of these

appear, on a close examination, not to be fundamental, the enumeration of

the different kinds of realities may be abridged accordingly. But to

impose upon the facts in the first instance the yoke of a theory, while

the grounds of the theory are reserved for discussion in a subsequent

stage, is not a course which a logician can reasonably adopt.

Chapter II.

Of Names.

§ 1. “A name,” says Hobbes,(7) “is a word taken at pleasure to serve for a

mark which may raise in our mind a thought like to some thought we had

before, and which being pronounced to others, may be to them a sign of

what thought the speaker had(8) before in his mind.” This simple

definition of a name, as a word (or set of words) serving the double

purpose of a mark to recall to ourselves the likeness of a former thought,

and a sign to make it known to others, appears unexceptionable. Names,

indeed, do much more than this; but whatever else they do, grows out of,

and is the result of this: as will appear in its proper place.

Are names more properly said to be the names of things, or of our ideas of

things? The first is the expression in common use; the last is that of

some metaphysicians, who conceived that in adopting it they were

introducing a highly important distinction. The eminent thinker, just

quoted, seems to countenance the latter opinion. “But seeing,” he

continues, “names ordered in speech (as is defined) are signs of our

conceptions, it is manifest they are not signs of the things themselves;

for that the sound of this word _stone_ should be the sign of a stone, can

not be understood in any sense but this, that he that hears it collects

that he that pronounces it thinks of a stone.”

If it be merely meant that the conception alone, and not the thing itself,

is recalled by the name, or imparted to the hearer, this of course can not

be denied. Nevertheless, there seems good reason for adhering to the

common usage, and calling (as indeed Hobbes himself does in other places)

the word _sun_ the name of the sun, and not the name of our idea of the

sun. For names are not intended only to make the hearer conceive what we

conceive, but also to inform him what we believe. Now, when I use a name

for the purpose of expressing a belief, it is a belief concerning the

thing itself, not concerning my idea of it. When I say, “the sun is the

cause of day,” I do not mean that my idea of the sun causes or excites in

me the idea of day; or in other words, that thinking of the sun makes me

think of day. I mean, that a certain physical fact, which is called the

sun’s presence (and which, in the ultimate analysis, resolves itself into

sensations, not ideas) causes another physical fact, which is called day.

It seems proper to consider a word as the _name_ of that which we intend

to be understood by it when we use it; of that which any fact that we

assert of it is to be understood of; that, in short, concerning which,

when we employ the word, we intend to give information. Names, therefore,

shall always be spoken of in this work as the names of things themselves,

and not merely of our ideas of things.

But the question now arises, of what things? and to answer this it is

necessary to take into consideration the different kinds of names.

§ 2. It is usual, before examining the various classes into which names

are commonly divided, to begin by distinguishing from names of every

description, those words which are not names, but only parts of names.

Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the

inflected cases of nouns substantive, as _me_, _him_, _John’s_; and even

adjectives, as _large_, _heavy_. These words do not express things of

which any thing can be affirmed or denied. We can not say, Heavy fell, or

A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the

room. Unless, indeed, we are speaking of the mere words themselves, as

when we say, Truly is an English word, or, Heavy is an adjective. In that

case they are complete names—viz., names of those particular sounds, or of

those particular collections of written characters. This employment of a

word to denote the mere letters and syllables of which it is composed, was

termed by the schoolmen the _suppositio materialis_ of the word. In any

other sense we can not introduce one of these words into the subject of a

proposition, unless in combination with other words; as, A heavy _body_

fell, A truly _important fact_ was asserted, A _member_ of _parliament_

was in the room.

An adjective, however, is capable of standing by itself as the predicate

of a proposition; as when we say, Snow is white; and occasionally even as

the subject, for we may say, White is an agreeable color. The adjective is

often said to be so used by a grammatical ellipsis: Snow is white, instead

of Snow is a white object; White is an agreeable color, instead of, A

white color, or, The color white, is agreeable. The Greeks and Romans were

allowed, by the rules of their language, to employ this ellipsis

universally in the subject as well as in the predicate of a proposition.

In English this can not, generally speaking, be done. We may say, The

earth is round; but we can not say, Round is easily moved; we must say, A

round object. This distinction, however, is rather grammatical than

logical. Since there is no difference of meaning between _round_, and _a

round object_, it is only custom which prescribes that on any given

occasion one shall be used, and not the other. We shall, therefore,

without scruple, speak of adjectives as names, whether in their own right,

or as representative of the more circuitous forms of expression above

exemplified. The other classes of subsidiary words have no title whatever

to be considered as names. An adverb, or an accusative case, can not under

any circumstances (except when their mere letters and syllables are spoken

of) figure as one of the terms of a proposition.

Words which are not capable of being used as names, but only as parts of

names, were called by some of the schoolmen Syncategorematic terms: from

σὺν, with, and κατηγορέω, to predicate, because it was only _with_ some

other word that they could be predicated. A word which could be used

either as the subject or predicate of a proposition without being

accompanied by any other word, was termed by the same authorities a

Categorematic term. A combination of one or more Categorematic, and one or

more Syncategorematic words, as A heavy body, or A court of justice, they

sometimes called a _mixed_ term; but this seems a needless multiplication

of technical expressions. A mixed term is, in the only useful sense of the

word, Categorematic. It belongs to the class of what have been called

many-worded names.

For, as one word is frequently not a name, but only part of a name, so a

number of words often compose one single name, and no more. These words,

“The place which the wisdom or policy of antiquity had destined for the

residence of the Abyssinian princes,” form in the estimation of the

logician only one name; one Categorematic term. A mode of determining

whether any set of words makes only one name, or more than one, is by

predicating something of it, and observing whether, by this predication,

we make only one assertion or several. Thus, when we say, John Nokes, who

was the mayor of the town, died yesterday—by this predication we make but

one assertion; whence it appears that “John Nokes, who was the mayor of

the town,” is no more than one name. It is true that in this proposition,

besides the assertion that John Nokes died yesterday, there is included

another assertion, namely, that John Nokes was mayor of the town. But this

last assertion was already made: we did not make it by adding the

predicate, “died yesterday.” Suppose, however, that the words had been,

John Nokes _and_ the mayor of the town, they would have formed two names

instead of one. For when we say, John Nokes and the mayor of the town died

yesterday, we make two assertions: one, that John Nokes died yesterday;

the other, that the mayor of the town died yesterday.

It being needless to illustrate at any greater length the subject of

many-worded names, we proceed to the distinctions which have been

established among names, not according to the words they are composed of,

but according to their signification.

§ 3. All names are names of something, real or imaginary; but all things

have not names appropriated to them individually. For some individual

objects we require, and consequently have, separate distinguishing names;

there is a name for every person, and for every remarkable place. Other

objects, of which we have not occasion to speak so frequently, we do not

designate by a name of their own; but when the necessity arises for naming

them, we do so by putting together several words, each of which, by

itself, might be and is used for an indefinite number of other objects; as

when I say, _this stone_: “this” and “stone” being, each of them, names

that may be used of many other objects besides the particular one meant,

though the only object of which they can both be used at the given moment,

consistently with their signification, may be the one of which I wish to

speak.

Were this the sole purpose for which names, that are common to more things

than one, could be employed; if they only served, by mutually limiting

each other, to afford a designation for such individual objects as have no

names of their own: they could only be ranked among contrivances for

economizing the use of language. But it is evident that this is not their

sole function. It is by their means that we are enabled to assert

_general_ propositions; to affirm or deny any predicate of an indefinite

number of things at once. The distinction, therefore, between _general_

names, and _individual_ or _singular_ names, is fundamental; and may be

considered as the first grand division of names.

A general name is familiarly defined, a name which is capable of being

truly affirmed, in the same sense, of each of an indefinite number of

things. An individual or singular name is a name which is only capable of

being truly affirmed, in the same sense, of one thing.

Thus, _man_ is capable of being truly affirmed of John, George, Mary, and

other persons without assignable limit; and it is affirmed of all of them

in the same sense; for the word man expresses certain qualities, and when

we predicate it of those persons, we assert that they all possess those

qualities. But _John_ is only capable of being truly affirmed of one

single person, at least in the same sense. For, though there are many

persons who bear that name, it is not conferred upon them to indicate any

qualities, or any thing which belongs to them in common; and can not be

said to be affirmed of them in any _sense_ at all, consequently not in the

same sense. “The king who succeeded William the Conqueror,” is also an

individual name. For, that there can not be more than one person of whom

it can be truly affirmed, is implied in the meaning of the words. Even

“_the_ king,” when the occasion or the context defines the individual of

whom it is to be understood, may justly be regarded as an individual name.

It is not unusual, by way of explaining what is meant by a general name,

to say that it is the name of a _class_. But this, though a convenient

mode of expression for some purposes, is objectionable as a definition,

since it explains the clearer of two things by the more obscure. It would

be more logical to reverse the proposition, and turn it into a definition

of the word _class_: “A class is the indefinite multitude of individuals

denoted by a general name.”

It is necessary to distinguish _general_ from _collective_ names. A

general name is one which can be predicated of _each_ individual of a

multitude; a collective name can not be predicated of each separately, but

only of all taken together. “The 76th regiment of foot in the British

army,” which is a collective name, is not a general but an individual

name; for though it can be predicated of a multitude of individual

soldiers taken jointly, it can not be predicated of them severally. We may

say, Jones is a soldier, and Thompson is a soldier, and Smith is a

soldier, but we can not say, Jones is the 76th regiment, and Thompson is

the 76th regiment, and Smith is the 76th regiment. We can only say, Jones,

and Thompson, and Smith, and Brown, and so forth (enumerating all the

soldiers), are the 76th regiment.

“The 76th regiment” is a collective name, but not a general one: “a

regiment” is both a collective and a general name. General with respect to

all individual regiments, of each of which separately it can be affirmed:

collective with respect to the individual soldiers of whom any regiment is

composed.

§ 4. The second general division of names is into _concrete_ and

_abstract_. A concrete name is a name which stands for a thing; an

abstract name is a name which stands for an attribute of a thing. Thus

_John_, _the sea_, _this table_, are names of things. _White_, also, is a

name of a thing, or rather of things. Whiteness, again, is the name of a

quality or attribute of those things. Man is a name of many things;

humanity is a name of an attribute of those things. _Old_ is a name of

things: _old age_ is a name of one of their attributes.

I have used the words concrete and abstract in the sense annexed to them

by the schoolmen, who, notwithstanding the imperfections of their

philosophy, were unrivaled in the construction of technical language, and

whose definitions, in logic at least, though they never went more than a

little way into the subject, have seldom, I think, been altered but to be

spoiled. A practice, however, has grown up in more modern times, which, if

not introduced by Locke, has gained currency chiefly from his example, of

applying the expression “abstract name” to all names which are the result

of abstraction or generalization, and consequently to all general names,

instead of confining it to the names of attributes. The metaphysicians of

the Condillac school—whose admiration of Locke, passing over the

profoundest speculations of that truly original genius, usually fastens

with peculiar eagerness upon his weakest points—have gone on imitating him

in this abuse of language, until there is now some difficulty in restoring

the word to its original signification. A more wanton alteration in the

meaning of a word is rarely to be met with; for the expression _general

name_, the exact equivalent of which exists in all languages I am

acquainted with, was already available for the purpose to which _abstract_

has been misappropriated, while the misappropriation leaves that important

class of words, the names of attributes, without any compact distinctive

appellation. The old acceptation, however, has not gone so completely out

of use as to deprive those who still adhere to it of all chance of being

understood. By _abstract_, then, I shall always, in Logic proper, mean the

opposite of _concrete_; by an abstract name, the name of an attribute; by

a concrete name, the name of an object.

Do abstract names belong to the class of general, or to that of singular

names? Some of them are certainly general. I mean those which are names

not of one single and definite attribute, but of a class of attributes.

Such is the word _color_, which is a name common to whiteness, redness,

etc. Such is even the word whiteness, in respect of the different shades

of whiteness to which it is applied in common: the word magnitude, in

respect of the various degrees of magnitude and the various dimensions of

space; the word weight, in respect of the various degrees of weight. Such

also is the word _attribute_ itself, the common name of all particular

attributes. But when only one attribute, neither variable in degree nor in

kind, is designated by the name; as visibleness; tangibleness; equality;

squareness; milk-whiteness; then the name can hardly be considered

general; for though it denotes an attribute of many different objects, the

attribute itself is always conceived as one, not many.(9) To avoid

needless logomachies, the best course would probably be to consider these

names as neither general nor individual, and to place them in a class

apart.

It may be objected to our definition of an abstract name, that not only

the names which we have called abstract, but adjectives, which we have

placed in the concrete class, are names of attributes; that _white_, for

example, is as much the name of the color as _whiteness_ is. But (as

before remarked) a word ought to be considered as the name of that which

we intend to be understood by it when we put it to its principal use, that

is, when we employ it in predication. When we say snow is white, milk is

white, linen is white, we do not mean it to be understood that snow, or

linen, or milk, is a color. We mean that they are things having the color.

The reverse is the case with the word whiteness; what we affirm to _be_

whiteness is not snow, but the color of snow. Whiteness, therefore, is the

name of the color exclusively: white is a name of all things whatever

having the color; a name, not of the quality whiteness, but of every white

object. It is true, this name was given to all those various objects on

account of the quality; and we may therefore say, without impropriety,

that the quality forms part of its signification; but a name can only be

said to stand for, or to be a name of, the things of which it can be

predicated. We shall presently see that all names which can be said to

have any signification, all names by applying which to an individual we

give any information respecting that individual, may be said to _imply_ an

attribute of some sort; but they are not names of the attribute; it has

its own proper abstract name.

§ 5. This leads to the consideration of a third great division of names,

into _connotative_ and _non-connotative_, the latter sometimes, but

improperly, called _absolute_. This is one of the most important

distinctions which we shall have occasion to point out, and one of those

which go deepest into the nature of language.

A non-connotative term is one which signifies a subject only, or an

attribute only. A connotative term is one which denotes a subject, and

implies an attribute. By a subject is here meant any thing which possesses

attributes. Thus John, or London, or England, are names which signify a

subject only. Whiteness, length, virtue, signify an attribute only. None

of these names, therefore, are connotative. But _white_, _long_,

_virtuous_, are connotative. The word white, denotes all white things, as

snow, paper, the foam of the sea, etc., and implies, or in the language of

the schoolmen, _connotes_,(10) the attribute _whiteness_. The word white

is not predicated of the attribute, but of the subjects, snow, etc.; but

when we predicate it of them, we convey the meaning that the attribute

whiteness belongs to them. The same may be said of the other words above

cited. Virtuous, for example, is the name of a class, which includes

Socrates, Howard, the Man of Ross, and an undefinable number of other

individuals, past, present, and to come. These individuals, collectively

and severally, can alone be said with propriety to be denoted by the word:

of them alone can it properly be said to be a name. But it is a name

applied to all of them in consequence of an attribute which they are

supposed to possess in common, the attribute which has received the name

of virtue. It is applied to all beings that are considered to possess this

attribute; and to none which are not so considered.

All concrete general names are connotative. The word _man_, for example,

denotes Peter, Jane, John, and an indefinite number of other individuals,

of whom, taken as a class, it is the name. But it is applied to them,

because they possess, and to signify that they possess, certain

attributes. These seem to be, corporeity, animal life, rationality, and a

certain external form, which for distinction we call the human. Every

existing thing, which possessed all these attributes, would be called a

man; and any thing which possessed none of them, or only one, or two, or

even three of them without the fourth, would not be so called. For

example, if in the interior of Africa there were to be discovered a race

of animals possessing reason equal to that of human beings, but with the

form of an elephant, they would not be called men. Swift’s Houyhnhnms

would not be so called. Or if such newly-discovered beings possessed the

form of man without any vestige of reason, it is probable that some other

name than that of man would be found for them. How it happens that there

can be any doubt about the matter, will appear hereafter. The word _man_,

therefore, signifies all these attributes, and all subjects which possess

these attributes. But it can be predicated only of the subjects. What we

call men, are the subjects, the individual Stiles and Nokes; not the

qualities by which their humanity is constituted. The name, therefore, is

said to signify the subjects _directly_, the attributes _indirectly_; it

_denotes_ the subjects, and implies, or involves, or indicates, or as we

shall say henceforth _connotes_, the attributes. It is a connotative name.

Connotative names have hence been also called _denominative_, because the

subject which they denote is denominated by, or receives a name from the

attribute which they connote. Snow, and other objects, receive the name

white, because they possess the attribute which is called whiteness;

Peter, James, and others receive the name man because they possess the

attributes which are considered to constitute humanity. The attribute, or

attributes, may therefore be said to denominate those objects, or to give

them a common name.(11)

It has been seen that all concrete general names are connotative. Even

abstract names, though the names only of attributes, may in some instances

be justly considered as connotative; for attributes themselves may have

attributes ascribed to them; and a word which denotes attributes may

connote an attribute of those attributes. Of this description, for

example, is such a word as _fault_; equivalent to _bad_ or _hurtful

quality_. This word is a name common to many attributes, and connotes

hurtfulness, an attribute of those various attributes. When, for example,

we say that slowness, in a horse, is a fault, we do not mean that the slow

movement, the actual change of pace of the slow horse, is a bad thing, but

that the property or peculiarity of the horse, from which it derives that

name, the quality of being a slow mover, is an undesirable peculiarity.

In regard to those concrete names which are not general but individual, a

distinction must be made.

Proper names are not connotative: they denote the individuals who are

called by them; but they do not indicate or imply any attributes as

belonging to those individuals. When we name a child by the name Paul, or

a dog by the name Cæsar, these names are simply marks used to enable those

individuals to be made subjects of discourse. It may be said, indeed, that

we must have had some reason for giving them those names rather than any

others; and this is true; but the name, once given, is independent of the

reason. A man may have been named John, because that was the name of his

father; a town may have been named Dartmouth, because it is situated at

the mouth of the Dart. But it is no part of the signification of the word

John, that the father of the person so called bore the same name; nor even

of the word Dartmouth, to be situated at the mouth of the Dart. If sand

should choke up the mouth of the river, or an earthquake change its

course, and remove it to a distance from the town, the name of the town

would not necessarily be changed. That fact, therefore, can form no part

of the signification of the word; for otherwise, when the fact confessedly

ceased to be true, no one would any longer think of applying the name.

Proper names are attached to the objects themselves, and are not dependent

on the continuance of any attribute of the object.

But there is another kind of names, which, although they are individual

names—that is, predicable only of one object—are really connotative. For,

though we may give to an individual a name utterly unmeaning, which we

call a proper name—a word which answers the purpose of showing what thing

it is we are talking about, but not of telling any thing about it; yet a

name peculiar to an individual is not necessarily of this description. It

may be significant of some attribute, or some union of attributes, which,

being possessed by no object but one, determines the name exclusively to

that individual. “The sun” is a name of this description; “God,” when used

by a monotheist, is another. These, however, are scarcely examples of what

we are now attempting to illustrate, being, in strictness of language,

general, not individual names: for, however they may be _in fact_

predicable only of one object, there is nothing in the meaning of the

words themselves which implies this: and, accordingly, when we are

imagining and not affirming, we may speak of many suns; and the majority

of mankind have believed, and still believe, that there are many gods. But

it is easy to produce words which are real instances of connotative

individual names. It may be part of the meaning of the connotative name

itself, that there can exist but one individual possessing the attribute

which it connotes: as, for instance, “the _only_ son of John Stiles;” “the

_first_ emperor of Rome.” Or the attribute connoted may be a connection

with some determinate event, and the connection may be of such a kind as

only one individual could have; or may at least be such as only one

individual actually had; and this may be implied in the form of the

expression. “The father of Socrates” is an example of the one kind (since

Socrates could not have had two fathers); “the author of the Iliad,” “the

murderer of Henri Quatre,” of the second. For, though it is conceivable

that more persons than one might have participated in the authorship of

the Iliad, or in the murder of Henri Quatre, the employment of the article

_the_ implies that, in fact, this was not the case. What is here done by

the word _the_, is done in other cases by the context: thus, “Cæsar’s

army” is an individual name, if it appears from the context that the army

meant is that which Cæsar commanded in a particular battle. The still more

general expressions, “the Roman army,” or “the Christian army,” may be

individualized in a similar manner. Another case of frequent occurrence

has already been noticed; it is the following: The name, being a

many-worded one, may consist, in the first place, of a _general_ name,

capable therefore in itself of being affirmed of more things than one, but

which is, in the second place, so limited by other words joined with it,

that the entire expression can only be predicated of one object,

consistently with the meaning of the general term. This is exemplified in

such an instance as the following: “the present prime minister of

England.” Prime Minister of England is a general name; the attributes

which it connotes may be possessed by an indefinite number of persons: in

succession however, not simultaneously; since the meaning of the name

itself imports (among other things) that there can be only one such person

at a time. This being the case, and the application of the name being

afterward limited by the article and the word _present_, to such

individuals as possess the attributes at one indivisible point of time, it

becomes applicable only to one individual. And as this appears from the

meaning of the name, without any extrinsic proof, it is strictly an

individual name.

From the preceding observations it will easily be collected, that whenever

the names given to objects convey any information—that is, whenever they

have properly any meaning—the meaning resides not in what they _denote_,

but in what they _connote_. The only names of objects which connote

nothing are _proper_ names; and these have, strictly speaking, no

signification.(12)

If, like the robber in the Arabian Nights, we make a mark with chalk on a

house to enable us to know it again, the mark has a purpose, but it has

not properly any meaning. The chalk does not declare any thing about the

house; it does not mean, This is such a person’s house, or This is a house

which contains booty. The object of making the mark is merely distinction.

I say to myself, All these houses are so nearly alike that if I lose sight

of them I shall not again be able to distinguish that which I am now

looking at, from any of the others; I must therefore contrive to make the

appearance of this one house unlike that of the others, that I may

hereafter know when I see the mark—not indeed any attribute of the

house—but simply that it is the same house which I am now looking at.

Morgiana chalked all the other houses in a similar manner, and defeated

the scheme: how? simply by obliterating the difference of appearance

between that house and the others. The chalk was still there, but it no

longer served the purpose of a distinctive mark.

When we impose a proper name, we perform an operation in some degree

analogous to what the robber intended in chalking the house. We put a

mark, not indeed upon the object itself, but, so to speak, upon the idea

of the object. A proper name is but an unmeaning mark which we connect in

our minds with the idea of the object, in order that whenever the mark

meets our eyes or occurs to our thoughts, we may think of that individual

object. Not being attached to the thing itself, it does not, like the

chalk, enable us to distinguish the object when we see it; but it enables

us to distinguish it when it is spoken of, either in the records of our

own experience, or in the discourse of others; to know that what we find

asserted in any proposition of which it is the subject, is asserted of the

individual thing with which we were previously acquainted.

When we predicate of any thing its proper name; when we say, pointing to a

man, this is Brown or Smith, or pointing to a city, that it is York, we do

not, merely by so doing, convey to the reader any information about them,

except that those are their names. By enabling him to identify the

individuals, we may connect them with information previously possessed by

him; by saying, This is York, we may tell him that it contains the

Minster. But this is in virtue of what he has previously heard concerning

York; not by any thing implied in the name. It is otherwise when objects

are spoken of by connotative names. When we say, The town is built of

marble, we give the hearer what may be entirely new information, and this

merely by the signification of the many-worded connotative name, “built of

marble.” Such names are not signs of the mere objects, invented because we

have occasion to think and speak of those objects individually; but signs

which accompany an attribute; a kind of livery in which the attribute

clothes all objects which are recognized as possessing it. They are not

mere marks, but more, that is to say, significant marks; and the

connotation is what constitutes their significance.

As a proper name is said to be the name of the one individual which it is

predicated of, so (as well from the importance of adhering to analogy, as

for the other reasons formerly assigned) a connotative name ought to be

considered a name of all the various individuals which it is predicable

of, or in other words _denotes_, and not of what it connotes. But by

learning what things it is a name of, we do not learn the meaning of the

name: for to the same thing we may, with equal propriety, apply many

names, not equivalent in meaning. Thus, I call a certain man by the name

Sophroniscus: I call him by another name, The father of Socrates. Both

these are names of the same individual, but their meaning is altogether

different; they are applied to that individual for two different purposes:

the one, merely to distinguish him from other persons who are spoken of;

the other to indicate a fact relating to him, the fact that Socrates was

his son. I further apply to him these other expressions: a man, a Greek,

an Athenian, a sculptor, an old man, an honest man, a brave man. All these

are, or may be, names of Sophroniscus, not indeed of him alone, but of him

and each of an indefinite number of other human beings. Each of these

names is applied to Sophroniscus for a different reason, and by each

whoever understands its meaning is apprised of a distinct fact or number

of facts concerning him; but those who knew nothing about the names except

that they were applicable to Sophroniscus, would be altogether ignorant of

their meaning. It is even possible that I might know every single

individual of whom a given name could be with truth affirmed, and yet

could not be said to know the meaning of the name. A child knows who are

its brothers and sisters, long before it has any definite conception of

the nature of the facts which are involved in the signification of those

words.

In some cases it is not easy to decide precisely how much a particular

word does or does not connote; that is, we do not exactly know (the case

not having arisen) what degree of difference in the object would occasion

a difference in the name. Thus, it is clear that the word man, besides

animal life and rationality, connotes also a certain external form; but it

would be impossible to say precisely what form; that is, to decide how

great a deviation from the form ordinarily found in the beings whom we are

accustomed to call men, would suffice in a newly-discovered race to make

us refuse them the name of man. Rationality, also, being a quality which

admits of degrees, it has never been settled what is the lowest degree of

that quality which would entitle any creature to be considered a human

being. In all such cases, the meaning of the general name is so far

unsettled and vague; mankind have not come to any positive agreement about

the matter. When we come to treat of Classification, we shall have

occasion to show under what conditions this vagueness may exist without

practical inconvenience; and cases will appear in which the ends of

language are better promoted by it than by complete precision; in order

that, in natural history for instance, individuals or species of no very

marked character may be ranged with those more strongly characterized

individuals or species to which, in all their properties taken together,

they bear the nearest resemblance.

But this partial uncertainty in the connotation of names can only be free

from mischief when guarded by strict precautions. One of the chief

sources, indeed, of lax habits of thought, is the custom of using

connotative terms without a distinctly ascertained connotation, and with

no more precise notion of their meaning than can be loosely collected from

observing what objects they are used to denote. It is in this manner that

we all acquire, and inevitably so, our first knowledge of our vernacular

language. A child learns the meaning of the words _man_, or _white_, by

hearing them applied to a variety of individual objects, and finding out,

by a process of generalization and analysis which he could not himself

describe, what those different objects have in common. In the case of

these two words the process is so easy as to require no assistance from

culture; the objects called human beings, and the objects called white,

differing from all others by qualities of a peculiarly definite and

obvious character. But in many other cases, objects bear a general

resemblance to one another, which leads to their being familiarly classed

together under a common name, while, without more analytic habits than the

generality of mankind possess, it is not immediately apparent what are the

particular attributes, upon the possession of which in common by them all,

their general resemblance depends. When this is the case, people use the

name without any recognized connotation, that is, without any precise

meaning; they talk, and consequently think, vaguely, and remain contented

to attach only the same degree of significance to their own words, which a

child three years old attaches to the words brother and sister. The child

at least is seldom puzzled by the starting up of new individuals, on whom

he is ignorant whether or not to confer the title; because there is

usually an authority close at hand competent to solve all doubts. But a

similar resource does not exist in the generality of cases; and new

objects are continually presenting themselves to men, women, and children,

which they are called upon to class _proprio motu_. They, accordingly, do

this on no other principle than that of superficial similarity, giving to

each new object the name of that familiar object, the idea of which it

most readily recalls, or which, on a cursory inspection, it seems to them

most to resemble: as an unknown substance found in the ground will be

called, according to its texture, earth, sand, or a stone. In this manner,

names creep on from subject to subject, until all traces of a common

meaning sometimes disappear, and the word comes to denote a number of

things not only independently of any common attribute, but which have

actually no attribute in common; or none but what is shared by other

things to which the name is capriciously refused.(13) Even scientific

writers have aided in this perversion of general language from its

purpose; sometimes because, like the vulgar, they knew no better; and

sometimes in deference to that aversion to admit new words, which induces

mankind, on all subjects not considered technical, to attempt to make the

original stock of names serve with but little augmentation to express a

constantly increasing number of objects and distinctions, and,

consequently, to express them in a manner progressively more and more

imperfect.

To what a degree this loose mode of classing and denominating objects has

rendered the vocabulary of mental and moral philosophy unfit for the

purposes of accurate thinking, is best known to whoever has most meditated

on the present condition of those branches of knowledge. Since, however,

the introduction of a new technical language as the vehicle of

speculations on subjects belonging to the domain of daily discussion, is

extremely difficult to effect, and would not be free from inconvenience

even if effected, the problem for the philosopher, and one of the most

difficult which he has to resolve, is, in retaining the existing

phraseology, how best to alleviate its imperfections. This can only be

accomplished by giving to every general concrete name which there is

frequent occasion to predicate, a definite and fixed connotation; in order

that it may be known what attributes, when we call an object by that name,

we really mean to predicate of the object. And the question of most nicety

is, how to give this fixed connotation to a name, with the least possible

change in the objects which the name is habitually employed to denote;

with the least possible disarrangement, either by adding or subtraction,

of the group of objects which, in however imperfect a manner, it serves to

circumscribe and hold together; and with the least vitiation of the truth

of any propositions which are commonly received as true.

This desirable purpose, of giving a fixed connotation where it is wanting,

is the end aimed at whenever any one attempts to give a definition of a

general name already in use; every definition of a connotative name being

an attempt either merely to declare, or to declare and analyze, the

connotation of the name. And the fact, that no questions which have arisen

in the moral sciences have been subjects of keener controversy than the

definitions of almost all the leading expressions, is a proof how great an

extent the evil to which we have adverted has attained.

Names with indeterminate connotation are not to be confounded with names

which have more than one connotation, that is to say, ambiguous words. A

word may have several meanings, but all of them fixed and recognized ones;

as the word _post_, for example, or the word _box_, the various senses of

which it would be endless to enumerate. And the paucity of existing names,

in comparison with the demand for them, may often render it advisable and

even necessary to retain a name in this multiplicity of acceptations,

distinguishing these so clearly as to prevent their being confounded with

one another. Such a word may be considered as two or more names,

accidentally written and spoken alike.(14)

§ 6. The fourth principal division of names, is into _positive_ and

_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,

_not-tree_, _not-good_. To every positive concrete name, a corresponding

negative one might be framed. After giving a name to any one thing, or to

any plurality of things, we might create a second name which should be a

name of all things whatever, except that particular thing or things. These

negative names are employed whenever we have occasion to speak

collectively of all things other than some thing or class of things. When

the positive name is connotative, the corresponding negative name is

connotative likewise; but in a peculiar way, connoting not the presence

but the absence of an attribute. Thus, _not-white_ denotes all things

whatever except white things; and connotes the attribute of not possessing

whiteness. For the non-possession of any given attribute is also an

attribute, and may receive a name as such; and thus negative concrete

names may obtain negative abstract names to correspond to them.(15)

Names which are positive in form are often negative in reality, and others

are really positive though their form is negative. The word

_inconvenient_, for example, does not express the mere absence of

convenience; it expresses a positive attribute—that of being the cause of

discomfort or annoyance. So the word _unpleasant_, notwithstanding its

negative form, does not connote the mere absence of pleasantness, but a

less degree of what is signified by the word _painful_, which, it is

hardly necessary to say, is positive. _Idle_, on the other hand, is a word

which, though positive in form, expresses nothing but what would be

signified either by the phrase _not working_, or by the phrase _not

disposed to work_; and _sober_, either by _not drunk_ or by _not drunken_.

There is a class of names called _privative_. A privative name is

equivalent in its signification to a positive and a negative name taken

together; being the name of something which has once had a particular

attribute, or for some other reason might have been expected to have it,

but which has it not. Such is the word _blind_, which is not equivalent to

_not seeing_, or to _not capable of seeing_, for it would not, except by a

poetical or rhetorical figure, be applied to stocks and stones. A thing is

not usually said to be blind, unless the class to which it is most

familiarly referred, or to which it is referred on the particular

occasion, be chiefly composed of things which can see, as in the case of a

blind man, or a blind horse; or unless it is supposed for any reason that

it ought to see; as in saying of a man, that he rushed blindly into an

abyss, or of philosophers or the clergy that the greater part of them are

blind guides. The names called privative, therefore, connote two things;

the absence of certain attributes, and the presence of others, from which

the presence also of the former might naturally have been expected.

§ 7. The fifth leading division of names is into _relative_ and

_absolute_, or let us rather say, _relative_ and _non-relative_; for the

word absolute is put upon much too hard duty in metaphysics, not to be

willingly spared when its services can be dispensed with. It resembles the

word _civil_ in the language of jurisprudence, which stands for the

opposite of criminal, the opposite of ecclesiastical, the opposite of

military, the opposite of political—in short, the opposite of any positive

word which wants a negative.

Relative names are such as father, son; ruler, subject; like; equal;

unlike; unequal; longer, shorter; cause, effect. Their characteristic

property is, that they are always given in pairs. Every relative name

which is predicated of an object, supposes another object (or objects), of

which we may predicate either that same name or another relative name

which is said to be the _correlative_ of the former. Thus, when we call

any person a son, we suppose other persons who must be called parents.

When we call any event a cause, we suppose another event which is an

effect. When we say of any distance that it is longer, we suppose another

distance which is shorter. When we say of any object that it is like, we

mean that it is like some other object, which is also said to be like the

first. In this last case both objects receive the same name; the relative

term is its own correlative.

It is evident that these words, when concrete, are, like other concrete

general names, connotative; they denote a subject, and connote an

attribute; and each of them has, or might have, a corresponding abstract

name, to denote the attribute connoted by the concrete. Thus the concrete

_like_ has its abstract _likeness_; the concretes, father and son, have,

or might have, the abstracts, paternity, and filiety, or sonship. The

concrete name connotes an attribute, and the abstract name which answers

to it denotes that attribute. But of what nature is the attribute? Wherein

consists the peculiarity in the connotation of a relative name?

The attribute signified by a relative name, say some, is a relation; and

this they give, if not as a sufficient explanation, at least as the only

one attainable. If they are asked, What then is a relation? they do not

profess to be able to tell. It is generally regarded as something

peculiarly recondite and mysterious. I can not, however, perceive in what

respect it is more so than any other attribute; indeed, it appears to me

to be so in a somewhat less degree. I conceive rather, that it is by

examining into the signification of relative names, or, in other words,

into the nature of the attribute which they connote, that a clear insight

may best be obtained into the nature of all attributes: of all that is

meant by an attribute.

It is obvious, in fact, that if we take any two correlative names,

_father_ and _son_ for instance, though the objects _de_noted by the names

are different, they both, in a certain sense, connote the same thing. They

can not, indeed, be said to connote the same _attribute_: to be a father,

is not the same thing as to be a son. But when we call one man a father,

another a son, what we mean to affirm is a set of facts, which are exactly

the same in both cases. To predicate of A that he is the father of B, and

of B that he is the son of A, is to assert one and the same fact in

different words. The two propositions are exactly equivalent: neither of

them asserts more or asserts less than the other. The paternity of A and

the filiety of B are not two facts, but two modes of expressing the same

fact. That fact, when analysed, consists of a series of physical events or

phenomena, in which both A and B are parties concerned, and from which

they both derive names. What those names really connote, is this series of

events: that is the meaning, and the whole meaning, which either of them

is intended to convey. The series of events may be said to _constitute_

the relation; the schoolmen called it the foundation of the relation,

_fundamentum relationis_.

In this manner any fact, or series of facts, in which two different

objects are implicated, and which is therefore predicable of both of them,

may be either considered as constituting an attribute of the one, or an

attribute of the other. According as we consider it in the former, or in

the latter aspect, it is connoted by the one or the other of the two

correlative names. _Father_ connotes the fact, regarded as constituting an

attribute of A; _son_ connotes the same fact, as constituting an attribute

of B. It may evidently be regarded with equal propriety in either light.

And all that appears necessary to account for the existence of relative

names, is, that whenever there is a fact in which two individuals are

concerned, an attribute grounded on that fact may be ascribed to either of

these individuals.

A name, therefore, is said to be relative, when, over and above the object

which it denotes, it implies in its signification the existence of another

object, also deriving a denomination from the same fact which is the

ground of the first name. Or (to express the same meaning in other words)

a name is relative, when, being the name of one thing, its signification

can not be explained but by mentioning another. Or we may state it

thus—when the name can not be employed in discourse so as to have a

meaning, unless the name of some other thing than what it is itself the

name of, be either expressed or understood. These definitions are all, at

bottom, equivalent, being modes of variously expressing this one

distinctive circumstance—that every other attribute of an object might,

without any contradiction, be conceived still to exist if no object

besides that one had ever existed;(16) but those of its attributes which

are expressed by relative names, would on that supposition be swept away.

§ 8. Names have been further distinguished into _univocal_ and

_æquivocal_: these, however, are not two kinds of names, but two different

modes of employing names. A name is univocal, or applied univocally, with

respect to all things of which it can be predicated _in the same sense_;

it is æquivocal, or applied æquivocally, as respects those things of which

it is predicated in different senses. It is scarcely necessary to give

instances of a fact so familiar as the double meaning of a word. In

reality, as has been already observed, an æquivocal or ambiguous word is

not one name, but two names, accidentally coinciding in sound. _File_

meaning a steel instrument, and _file_ meaning a line of soldiers, have no

more title to be considered one word, because written alike, than _grease_

and _Greece_ have, because they are pronounced alike. They are one sound,

appropriated to form two different words.

An intermediate case is that of a name used _analogically_ or

metaphorically; that is, a name which is predicated of two things, not

univocally, or exactly in the same signification, but in significations

somewhat similar, and which being derived one from the other, one of them

may be considered the primary, and the other a secondary signification. As

when we speak of a brilliant light and a brilliant achievement. The word

is not applied in the same sense to the light and to the achievement; but

having been applied to the light in its original sense, that of brightness

to the eye, it is transferred to the achievement in a derivative

signification, supposed to be somewhat like the primitive one. The word,

however, is just as properly two names instead of one, in this case, as in

that of the most perfect ambiguity. And one of the commonest forms of

fallacious reasoning arising from ambiguity, is that of arguing from a

metaphorical expression as if it were literal; that is, as if a word, when

applied metaphorically, were the same name as when taken in its original

sense: which will be seen more particularly in its place.

Chapter III.

Of The Things Denoted By Names.

§ 1. Looking back now to the commencement of our inquiry, let us attempt

to measure how far it has advanced. Logic, we found, is the Theory of

Proof. But proof supposes something provable, which must be a Proposition

or Assertion; since nothing but a Proposition can be an object of belief,

or therefore of proof. A Proposition is, discourse which affirms or denies

something of some other thing. This is one step: there must, it seems, be

two things concerned in every act of belief. But what are these Things?

They can be no other than those signified by the two names, which being

joined together by a copula constitute the Proposition. If, therefore, we

knew what all names signify, we should know every thing which, in the

existing state of human knowledge, is capable either of being made a

subject of affirmation or denial, or of being itself affirmed or denied of

a subject. We have accordingly, in the preceding chapter, reviewed the

various kinds of Names, in order to ascertain what is signified by each of

them. And we have now carried this survey far enough to be able to take an

account of its results, and to exhibit an enumeration of all kinds of

Things which are capable of being made predicates, or of having any thing

predicated of them: after which to determine the import of Predication,

that is, of Propositions, can be no arduous task.

The necessity of an enumeration of Existences, as the basis of Logic, did

not escape the attention of the schoolmen, and of their master Aristotle,

the most comprehensive, if not also the most sagacious, of the ancient

philosophers. The Categories, or Predicaments—the former a Greek word, the

latter its literal translation in the Latin language—were believed to be

an enumeration of all things capable of being named; an enumeration by the

_summa genera_, _i.e._, the most extensive classes into which things could

be distributed; which, therefore, were so many highest Predicates, one or

other of which was supposed capable of being affirmed with truth of every

namable thing whatsoever. The following are the classes into which,

according to this school of philosophy, Things in general might be

reduced:

Οὐσία, Substantia.

Ποσὸν, Quantitas.

Ποιόν, Qualitas.

Πρός τι, Relatio.

Ποιεῖν, Actio.

Πάσχειν, Passio.

Ποῦ, Ubi.

Πότε, Quando.

Κεῖσθακ, Situs.

Ἔχειν, Habitus.

The imperfections of this classification are too obvious to require, and

its merits are not sufficient to reward, a minute examination. It is a

mere catalogue of the distinctions rudely marked out by the language of

familiar life, with little or no attempt to penetrate, by philosophic

analysis, to the _rationale_ even of those common distinctions. Such an

analysis, however superficially conducted, would have shown the

enumeration to be both redundant and defective. Some objects are omitted,

and others repeated several times under different heads. It is like a

division of animals into men, quadrupeds, horses, asses, and ponies. That,

for instance, could not be a very comprehensive view of the nature of

Relation which could exclude action, passivity, and local situation from

that category. The same observation applies to the categories Quando (or

position in time), and Ubi (or position in space); while the distinction

between the latter and Situs is merely verbal. The incongruity of erecting

into a _summum genus_ the class which forms the tenth category is

manifest. On the other hand, the enumeration takes no notice of any thing

besides substances and attributes. In what category are we to place

sensations, or any other feelings and states of mind; as hope, joy, fear;

sound, smell, taste; pain, pleasure; thought, judgment, conception, and

the like? Probably all these would have been placed by the Aristotelian

school in the categories of _actio_ and _passio_; and the relation of such

of them as are active, to their objects, and of such of them as are

passive, to their causes, would rightly be so placed; but the things

themselves, the feelings or states of mind, wrongly. Feelings, or states

of consciousness, are assuredly to be accounted among realities, but they

can not be reckoned either among substances or attributes.(17)

§ 2. Before recommencing, under better auspices, the attempt made with

such imperfect success by the early logicians, we must take notice of an

unfortunate ambiguity in all the concrete names which correspond to the

most general of all abstract terms, the word Existence. When we have

occasion for a name which shall be capable of denoting whatever exists, as

contradistinguished from non-entity or Nothing, there is hardly a word

applicable to the purpose which is not also, and even more familiarly,

taken in a sense in which it denotes only substances. But substances are

not all that exists; attributes, if such things are to be spoken of, must

be said to exist; feelings certainly exist. Yet when we speak of an

_object_, or of a _thing_, we are almost always supposed to mean a

substance. There seems a kind of contradiction in using such an expression

as that one _thing_ is merely an attribute of another thing. And the

announcement of a Classification of Things would, I believe, prepare most

readers for an enumeration like those in natural history, beginning with

the great divisions of animal, vegetable, and mineral, and subdividing

them into classes and orders. If, rejecting the word Thing, we endeavor to

find another of a more general import, or at least more exclusively

confined to that general import, a word denoting all that exists, and

connoting only simple existence; no word might be presumed fitter for such

a purpose than _being_: originally the present participle of a verb which

in one of its meanings is exactly equivalent to the verb _exists_; and

therefore suitable, even by its grammatical formation, to be the concrete

of the abstract _existence_. But this word, strange as the fact may

appear, is still more completely spoiled for the purpose which it seemed

expressly made for, than the word Thing. _Being_ is, by custom, exactly

synonymous with substance; except that it is free from a slight taint of a

second ambiguity; being implied impartially to matter and to mind, while

substance, though originally and in strictness applicable to both, is apt

to suggest in preference the idea of matter. Attributes are never called

Beings; nor are feelings. A Being is that which excites feelings, and

which possesses attributes. The soul is called a Being; God and angels are

called Beings; but if we were to say, extension, color, wisdom, virtue,

are beings, we should perhaps be suspected of thinking with some of the

ancients, that the cardinal virtues are animals; or, at the least, of

holding with the Platonic school the doctrine of self-existent Ideas, or

with the followers of Epicurus that of Sensible Forms, which detach

themselves in every direction from bodies, and by coming in contact with

our organs, cause our perceptions. We should be supposed, in short, to

believe that Attributes are Substances.

In consequence of this perversion of the word Being, philosophers looking

about for something to supply its place, laid their hands upon the word

Entity, a piece of barbarous Latin, invented by the schoolmen to be used

as an abstract name, in which class its grammatical form would seem to

place it: but being seized by logicians in distress to stop a leak in

their terminology, it has ever since been used as a concrete name. The

kindred word _essence_, born at the same time and of the same parents,

scarcely underwent a more complete transformation when, from being the

abstract of the verb _to be_, it came to denote something sufficiently

concrete to be inclosed in a glass bottle. The word Entity, since it

settled down into a concrete name, has retained its universality of

signification somewhat less impaired than any of the names before

mentioned. Yet the same gradual decay to which, after a certain age, all

the language of psychology seems liable, has been at work even here. If

you call virtue an _entity_, you are indeed somewhat less strongly

suspected of believing it to be a substance than if you called it a

_being_; but you are by no means free from the suspicion. Every word which

was originally intended to connote mere existence, seems, after a time, to

enlarge its connotation to _separate_ existence, or existence freed from

the condition of belonging to a substance; which condition being precisely

what constitutes an attribute, attributes are gradually shut out; and

along with them feelings, which in ninety-nine cases out of a hundred have

no other name than that of the attribute which is grounded on them.

Strange that when the greatest embarrassment felt by all who have any

considerable number of thoughts to express, is to find a sufficient

variety of precise words fitted to express them, there should be no

practice to which even scientific thinkers are more addicted than that of

taking valuable words to express ideas which are sufficiently expressed by

other words already appropriated to them.

When it is impossible to obtain good tools, the next best thing is to

understand thoroughly the defects of those we have. I have therefore

warned the reader of the ambiguity of the names which, for want of better,

I am necessitated to employ. It must now be the writer’s endeavor so to

employ them as in no case to leave the meaning doubtful or obscure. No one

of the above terms being altogether unambiguous, I shall not confine

myself to any one, but shall employ on each occasion the word which seems

least likely in the particular case to lead to misunderstanding; nor do I

pretend to use either these or any other words with a rigorous adherence

to one single sense. To do so would often leave us without a word to

express what is signified by a known word in some one or other of its

senses: unless authors had an unlimited license to coin new words,

together with (what it would be more difficult to assume) unlimited power

of making readers understand them. Nor would it be wise in a writer, on a

subject involving so much of abstraction, to deny himself the advantage

derived from even an improper use of a term, when, by means of it, some

familiar association is called up which brings the meaning home to the

mind, as it were by a flash.

The difficulty both to the writer and reader, of the attempt which must be

made to use vague words so as to convey a precise meaning, is not wholly a

matter of regret. It is not unfitting that logical treatises should afford

an example of that, to facilitate which is among the most important uses

of logic. Philosophical language will for a long time, and popular

language still longer, retain so much of vagueness and ambiguity, that

logic would be of little value if it did not, among its other advantages,

exercise the understanding in doing its work neatly and correctly with

these imperfect tools.

After this preamble it is time to proceed to our enumeration. We shall

commence with Feelings, the simplest class of namable things; the term

Feeling being of course understood in its most enlarged sense.

I. Feelings, Or States of Consciousness.

§ 3. A Feeling and a State of consciousness are, in the language of

philosophy, equivalent expressions: every thing is a feeling of which the

mind is conscious; every thing which it _feels_, or, in other words, which

forms a part of its own sentient existence. In popular language Feeling is

not always synonymous with State of Consciousness; being often taken more

peculiarly for those states which are conceived as belonging to the

sensitive, or to the emotional, phasis of our nature, and sometimes, with

a still narrower restriction, to the emotional alone, as distinguished

from what are conceived as belonging to the percipient or to the

intellectual phasis. But this is an admitted departure from correctness of

language; just as, by a popular perversion the exact converse of this, the

word Mind is withdrawn from its rightful generality of signification, and

restricted to the intellect. The still greater perversion by which Feeling

is sometimes confined not only to bodily sensations, but to the sensations

of a single sense, that of touch, needs not be more particularly adverted

to.

Feeling, in the proper sense of the term, is a genus, of which Sensation,

Emotion, and Thought, are subordinate species. Under the word Thought is

here to be included whatever we are internally conscious of when we are

said to think; from the consciousness we have when we think of a red color

without having it before our eyes, to the most recondite thoughts of a

philosopher or poet. Be it remembered, however, that by a thought is to be

understood what passes in the mind itself, and not any object external to

the mind, which the person is commonly said to be thinking of. He may be

thinking of the sun, or of God, but the sun and God are not thoughts; his

mental image, however, of the sun, and his idea of God, are thoughts;

states of his mind, not of the objects themselves; and so also is his

belief of the existence of the sun, or of God; or his disbelief, if the

case be so. Even imaginary objects (which are said to exist only in our

ideas) are to be distinguished from our ideas of them. I may think of a

hobgoblin, as I may think of the loaf which was eaten yesterday, or of the

flower which will bloom to-morrow. But the hobgoblin which never existed

is not the same thing with my idea of a hobgoblin, any more than the loaf

which once existed is the same thing with my idea of a loaf, or the flower

which does not yet exist, but which will exist, is the same with my idea

of a flower. They are all, not thoughts, but objects of thought; though at

the present time all the objects are alike non-existent.

In like manner, a Sensation is to be carefully distinguished from the

object which causes the sensation; our sensation of white from a white

object: nor is it less to be distinguished from the attribute whiteness,

which we ascribe to the object in consequence of its exciting the

sensation. Unfortunately for clearness and due discrimination in

considering these subjects, our sensations seldom receive separate names.

We have a name for the objects which produce in us a certain sensation:

the word _white_. We have a name for the quality in those objects, to

which we ascribe the sensation: the name _whiteness_. But when we speak of

the sensation itself (as we have not occasion to do this often except in

our scientific speculations), language, which adapts itself for the most

part only to the common uses of life, has provided us with no

single-worded or immediate designation; we must employ a circumlocution,

and say, The sensation of white, or The sensation of whiteness; we must

denominate the sensation either from the object, or from the attribute, by

which it is excited. Yet the sensation, though it never _does_, might very

well be _conceived_ to exist, without any thing whatever to excite it. We

can conceive it as arising spontaneously in the mind. But if it so arose,

we should have no name to denote it which would not be a misnomer. In the

case of our sensations of hearing we are better provided; we have the word

Sound, and a whole vocabulary of words to denote the various kinds of

sounds. For as we are often conscious of these sensations in the absence

of any perceptible object, we can more easily conceive having them in the

absence of any object whatever. We need only shut our eyes and listen to

music, to have a conception of a universe with nothing in it except

sounds, and ourselves hearing them: and what is easily conceived

separately, easily obtains a separate name. But in general our names of

sensations denote indiscriminately the sensation and the attribute. Thus,

_color_ stands for the sensations of white, red, etc., but also for the

quality in the colored object. We talk of the colors of things as among

their _properties_.

§ 4. In the case of sensations, another distinction has also to be kept in

view, which is often confounded, and never without mischievous

consequences. This is, the distinction between the sensation itself, and

the state of the bodily organs which precedes the sensation, and which

constitutes the physical agency by which it is produced. One of the

sources of confusion on this subject is the division commonly made of

feelings into Bodily and Mental. Philosophically speaking, there is no

foundation at all for this distinction: even sensations are states of the

sentient mind, not states of the body, as distinguished from it. What I am

conscious of when I see the color blue, is a feeling of blue color, which

is one thing; the picture on my retina, or the phenomenon of hitherto

mysterious nature which takes place in my optic nerve or in my brain, is

another thing, of which I am not at all conscious, and which scientific

investigation alone could have apprised me of. These are states of my

body; but the sensation of blue, which is the consequence of these states

of body, is not a state of body: that which perceives and is conscious is

called Mind. When sensations are called bodily feelings, it is only as

being the class of feelings which are immediately occasioned by bodily

states; whereas the other kinds of feelings, thoughts, for instance, or

emotions, are immediately excited not by any thing acting upon the bodily

organs, but by sensations, or by previous thoughts. This, however, is a

distinction not in our feelings, but in the agency which produces our

feelings: all of them when actually produced are states of mind.

Besides the affection of our bodily organs from without, and the sensation

thereby produced in our minds, many writers admit a third link in the

chain of phenomena, which they call a Perception, and which consists in

the recognition of an external object as the exciting cause of the

sensation. This perception, they say, is an _act_ of the mind, proceeding

from its own spontaneous activity; while in a sensation the mind is

passive, being merely acted upon by the outward object. And according to

some metaphysicians, it is by an act of the mind, similar to perception,

except in not being preceded by any sensation, that the existence of God,

the soul, and other hyperphysical objects, is recognized.

These acts of what is termed perception, whatever be the conclusion

ultimately come to respecting their nature, must, I conceive, take their

place among the varieties of feelings or states of mind. In so classing

them, I have not the smallest intention of declaring or insinuating any

theory as to the law of mind in which these mental processes may be

supposed to originate, or the conditions under which they may be

legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to

suppose must be meant in an analogous case(18)) to indicate that as they

are “_merely_ states of mind,” it is superfluous to inquire into their

distinguishing peculiarities. I abstain from the inquiry as irrelevant to

the science of logic. In these so-called perceptions, or direct

recognitions by the mind, of objects, whether physical or spiritual, which

are external to itself, I can see only cases of belief; but of belief

which claims to be intuitive, or independent of external evidence. When a

stone lies before me, I am conscious of certain sensations which I receive

from it; but if I say that these sensations come to me from an external

object which I _perceive_, the meaning of these words is, that receiving

the sensations, I intuitively _believe_ that an external cause of those

sensations exists. The laws of intuitive belief, and the conditions under

which it is legitimate, are a subject which, as we have already so often

remarked, belongs not to logic, but to the science of the ultimate laws of

the human mind.

To the same region of speculation belongs all that can be said respecting

the distinction which the German metaphysicians and their French and

English followers so elaborately draw between the _acts_ of the mind and

its merely passive _states_; between what it receives from, and what it

gives to, the crude materials of its experience. I am aware that with

reference to the view which those writers take of the primary elements of

thought and knowledge, this distinction is fundamental. But for the

present purpose, which is to examine, not the original groundwork of our

knowledge, but how we come by that portion of it which is not original;

the difference between active and passive states of mind is of secondary

importance. For us, they all are states of mind, they all are feelings; by

which, let it be said once more, I mean to imply nothing of passivity, but

simply that they are psychological facts, facts which take place in the

mind, and are to be carefully distinguished from the external or physical

facts with which they may be connected either as effects or as causes.

§ 5. Among active states of mind, there is, however, one species which

merits particular attention, because it forms a principal part of the

connotation of some important classes of names. I mean _volitions_, or

acts of the will. When we speak of sentient beings by relative names, a

large portion of the connotation of the name usually consists of the

actions of those beings; actions past, present, and possible or probable

future. Take, for instance, the words Sovereign and Subject. What meaning

do these words convey, but that of innumerable actions, done or to be done

by the sovereign and the subjects, to or in regard to one another

reciprocally? So with the words physician and patient, leader and

follower, tutor and pupil. In many cases the words also connote actions

which would be done under certain contingencies by persons other than

those denoted: as the words mortgagor and mortgagee, obligor and obligee,

and many other words expressive of legal relation, which connote what a

court of justice would do to enforce the legal obligation if not

fulfilled. There are also words which connote actions previously done by

persons other than those denoted either by the name itself or by its

correlative; as the word brother. From these instances, it may be seen how

large a portion of the connotation of names consists of actions. Now what

is an action? Not one thing, but a series of two things: the state of mind

called a volition, followed by an effect. The volition or intention to

produce the effect, is one thing; the effect produced in consequence of

the intention, is another thing; the two together constitute the action. I

form the purpose of instantly moving my arm; that is a state of my mind:

my arm (not being tied or paralytic) moves in obedience to my purpose;

that is a physical fact, consequent on a state of mind. The intention,

followed by the fact, or (if we prefer the expression) the fact when

preceded and caused by the intention, is called the action of moving my

arm.

§ 6. Of the first leading division of namable things, viz., Feelings or

States of Consciousness, we began by recognizing three subdivisions;

Sensations, Thoughts, and Emotions. The first two of these we have

illustrated at considerable length; the third, Emotions, not being

perplexed by similar ambiguities, does not require similar

exemplification. And, finally, we have found it necessary to add to these

three a fourth species, commonly known by the name Volitions. We shall now

proceed to the two remaining classes of namable things; all things which

are regarded as external to the mind being considered as belonging either

to the class of Substances or to that of Attributes.

II. Substances.

Logicians have endeavored to define Substance and Attribute; but their

definitions are not so much attempts to draw a distinction between the

things themselves, as instructions what difference it is customary to make

in the grammatical structure of the sentence, according as we are speaking

of substances or of attributes. Such definitions are rather lessons of

English, or of Greek, Latin, or German, than of mental philosophy. An

attribute, say the school logicians, must be the attribute _of_ something;

color, for example, must be the color _of_ something; goodness must be the

goodness _of_ something; and if this something should cease to exist, or

should cease to be connected with the attribute, the existence of the

attribute would be at an end. A substance, on the contrary, is

self-existent; in speaking about it, we need not put _of_ after its name.

A stone is not the stone of any thing; the moon is not the moon _of_ any

thing, but simply the moon. Unless, indeed, the name which we choose to

give to the substance be a relative name; if so, it must be followed

either by _of_, or by some other particle, implying, as that preposition

does, a reference to something else: but then the other characteristic

peculiarity of an attribute would fail; the _something_ might be

destroyed, and the substance might still subsist. Thus, a father must be

the father _of_ something, and so far resembles an attribute, in being

referred to something besides himself: if there were no child, there would

be no father: but this, when we look into the matter, only means that we

should not call him father. The man called father might still exist though

there were no child, as he existed before there was a child; and there

would be no contradiction in supposing him to exist, though the whole

universe except himself were destroyed. But destroy all white substances,

and where would be the attribute whiteness? Whiteness, without any white

thing, is a contradiction in terms.

This is the nearest approach to a solution of the difficulty, that will be

found in the common treatises on logic. It will scarcely be thought to be

a satisfactory one. If an attribute is distinguished from a substance by

being the attribute _of_ something, it seems highly necessary to

understand what is meant by _of_; a particle which needs explanation too

much itself, to be placed in front of the explanation of any thing else.

And as for the self-existence of substance, it is very true that a

substance may be conceived to exist without any other substance, but so

also may an attribute without any other attribute: and we can no more

imagine a substance without attributes than we can imagine attributes

without a substance.

Metaphysicians, however, have probed the question deeper, and given an

account of Substance considerably more satisfactory than this. Substances

are usually distinguished as Bodies or Minds. Of each of these,

philosophers have at length provided us with a definition which seems

unexceptionable.

§ 7. A body, according to the received doctrine of modern metaphysicians,

may be defined, the external cause to which we ascribe our sensations.

When I see and touch a piece of gold, I am conscious of a sensation of

yellow color, and sensations of hardness and weight; and by varying the

mode of handling, I may add to these sensations many others completely

distinct from them. The sensations are all of which I am directly

conscious; but I consider them as produced by something not only existing

independently of my will, but external to my bodily organs and to my mind.

This external something I call a body.

It may be asked, how come we to ascribe our sensations to any external

cause? And is there sufficient ground for so ascribing them? It is known,

that there are metaphysicians who have raised a controversy on the point;

maintaining that we are not warranted in referring our sensations to a

cause such as we understand by the word Body, or to any external cause

whatever. Though we have no concern here with this controversy, nor with

the metaphysical niceties on which it turns, one of the best ways of

showing what is meant by Substance is, to consider what position it is

necessary to take up, in order to maintain its existence against

opponents.

It is certain, then, that a part of our notion of a body consists of the

notion of a number of sensations of our own, or of other sentient beings,

habitually occurring simultaneously. My conception of the table at which I

am writing is compounded of its visible form and size, which are complex

sensations of sight; its tangible form and size, which are complex

sensations of our organs of touch and of our muscles; its weight, which is

also a sensation of touch and of the muscles; its color, which is a

sensation of sight; its hardness, which is a sensation of the muscles; its

composition, which is another word for all the varieties of sensation

which we receive under various circumstances from the wood of which it is

made, and so forth. All or most of these various sensations frequently

are, and, as we learn by experience, always might be, experienced

simultaneously, or in many different orders of succession at our own

choice: and hence the thought of any one of them makes us think of the

others, and the whole becomes mentally amalgamated into one mixed state of

consciousness, which, in the language of the school of Locke and Hartley,

is termed a Complex Idea.

Now, there are philosophers who have argued as follows: If we conceive an

orange to be divested of its natural color without acquiring any new one;

to lose its softness without becoming hard, its roundness without becoming

square or pentagonal, or of any other regular or irregular figure

whatever; to be deprived of size, of weight, of taste, of smell; to lose

all its mechanical and all its chemical properties, and acquire no new

ones; to become, in short, invisible, intangible, imperceptible not only

by all our senses, but by the senses of all other sentient beings, real or

possible; nothing, say these thinkers, would remain. For of what nature,

they ask, could be the residuum? and by what token could it manifest its

presence? To the unreflecting its existence seems to rest on the evidence

of the senses. But to the senses nothing is apparent except the

sensations. We know, indeed, that these sensations are bound together by

some law; they do not come together at random, but according to a

systematic order, which is part of the order established in the universe.

When we experience one of these sensations, we usually experience the

others also, or know that we have it in our power to experience them. But

a fixed law of connection, making the sensations occur together, does not,

say these philosophers, necessarily require what is called a substratum to

support them. The conception of a substratum is but one of many possible

forms in which that connection presents itself to our imagination; a mode

of, as it were, realizing the idea. If there be such a substratum, suppose

it at this instant miraculously annihilated, and let the sensations

continue to occur in the same order, and how would the substratum be

missed? By what signs should we be able to discover that its existence had

terminated? Should we not have as much reason to believe that it still

existed as we now have? And if we should not then be warranted in

believing it, how can we be so now? A body, therefore, according to these

metaphysicians, is not any thing intrinsically different from the

sensations which the body is said to produce in us; it is, in short, a set

of sensations, or rather, of possibilities of sensation, joined together

according to a fixed law.

The controversies to which these speculations have given rise, and the

doctrines which have been developed in the attempt to find a conclusive

answer to them, have been fruitful of important consequences to the

Science of Mind. The sensations (it was answered) which we are conscious

of, and which we receive, not at random, but joined together in a certain

uniform manner, imply not only a law or laws of connection, but a cause

external to our mind, which cause, by its own laws, determines the laws

according to which the sensations are connected and experienced. The

schoolmen used to call this external cause by the name we have already

employed, a _substratum_; and its attributes (as they expressed

themselves) _inhered_, literally _stuck_, in it. To this substratum the

name Matter is usually given in philosophical discussions. It was soon,

however, acknowledged by all who reflected on the subject, that the

existence of matter can not be proved by extrinsic evidence. The answer,

therefore, now usually made to Berkeley and his followers, is, that the

belief is intuitive; that mankind, in all ages, have felt themselves

compelled, by a necessity of their nature, to refer their sensations to an

external cause: that even those who deny it in theory, yield to the

necessity in practice, and both in speech, thought, and feeling, do,

equally with the vulgar, acknowledge their sensations to be the effects of

something external to them: this knowledge, therefore, it is affirmed, is

as evidently intuitive as our knowledge of our sensations themselves is

intuitive. And here the question merges in the fundamental problem of

metaphysics properly so called: to which science we leave it.

But although the extreme doctrine of the Idealist metaphysicians, that

objects are nothing but our sensations and the laws which connect them,

has not been generally adopted by subsequent thinkers; the point of most

real importance is one on which those metaphysicians are now very

generally considered to have made out their case: viz., that _all we know_

of objects is the sensations which they give us, and the order of the

occurrence of those sensations. Kant himself, on this point, is as

explicit as Berkeley or Locke. However firmly convinced that there exists

a universe of “Things in themselves,” totally distinct from the universe

of phenomena, or of things as they appear to our senses; and even when

bringing into use a technical expression (_Noumenon_) to denote what the

thing is in itself, as contrasted with the _representation_ of it in our

minds; he allows that this representation (the matter of which, he says,

consists of our sensations, though the form is given by the laws of the

mind itself) is all we know of the object: and that the real nature of the

Thing is, and by the constitution of our faculties ever must remain, at

least in the present state of existence, an impenetrable mystery to us.

“Of things absolutely or in themselves,” says Sir William Hamilton,(19)

“be they external, be they internal, we know nothing, or know them only as

incognizable; and become aware of their incomprehensible existence, only

as this is indirectly and accidentally revealed to us, through certain

qualities related to our faculties of knowledge, and which qualities,

again, we can not think as unconditional, irrelative, existent in and of

ourselves. All that we know is therefore phenomenal—phenomenal of the

unknown.”(20) The same doctrine is laid down in the clearest and strongest

terms by M. Cousin, whose observations on the subject are the more worthy

of attention, as, in consequence of the ultra-German and ontological

character of his philosophy in other respects, they may be regarded as the

admissions of an opponent.(21)

There is not the slightest reason for believing that what we call the

sensible qualities of the object are a type of any thing inherent in

itself, or bear any affinity to its own nature. A cause does not, as such,

resemble its effects; an east wind is not like the feeling of cold, nor

heat like the steam of boiling water. Why then should matter resemble our

sensations? Why should the inmost nature of fire or water resemble the

impressions made by those objects upon our senses?(22) Or on what

principle are we authorized to deduce from the effects, any thing

concerning the cause, except that it is a cause adequate to produce those

effects? It may, therefore, safely be laid down as a truth both obvious in

itself, and admitted by all whom it is at present necessary to take into

consideration, that, of the outward world, we know and can know absolutely

nothing, except the sensations which we experience from it.(23)

§ 8. Body having now been defined the external cause, and (according to

the more reasonable opinion) the unknown external cause, to which we refer

our sensations; it remains to frame a definition of Mind. Nor, after the

preceding observations, will this be difficult. For, as our conception of

a body is that of an unknown exciting cause of sensations, so our

conception of a mind is that of an unknown recipient or percipient, of

them; and not of them alone, but of all our other feelings. As body is

understood to be the mysterious something which excites the mind to feel,

so mind is the mysterious something which feels and thinks. It is

unnecessary to give in the case of mind, as we gave in the case of matter,

a particular statement of the skeptical system by which its existence as a

Thing in itself, distinct from the series of what are denominated its

states, is called in question. But it is necessary to remark, that on the

inmost nature (whatever be meant by inmost nature) of the thinking

principle, as well as on the inmost nature of matter, we are, and with our

faculties must always remain, entirely in the dark. All which we are aware

of, even in our own minds, is (in the words of James Mill) a certain

“thread of consciousness;” a series of feelings, that is, of sensations,

thoughts, emotions, and volitions, more or less numerous and complicated.

There is a something I call Myself, or, by another form of expression, my

mind, which I consider as distinct from these sensations, thoughts, etc.;

a something which I conceive to be not the thoughts, but the being that

has the thoughts, and which I can conceive as existing forever in a state

of quiescence, without any thoughts at all. But what this being is, though

it is myself, I have no knowledge, other than the series of its states of

consciousness. As bodies manifest themselves to me only through the

sensations of which I regard them as the causes, so the thinking

principle, or mind, in my own nature, makes itself known to me only by the

feelings of which it is conscious. I know nothing about myself, save my

capacities of feeling or being conscious (including, of course, thinking

and willing): and were I to learn any thing new concerning my own nature,

I can not with my present faculties conceive this new information to be

any thing else, than that I have some additional capacities, as yet

unknown to me, of feeling, thinking, or willing.

Thus, then, as body is the unsentient cause to which we are naturally

prompted to refer a certain portion of our feelings, so mind may be

described as the sentient _subject_ (in the scholastic sense of the term)

of all feelings; that which has or feels them. But of the nature of either

body or mind, further than the feelings which the former excites, and

which the latter experiences, we do not, according to the best existing

doctrine, know any thing; and if any thing, logic has nothing to do with

it, or with the manner in which the knowledge is acquired. With this

result we may conclude this portion of our subject, and pass to the third

and only remaining class or division of Namable Things.

III. Attributes: and, first, Qualities.

§ 9. From what has already been said of Substance, what is to be said of

Attribute is easily deducible. For if we know not, and can not know, any

thing of bodies but the sensations which they excite in us or in others,

those sensations must be all that we can, at bottom, mean by their

attributes; and the distinction which we verbally make between the

properties of things and the sensations we receive from them, must

originate in the convenience of discourse rather than in the nature of

what is signified by the terms.

Attributes are usually distributed under the three heads of Quality,

Quantity, and Relation. We shall come to the two latter presently: in the

first place we shall confine ourselves to the former.

Let us take, then, as our example, one of what are termed the sensible

qualities of objects, and let that example be whiteness. When we ascribe

whiteness to any substance, as, for instance, snow; when we say that snow

has the quality whiteness, what do we really assert? Simply, that when

snow is present to our organs, we have a particular sensation, which we

are accustomed to call the sensation of white. But how do I know that snow

is present? Obviously by the sensations which I derive from it, and not

otherwise. I infer that the object is present, because it gives me a

certain assemblage or series of sensations. And when I ascribe to it the

attribute whiteness, my meaning is only, that, of the sensations composing

this group or series, that which I call the sensation of white color is

one.

This is one view which may be taken of the subject. But there is also

another and a different view. It may be said, that it is true we _know_

nothing of sensible objects, except the sensations they excite in us; that

the fact of our receiving from snow the particular sensation which is

called a sensation of white, is the _ground_ on which we ascribe to that

substance the quality whiteness; the sole proof of its possessing that

quality. But because one thing may be the sole evidence of the existence

of another thing, it does not follow that the two are one and the same.

The attribute whiteness (it may be said) is not the fact of receiving the

sensation, but something in the object itself; a _power_ inherent in it;

something _in virtue_ of which the object produces the sensation. And when

we affirm that snow possesses the attribute whiteness, we do not merely

assert that the presence of snow produces in us that sensation, but that

it does so through, and by reason of, that power or quality.

For the purposes of logic it is not of material importance which of these

opinions we adopt. The full discussion of the subject belongs to the other

department of scientific inquiry, so often alluded to under the name of

metaphysics; but it may be said here, that for the doctrine of the

existence of a peculiar species of entities called qualities, I can see no

foundation except in a tendency of the human mind which is the cause of

many delusions. I mean, the disposition, wherever we meet with two names

which are not precisely synonymous, to suppose that they must be the names

of two different things; whereas in reality they may be names of the same

thing viewed in two different lights, or under different suppositions as

to surrounding circumstances. Because _quality_ and _sensation_ can not be

put indiscriminately one for the other, it is supposed that they can not

both signify the same thing, namely, the impression or feeling with which

we are affected through our senses by the presence of an object; though

there is at least no absurdity in supposing that this identical impression

or feeling may be called a sensation when considered merely in itself, and

a quality when looked at in relation to any one of the numerous objects,

the presence of which to our organs excites in our minds that among

various other sensations or feelings. And if this be admissible as a

supposition, it rests with those who contend for an entity _per se_ called

a quality, to show that their opinion is preferable, or is any thing in

fact but a lingering remnant of the old doctrine of occult causes; the

very absurdity which Molière so happily ridiculed when he made one of his

pedantic physicians account for the fact that opium produces sleep by the

maxim, Because it has a soporific virtue.

It is evident that when the physician stated that opium has a soporific

virtue, he did not account for, but merely asserted over again, the fact

that it produces sleep. In like manner, when we say that snow is white

because it has the quality of whiteness, we are only re-asserting in more

technical language the fact that it excites in us the sensation of white.

If it be said that the sensation must have some cause, I answer, its cause

is the presence of the assemblage of phenomena which is termed the object.

When we have asserted that as often as the object is present, and our

organs in their normal state, the sensation takes place, we have stated

all that we know about the matter. There is no need, after assigning a

certain and intelligible cause, to suppose an occult cause besides, for

the purpose of enabling the real cause to produce its effect. If I am

asked, why does the presence of the object cause this sensation in me, I

can not tell: I can only say that such is my nature, and the nature of the

object; that the fact forms a part of the constitution of things. And to

this we must at last come, even after interpolating the imaginary entity.

Whatever number of links the chain of causes and effects may consist of,

how any one link produces the one which is next to it, remains equally

inexplicable to us. It is as easy to comprehend that the object should

produce the sensation directly and at once, as that it should produce the

same sensation by the aid of something else called the _power_ of

producing it.

But, as the difficulties which may be felt in adopting this view of the

subject can not be removed without discussions transcending the bounds of

our science, I content myself with a passing indication, and shall, for

the purposes of logic, adopt a language compatible with either view of the

nature of qualities. I shall say—what at least admits of no dispute—that

the quality of whiteness ascribed to the object snow, is _grounded_ on its

exciting in us the sensation of white; and adopting the language already

used by the school logicians in the case of the kind of attributes called

Relations, I shall term the sensation of white the _foundation_ of the

quality whiteness. For logical purposes the sensation is the only

essential part of what is meant by the word; the only part which we ever

can be concerned in proving. When that is proved, the quality is proved;

if an object excites a sensation, it has, of course, the power of exciting

it.

IV. Relations.

§ 10. The _qualities_ of a body, we have said, are the attributes grounded

on the sensations which the presence of that particular body to our organs

excites in our minds. But when we ascribe to any object the kind of

attribute called a Relation, the foundation of the attribute must be

something in which other objects are concerned besides itself and the

percipient.

As there may with propriety be said to be a relation between any two

things to which two correlative names are or may be given, we may expect

to discover what constitutes a relation in general, if we enumerate the

principal cases in which mankind have imposed correlative names, and

observe what these cases have in common.

What, then, is the character which is possessed in common by states of

circumstances so heterogeneous and discordant as these: one thing _like_

another; one thing _unlike_ another; one thing _near_ another; one thing

_far from_ another; one thing _before_, _after_, _along with_ another; one

thing _greater_, _equal_, _less_, than another; one thing the _cause_ of

another, the _effect_ of another; one person the _master_, _servant_,

_child_, _parent_, _debtor_, _creditor_, _sovereign_, _subject_,

_attorney_, _client_, of another, and so on?

Omitting, for the present, the case of Resemblance, (a relation which

requires to be considered separately,) there seems to be one thing common

to all these cases, and only one; that in each of them there exists or

occurs, or has existed or occurred, or may be expected to exist or occur,

some fact or phenomenon, into which the two things which are said to be

related to each other, both enter as parties concerned. This fact, or

phenomenon, is what the Aristotelian logicians called the _fundamentum

relationis_. Thus in the relation of greater and less between two

magnitudes, the _fundamentum relationis_ is the fact that one of the two

magnitudes could, under certain conditions, be included in, without

entirely filling, the space occupied by the other magnitude. In the

relation of master and servant, the _fundamentum relationis_ is the fact

that the one has undertaken, or is compelled, to perform certain services

for the benefit and at the bidding of the other. Examples might be

indefinitely multiplied; but it is already obvious that whenever two

things are said to be related, there is some fact, or series of facts,

into which they both enter; and that whenever any two things are involved

in some one fact, or series of facts, we may ascribe to those two things a

mutual relation grounded on the fact. Even if they have nothing in common

but what is common to all things, that they are members of the universe,

we call that a relation, and denominate them fellow-creatures,

fellow-beings, or fellow-denizens of the universe. But in proportion as

the fact into which the two objects enter as parts is of a more special

and peculiar, or of a more complicated nature, so also is the relation

grounded upon it. And there are as many conceivable relations as there are

conceivable kinds of fact in which two things can be jointly concerned.

In the same manner, therefore, as a quality is an attribute grounded on

the fact that a certain sensation or sensations are produced in us by the

object, so an attribute grounded on some fact into which the object enters

jointly with another object, is a relation between it and that other

object. But the fact in the latter case consists of the very same kind of

elements as the fact in the former; namely, states of consciousness. In

the case, for example, of any legal relation, as debtor and creditor,

principal and agent, guardian and ward, the _fundamentum relationis_

consists entirely of thoughts, feelings, and volitions (actual or

contingent), either of the persons themselves or of other persons

concerned in the same series of transactions; as, for instance, the

intentions which would be formed by a judge, in case a complaint were made

to his tribunal of the infringement of any of the legal obligations

imposed by the relation; and the acts which the judge would perform in

consequence; acts being (as we have already seen) another word for

intentions followed by an effect, and that effect being but another word

for sensations, or some other feelings, occasioned either to the agent

himself or to somebody else. There is no part of what the names expressive

of the relation imply, that is not resolvable into states of

consciousness; outward objects being, no doubt, supposed throughout as the

causes by which some of those states of consciousness are excited, and

minds as the subjects by which all of them are experienced, but neither

the external objects nor the minds making their existence known otherwise

than by the states of consciousness.

Cases of relation are not always so complicated as those to which we last

alluded. The simplest of all cases of relation are those expressed by the

words antecedent and consequent, and by the word simultaneous. If we say,

for instance, that dawn preceded sunrise, the fact in which the two

things, dawn and sunrise, were jointly concerned, consisted only of the

two things themselves; no third thing entered into the fact or phenomenon

at all. Unless, indeed, we choose to call the succession of the two

objects a third thing; but their succession is not something added to the

things themselves; it is something involved in them. Dawn and sunrise

announce themselves to our consciousness by two successive sensations. Our

consciousness of the succession of these sensations is not a third

sensation or feeling added to them; we have not first the two feelings,

and then a feeling of their succession. To have two feelings at all,

implies having them either successively, or else simultaneously.

Sensations, or other feelings, being given, succession and

simultaneousness are the two conditions, to the alternative of which they

are subjected by the nature of our faculties; and no one has been able, or

needs expect, to analyze the matter any further.

§ 11. In a somewhat similar position are two other sorts of relations,

Likeness and Unlikeness. I have two sensations; we will suppose them to be

simple ones; two sensations of white, or one sensation of white and

another of black. I call the first two sensations _like_; the last two

_unlike_. What is the fact or phenomenon constituting the _fundamentum_ of

this relation? The two sensations first, and then what we call a feeling

of resemblance, or of want of resemblance. Let us confine ourselves to the

former case. Resemblance is evidently a feeling; a state of the

consciousness of the observer. Whether the feeling of the resemblance of

the two colors be a third state of consciousness, which I have _after_

having the two sensations of color, or whether (like the feeling of their

succession) it is involved in the sensations themselves, may be a matter

of discussion. But in either case, these feelings of resemblance, and of

its opposite dissimilarity, are parts of our nature; and parts so far from

being capable of analysis, that they are presupposed in every attempt to

analyze any of our other feelings. Likeness and unlikeness, therefore, as

well as antecedence, sequence, and simultaneousness, must stand apart

among relations, as things _sui generis_. They are attributes grounded on

facts, that is, on states of consciousness, but on states which are

peculiar, unresolvable, and inexplicable.

But, though likeness or unlikeness can not be resolved into any thing

else, complex cases of likeness or unlikeness can be resolved into simpler

ones. When we say of two things which consist of parts, that they are like

one another, the likeness of the wholes does admit of analysis; it is

compounded of likenesses between the various parts respectively, and of

likeness in their arrangement. Of how vast a variety of resemblances of

parts must that resemblance be composed, which induces us to say that a

portrait, or a landscape, is like its original. If one person mimics

another with any success, of how many simple likenesses must the general

or complex likeness be compounded: likeness in a succession of bodily

postures; likeness in voice, or in the accents and intonations of the

voice; likeness in the choice of words, and in the thoughts or sentiments

expressed, whether by word, countenance, or gesture.

All likeness and unlikeness of which we have any cognizance, resolve

themselves into likeness and unlikeness between states of our own, or some

other, mind. When we say that one body is like another, (since we know

nothing of bodies but the sensations which they excite,) we mean really

that there is a resemblance between the sensations excited by the two

bodies, or between some portions at least of those sensations. If we say

that two attributes are like one another (since we know nothing of

attributes except the sensations or states of feeling on which they are

grounded), we mean really that those sensations, or states of feeling,

resemble each other. We may also say that two relations are alike. The

fact of resemblance between relations is sometimes called _analogy_,

forming one of the numerous meanings of that word. The relation in which

Priam stood to Hector, namely, that of father and son, resembles the

relation in which Philip stood to Alexander; resembles it so closely that

they are called the same relation. The relation in which Cromwell stood to

England resembles the relation in which Napoleon stood to France, though

not so closely as to be called the same relation. The meaning in both

these instances must be, that a resemblance existed between the facts

which constituted the _fundamentum relationis_.

This resemblance may exist in all conceivable gradations, from perfect

undistinguishableness to something extremely slight. When we say, that a

thought suggested to the mind of a person of genius is like a seed cast

into the ground, because the former produces a multitude of other

thoughts, and the latter a multitude of other seeds, this is saying that

between the relation of an inventive mind to a thought contained in it,

and the relation of a fertile soil to a seed contained in it, there exists

a resemblance: the real resemblance being in the two _fundamenta

relationis_, in each of which there occurs a germ, producing by its

development a multitude of other things similar to itself. And as,

whenever two objects are jointly concerned in a phenomenon, this

constitutes a relation between those objects, so, if we suppose a second

pair of objects concerned in a second phenomenon, the slightest

resemblance between the two phenomena is sufficient to admit of its being

said that the two relations resemble; provided, of course, the points of

resemblance are found in those portions of the two phenomena respectively

which are connoted by the relative names.

While speaking of resemblance, it is necessary to take notice of an

ambiguity of language, against which scarcely any one is sufficiently on

his guard. Resemblance, when it exists in the highest degree of all,

amounting to undistinguishableness, is often called identity, and the two

similar things are said to be the same. I say often, not always; for we do

not say that two visible objects, two persons, for instance, are the same,

because they are so much alike that one might be mistaken for the other:

but we constantly use this mode of expression when speaking of feelings;

as when I say that the sight of any object gives me the _same_ sensation

or emotion to-day that it did yesterday, or the _same_ which it gives to

some other person. This is evidently an incorrect application of the word

_same_; for the feeling which I had yesterday is gone, never to return;

what I have to-day is another feeling, exactly like the former, perhaps,

but distinct from it; and it is evident that two different persons can not

be experiencing the same feeling, in the sense in which we say that they

are both sitting at the same table. By a similar ambiguity we say, that

two persons are ill of the _same_ disease; that two persons hold the

_same_ office; not in the sense in which we say that they are engaged in

the same adventure, or sailing in the same ship, but in the sense that

they fill offices exactly similar, though, perhaps, in distant places.

Great confusion of ideas is often produced, and many fallacies engendered,

in otherwise enlightened understandings, by not being sufficiently alive

to the fact (in itself not always to be avoided), that they use the same

name to express ideas so different as those of identity and

undistinguishable resemblance. Among modern writers, Archbishop Whately

stands almost alone in having drawn attention to this distinction, and to

the ambiguity connected with it.

Several relations, generally called by other names, are really cases of

resemblance. As, for example, equality; which is but another word for the

exact resemblance commonly called identity, considered as subsisting

between things in respect of their _quantity_. And this example forms a

suitable transition to the third and last of the three heads under which,

as already remarked, Attributes are commonly arranged.

V. Quantity.

§ 12. Let us imagine two things, between which there is no difference

(that is, no dissimilarity), except in quantity alone; for instance, a

gallon of water, and more than a gallon of water. A gallon of water, like

any other external object, makes its presence known to us by a set of

sensations which it excites. Ten gallons of water are also an external

object, making its presence known to us in a similar manner; and as we do

not mistake ten gallons of water for a gallon of water, it is plain that

the set of sensations is more or less different in the two cases. In like

manner, a gallon of water, and a gallon of wine, are two external objects,

making their presence known by two sets of sensations, which sensations

are different from each other. In the first case, however, we say that the

difference is in quantity; in the last there is a difference in quality,

while the quantity of the water and of the wine is the same. What is the

real distinction between the two cases? It is not within the province of

Logic to analyze it; nor to decide whether it is susceptible of analysis

or not. For us the following considerations are sufficient: It is evident

that the sensations I receive from the gallon of water, and those I

receive from the gallon of wine, are not the same, that is, not precisely

alike; neither are they altogether unlike: they are partly similar, partly

dissimilar; and that in which they resemble is precisely that in which

alone the gallon of water and the ten gallons do not resemble. That in

which the gallon of water and the gallon of wine are like each other, and

in which the gallon and the ten gallons of water are unlike each other, is

called their quantity. This likeness and unlikeness I do not pretend to

explain, no more than any other kind of likeness or unlikeness. But my

object is to show, that when we say of two things that they differ in

quantity, just as when we say that they differ in quality, the assertion

is always grounded on a difference in the sensations which they excite.

Nobody, I presume, will say, that to see, or to lift, or to drink, ten

gallons of water, does not include in itself a different set of sensations

from those of seeing, lifting, or drinking one gallon; or that to see or

handle a foot-rule, and to see or handle a yard-measure made exactly like

it, are the same sensations. I do not undertake to say what the difference

in the sensations is. Every body knows, and nobody can tell; no more than

any one could tell what white is to a person who had never had the

sensation. But the difference, so far as cognizable by our faculties, lies

in the sensations. Whatever difference we say there is in the things

themselves, is, in this as in all other cases, grounded, and grounded

exclusively, on a difference in the sensations excited by them.

VI. Attributes Concluded.

§ 13. Thus, then, all the attributes of bodies which are classed under

Quality or Quantity, are grounded on the sensations which we receive from

those bodies, and may be defined, the powers which the bodies have of

exciting those sensations. And the same general explanation has been found

to apply to most of the attributes usually classed under the head of

Relation. They, too, are grounded on some fact or phenomenon into which

the related objects enter as parts; that fact or phenomenon having no

meaning and no existence to us, except the series of sensations or other

states of consciousness by which it makes itself known; and the relation

being simply the power or capacity which the object possesses of taking

part along with the correlated object in the production of that series of

sensations or states of consciousness. We have been obliged, indeed, to

recognize a somewhat different character in certain peculiar relations,

those of succession and simultaneity, of likeness and unlikeness. These,

not being grounded on any fact or phenomenon distinct from the related

objects themselves, do not admit of the same kind of analysis. But these

relations, though not, like other relations, grounded on states of

consciousness, are themselves states of consciousness: resemblance is

nothing but our feeling of resemblance; succession is nothing but our

feeling of succession. Or, if this be disputed (and we can not, without

transgressing the bounds of our science, discuss it here), at least our

knowledge of these relations, and even our possibility of knowledge, is

confined to those which subsist between sensations, or other states of

consciousness; for, though we ascribe resemblance, or succession, or

simultaneity, to objects and to attributes, it is always in virtue of

resemblance or succession or simultaneity in the sensations or states of

consciousness which those objects excite, and on which those attributes

are grounded.

§ 14. In the preceding investigation we have, for the sake of simplicity,

considered bodies only, and omitted minds. But what we have said, is

applicable, _mutatis mutandis_, to the latter. The attributes of minds, as

well as those of bodies, are grounded on states of feeling or

consciousness. But in the case of a mind, we have to consider its own

states, as well as those which it produces in other minds. Every attribute

of a mind consists either in being itself affected in a certain way, or

affecting other minds in a certain way. Considered in itself, we can

predicate nothing of it but the series of its own feelings. When we say of

any mind, that it is devout, or superstitious, or meditative, or cheerful,

we mean that the ideas, emotions, or volitions implied in those words,

form a frequently recurring part of the series of feelings, or states of

consciousness, which fill up the sentient existence of that mind.

In addition, however, to those attributes of a mind which are grounded on

its own states of feeling, attributes may also be ascribed to it, in the

same manner as to a body, grounded on the feelings which it excites in

other minds. A mind does not, indeed, like a body, excite sensations, but

it may excite thoughts or emotions. The most important example of

attributes ascribed on this ground, is the employment of terms expressive

of approbation or blame. When, for example, we say of any character, or

(in other words) of any mind, that it is admirable, we mean that the

contemplation of it excites the sentiment of admiration; and indeed

somewhat more, for the word implies that we not only feel admiration, but

approve that sentiment in ourselves. In some cases, under the semblance of

a single attribute, two are really predicated: one of them, a state of the

mind itself; the other, a state with which other minds are affected by

thinking of it. As when we say of any one that he is generous. The word

generosity expresses a certain state of mind, but being a term of praise,

it also expresses that this state of mind excites in us another mental

state, called approbation. The assertion made, therefore, is twofold, and

of the following purport: Certain feelings form habitually a part of this

person’s sentient existence; and the idea of those feelings of his,

excites the sentiment of approbation in ourselves or others.

As we thus ascribe attributes to minds on the ground of ideas and

emotions, so may we to bodies on similar grounds, and not solely on the

ground of sensations: as in speaking of the beauty of a statue; since this

attribute is grounded on the peculiar feeling of pleasure which the statue

produces in our minds; which is not a sensation, but an emotion.

VII. General Results.

§ 15. Our survey of the varieties of Things which have been, or which are

capable of being, named—which have been, or are capable of being, either

predicated of other Things, or themselves made the subject of

predications—is now concluded.

Our enumeration commenced with Feelings. These we scrupulously

distinguished from the objects which excite them, and from the organs by

which they are, or may be supposed to be, conveyed. Feelings are of four

sorts: Sensations, Thoughts, Emotions, and Volitions. What are called

Perceptions are merely a particular case of Belief, and Belief is a kind

of thought. Actions are merely volitions followed by an effect.

After Feelings we proceeded to Substances. These are either Bodies or

Minds. Without entering into the grounds of the metaphysical doubts which

have been raised concerning the existence of Matter and Mind as objective

realities, we stated as sufficient for us the conclusion in which the best

thinkers are now for the most part agreed, that all we can know of Matter

is the sensations which it gives us, and the order of occurrence of those

sensations; and that while the substance Body is the unknown cause of our

sensations, the substance Mind is the unknown recipient.

The only remaining class of Namable Things is Attributes; and these are of

three kinds, Quality, Relation, and Quantity. Qualities, like substances,

are known to us no otherwise than by the sensations or other states of

consciousness which they excite: and while, in compliance with common

usage, we have continued to speak of them as a distinct class of Things,

we showed that in predicating them no one means to predicate any thing but

those sensations or states of consciousness, on which they may be said to

be grounded, and by which alone they can be defined or described.

Relations, except the simple cases of likeness and unlikeness, succession

and simultaneity, are similarly grounded on some fact or phenomenon, that

is, on some series of sensations or states of consciousness, more or less

complicated. The third species of Attribute, Quantity, is also manifestly

grounded on something in our sensations or states of feeling, since there

is an indubitable difference in the sensations excited by a larger and a

smaller bulk, or by a greater or a less degree of intensity, in any object

of sense or of consciousness. All attributes, therefore, are to us nothing

but either our sensations and other states of feeling, or something

inextricably involved therein; and to this even the peculiar and simple

relations just adverted to are not exceptions. Those peculiar relations,

however, are so important, and, even if they might in strictness be

classed among states of consciousness, are so fundamentally distinct from

any other of those states, that it would be a vain subtlety to bring them

under that common description, and it is necessary that they should be

classed apart.(24)

As the result, therefore, of our analysis, we obtain the following as an

enumeration and classification of all Namable Things:

1st. Feelings, or States of Consciousness.

2d. The Minds which experience those feelings.

3d. The Bodies, or external objects which excite certain of those

feelings, together with the powers or properties whereby they excite them;

these latter (at least) being included rather in compliance with common

opinion, and because their existence is taken for granted in the common

language from which I can not prudently deviate, than because the

recognition of such powers or properties as real existences appears to be

warranted by a sound philosophy.

4th, and last. The Successions and Co-existences, the Likenesses and

Unlikenesses, between feelings or states of consciousness. Those

relations, when considered as subsisting between other things, exist in

reality only between the states of consciousness which those things, if

bodies, excite, if minds, either excite or experience.

This, until a better can be suggested, may serve as a substitute for the

Categories of Aristotle considered as a classification of Existences. The

practical application of it will appear when we commence the inquiry into

the Import of Propositions; in other words, when we inquire what it is

which the mind actually believes, when it gives what is called its assent

to a proposition.

These four classes comprising, if the classification be correct, all

Namable Things, these or some of them must of course compose the

signification of all names: and of these, or some of them, is made up

whatever we call a fact.

For distinction’s sake, every fact which is solely composed of feelings or

states of consciousness considered as such, is often called a

Psychological or Subjective fact; while every fact which is composed,

either wholly or in part, of something different from these, that is, of

substances and attributes, is called an Objective fact. We may say, then,

that every objective fact is grounded on a corresponding subjective one;

and has no meaning to us (apart from the subjective fact which corresponds

to it), except as a name for the unknown and inscrutable process by which

that subjective or psychological fact is brought to pass.

Chapter IV.

Of Propositions.

§ 1. In treating of Propositions, as already in treating of Names, some

considerations of a comparatively elementary nature respecting their form

and varieties must be premised, before entering upon that analysis of the

import conveyed by them, which is the real subject and purpose of this

preliminary book.

A proposition, we have before said, is a portion of discourse in which a

predicate is affirmed or denied of a subject. A predicate and a subject

are all that is necessarily required to make up a proposition: but as we

can not conclude from merely seeing two names put together, that they are

a predicate and a subject, that is, that one of them is intended to be

affirmed or denied of the other, it is necessary that there should be some

mode or form of indicating that such is the intention; some sign to

distinguish a predication from any other kind of discourse. This is

sometimes done by a slight alteration of one of the words, called an

_inflection_; as when we say, Fire burns; the change of the second word

from _burn_ to _burns_ showing that we mean to affirm the predicate burn

of the subject fire. But this function is more commonly fulfilled by the

word _is_, when an affirmation is intended, _is not_, when a negation; or

by some other part of the verb _to be_. The word which thus serves the

purpose of a sign of predication is called, as we formerly observed, the

_copula_. It is important that there should be no indistinctness in our

conception of the nature and office of the copula; for confused notions

respecting it are among the causes which have spread mysticism over the

field of logic, and perverted its speculations into logomachies.

It is apt to be supposed that the copula is something more than a mere

sign of predication; that it also signifies existence. In the proposition,

Socrates is just, it may seem to be implied not only that the quality

_just_ can be affirmed of Socrates, but moreover that Socrates _is_, that

is to say, exists. This, however, only shows that there is an ambiguity in

the word _is_; a word which not only performs the function of the copula

in affirmations, but has also a meaning of its own, in virtue of which it

may itself be made the predicate of a proposition. That the employment of

it as a copula does not necessarily include the affirmation of existence,

appears from such a proposition as this, A centaur is a fiction of the

poets; where it can not possibly be implied that a centaur exists, since

the proposition itself expressly asserts that the thing has no real

existence.

Many volumes might be filled with the frivolous speculations concerning

the nature of Being (το ὄν, οὐσία, Ens, Entitas, Essentia, and the like),

which have arisen from overlooking this double meaning of the word _to

be_; from supposing that when it signifies _to exist_, and when it

signifies to _be_ some specified thing, as to _be_ a man, to _be_

Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a

nonentity, it must still, at bottom, answer to the same idea; and that a

meaning must be found for it which shall suit all these cases. The fog

which rose from this narrow spot diffused itself at an early period over

the whole surface of metaphysics. Yet it becomes us not to triumph over

the great intellects of Plato and Aristotle because we are now able to

preserve ourselves from many errors into which they, perhaps inevitably,

fell. The fire-teazer of a modern steam-engine produces by his exertions

far greater effects than Milo of Crotona could, but he is not therefore a

stronger man. The Greeks seldom knew any language but their own. This

rendered it far more difficult for them than it is for us, to acquire a

readiness in detecting ambiguities. One of the advantages of having

accurately studied a plurality of languages, especially of those languages

which eminent thinkers have used as the vehicle of their thoughts, is the

practical lesson we learn respecting the ambiguities of words, by finding

that the same word in one language corresponds, on different occasions, to

different words in another. When not thus exercised, even the strongest

understandings find it difficult to believe that things which have a

common name, have not in some respect or other a common nature; and often

expend much labor very unprofitably (as was frequently done by the two

philosophers just mentioned) in vain attempts to discover in what this

common nature consists. But, the habit once formed, intellects much

inferior are capable of detecting even ambiguities which are common to

many languages: and it is surprising that the one now under consideration,

though it exists in the modern languages as well as in the ancient, should

have been overlooked by almost all authors. The quantity of futile

speculation which had been caused by a misapprehension of the nature of

the copula, was hinted at by Hobbes; but Mr. James Mill(25) was, I

believe, the first who distinctly characterized the ambiguity, and pointed

out how many errors in the received systems of philosophy it has had to

answer for. It has, indeed, misled the moderns scarcely less than the

ancients, though their mistakes, because our understandings are not yet so

completely emancipated from their influence, do not appear equally

irrational.

We shall now briefly review the principal distinctions which exist among

propositions, and the technical terms most commonly in use to express

those distinctions.

§ 2. A proposition being a portion of discourse in which something is

affirmed or denied of something, the first division of propositions is

into affirmative and negative. An affirmative proposition is that in which

the predicate is _affirmed_ of the subject; as, Cæsar is dead. A negative

proposition is that in which the predicate is _denied_ of the subject; as,

Cæsar is not dead. The copula, in this last species of proposition,

consists of the words _is not_, which are the sign of negation; _is_ being

the sign of affirmation.

Some logicians, among whom may be mentioned Hobbes, state this distinction

differently; they recognize only one form of copula, _is_, and attach the

negative sign to the predicate. “Cæsar is dead,” and “Cæsar is not dead,”

according to these writers, are propositions agreeing not in the subject

and predicate, but in the subject only. They do not consider “dead,” but

“not dead,” to be the predicate of the second proposition, and they

accordingly define a negative proposition to be one in which the predicate

is a negative name. The point, though not of much practical moment,

deserves notice as an example (not unfrequent in logic) where by means of

an apparent simplification, but which is merely verbal, matters are made

more complex than before. The notion of these writers was, that they could

get rid of the distinction between affirming and denying, by treating

every case of denying as the affirming of a negative name. But what is

meant by a negative name? A name expressive of the _absence_ of an

attribute. So that when we affirm a negative name, what we are really

predicating is absence and not presence; we are asserting not that any

thing is, but that something is not; to express which operation no word

seems so proper as the word denying. The fundamental distinction is

between a fact and the non-existence of that fact; between seeing

something and not seeing it, between Cæsar’s being dead and his not being

dead; and if this were a merely verbal distinction, the generalization

which brings both within the same form of assertion would be a real

simplification: the distinction, however, being real, and in the facts, it

is the generalization confounding the distinction that is merely verbal;

and tends to obscure the subject, by treating the difference between two

kinds of truths as if it were only a difference between two kinds of

words. To put things together, and to put them or keep them asunder, will

remain different operations, whatever tricks we may play with language.

A remark of a similar nature may be applied to most of those distinctions

among propositions which are said to have reference to their _modality_;

as, difference of tense or time; the sun _did_ rise, the sun _is_ rising,

the sun _will_ rise. These differences, like that between affirmation and

negation, might be glossed over by considering the incident of time as a

mere modification of the predicate: thus, The sun is _an object having

risen_, The sun is _an object now rising_, The sun is _an object to rise

hereafter_. But the simplification would be merely verbal. Past, present,

and future, do not constitute so many different kinds of rising; they are

designations belonging to the event asserted, to the _sun’s_ rising

to-day. They affect, not the predicate, but the applicability of the

predicate to the particular subject. That which we affirm to be past,

present, or future, is not what the subject signifies, nor what the

predicate signifies, but specifically and expressly what the predication

signifies; what is expressed only by the proposition as such, and not by

either or both of the terms. Therefore the circumstance of time is

properly considered as attaching to the copula, which is the sign of

predication, and not to the predicate. If the same can not be said of such

modifications as these, Cæsar _may_ be dead; Cæsar is _perhaps_ dead; it

is _possible_ that Cæsar is dead; it is only because these fall altogether

under another head, being properly assertions not of any thing relating to

the fact itself, but of the state of our own mind in regard to it; namely,

our absence of disbelief of it. Thus “Cæsar may be dead” means “I am not

sure that Cæsar is alive.”

§ 3. The next division of propositions is into Simple and Complex; more

aptly (by Professor Bain(26)) termed Compound. A simple proposition is

that in which one predicate is affirmed or denied of one subject. A

compound proposition is that in which there is more than one predicate, or

more than one subject, or both.

At first sight this division has the air of an absurdity; a solemn

distinction of things into one and more than one; as if we were to divide

horses into single horses and teams of horses. And it is true that what is

called a complex (or compound) proposition is often not a proposition at

all, but several propositions, held together by a conjunction. Such, for

example, is this: Cæsar is dead, and Brutus is alive: or even this, Cæsar

is dead, _but_ Brutus is alive. There are here two distinct assertions;

and we might as well call a street a complex house, as these two

propositions a complex proposition. It is true that the syncategorematic

words _and_ and _but_ have a meaning; but that meaning is so far from

making the two propositions one, that it adds a third proposition to them.

All particles are abbreviations, and generally abbreviations of

propositions; a kind of short-hand, whereby something which, to be

expressed fully, would have required a proposition or a series of

propositions, is suggested to the mind at once. Thus the words, Cæsar is

dead and Brutus is alive, are equivalent to these: Cæsar is dead; Brutus

is alive; it is desired that the two preceding propositions should be

thought of together. If the words were, Cæsar is dead, _but_ Brutus is

alive, the sense would be equivalent to the same three propositions

together with a fourth; “between the two preceding propositions there

exists a contrast:” viz., either between the two facts themselves, or

between the feelings with which it is desired that they should be

regarded.

In the instances cited the two propositions are kept visibly distinct,

each subject having its separate predicate, and each predicate its

separate subject. For brevity, however, and to avoid repetition, the

propositions are often blended together: as in this, “Peter and James

preached at Jerusalem and in Galilee,” which contains four propositions:

Peter preached at Jerusalem, Peter preached in Galilee, James preached at

Jerusalem, James preached in Galilee.

We have seen that when the two or more propositions comprised in what is

called a complex proposition are stated absolutely, and not under any

condition or proviso, it is not a proposition at all, but a plurality of

propositions; since what it expresses is not a single assertion, but

several assertions, which, if true when joined, are true also when

separated. But there is a kind of proposition which, though it contains a

plurality of subjects and of predicates, and may be said in one sense of

the word to consist of several propositions, contains but one assertion;

and its truth does not at all imply that of the simple propositions which

compose it. An example of this is, when the simple propositions are

connected by the particle _or_; as, either A is B or C is D; or by the

particle _if_; as, A is B if C is D. In the former case, the proposition

is called _disjunctive_, in the latter, _conditional_: the name

_hypothetical_ was originally common to both.

As has been well remarked by Archbishop Whately and others, the

disjunctive form is resolvable into the conditional; every disjunctive

proposition being equivalent to two or more conditional ones. “Either A is

B or C is D,” means, “if A is not B, C is D; and if C is not D, A is B.”

All hypothetical propositions, therefore, though disjunctive in form, are

conditional in meaning; and the words hypothetical and conditional may be,

as indeed they generally are, used synonymously. Propositions in which the

assertion is not dependent on a condition, are said, in the language of

logicians, to be _categorical_.

A hypothetical proposition is not, like the pretended complex propositions

which we previously considered, a mere aggregation of simple propositions.

The simple propositions which form part of the words in which it is

couched, form no part of the assertion which it conveys. When we say, If

the Koran comes from God, Mohammed is the prophet of God, we do not intend

to affirm either that the Koran does come from God, or that Mohammed is

really his prophet. Neither of these simple propositions may be true, and

yet the truth of the hypothetical proposition may be indisputable. What is

asserted is not the truth of either of the propositions, but the

inferribility of the one from the other. What, then, is the subject, and

what the predicate of the hypothetical proposition? “The Koran” is not the

subject of it, nor is “Mohammed:” for nothing is affirmed or denied either

of the Koran or of Mohammed. The real subject of the predication is the

entire proposition, “Mohammed is the prophet of God;” and the affirmation

is, that this is a legitimate inference from the proposition, “The Koran

comes from God.” The subject and predicate, therefore, of a hypothetical

proposition are names of propositions. The subject is some one

proposition. The predicate is a general relative name applicable to

propositions; of this form—“an inference from so and so.” A fresh instance

is here afforded of the remark, that particles are abbreviations; since

“_If_ A is B, C is D,” is found to be an abbreviation of the following:

“The proposition C is D, is a legitimate inference from the proposition A

is B.”

The distinction, therefore, between hypothetical and categorical

propositions is not so great as it at first appears. In the conditional,

as well as in the categorical form, one predicate is affirmed of one

subject, and no more: but a conditional proposition is a proposition

concerning a proposition; the subject of the assertion is itself an

assertion. Nor is this a property peculiar to hypothetical propositions.

There are other classes of assertions concerning propositions. Like other

things, a proposition has attributes which may be predicated of it. The

attribute predicated of it in a hypothetical proposition, is that of being

an inference from a certain other proposition. But this is only one of

many attributes that might be predicated. We may say, That the whole is

greater than its part, is an axiom in mathematics: That the Holy Ghost

proceeds from the Father alone, is a tenet of the Greek Church: The

doctrine of the divine right of kings was renounced by Parliament at the

Revolution: The infallibility of the Pope has no countenance from

Scripture. In all these cases the subject of the predication is an entire

proposition. That which these different predicates are affirmed of, is

_the proposition_, “the whole is greater than its part;” _the

proposition_, “the Holy Ghost proceeds from the Father alone;” _the

proposition_, “kings have a divine right;” _the proposition_, “the Pope is

infallible.”

Seeing, then, that there is much less difference between hypothetical

propositions and any others, than one might be led to imagine from their

form, we should be at a loss to account for the conspicuous position which

they have been selected to fill in treatises on logic, if we did not

remember that what they predicate of a proposition, namely, its being an

inference from something else, is precisely that one of its attributes

with which most of all a logician is concerned.

§ 4. The next of the common divisions of Propositions is into Universal,

Particular, Indefinite, and Singular: a distinction founded on the degree

of generality in which the name, which is the subject of the proposition,

is to be understood. The following are examples:

_All men_ are mortal—Universal.

_Some men_ are mortal—Particular.

_Man_ is mortal—Indefinite.

_Julius Cæsar_ is mortal—Singular.

The proposition is Singular, when the subject is an individual name. The

individual name needs not be a proper name. “The Founder of Christianity

was crucified,” is as much a singular proposition as “Christ was

crucified.”

When the name which is the subject of the proposition is a general name,

we may intend to affirm or deny the predicate, either of all the things

that the subject denotes, or only of some. When the predicate is affirmed

or denied of all and each of the things denoted by the subject, the

proposition is universal; when of some undefined portion of them only, it

is particular. Thus, All men are mortal; Every man is mortal; are

universal propositions. No man is immortal, is also a universal

proposition, since the predicate, immortal, is denied of each and every

individual denoted by the term man; the negative proposition being exactly

equivalent to the following, Every man is not-immortal. But “some men are

wise,” “some men are not wise,” are particular propositions; the predicate

_wise_ being in the one case affirmed and in the other denied not of each

and every individual denoted by the term man, but only of each and every

one of some portion of those individuals, without specifying what portion;

for if this were specified, the proposition would be changed either into a

singular proposition, or into a universal proposition with a different

subject; as, for instance, “all _properly instructed_ men are wise.” There

are other forms of particular propositions; as, “_Most_ men are

imperfectly educated:” it being immaterial how large a portion of the

subject the predicate is asserted of, as long as it is left uncertain how

that portion is to be distinguished from the rest.(27)

When the form of the expression does not clearly show whether the general

name which is the subject of the proposition is meant to stand for all the

individuals denoted by it, or only for some of them, the proposition is,

by some logicians, called Indefinite; but this, as Archbishop Whately

observes, is a solecism, of the same nature as that committed by some

grammarians when in their list of genders they enumerate the _doubtful_

gender. The speaker must mean to assert the proposition either as a

universal or as a particular proposition, though he has failed to declare

which: and it often happens that though the words do not show which of the

two he intends, the context, or the custom of speech, supplies the

deficiency. Thus, when it is affirmed that “Man is mortal,” nobody doubts

that the assertion is intended of all human beings; and the word

indicative of universality is commonly omitted, only because the meaning

is evident without it. In the proposition, “Wine is good,” it is

understood with equal readiness, though for somewhat different reasons,

that the assertion is not intended to be universal, but particular.(28) As

is observed by Professor Bain,(29) the chief examples of Indefinite

propositions occur “with names of material, which are the subjects

sometimes of universal, and at other times of particular predication.

‘Food is chemically constituted by carbon, oxygen, etc.,’ is a proposition

of universal quantity; the meaning is all food—all kinds of food. ‘Food is

necessary to animal life’ is a case of particular quantity; the meaning is

some sort of food, not necessarily all sorts. ‘Metal is requisite in order

to strength’ does not mean all kinds of metal. ‘Gold will make a way,’

means a portion of gold.”

When a general name stands for each and every individual which it is a

name of, or in other words, which it denotes, it is said by logicians to

be _distributed_, or taken distributively. Thus, in the proposition, All

men are mortal, the subject, Man, is distributed, because mortality is

affirmed of each and every man. The predicate, Mortal, is not distributed,

because the only mortals who are spoken of in the proposition are those

who happen to be men; while the word may, for aught that appears, and in

fact does, comprehend within it an indefinite number of objects besides

men. In the proposition, Some men are mortal, both the predicate and the

subject are undistributed. In the following, No men have wings, both the

predicate and the subject are distributed. Not only is the attribute of

having wings denied of the entire class Man, but that class is severed and

cast out from the whole of the class Winged, and not merely from some part

of that class.

This phraseology, which is of great service in stating and demonstrating

the rules of the syllogism, enables us to express very concisely the

definitions of a universal and a particular proposition. A universal

proposition is that of which the subject is distributed; a particular

proposition is that of which the subject is undistributed.

There are many more distinctions among propositions than those we have

here stated, some of them of considerable importance. But, for explaining

and illustrating these, more suitable opportunities will occur in the

sequel.

Chapter V.

Of The Import Of Propositions.

§ 1. An inquiry into the nature of propositions must have one of two

objects: to analyze the state of mind called Belief, or to analyze what is

believed. All language recognizes a difference between a doctrine or

opinion, and the fact of entertaining the opinion; between assent, and

what is assented to.

Logic, according to the conception here formed of it, has no concern with

the nature of the act of judging or believing; the consideration of that

act, as a phenomenon of the mind, belongs to another science.

Philosophers, however, from Descartes downward, and especially from the

era of Leibnitz and Locke, have by no means observed this distinction; and

would have treated with great disrespect any attempt to analyze the import

of Propositions, unless founded on an analysis of the act of Judgment. A

proposition, they would have said, is but the expression in words of a

Judgment. The thing expressed, not the mere verbal expression, is the

important matter. When the mind assents to a proposition, it judges. Let

us find out what the mind does when it judges, and we shall know what

propositions mean, and not otherwise.

Conformably to these views, almost all the writers on Logic in the last

two centuries, whether English, German, or French, have made their theory

of Propositions, from one end to the other, a theory of Judgments. They

considered a Proposition, or a Judgment, for they used the two words

indiscriminately, to consist in affirming or denying one _idea_ of

another. To judge, was to put two ideas together, or to bring one idea

under another, or to compare two ideas, or to perceive the agreement or

disagreement between two ideas: and the whole doctrine of Propositions,

together with the theory of Reasoning (always necessarily founded on the

theory of Propositions), was stated as if Ideas, or Conceptions, or

whatever other term the writer preferred as a name for mental

representations generally, constituted essentially the subject-matter and

substance of those operations.

It is, of course, true, that in any case of judgment, as for instance when

we judge that gold is yellow, a process takes place in our minds, of which

some one or other of these theories is a partially correct account. We

must have the idea of gold and the idea of yellow, and these two ideas

must be brought together in our mind. But in the first place, it is

evident that this is only a part of what takes place; for we may put two

ideas together without any act of belief; as when we merely imagine

something, such as a golden mountain; or when we actually disbelieve: for

in order even to disbelieve that Mohammed was an apostle of God, we must

put the idea of Mohammed and that of an apostle of God together. To

determine what it is that happens in the case of assent or dissent besides

putting two ideas together, is one of the most intricate of metaphysical

problems. But whatever the solution may be, we may venture to assert that

it can have nothing whatever to do with the import of propositions; for

this reason, that propositions (except sometimes when the mind itself is

the subject treated of) are not assertions respecting our ideas of things,

but assertions respecting the things themselves. In order to believe that

gold is yellow, I must, indeed, have the idea of gold, and the idea of

yellow, and something having reference to those ideas must take place in

my mind; but my belief has not reference to the ideas, it has reference to

the things. What I believe, is a fact relating to the outward thing, gold,

and to the impression made by that outward thing upon the human organs;

not a fact relating to my conception of gold, which would be a fact in my

mental history, not a fact of external nature. It is true, that in order

to believe this fact in external nature, another fact must take place in

my mind, a process must be performed upon my ideas; but so it must in

every thing else that I do. I can not dig the ground unless I have the

idea of the ground, and of a spade, and of all the other things I am

operating upon, and unless I put those ideas together.(30) But it would be

a very ridiculous description of digging the ground to say that it is

putting one idea into another. Digging is an operation which is performed

upon the things themselves, though it can not be performed unless I have

in my mind the ideas of them. And in like manner, believing is an act

which has for its subject the facts themselves, though a previous mental

conception of the facts is an indispensable condition. When I say that

fire causes heat, do I mean that my idea of fire causes my idea of heat?

No: I mean that the natural phenomenon, fire, causes the natural

phenomenon, heat. When I mean to assert any thing respecting the ideas, I

give them their proper name, I call them ideas: as when I say, that a

child’s idea of a battle is unlike the reality, or that the ideas

entertained of the Deity have a great effect on the characters of mankind.

The notion that what is of primary importance to the logician in a

proposition, is the relation between the two _ideas_ corresponding to the

subject and predicate (instead of the relation between the two _phenomena_

which they respectively express), seems to me one of the most fatal errors

ever introduced into the philosophy of Logic; and the principal cause why

the theory of the science has made such inconsiderable progress during the

last two centuries. The treatises on Logic, and on the branches of Mental

Philosophy connected with Logic, which have been produced since the

intrusion of this cardinal error, though sometimes written by men of

extraordinary abilities and attainments, almost always tacitly imply a

theory that the investigation of truth consists in contemplating and

handling our ideas, or conceptions of things, instead of the things

themselves: a doctrine tantamount to the assertion, that the only mode of

acquiring knowledge of nature is to study it at second hand, as

represented in our own minds. Meanwhile, inquiries into every kind of

natural phenomena were incessantly establishing great and fruitful truths

on most important subjects, by processes upon which these views of the

nature of Judgment and Reasoning threw no light, and in which they

afforded no assistance whatever. No wonder that those who knew by

practical experience how truths are arrived at, should deem a science

futile, which consisted chiefly of such speculations. What has been done

for the advancement of Logic since these doctrines came into vogue, has

been done not by professed logicians, but by discoverers in the other

sciences; in whose methods of investigation many principles of logic, not

previously thought of, have successively come forth into light, but who

have generally committed the error of supposing that nothing whatever was

known of the art of philosophizing by the old logicians, because their

modern interpreters have written to so little purpose respecting it.

We have to inquire, then, on the present occasion, not into Judgment, but

judgments; not into the act of believing, but into the thing believed.

What is the immediate object of belief in a Proposition? What is the

matter of fact signified by it? What is it to which, when I assert the

proposition, I give my assent, and call upon others to give theirs? What

is that which is expressed by the form of discourse called a Proposition,

and the conformity of which to fact constitutes the truth of the

proposition?

§ 2. One of the clearest and most consecutive thinkers whom this country

or the world has produced, I mean Hobbes, has given the following answer

to this question. In every proposition (says he) what is signified is, the

belief of the speaker that the predicate is a name of the same thing of

which the subject is a name; and if it really is so, the proposition is

true. Thus the proposition, All men are living beings (he would say) is

true, because _living being_ is a name of every thing of which _man_ is a

name. All men are six feet high, is not true, because _six feet high_ is

not a name of every thing (though it is of some things) of which _man_ is

a name.

What is stated in this theory as the definition of a true proposition,

must be allowed to be a property which all true propositions possess. The

subject and predicate being both of them names of things, if they were

names of quite different things the one name could not, consistently with

its signification, be predicated of the other. If it be true that some men

are copper-colored, it must be true—and the proposition does really

assert—that among the individuals denoted by the name man, there are some

who are also among those denoted by the name copper-colored. If it be true

that all oxen ruminate, it must be true that all the individuals denoted

by the name ox are also among those denoted by the name ruminating; and

whoever asserts that all oxen ruminate, undoubtedly does assert that this

relation subsists between the two names.

The assertion, therefore, which, according to Hobbes, is the only one made

in any proposition, really is made in every proposition: and his analysis

has consequently one of the requisites for being the true one. We may go a

step further; it is the only analysis that is rigorously true of all

propositions without exception. What he gives as the meaning of

propositions, is part of the meaning of all propositions, and the whole

meaning of some. This, however, only shows what an extremely minute

fragment of meaning it is quite possible to include within the logical

formula of a proposition. It does not show that no proposition means more.

To warrant us in putting together two words with a copula between them, it

is really enough that the thing or things denoted by one of the names

should be capable, without violation of usage, of being called by the

other name also. If, then, this be all the meaning necessarily implied in

the form of discourse called a Proposition, why do I object to it as the

scientific definition of what a proposition means? Because, though the

mere collocation which makes the proposition a proposition, conveys no

more than this scanty amount of meaning, that same collocation combined

with other circumstances, that _form_ combined with other _matter_, does

convey more, and the proposition in those other circumstances does assert

more, than merely that relation between the two names.

The only propositions of which Hobbes’s principle is a sufficient account,

are that limited and unimportant class in which both the predicate and the

subject are proper names. For, as has already been remarked, proper names

have strictly no meaning; they are mere marks for individual objects: and

when a proper name is predicated of another proper name, all the

signification conveyed is, that both the names are marks for the same

object. But this is precisely what Hobbes produces as a theory of

predication in general. His doctrine is a full explanation of such

predications as these: Hyde was Clarendon, or, Tully is Cicero. It

exhausts the meaning of those propositions. But it is a sadly inadequate

theory of any others. That it should ever have been thought of as such,

can be accounted for only by the fact, that Hobbes, in common with the

other Nominalists, bestowed little or no attention upon the _connotation_

of words; and sought for their meaning exclusively in what they _denote_:

as if all names had been (what none but proper names really are) marks put

upon individuals; and as if there were no difference between a proper and

a general name, except that the first denotes only one individual, and the

last a greater number.

It has been seen, however, that the meaning of all names, except proper

names and that portion of the class of abstract names which are not

connotative, resides in the connotation. When, therefore, we are analyzing

the meaning of any proposition in which the predicate and the subject, or

either of them, are connotative names, it is to the connotation of those

terms that we must exclusively look, and not to what they _denote_, or in

the language of Hobbes (language so far correct) are names of.

In asserting that the truth of a proposition depends on the conformity of

import between its terms, as, for instance, that the proposition, Socrates

is wise, is a true proposition, because Socrates and wise are names

applicable to, or, as he expresses it, names of, the same person; it is

very remarkable that so powerful a thinker should not have asked himself

the question, But how came they to be names of the same person? Surely not

because such was the intention of those who invented the words. When

mankind fixed the meaning of the word wise, they were not thinking of

Socrates, nor, when his parents gave him the name of Socrates, were they

thinking of wisdom. The names _happen_ to fit the same person because of a

certain _fact_, which fact was not known, nor in being, when the names

were invented. If we want to know what the fact is, we shall find the clue

to it in the _connotation_ of the names.

A bird or a stone, a man, or a wise man, means simply, an object having

such and such attributes. The real meaning of the word man, is those

attributes, and not Smith, Brown, and the remainder of the individuals.

The word _mortal_, in like manner connotes a certain attribute or

attributes; and when we say, All men are mortal, the meaning of the

proposition is, that all beings which possess the one set of attributes,

possess also the other. If, in our experience, the attributes connoted by

_man_ are always accompanied by the attribute connoted by _mortal_, it

will follow as a consequence, that the class _man_ will be wholly included

in the class _mortal_, and that _mortal_ will be a name of all things of

which _man_ is a name: but why? Those objects are brought under the name,

by possessing the attributes connoted by it: but their possession of the

attributes is the real condition on which the truth of the proposition

depends; not their being called by the name. Connotative names do not

precede, but follow, the attributes which they connote. If one attribute

happens to be always found in conjunction with another attribute, the

concrete names which answer to those attributes will of course be

predicable of the same subjects, and may be said, in Hobbes’s language (in

the propriety of which on this occasion I fully concur), to be two names

for the same things. But the possibility of a concurrent application of

the two names, is a mere consequence of the conjunction between the two

attributes, and was, in most cases, never thought of when the names were

introduced and their signification fixed. That the diamond is combustible,

was a proposition certainly not dreamed of when the words Diamond and

Combustible first received their meaning; and could not have been

discovered by the most ingenious and refined analysis of the signification

of those words. It was found out by a very different process, namely, by

exerting the senses, and learning from them, that the attribute of

combustibility existed in the diamonds upon which the experiment was

tried; the number or character of the experiments being such, that what

was true of those individuals might be concluded to be true of all

substances “called by the name,” that is, of all substances possessing the

attributes which the name connotes. The assertion, therefore, when

analyzed, is, that wherever we find certain attributes, there will be

found a certain other attribute: which is not a question of the

signification of names, but of laws of nature; the order existing among

phenomena.

§ 3. Although Hobbes’s theory of Predication has not, in the terms in

which he stated it, met with a very favorable reception from subsequent

thinkers, a theory virtually identical with it, and not by any means so

perspicuously expressed, may almost be said to have taken the rank of an

established opinion. The most generally received notion of Predication

decidedly is that it consists in referring something to a class, _i.e._,

either placing an individual under a class, or placing one class under

another class. Thus, the proposition, Man is mortal, asserts, according to

this view of it, that the class man is included in the class mortal.

“Plato is a philosopher,” asserts that the individual Plato is one of

those who compose the class philosopher. If the proposition is negative,

then instead of placing something in a class, it is said to exclude

something from a class. Thus, if the following be the proposition, The

elephant is not carnivorous; what is asserted (according to this theory)

is, that the elephant is excluded from the class carnivorous, or is not

numbered among the things comprising that class. There is no real

difference, except in language, between this theory of Predication and the

theory of Hobbes. For a class _is_ absolutely nothing but an indefinite

number of individuals denoted by a general name. The name given to them in

common, is what makes them a class. To refer any thing to a class,

therefore, is to look upon it as one of the things which are to be called

by that common name. To exclude it from a class, is to say that the common

name is not applicable to it.

How widely these views of predication have prevailed, is evident from

this, that they are the basis of the celebrated _dictum de omni et nullo_.

When the syllogism is resolved, by all who treat of it, into an inference

that what is true of a class is true of all things whatever that belong to

the class; and when this is laid down by almost all professed logicians as

the ultimate principle to which all reasoning owes its validity; it is

clear that in the general estimation of logicians, the propositions of

which reasonings are composed can be the expression of nothing but the

process of dividing things into classes, and referring every thing to its

proper class.

This theory appears to me a signal example of a logical error very often

committed in logic, that of ὕστερον προτέρον, or explaining a thing by

something which presupposes it. When I say that snow is white, I may and

ought to be thinking of snow as a class, because I am asserting a

proposition as true of all snow: but I am certainly not thinking of white

objects as a class; I am thinking of no white object whatever except snow,

but only of that, and of the sensation of white which it gives me. When,

indeed, I have judged, or assented to the propositions, that snow is

white, and that several other things are also white, I gradually begin to

think of white objects as a class, including snow and those other things.

But this is a conception which followed, not preceded, those judgments,

and therefore can not be given as an explanation of them. Instead of

explaining the effect by the cause, this doctrine explains the cause by

the effect, and is, I conceive, founded on a latent misconception of the

nature of classification.

There is a sort of language very generally prevalent in these discussions,

which seems to suppose that classification is an arrangement and grouping

of definite and known individuals: that when names were imposed, mankind

took into consideration all the individual objects in the universe,

distributed them into parcels or lists, and gave to the objects of each

list a common name, repeating this operation _toties quoties_ until they

had invented all the general names of which language consists; which

having been once done, if a question subsequently arises whether a certain

general name can be truly predicated of a certain particular object, we

have only (as it were) to read the roll of the objects upon which that

name was conferred, and see whether the object about which the question

arises is to be found among them. The framers of language (it would seem

to be supposed) have predetermined all the objects that are to compose

each class, and we have only to refer to the record of an antecedent

decision.

So absurd a doctrine will be owned by nobody when thus nakedly stated; but

if the commonly received explanations of classification and naming do not

imply this theory, it requires to be shown how they admit of being

reconciled with any other.

General names are not marks put upon definite objects; classes are not

made by drawing a line round a given number of assignable individuals. The

objects which compose any given class are perpetually fluctuating. We may

frame a class without knowing the individuals, or even any of the

individuals, of which it may be composed; we may do so while believing

that no such individuals exist. If by the _meaning_ of a general name are

to be understood the things which it is the name of, no general name,

except by accident, has a fixed meaning at all, or ever long retains the

same meaning. The only mode in which any general name has a definite

meaning, is by being a name of an indefinite variety of things; namely, of

all things, known or unknown, past, present, or future, which possess

certain definite attributes. When, by studying not the meaning of words,

but the phenomena of nature, we discover that these attributes are

possessed by some object not previously known to possess them (as when

chemists found that the diamond was combustible), we include this new

object in the class; but it did not already belong to the class. We place

the individual in the class because the proposition is true; the

proposition is not true because the object is placed in the class.(31)

It will appear hereafter, in treating of reasoning, how much the theory of

that intellectual process has been vitiated by the influence of these

erroneous notions, and by the habit which they exemplify of assimilating

all the operations of the human understanding which have truth for their

object, to processes of mere classification and naming. Unfortunately, the

minds which have been entangled in this net are precisely those which have

escaped the other cardinal error commented upon in the beginning of the

present chapter. Since the revolution which dislodged Aristotle from the

schools, logicians may almost be divided into those who have looked upon

reasoning as essentially an affair of Ideas, and those who have looked

upon it as essentially an affair of Names.

Although, however, Hobbes’s theory of Predication, according to the

well-known remark of Leibnitz, and the avowal of Hobbes himself,(32)

renders truth and falsity completely arbitrary, with no standard but the

will of men, it must not be concluded that either Hobbes, or any of the

other thinkers who have in the main agreed with him, did in fact consider

the distinction between truth and error as less real, or attached less

importance to it, than other people. To suppose that they did so would

argue total unacquaintance with their other speculations. But this shows

how little hold their doctrine possessed over their own minds. No person,

at bottom, ever imagined that there was nothing more in truth than

propriety of expression; than using language in conformity to a previous

convention. When the inquiry was brought down from generals to a

particular case, it has always been acknowledged that there is a

distinction between verbal and real questions; that some false

propositions are uttered from ignorance of the meaning of words, but that

in others the source of the error is a misapprehension of things; that a

person who has not the use of language at all may form propositions

mentally, and that they may be untrue—that is, he may believe as matters

of fact what are not really so. This last admission can not be made in

stronger terms than it is by Hobbes himself,(33) though he will not allow

such erroneous belief to be called falsity, but only error. And he has

himself laid down, in other places, doctrines in which the true theory of

predication is by implication contained. He distinctly says that general

names are given to things on account of their attributes, and that

abstract names are the names of those attributes. “Abstract is that which

in any subject denotes the cause of the concrete name.... And these causes

of names are the same with the causes of our conceptions, namely, some

power of action, or affection, of the thing conceived, which some call the

manner by which any thing works upon our senses, but by most men they are

called _accidents_.”(34) It is strange that having gone so far, he should

not have gone one step further, and seen that what he calls the cause of

the concrete name, is in reality the meaning of it; and that when we

predicate of any subject a name which is given _because_ of an attribute

(or, as he calls it, an accident), our object is not to affirm the name,

but, by means of the name, to affirm the attribute.

§ 4. Let the predicate be, as we have said, a connotative term; and to

take the simplest case first, let the subject be a proper name: “The

summit of Chimborazo is white.” The word white connotes an attribute which

is possessed by the individual object designated by the words “summit of

Chimborazo;” which attribute consists in the physical fact, of its

exciting in human beings the sensation which we call a sensation of white.

It will be admitted that, by asserting the proposition, we wish to

communicate information of that physical fact, and are not thinking of the

names, except as the necessary means of making that communication. The

meaning of the proposition, therefore, is, that the individual thing

denoted by the subject, has the attributes connoted by the predicate.

If we now suppose the subject also to be a connotative name, the meaning

expressed by the proposition has advanced a step further in complication.

Let us first suppose the proposition to be universal, as well as

affirmative: “All men are mortal.” In this case, as in the last, what the

proposition asserts (or expresses a belief of) is, of course, that the

objects denoted by the subject (man) possess the attributes connoted by

the predicate (mortal). But the characteristic of this case is, that the

objects are no longer _individually_ designated. They are pointed out only

by some of their attributes: they are the objects called men, that is,

possessing the attributes connoted by the name man; and the only thing

known of them may be those attributes: indeed, as the proposition is

general, and the objects denoted by the subject are therefore indefinite

in number, most of them are not known individually at all. The assertion,

therefore, is not, as before, that the attributes which the predicate

connotes are possessed by any given individual, or by any number of

individuals previously known as John, Thomas, etc., but that those

attributes are possessed by each and every individual possessing certain

other attributes; that whatever has the attributes connoted by the

subject, has also those connoted by the predicate; that the latter set of

attributes _constantly accompany_ the former set. Whatever has the

attributes of man has the attribute of mortality; mortality constantly

accompanies the attributes of man.(35)

If it be remembered that every attribute is _grounded_ on some fact or

phenomenon, either of outward sense or of inward consciousness, and that

to _possess_ an attribute is another phrase for being the cause of, or

forming part of, the fact or phenomenon upon which the attribute is

grounded; we may add one more step to complete the analysis. The

proposition which asserts that one attribute always accompanies another

attribute, really asserts thereby no other thing than this, that one

phenomenon always accompanies another phenomenon; insomuch that where we

find the latter, we have assurance of the existence of the former. Thus,

in the proposition, All men are mortal, the word man connotes the

attributes which we ascribe to a certain kind of living creatures, on the

ground of certain phenomena which they exhibit, and which are partly

physical phenomena, namely the impressions made on our senses by their

bodily form and structure, and partly mental phenomena, namely the

sentient and intellectual life which they have of their own. All this is

understood when we utter the word man, by any one to whom the meaning of

the word is known. Now, when we say, Man is mortal, we mean that wherever

these various physical and mental phenomena are all found, there we have

assurance that the other physical and mental phenomenon, called death,

will not fail to take place. The proposition does not affirm _when_; for

the connotation of the word _mortal_ goes no further than to the

occurrence of the phenomenon at some time or other, leaving the particular

time undecided.

§ 5. We have already proceeded far enough, not only to demonstrate the

error of Hobbes, but to ascertain the real import of by far the most

numerous class of propositions. The object of belief in a proposition,

when it asserts any thing more than the meaning of words, is generally, as

in the cases which we have examined, either the co-existence or the

sequence of two phenomena. At the very commencement of our inquiry, we

found that every act of belief implied two Things: we have now ascertained

what, in the most frequent case, these two things are, namely, two

Phenomena; in other words, two states of consciousness; and what it is

which the proposition affirms (or denies) to subsist between them, namely,

either succession or co-existence. And this case includes innumerable

instances which no one, previous to reflection, would think of referring

to it. Take the following example: A generous person is worthy of honor.

Who would expect to recognize here a case of co-existence between

phenomena? But so it is. The attribute which causes a person to be termed

generous, is ascribed to him on the ground of states of his mind, and

particulars of his conduct: both are phenomena: the former are facts of

internal consciousness; the latter, so far as distinct from the former,

are physical facts, or perceptions of the senses. Worthy of honor admits

of a similar analysis. Honor, as here used, means a state of approving and

admiring emotion, followed on occasion by corresponding outward acts.

“Worthy of honor” connotes all this, together with our approval of the act

of showing honor. All these are phenomena; states of internal

consciousness, accompanied or followed by physical facts. When we say, A

generous person is worthy of honor, we affirm co-existence between the two

complicated phenomena connoted by the two terms respectively. We affirm,

that wherever and whenever the inward feelings and outward facts implied

in the word generosity have place, then and there the existence and

manifestation of an inward feeling, honor, would be followed in our minds

by another inward feeling, approval.

After the analysis, in a former chapter, of the import of names, many

examples are not needed to illustrate the import of propositions. When

there is any obscurity, or difficulty, it does not lie in the meaning of

the proposition, but in the meaning of the names which compose it; in the

extremely complicated connotation of many words; the immense multitude and

prolonged series of facts which often constitute the phenomenon connoted

by a name. But where it is seen what the phenomenon is, there is seldom

any difficulty in seeing that the assertion conveyed by the proposition

is, the co-existence of one such phenomenon with another; or the

succession of one such phenomenon to another: so that where the one is

found, we may calculate on finding the other, though perhaps not

conversely.

This, however, though the most common, is not the only meaning which

propositions are ever intended to convey. In the first place, sequences

and co-existences are not only asserted respecting Phenomena; we make

propositions also respecting those hidden causes of phenomena, which are

named substances and attributes. A substance, however, being to us nothing

but either that which causes, or that which is conscious of, phenomena;

and the same being true, _mutatis mutandis_, of attributes; no assertion

can be made, at least with a meaning, concerning these unknown and

unknowable entities, except in virtue of the Phenomena by which alone they

manifest themselves to our faculties. When we say Socrates was

contemporary with the Peloponnesian war, the foundation of this assertion,

as of all assertions concerning substances, is an assertion concerning the

phenomena which they exhibit—namely, that the series of facts by which

Socrates manifested himself to mankind, and the series of mental states

which constituted his sentient existence, went on simultaneously with the

series of facts known by the name of the Peloponnesian war. Still, the

proposition as commonly understood does not assert that alone; it asserts

that the Thing in itself, the _noumenon_ Socrates, was existing, and doing

or experiencing those various facts during the same time. Co-existence and

sequence, therefore, may be affirmed or denied not only between phenomena,

but between noumena, or between a noumenon and phenomena. And both of

noumena and of phenomena we may affirm simple existence. But what is a

noumenon? An unknown cause. In affirming, therefore, the existence of a

noumenon, we affirm causation. Here, therefore, are two additional kinds

of fact, capable of being asserted in a proposition. Besides the

propositions which assert Sequence or Co-existence, there are some which

assert simple Existence;(36) and others assert Causation, which, subject

to the explanations which will follow in the Third Book, must be

considered provisionally as a distinct and peculiar kind of assertion.

§ 6. To these four kinds of matter-of-fact or assertion, must be added a

fifth, Resemblance. This was a species of attribute which we found it

impossible to analyze; for which no _fundamentum_, distinct from the

objects themselves, could be assigned. Besides propositions which assert a

sequence or co-existence between two phenomena, there are therefore also

propositions which assert resemblance between them; as, This color is like

that color; The heat of to-day is _equal_ to the heat of yesterday. It is

true that such an assertion might with some plausibility be brought within

the description of an affirmation of sequence, by considering it as an

assertion that the simultaneous contemplation of the two colors is

_followed_ by a specific feeling termed the feeling of resemblance. But

there would be nothing gained by incumbering ourselves, especially in this

place, with a generalization which may be looked upon as strained. Logic

does not undertake to analyze mental facts into their ultimate elements.

Resemblance between two phenomena is more intelligible in itself than any

explanation could make it, and under any classification must remain

specifically distinct from the ordinary cases of sequence and

co-existence.

It is sometimes said, that all propositions whatever, of which the

predicate is a general name, do, in point of fact, affirm or deny

resemblance. All such propositions affirm that a thing belongs to a class;

but things being classed together according to their resemblance, every

thing is of course classed with the things which it is supposed to

resemble most; and thence, it may be said, when we affirm that Gold is a

metal, or that Socrates is a man, the affirmation intended is, that gold

resembles other metals, and Socrates other men, more nearly than they

resemble the objects contained in any other of the classes co-ordinate

with these.

There is some slight degree of foundation for this remark, but no more

than a slight degree. The arrangement of things into classes, such as the

class _metal_, or the class _man_, is grounded indeed on a resemblance

among the things which are placed in the same class, but not on a mere

general resemblance: the resemblance it is grounded on consists in the

possession by all those things, of certain common peculiarities; and those

peculiarities it is which the terms connote, and which the propositions

consequently assert; not the resemblance. For though when I say, Gold is a

metal, I say by implication that if there be any other metals it must

resemble them, yet if there were no other metals I might still assert the

proposition with the same meaning as at present, namely, that gold has the

various properties implied in the word metal; just as it might be said,

Christians are men, even if there were no men who were not Christians.

Propositions, therefore, in which objects are referred to a class because

they possess the attributes constituting the class, are so far from

asserting nothing but resemblance, that they do not, properly speaking,

assert resemblance at all.

But we remarked some time ago (and the reasons of the remark will be more

fully entered into in a subsequent Book(37)) that there is sometimes a

convenience in extending the boundaries of a class so as to include things

which possess in a very inferior degree, if in any, some of the

characteristic properties of the class—provided they resemble that class

more than any other, insomuch that the general propositions which are true

of the class, will be nearer to being true of those things than any other

equally general propositions. For instance, there are substances called

metals which have very few of the properties by which metals are commonly

recognized; and almost every great family of plants or animals has a few

anomalous genera or species on its borders, which are admitted into it by

a sort of courtesy, and concerning which it has been matter of discussion

to what family they properly belonged. Now when the class-name is

predicated of any object of this description, we do, by so predicating it,

affirm resemblance and nothing more. And in order to be scrupulously

correct it ought to be said, that in every case in which we predicate a

general name, we affirm, not absolutely that the object possesses the

properties designated by the name, but that it _either_ possesses those

properties, or if it does not, at any rate resembles the things which do

so, more than it resembles any other things. In most cases, however, it is

unnecessary to suppose any such alternative, the latter of the two grounds

being very seldom that on which the assertion is made: and when it is,

there is generally some slight difference in the form of the expression,

as, This species (or genus) is _considered_, or _may be ranked_, as

belonging to such and such a family: we should hardly say positively that

it does belong to it, unless it possessed unequivocally the properties of

which the class-name is scientifically significant.

There is still another exceptional case, in which, though the predicate is

the name of a class, yet in predicating it we affirm nothing but

resemblance, the class being founded not on resemblance in any given

particular, but on general unanalyzable resemblance. The classes in

question are those into which our simple sensations, or other simple

feelings, are divided. Sensations of white, for instance, are classed

together, not because we can take them to pieces, and say they are alike

in this, and not alike in that, but because we feel them to be alike

altogether, though in different degrees. When, therefore, I say, The color

I saw yesterday was a white color, or, The sensation I feel is one of

tightness, in both cases the attribute I affirm of the color or of the

other sensation is mere resemblance—simple _likeness_ to sensations which

I have had before, and which have had those names bestowed upon them. The

names of feelings, like other concrete general names, are connotative; but

they connote a mere resemblance. When predicated of any individual

feeling, the information they convey is that of its likeness to the other

feelings which we have been accustomed to call by the same name. Thus much

may suffice in illustration of the kind of propositions in which the

matter-of-fact asserted (or denied) is simple Resemblance.

Existence, Co-existence, Sequence, Causation, Resemblance: one or other of

these is asserted (or denied) in every proposition which is not merely

verbal. This five-fold division is an exhaustive classification of

matters-of-fact; of all things that can be believed, or tendered for

belief; of all questions that can be propounded, and all answers that can

be returned to them.

Professor Bain(38) distinguishes two kinds of Propositions of

Co-existence. “In the one kind, account is taken of Place; they may be

described as propositions of Order in Place.” In the other kind, the

co-existence which is predicated is termed by Mr. Bain Co-inherence of

Attributes. “This is a distinct variety of Propositions of Co-existence.

Instead of an arrangement in place with numerical intervals, we have the

concurrence of two or more attributes or powers in the same part or

locality. A mass of gold contains, in every atom, the concurring

attributes that mark the substance—weight, hardness, color, lustre,

incorrosibility, etc. An animal, besides having parts situated in place,

has co-inhering functions in the same parts, exerted by the very same

masses and molecules of its substance.... The Mind, which affords no

Propositions of Order in Place, has co-inhering functions. We affirm mind

to contain Feeling, Will, and Thought, not in local separation, but in

commingling exercise. The concurring properties of minerals, of plants,

and of the bodily and the mental structure of animals, are united in

affirmations of co-inherence.”

The distinction is real and important. But, as has been seen, an

Attribute, when it is any thing but a simple unanalyzable Resemblance

between the subject and some other things, consists in causing impressions

of some sort on consciousness. Consequently, the co-inherence of two

attributes is but the co-existence of the two states of consciousness

implied in their meaning: with the difference, however, that this

co-existence is sometimes potential only, the attribute being considered

as in existence, though the fact on which it is grounded may not be

actually, but only potentially present. Snow, for instance, is, with great

convenience, said to be white even in a state of total darkness, because,

though we are not now conscious of the color, we shall be conscious of it

as soon as morning breaks. Co-inherence of attributes is therefore still a

case, though a complex one, of co-existence of states of consciousness; a

totally different thing, however, from Order in Place. Being a part of

simultaneity, it belongs not to Place but to Time.

We may therefore (and we shall sometimes find it a convenience) instead of

Co-existence and Sequence, say, for greater particularity, Order in Place

and Order in Time: Order in Place being a specific mode of co-existence,

not necessary to be more particularly analyzed here; while the mere fact

of co-existence, whether between actual sensations, or between the

potentialities of causing them, known by the name of attributes, may be

classed, together with Sequence, under the head of Order in Time.

§ 7. In the foregoing inquiry into the import of propositions, we have

thought it necessary to analyze directly those alone, in which the terms

of the proposition (or the predicate at least) are concrete terms. But, in

doing so, we have indirectly analyzed those in which the terms are

abstract. The distinction between an abstract term and its corresponding

concrete, does not turn upon any difference in what they are appointed to

signify; for the real signification of a concrete general name is, as we

have so often said, its connotation; and what the concrete term connotes,

forms the entire meaning of the abstract name. Since there is nothing in

the import of an abstract name which is not in the import of the

corresponding concrete, it is natural to suppose that neither can there be

any thing in the import of a proposition of which the terms are abstract,

but what there is in some proposition which can be framed of concrete

terms.

And this presumption a closer examination will confirm. An abstract name

is the name of an attribute, or combination of attributes. The

corresponding concrete is a name given to things, because of, and in order

to express, their possessing that attribute, or that combination of

attributes. When, therefore, we predicate of any thing a concrete name,

the attribute is what we in reality predicate of it. But it has now been

shown that in all propositions of which the predicate is a concrete name,

what is really predicated is one of five things: Existence, Co-existence,

Causation, Sequence, or Resemblance. An attribute, therefore, is

necessarily either an existence, a co-existence, a causation, a sequence,

or a resemblance. When a proposition consists of a subject and predicate

which are abstract terms, it consists of terms which must necessarily

signify one or other of these things. When we predicate of any thing an

abstract name, we affirm of the thing that it is one or other of these

five things; that it is a case of Existence, or of Co-existence, or of

Causation, or of Sequence, or of Resemblance.

It is impossible to imagine any proposition expressed in abstract terms,

which can not be transformed into a precisely equivalent proposition in

which the terms are concrete; namely, either the concrete names which

connote the attributes themselves, or the names of the _fundamenta_ of

those attributes; the facts or phenomena on which they are grounded. To

illustrate the latter case, let us take this proposition, of which the

subject only is an abstract name, “Thoughtlessness is dangerous.”

Thoughtlessness is an attribute, grounded on the facts which we call

thoughtless actions; and the proposition is equivalent to this,

Thoughtless actions are dangerous. In the next example the predicate as

well as the subject are abstract names: “Whiteness is a color;” or “The

color of snow is a whiteness.” These attributes being grounded on

sensations, the equivalent propositions in the concrete would be, The

sensation of white is one of the sensations called those of color—The

sensation of sight, caused by looking at snow, is one of the sensations

called sensations of white. In these propositions, as we have before seen,

the matter-of-fact asserted is a Resemblance. In the following examples,

the concrete terms are those which directly correspond to the abstract

names; connoting the attribute which these denote. “Prudence is a virtue:”

this may be rendered, “All prudent persons, _in so far as_ prudent, are

virtuous:” “Courage is deserving of honor;” thus, “All courageous persons

are deserving of honor _in so far_ as they are courageous:” which is

equivalent to this—“All courageous persons deserve an addition to the

honor, or a diminution of the disgrace, which would attach to them on

other grounds.”

In order to throw still further light upon the import of propositions of

which the terms are abstract, we will subject one of the examples given

above to a minuter analysis. The proposition we shall select is the

following: “Prudence is a virtue.” Let us substitute for the word virtue

an equivalent but more definite expression, such as “a mental quality

beneficial to society,” or “a mental quality pleasing to God,” or whatever

else we adopt as the definition of virtue. What the proposition asserts is

a sequence, accompanied with causation; namely, that benefit to society,

or that the approval of God, is consequent on, and caused by, prudence.

Here is a sequence; but between what? We understand the consequent of the

sequence, but we have yet to analyze the antecedent. Prudence is an

attribute; and, in connection with it, two things besides itself are to be

considered; prudent persons, who are the _subjects_ of the attribute, and

prudential conduct, which may be called the _foundation_ of it. Now is

either of these the antecedent? and, first, is it meant, that the approval

of God, or benefit to society, is attendant upon all prudent _persons_?

No; except _in so far_ as they are prudent; for prudent persons who are

scoundrels can seldom, on the whole, be beneficial to society, nor can

they be acceptable to a good being. Is it upon prudential _conduct_, then,

that divine approbation and benefit to mankind are supposed to be

invariably consequent? Neither is this the assertion meant, when it is

said that prudence is a virtue; except with the same reservation as

before, and for the same reason, namely, that prudential conduct, although

in _so far as_ it is prudential it is beneficial to society, may yet, by

reason of some other of its qualities, be productive of an injury

outweighing the benefit, and deserve a displeasure exceeding the

approbation which would be due to the prudence. Neither the substance,

therefore (viz., the person), nor the phenomenon (the conduct), is an

antecedent on which the other term of the sequence is universally

consequent. But the proposition, “Prudence is a virtue,” is a universal

proposition. What is it, then, upon which the proposition affirms the

effects in question to be universally consequent? Upon that in the person,

and in the conduct, which causes them to be called prudent, and which is

equally in them when the action, though prudent, is wicked; namely, a

correct foresight of consequences, a just estimation of their importance

to the object in view, and repression of any unreflecting impulse at

variance with the deliberate purpose. These, which are states of the

person’s mind, are the real antecedent in the sequence, the real cause in

the causation, asserted by the proposition. But these are also the real

ground, or foundation, of the attribute Prudence; since wherever these

states of mind exist we may predicate prudence, even before we know

whether any conduct has followed. And in this manner every assertion

respecting an attribute, may be transformed into an assertion exactly

equivalent respecting the fact or phenomenon which is the ground of the

attribute. And no case can be assigned, where that which is predicated of

the fact or phenomenon, does not belong to one or other of the five

species formerly enumerated: it is either simple Existence, or it is some

Sequence, Co-existence, Causation, or Resemblance.

And as these five are the only things which can be affirmed, so are they

the only things which can be denied. “No horses are web-footed” denies

that the attributes of a horse ever co-exist with web-feet. It is scarcely

necessary to apply the same analysis to Particular affirmations and

negations. “Some birds are web-footed,” affirms that, with the attributes

connoted by _bird_, the phenomenon web-feet is sometimes co-existent:

“Some birds are not web-footed,” asserts that there are other instances in

which this co-existence does not have place. Any further explanation of a

thing which, if the previous exposition has been assented to, is so

obvious, may here be spared.

Chapter VI.

Of Propositions Merely Verbal.

§ 1. As a preparation for the inquiry which is the proper object of Logic,

namely, in what manner propositions are to be proved, we have found it

necessary to inquire what they contain which requires, or is susceptible

of, proof; or (which is the same thing) what they assert. In the course of

this preliminary investigation into the import of Propositions, we

examined the opinion of the Conceptualists, that a proposition is the

expression of a relation between two ideas; and the doctrine of the

extreme Nominalists, that it is the expression of an agreement or

disagreement between the meanings of two names. We decided that, as

general theories, both of these are erroneous; and that, though

propositions may be made both respecting names and respecting ideas,

neither the one nor the other are the subject-matter of Propositions

considered generally. We then examined the different kinds of

Propositions, and found that, with the exception of those which are merely

verbal, they assert five different kinds of matters of fact, namely,

Existence, Order in Place, Order in Time, Causation, and Resemblance; that

in every proposition one of these five is either affirmed, or denied, of

some fact or phenomenon, or of some object the unknown source of a fact or

phenomenon.

In distinguishing, however, the different kinds of matters of fact

asserted in propositions, we reserved one class of propositions, which do

not relate to any matter of fact, in the proper sense of the term at all,

but to the meaning of names. Since names and their signification are

entirely arbitrary, such propositions are not, strictly speaking,

susceptible of truth or falsity, but only of conformity or disconformity

to usage or convention; and all the proof they are capable of, is proof of

usage; proof that the words have been employed by others in the

acceptation in which the speaker or writer desires to use them. These

propositions occupy, however, a conspicuous place in philosophy; and their

nature and characteristics are of as much importance in logic, as those of

any of the other classes of propositions previously adverted to.

If all propositions respecting the signification of words were as simple

and unimportant as those which served us for examples when examining

Hobbes’s theory of predication, viz., those of which the subject and

predicate are proper names, and which assert only that those names have,

or that they have not, been conventionally assigned to the same

individual, there would be little to attract to such propositions the

attention of philosophers. But the class of merely verbal propositions

embraces not only much more than these, but much more than any

propositions which at first sight present themselves as verbal;

comprehending a kind of assertions which have been regarded not only as

relating to things, but as having actually a more intimate relation with

them than any other propositions whatever. The student in philosophy will

perceive that I allude to the distinction on which so much stress was laid

by the schoolmen, and which has been retained either under the same or

under other names by most metaphysicians to the present day, viz., between

what were called _essential_, and what were called _accidental_,

propositions, and between essential and accidental properties or

attributes.

§ 2. Almost all metaphysicians prior to Locke, as well as many since his

time, have made a great mystery of Essential Predication, and of

predicates which are said to be of the _essence_ of the subject. The

essence of a thing, they said, was that without which the thing could

neither be, nor be conceived to be. Thus, rationality was of the essence

of man, because without rationality, man could not be conceived to exist.

The different attributes which made up the essence of the thing were

called its essential properties; and a proposition in which any of these

were predicated of it was called an Essential Proposition, and was

considered to go deeper into the nature of the thing, and to convey more

important information respecting it, than any other proposition could do.

All properties, not of the essence of the thing, were called its

accidents; were supposed to have nothing at all, or nothing comparatively,

to do with its inmost nature; and the propositions in which any of these

were predicated of it were called Accidental Propositions. A connection

may be traced between this distinction, which originated with the

schoolmen, and the well-known dogmas of _substantiæ secundæ_ or general

substances, and _substantial forms_, doctrines which under varieties of

language pervaded alike the Aristotelian and the Platonic schools, and of

which more of the spirit has come down to modern times than might be

conjectured from the disuse of the phraseology. The false views of the

nature of classification and generalization which prevailed among the

schoolmen, and of which these dogmas were the technical expression, afford

the only explanation which can be given of their having misunderstood the

real nature of those Essences which held so conspicuous a place in their

philosophy. They said, truly, that _man_ can not be conceived without

rationality. But though _man_ can not, a being may be conceived exactly

like a man in all points except that one quality, and those others which

are the conditions or consequences of it. All, therefore, which is really

true in the assertion that man can not be conceived without rationality,

is only, that if he had not rationality, he would not be reputed a man.

There is no impossibility in conceiving the _thing_, nor, for aught we

know, in its existing: the impossibility is in the conventions of

language, which will not allow the thing, even if it exist, to be called

by the name which is reserved for rational beings. Rationality, in short,

is involved in the meaning of the word man: is one of the attributes

connoted by the name. The essence of man, simply means the whole of the

attributes connoted by the word; and any one of those attributes taken

singly, is an essential property of man.

But these reflections, so easy to us, would have been difficult to persons

who thought, as most of the later Aristotelians did, that objects were

made what they were called, that gold (for instance) was made gold, not by

the possession of certain properties to which mankind have chosen to

attach that name, but by participation in the nature of a general

substance, called gold in general, which substance, together with all the

properties that belonged to it, _inhered_ in every individual piece of

gold.(39) As they did not consider these universal substances to be

attached to all general names, but only to some, they thought that an

object borrowed only a part of its properties from a universal substance,

and that the rest belonged to it individually: the former they called its

essence, and the latter its accidents. The scholastic doctrine of essences

long survived the theory on which it rested, that of the existence of real

entities corresponding to general terms; and it was reserved for Locke, at

the end of the seventeenth century, to convince philosophers that the

supposed essences of classes were merely the signification of their names;

nor, among the signal services which his writings rendered to philosophy,

was there one more needful or more valuable.

Now, as the most familiar of the general names by which an object is

designated usually connotes not one only, but several attributes of the

object, each of which attributes separately forms also the bond of union

of some class, and the meaning of some general name; we may predicate of a

name which connotes a variety of attributes, another name which connotes

only one of these attributes, or some smaller number of them than all. In

such cases, the universal affirmative proposition will be true; since

whatever possesses the whole of any set of attributes, must possess any

part of that same set. A proposition of this sort, however, conveys no

information to any one who previously understood the whole meaning of the

terms. The propositions, Every man is a corporeal being, Every man is a

living creature, Every man is rational, convey no knowledge to any one who

was already aware of the entire meaning of the word _man_, for the meaning

of the word includes all this: and that every _man_ has the attributes

connoted by all these predicates, is already asserted when he is called a

man. Now, of this nature are all the propositions which have been called

essential. They are, in fact, identical propositions.

It is true that a proposition which predicates any attribute, even though

it be one implied in the name, is in most cases understood to involve a

tacit assertion that there _exists_ a thing corresponding to the name, and

possessing the attributes connoted by it; and this implied assertion may

convey information, even to those who understood the meaning of the name.

But all information of this sort, conveyed by all the essential

propositions of which man can be made the subject, is included in the

assertion, Men exist. And this assumption of real existence is, after all,

the result of an imperfection of language. It arises from the ambiguity of

the copula, which, in addition to its proper office of a mark to show that

an assertion is made, is also, as formerly remarked, a concrete word

connoting existence. The actual existence of the subject of the

proposition is therefore only apparently, not really, implied in the

predication, if an essential one: we may say, A ghost is a disembodied

spirit, without believing in ghosts. But an accidental, or non-essential,

affirmation, does imply the real existence of the subject, because in the

case of a non-existent subject there is nothing for the proposition to

assert. Such a proposition as, The ghost of a murdered person haunts the

couch of the murderer, can only have a meaning if understood as implying a

belief in ghosts; for since the signification of the word ghost implies

nothing of the kind, the speaker either means nothing, or means to assert

a thing which he wishes to be believed to have really taken place.

It will be hereafter seen that when any important consequences seem to

follow, as in mathematics, from an essential proposition, or, in other

words, from a proposition involved in the meaning of a name, what they

really flow from is the tacit assumption of the real existence of the

objects so named. Apart from this assumption of real existence, the class

of propositions in which the predicate is of the essence of the subject

(that is, in which the predicate connotes the whole or part of what the

subject connotes, but nothing besides) answer no purpose but that of

unfolding the whole or some part of the meaning of the name, to those who

did not previously know it. Accordingly, the most useful, and in

strictness the only useful kind of essential propositions, are

Definitions: which, to be complete, should unfold the whole of what is

involved in the meaning of the word defined; that is (when it is a

connotative word), the whole of what it connotes. In defining a name,

however, it is not usual to specify its entire connotation, but so much

only as is sufficient to mark out the objects usually denoted by it from

all other known objects. And sometimes a merely accidental property, not

involved in the meaning of the name, answers this purpose equally well.

The various kinds of definition which these distinctions give rise to, and

the purposes to which they are respectively subservient, will be minutely

considered in the proper place.

§ 3. According to the above view of essential propositions, no proposition

can be reckoned such which relates to an individual by name, that is, in

which the subject is a proper name. Individuals have no essences. When the

schoolmen talked of the essence of an individual, they did not mean the

properties implied in its name, for the names of individuals imply no

properties. They regarded as of the essence of an individual, whatever was

of the essence of the species in which they were accustomed to place that

individual; _i.e._, of the class to which it was most familiarly referred,

and to which, therefore, they conceived that it by nature belonged. Thus,

because the proposition Man is a rational being, was an essential

proposition, they affirmed the same thing of the proposition, Julius Cæsar

is a rational being. This followed very naturally if genera and species

were to be considered as entities, distinct from, but _inhering_ in, the

individuals composing them. If _man_ was a substance inhering in each

individual man, the _essence_ of man (whatever that might mean) was

naturally supposed to accompany it; to inhere in John Thompson, and to

form the _common essence_ of Thompson and Julius Cæsar. It might then be

fairly said, that rationality, being of the essence of Man, was of the

essence also of Thompson. But if Man altogether be only the individual men

and a name bestowed upon them in consequence of certain common properties,

what becomes of John Thompson’s essence?

A fundamental error is seldom expelled from philosophy by a single

victory. It retreats slowly, defends every inch of ground, and often,

after it has been driven from the open country, retains a footing in some

remote fastness. The essences of individuals were an unmeaning figment

arising from a misapprehension of the essences of classes, yet even Locke,

when he extirpated the parent error, could not shake himself free from

that which was its fruit. He distinguished two sorts of essences, Real and

Nominal. His nominal essences were the essences of classes, explained

nearly as we have now explained them. Nor is any thing wanting to render

the third book of Locke’s Essay a nearly unexceptional treatise on the

connotation of names, except to free its language from the assumption of

what are called Abstract Ideas, which unfortunately is involved in the

phraseology, though not necessarily connected with the thoughts contained

in that immortal Third Book.(40) But besides nominal essences, he admitted

real essences, or essences of individual objects, which he supposed to be

the causes of the sensible properties of those objects. We know not (said

he) what these are (and this acknowledgment rendered the fiction

comparatively innocuous); but if we did, we could, from them alone,

demonstrate the sensible properties of the object, as the properties of

the triangle are demonstrated from the definition of the triangle. I shall

have occasion to revert to this theory in treating of Demonstration, and

of the conditions under which one property of a thing admits of being

demonstrated from another property. It is enough here to remark that,

according to this definition, the real essence of an object has, in the

progress of physics, come to be conceived as nearly equivalent, in the

case of bodies, to their corpuscular structure: what it is now supposed to

mean in the case of any other entities, I would not take upon myself to

define.

§ 4. An essential proposition, then, is one which is purely verbal; which

asserts of a thing under a particular name, only what is asserted of it in

the fact of calling it by that name; and which, therefore, either gives no

information, or gives it respecting the name, not the thing.

Non-essential, or accidental propositions, on the contrary, may be called

Real Propositions, in opposition to Verbal. They predicate of a thing some

fact not involved in the signification of the name by which the

proposition speaks of it; some attribute not connoted by that name. Such

are all propositions concerning things individually designated, and all

general or particular propositions in which the predicate connotes any

attribute not connoted by the subject. All these, if true, add to our

knowledge: they convey information, not already involved in the names

employed. When I am told that all, or even that some objects, which have

certain qualities, or which stand in certain relations, have also certain

other qualities, or stand in certain other relations, I learn from this

proposition a new fact; a fact not included in my knowledge of the meaning

of the words, nor even of the existence of Things answering to the

signification of those words. It is this class of propositions only which

are in themselves instructive, or from which any instructive propositions

can be inferred.(41)

Nothing has probably contributed more to the opinion so long prevalent of

the futility of the school logic, than the circumstance that almost all

the examples used in the common school books to illustrate the doctrine of

predication and that of the syllogism, consist of essential propositions.

They were usually taken either from the branches or from the main trunk of

the Predicamental Tree, which included nothing but what was of the

_essence_ of the species: _Omne corpus est substantia_, _Omne animal est

corpus_, _Omnis homo est corpus_, _Omnis homo est animal_, _Omnis homo est

rationalis_, and so forth. It is far from wonderful that the syllogistic

art should have been thought to be of no use in assisting correct

reasoning, when almost the only propositions which, in the hands of its

professed teachers, it was employed to prove, were such as every one

assented to without proof the moment he comprehended the meaning of the

words; and stood exactly on a level, in point of evidence, with the

premises from which they were drawn. I have, therefore, throughout this

work, avoided the employment of essential propositions as examples, except

where the nature of the principle to be illustrated specifically required

them.

§ 5. With respect to propositions which do convey information—which assert

something of a Thing, under a name that does not already presuppose what

is about to be asserted; there are two different aspects in which these,

or rather such of them as are general propositions, may be considered: we

may either look at them as portions of speculative truth, or as memoranda

for practical use. According as we consider propositions in one or the

other of these lights, their import may be conveniently expressed in one

or in the other of two formulas.

According to the formula which we have hitherto employed, and which is

best adapted to express the import of the proposition as a portion of our

theoretical knowledge, All men are mortal, means that the attributes of

man are always accompanied by the attribute mortality: No men are gods,

means that the attributes of man are never accompanied by the attributes,

or at least never by all the attributes, signified by the word god. But

when the proposition is considered as a memorandum for practical use, we

shall find a different mode of expressing the same meaning better adapted

to indicate the office which the proposition performs. The practical use

of a proposition is, to apprise or remind us what we have to expect, in

any individual case which comes within the assertion contained in the

proposition. In reference to this purpose, the proposition, All men are

mortal, means that the attributes of man are _evidence of_, are a _mark_

of, mortality; an indication by which the presence of that attribute is

made manifest. No men are gods, means that the attributes of man are a

mark or evidence that some or all of the attributes understood to belong

to a god are not there; that where the former are, we need not expect to

find the latter.

These two forms of expression are at bottom equivalent; but the one points

the attention more directly to what a proposition means, the latter to the

manner in which it is to be used.

Now it is to be observed that Reasoning (the subject to which we are next

to proceed) is a process into which propositions enter not as ultimate

results, but as means to the establishment of other propositions. We may

expect, therefore, that the mode of exhibiting the import of a general

proposition which shows it in its application to practical use, will best

express the function which propositions perform in Reasoning. And

accordingly, in the theory of Reasoning, the mode of viewing the subject

which considers a Proposition as asserting that one fact or phenomenon is

a _mark_ or _evidence_ of another fact or phenomenon, will be found almost

indispensable. For the purposes of that Theory, the best mode of defining

the import of a proposition is not the mode which shows most clearly what

it is in itself, but that which most distinctly suggests the manner in

which it may be made available for advancing from it to other

propositions.

Chapter VII.

Of The Nature Of Classification, And The Five Predicables.

§ 1. In examining into the nature of general propositions, we have

adverted much less than is usual with logicians to the ideas of a Class,

and Classification; ideas which, since the Realist doctrine of General

Substances went out of vogue, have formed the basis of almost every

attempt at a philosophical theory of general terms and general

propositions. We have considered general names as having a meaning, quite

independently of their being the names of classes. That circumstance is in

truth accidental, it being wholly immaterial to the signification of the

name whether there are many objects, or only one, to which it happens to

be applicable, or whether there be any at all. God is as much a general

term to the Christian or Jew as to the Polytheist; and dragon, hippogriff,

chimera, mermaid, ghost, are as much so as if real objects existed,

corresponding to those names. Every name the signification of which is

constituted by attributes, is potentially a name of an indefinite number

of objects; but it needs not be actually the name of any; and if of any,

it may be the name of only one. As soon as we employ a name to connote

attributes, the things, be they more or fewer, which happen to possess

those attributes, are constituted _ipso facto_ a class. But in predicating

the name we predicate only the attributes; and the fact of belonging to a

class does not, in many cases, come into view at all.

Although, however, Predication does not presuppose Classification, and

though the theory of Names and of Propositions is not cleared up, but only

encumbered, by intruding the idea of classification into it, there is

nevertheless a close connection between Classification and the employment

of General Names. By every general name which we introduce, we create a

class, if there be any things, real or imaginary, to compose it; that is,

any Things corresponding to the signification of the name. Classes,

therefore, mostly owe their existence to general language. But general

language, also, though that is not the most common case, sometimes owes

its existence to classes. A general, which is as much as to say a

significant, name, is indeed mostly introduced because we have a

signification to express by it; because we need a word by means of which

to predicate the attributes which it connotes. But it is also true that a

name is sometimes introduced because we have found it convenient to create

a class; because we have thought it useful for the regulation of our

mental operations, that a certain group of objects should be thought of

together. A naturalist, for purposes connected with his particular

science, sees reason to distribute the animal or vegetable creation into

certain groups rather than into any others, and he requires a name to

bind, as it were, each of his groups together. It must not, however, be

supposed that such names, when introduced, differ in any respect, as to

their mode of signification, from other connotative names. The classes

which they denote are, as much as any other classes, constituted by

certain common attributes, and their names are significant of those

attributes, and of nothing else. The names of Cuvier’s classes and orders,

_Plantigrades_, _Digitigrades_, etc., are as much the expression of

attributes as if those names had preceded, instead of grown out of, his

classification of animals. The only peculiarity of the case is, that the

convenience of classification was here the primary motive for introducing

the names; while in other cases the name is introduced as a means of

predication, and the formation of a class denoted by it is only an

indirect consequence.

The principles which ought to regulate Classification, as a logical

process subservient to the investigation of truth, can not be discussed to

any purpose until a much later stage of our inquiry. But, of

Classification as resulting from, and implied in, the fact of employing

general language, we can not forbear to treat here, without leaving the

theory of general names, and of their employment in predication, mutilated

and formless.

§ 2. This portion of the theory of general language is the subject of what

is termed the doctrine of the Predicables; a set of distinctions handed

down from Aristotle, and his follower Porphyry, many of which have taken a

firm root in scientific, and some of them even in popular, phraseology.

The predicables are a fivefold division of General Names, not grounded as

usual on a difference in their meaning, that is, in the attribute which

they connote, but on a difference in the kind of class which they denote.

We may predicate of a thing five different varieties of class-name:

A _genus_ of the thing: (γὲνος).

A _species_: (εἶσος).

A _differentia_: (διαφορὰ).

A _proprium_: (ἰδιών).

An _accidens_: (συμβεβηκός).

It is to be remarked of these distinctions, that they express, not what

the predicate is in its own meaning, but what relation it bears to the

subject of which it happens on the particular occasion to be predicated.

There are not some names which are exclusively genera, and others which

are exclusively species, or differentiæ; but the same name is referred to

one or another predicable, according to the subject of which it is

predicated on the particular occasion. _Animal_, for instance, is a genus

with respect to man, or John; a species with respect to Substance, or

Being. _Rectangular_ is one of the Differentiæ of a geometrical square; it

is merely one of the Accidentia of the table at which I am writing. The

words genus, species, etc., are therefore relative terms; they are names

applied to certain predicates, to express the relation between them and

some given subject: a relation grounded, as we shall see, not on what the

predicate connotes, but on the class which it denotes, and on the place

which, in some given classification, that class occupies relatively to the

particular subject.

§ 3. Of these five names, two, Genus and Species, are not only used by

naturalists in a technical acceptation not precisely agreeing with their

philosophical meaning, but have also acquired a popular acceptation, much

more general than either. In this popular sense any two classes, one of

which includes the whole of the other and more, may be called a Genus and

a Species. Such, for instance, are Animal and Man; Man and Mathematician.

Animal is a Genus; Man and Brute are its two species; or we may divide it

into a greater number of species, as man, horse, dog, etc. _Biped_, or

_two-footed animal_, may also be considered a genus, of which man and bird

are two species. _Taste_ is a genus, of which sweet taste, sour taste,

salt taste, etc., are species. _Virtue_ is a genus; justice, prudence,

courage, fortitude, generosity, etc., are its species.

The same class which is a genus with reference to the sub-classes or

species included in it, may be itself a species with reference to a more

comprehensive, or, as it is often called, a superior genus. Man is a

species with reference to animal, but a genus with reference to the

species Mathematician. Animal is a genus, divided into two species, man

and brute; but animal is also a species, which, with another species,

vegetable, makes up the genus, organized being. Biped is a genus with

reference to man and bird, but a species with respect to the superior

genus, animal. Taste is a genus divided into species, but also a species

of the genus sensation. Virtue, a genus with reference to justice,

temperance, etc., is one of the species of the genus, mental quality.

In this popular sense the words Genus and Species have passed into common

discourse. And it should be observed that in ordinary parlance, not the

name of the class, but the class itself, is said to be the genus or

species; not, of course, the class in the sense of each individual of the

class, but the individuals collectively, considered as an aggregate whole;

the name by which the class is designated being then called not the genus

or species, but the generic or specific name. And this is an admissible

form of expression; nor is it of any importance which of the two modes of

speaking we adopt, provided the rest of our language is consistent with

it; but, if we call the class itself the genus, we must not talk of

predicating the genus. We predicate of man the _name_ mortal; and by

predicating the name, we may be said, in an intelligible sense, to

predicate what the name expresses, the _attribute_ mortality; but in no

allowable sense of the word predication do we predicate of man the _class_

mortal. We predicate of him the fact of belonging to the class.

By the Aristotelian logicians, the terms genus and species were used in a

more restricted sense. They did not admit every class which could be

divided into other classes to be a genus, or every class which could be

included in a larger class to be a species. Animal was by them considered

a genus; man and brute co-ordinate species under that genus: _biped_,

however, would not have been admitted to be a genus with reference to man,

but a _proprium_ or _accidens_ only. It was requisite, according to their

theory, that genus and species should be of the _essence_ of the subject.

Animal was of the essence of man; biped was not. And in every

classification they considered some one class as the lowest or _infima_

species. Man, for instance, was a lowest species. Any further divisions

into which the class might be capable of being broken down, as man into

white, black, and red man, or into priest and layman, they did not admit

to be species.

It has been seen, however, in the preceding chapter, that the distinction

between the essence of a class, and the attributes or properties which are

not of its essence—a distinction which has given occasion to so much

abstruse speculation, and to which so mysterious a character was formerly,

and by many writers is still, attached—amounts to nothing more than the

difference between those attributes of the class which are, and those

which are not, involved in the signification of the class-name. As applied

to individuals, the word Essence, we found, has no meaning, except in

connection with the exploded tenets of the Realists; and what the

schoolmen chose to call the essence of an individual, was simply the

essence of the class to which that individual was most familiarly

referred.

Is there no difference, then, save this merely verbal one, between the

classes which the schoolmen admitted to be genera or species, and those to

which they refused the title? Is it an error to regard some of the

differences which exist among objects as differences _in kind_ (_genere_

or _specie_), and others only as differences in the accidents? Were the

schoolmen right or wrong in giving to some of the classes into which

things may be divided, the name of _kinds_, and considering others as

secondary divisions, grounded on differences of a comparatively

superficial nature? Examination will show that the Aristotelians did mean

something by this distinction, and something important; but which, being

but indistinctly conceived, was inadequately expressed by the phraseology

of essences, and the various other modes of speech to which they had

recourse.

§ 4. It is a fundamental principle in logic, that the power of framing

classes is unlimited, as long as there is any (even the smallest)

difference to found a distinction upon. Take any attribute whatever, and

if some things have it, and others have not, we may ground on the

attribute a division of all things into two classes; and we actually do

so, the moment we create a name which connotes the attribute. The number

of possible classes, therefore, is boundless; and there are as many actual

classes (either of real or of imaginary things) as there are general

names, positive and negative together.

But if we contemplate any one of the classes so formed, such as the class

animal or plant, or the class sulphur or phosphorus, or the class white or

red, and consider in what particulars the individuals included in the

class differ from those which do not come within it, we find a very

remarkable diversity in this respect between some classes and others.

There are some classes, the things contained in which differ from other

things only in certain particulars which may be numbered, while others

differ in more than can be numbered, more even than we need ever expect to

know. Some classes have little or nothing in common to characterize them

by, except precisely what is connoted by the name: white things, for

example, are not distinguished by any common properties except whiteness;

or if they are, it is only by such as are in some way dependent on, or

connected with, whiteness. But a hundred generations have not exhausted

the common properties of animals or of plants, of sulphur or of

phosphorus; nor do we suppose them to be exhaustible, but proceed to new

observations and experiments, in the full confidence of discovering new

properties which were by no means implied in those we previously knew.

While, if any one were to propose for investigation the common properties

of all things which are of the same color, the same shape, or the same

specific gravity, the absurdity would be palpable. We have no ground to

believe that any such common properties exist, except such as may be shown

to be involved in the supposition itself, or to be derivable from it by

some law of causation. It appears, therefore, that the properties, on

which we ground our classes, sometimes exhaust all that the class has in

common, or contain it all by some mode of implication; but in other

instances we make a selection of a few properties from among not only a

greater number, but a number inexhaustible by us, and to which as we know

no bounds, they may, so far as we are concerned, be regarded as infinite.

There is no impropriety in saying that, of these two classifications, the

one answers to a much more radical distinction in the things themselves,

than the other does. And if any one even chooses to say that the one

classification is made by nature, the other by us for our convenience, he

will be right; provided he means no more than this: Where a certain

apparent difference between things (though perhaps in itself of little

moment) answers to we know not what number of other differences, pervading

not only their known properties, but properties yet undiscovered, it is

not optional but imperative to recognize this difference as the foundation

of a specific distinction; while, on the contrary, differences that are

merely finite and determinate, like those designated by the words white,

black, or red, may be disregarded if the purpose for which the

classification is made does not require attention to those particular

properties. The differences, however, are made by nature, in both cases;

while the recognition of those differences as grounds of classification

and of naming, is, equally in both cases, the act of man: only in the one

case, the ends of language and of classification would be subverted if no

notice were taken of the difference, while in the other case, the

necessity of taking notice of it depends on the importance or unimportance

of the particular qualities in which the difference happens to consist.

Now, these classes, distinguished by unknown multitudes of properties, and

not solely by a few determinate ones—which are parted off from one another

by an unfathomable chasm, instead of a mere ordinary ditch with a visible

bottom—are the only classes which, by the Aristotelian logicians, were

considered as genera or species. Differences which extended only to a

certain property or properties, and there terminated, they considered as

differences only in the _accidents_ of things; but where any class

differed from other things by an infinite series of differences, known and

unknown, they considered the distinction as one of _kind_, and spoke of it

as being an _essential_ difference, which is also one of the current

meanings of that vague expression at the present day.

Conceiving the schoolmen to have been justified in drawing a broad line of

separation between these two kinds of classes and of class-distinctions, I

shall not only retain the division itself, but continue to express it in

their language. According to that language, the proximate (or lowest) Kind

to which any individual is referrible, is called its species. Conformably

to this, Isaac Newton would be said to be of the species man. There are

indeed numerous sub-classes included in the class man, to which Newton

also belongs; for example, Christian, and Englishman, and Mathematician.

But these, though distinct classes, are not, in our sense of the term,

distinct Kinds of men. A Christian, for example, differs from other human

beings; but he differs only in the attribute which the word expresses,

namely, belief in Christianity, and whatever else that implies, either as

involved in the fact itself, or connected with it through some law of

cause and effect. We should never think of inquiring what properties,

unconnected with Christianity, either as cause or effect, are common to

all Christians and peculiar to them; while in regard to all Men,

physiologists are perpetually carrying on such an inquiry; nor is the

answer ever likely to be completed. Man, therefore, we may call a species;

Christian, or Mathematician, we can not.

Note here, that it is by no means intended to imply that there may not be

different Kinds, or logical species, of man. The various races and

temperaments, the two sexes, and even the various ages, may be differences

of kind, within our meaning of the term. I do not say that they are so.

For in the progress of physiology it may almost be said to be made out,

that the differences which really exist between different races, sexes,

etc., follow as consequences, under laws of nature, from a small number of

primary differences which can be precisely determined, and which, as the

phrase is, _account for_ all the rest. If this be so, these are not

distinctions in kind; no more than Christian, Jew, Mussulman, and Pagan, a

difference which also carries many consequences along with it. And in this

way classes are often mistaken for real Kinds, which are afterward proved

not to be so. But if it turned out that the differences were not capable

of being thus accounted for, then Caucasian, Mongolian, Negro, etc., would

be really different Kinds of human beings, and entitled to be ranked as

species by the logician; though not by the naturalist. For (as already

noticed) the word species is used in a different signification in logic

and in natural history. By the naturalist, organized beings are not

usually said to be of different species, if it is supposed that they have

descended from the same stock. That, however, is a sense artificially

given to the word, for the technical purposes of a particular science. To

the logician, if a negro and a white man differ in the same manner

(however less in degree) as a horse and a camel do, that is, if their

differences are inexhaustible, and not referrible to any common cause,

they are different species, whether they are descended from common

ancestors or not. But if their differences can all be traced to climate

and habits, or to some one or a few special differences in structure, they

are not, in the logician’s view, specifically distinct.

When the _infima species_, or proximate Kind, to which an individual

belongs, has been ascertained, the properties common to that Kind include

necessarily the whole of the common properties of every other real Kind to

which the individual can be referrible. Let the individual, for example,

be Socrates, and the proximate Kind, man. Animal, or living creature, is

also a real kind, and includes Socrates; but, since it likewise includes

man, or in other words, since all men are animals, the properties common

to animals form a portion of the common properties of the sub-class, man.

And if there be any class which includes Socrates without including man,

that class is not a real Kind. Let the class, for example, be

_flat-nosed_; that being a class which includes Socrates, without

including all men. To determine whether it is a real Kind, we must ask

ourselves this question: Have all flat-nosed animals, in addition to

whatever is implied in their flat noses, any common properties, other than

those which are common to all animals whatever? If they had; if a flat

nose were a mark or index to an indefinite number of other peculiarities,

not deducible from the former by an ascertainable law, then out of the

class man we might cut another class, flat-nosed man, which, according to

our definition, would be a Kind. But if we could do this, man would not

be, as it was assumed to be, the proximate Kind. Therefore, the properties

of the proximate Kind do comprehend those (whether known or unknown) of

all other Kinds to which the individual belongs; which was the point we

undertook to prove. And hence, every other Kind which is predicable of the

individual, will be to the proximate Kind in the relation of a genus,

according to even the popular acceptation of the terms genus and species;

that is, it will be a larger class, including it and more.

We are now able to fix the logical meaning of these terms. Every class

which is a real Kind, that is, which is distinguished from all other

classes by an indeterminate multitude of properties not derivable from one

another, is either a genus or a species. A Kind which is not divisible

into other Kinds, can not be a genus, because it has no species under it;

but it is itself a species, both with reference to the individuals below

and to the genera above (Species Prædicabilis and Species Subjicibilis).

But every Kind which admits of division into real Kinds (as animal into

mammal, bird, fish, etc., or bird into various species of birds) is a

genus to all below it, a species to all genera in which it is itself

included. And here we may close this part of the discussion, and pass to

the three remaining predicables, Differentia, Proprium, and Accidens.

§ 5. To begin with Differentia. This word is correlative with the words

genus and species, and as all admit, it signifies the attribute which

distinguishes a given species from every other species of the same genus.

This is so far clear: but we may still ask, which of the distinguishing

attributes it signifies. For we have seen that every Kind (and a species

must be a Kind) is distinguished from other Kinds, not by any one

attribute, but by an indefinite number. Man, for instance, is a species of

the genus animal: Rational (or rationality, for it is of no consequence

here whether we use the concrete or the abstract form) is generally

assigned by logicians as the Differentia; and doubtless this attribute

serves the purpose of distinction: but it has also been remarked of man,

that he is a cooking animal; the only animal that dresses its food. This,

therefore, is another of the attributes by which the species man is

distinguished from other species of the same genus: would this attribute

serve equally well for a differentia? The Aristotelians say No; having

laid it down that the differentia must, like the genus and species, be of

the _essence_ of the subject.

And here we lose even that vestige of a meaning grounded in the nature of

the things themselves, which may be supposed to be attached to the word

essence when it is said that genus and species must be of the essence of

the thing. There can be no doubt that when the schoolmen talked of the

essences of things as opposed to their accidents, they had confusedly in

view the distinction between differences of kind, and the differences

which are not of kind; they meant to intimate that genera and species must

be Kinds. Their notion of the essence of a thing was a vague notion of a

something which makes it what it is, _i.e._, which makes it the Kind of

thing that it is—which causes it to have all that variety of properties

which distinguish its Kind. But when the matter came to be looked at more

closely, nobody could discover what caused the thing to have all those

properties, nor even that there was any thing which caused it to have

them. Logicians, however, not liking to admit this, and being unable to

detect what made the thing to be what it was, satisfied themselves with

what made it to be what it was called. Of the innumerable properties,

known and unknown, that are common to the class man, a portion only, and

of course a very small portion, are connoted by its name; these few,

however, will naturally have been thus distinguished from the rest either

for their greater obviousness, or for greater supposed importance. These

properties, then, which were connoted by the name, logicians seized upon,

and called them the essence of the species; and not stopping there, they

affirmed them, in the case of the _infima species_, to be the essence of

the individual too; for it was their maxim, that the species contained the

“whole essence” of the thing. Metaphysics, that fertile field of delusion

propagated by language, does not afford a more signal instance of such

delusion. On this account it was that rationality, being connoted by the

name man, was allowed to be a differentia of the class; but the

peculiarity of cooking their food, not being connoted, was relegated to

the class of accidental properties.

The distinction, therefore, between Differentia, Proprium, and Accidens,

is not grounded in the nature of things, but in the connotation of names;

and we must seek it there, if we wish to find what it is.

From the fact that the genus includes the species, in other words

_de_notes more than the species, or is predicable of a greater number of

individuals, it follows that the species must connote more than the genus.

It must connote all the attributes which the genus connotes, or there

would be nothing to prevent it from denoting individuals not included in

the genus. And it must connote something besides, otherwise it would

include the whole genus. Animal denotes all the individuals denoted by

man, and many more. Man, therefore, must connote all that animal connotes,

otherwise there might be men who are not animals; and it must connote

something more than animal connotes, otherwise all animals would be men.

This surplus of connotation—this which the species connotes over and above

the connotation of the genus—is the Differentia, or specific difference;

or, to state the same proposition in other words, the Differentia is that

which must be added to the connotation of the genus, to complete the

connotation of the species.

The word man, for instance, exclusively of what it connotes in common with

animal, also connotes rationality, and at least some approximation to that

external form which we all know, but which as we have no name for it

considered in itself, we are content to call the human. The Differentia,

or specific difference, therefore, of man, as referred to the genus

animal, is that outward form and the possession of reason. The

Aristotelians said, the possession of reason, without the outward form.

But if they adhered to this, they would have been obliged to call the

Houyhnhnms men. The question never arose, and they were never called upon

to decide how such a case would have affected their notion of

essentiality. However this may be, they were satisfied with taking such a

portion of the differentia as sufficed to distinguish the species from all

other _existing_ things, though by so doing they might not exhaust the

connotation of the name.

§ 6. And here, to prevent the notion of differentia from being restricted

within too narrow limits, it is necessary to remark, that a species, even

as referred to the same genus, will not always have the same differentia,

but a different one, according to the principle and purpose which preside

over the particular classification. For example, a naturalist surveys the

various kinds of animals, and looks out for the classification of them

most in accordance with the order in which, for zoological purposes, he

considers it desirable that we should think of them. With this view he

finds it advisable that one of his fundamental divisions should be into

warm-blooded and cold-blooded animals; or into animals which breathe with

lungs and those which breathe with gills; or into carnivorous, and

frugivorous or graminivorous; or into those which walk on the flat part

and those which walk on the extremity of the foot, a distinction on which

two of Cuvier’s families are founded. In doing this, the naturalist

creates as many new classes; which are by no means those to which the

individual animal is familiarly and spontaneously referred; nor should we

ever think of assigning to them so prominent a position in our arrangement

of the animal kingdom, unless for a preconceived purpose of scientific

convenience. And to the liberty of doing this there is no limit. In the

examples we have given, most of the classes are real Kinds, since each of

the peculiarities is an index to a multitude of properties belonging to

the class which it characterizes: but even if the case were otherwise—if

the other properties of those classes could all be derived, by any process

known to us, from the one peculiarity on which the class is founded—even

then, if these derivative properties were of primary importance for the

purposes of the naturalist, he would be warranted in founding his primary

divisions on them.

If, however, practical convenience is a sufficient warrant for making the

main demarcations in our arrangement of objects run in lines not

coinciding with any distinction of Kind, and so creating genera and

species in the popular sense which are not genera or species in the

rigorous sense at all; _à fortiori_ must we be warranted, when our genera

and species _are_ real genera and species, in marking the distinction

between them by those of their properties which considerations of

practical convenience most strongly recommend. If we cut a species out of

a given genus—the species man, for instance, out of the genus animal—with

an intention on our part that the peculiarity by which we are to be guided

in the application of the name man should be rationality, then rationality

is the differentia of the species man. Suppose, however, that being

naturalists, we, for the purposes of our particular study, cut out of the

genus animal the same species man, but with an intention that the

distinction between man and all other species of animal should be, not

rationality, but the possession of “four incisors in each jaw, tusks

solitary, and erect posture.” It is evident that the word man, when used

by us as naturalists, no longer connotes rationality, but connotes the

three other properties specified; for that which we have expressly in view

when we impose a name, assuredly forms part of the meaning of that name.

We may, therefore, lay it down as a maxim, that wherever there is a Genus,

and a Species marked out from that genus by an assignable differentia, the

name of the species must be connotative, and must connote the differentia;

but the connotation may be special—not involved in the signification of

the term as ordinarily used, but given to it when employed as a term of

art or science. The word Man in common use, connotes rationality and a

certain form, but does not connote the number or character of the teeth;

in the Linnæan system it connotes the number of incisor and canine teeth,

but does not connote rationality nor any particular form. The word _man_

has, therefore, two different meanings; though not commonly considered as

ambiguous, because it happens in both cases to _de_note the same

individual objects. But a case is conceivable in which the ambiguity would

become evident: we have only to imagine that some new kind of animal were

discovered, having Linnæus’s three characteristics of humanity, but not

rational, or not of the human form. In ordinary parlance, these animals

would not be called men; but in natural history they must still be called

so by those, if any there should be, who adhere to the Linnæan

classification; and the question would arise, whether the word should

continue to be used in two senses, or the classification be given up, and

the technical sense of the term be abandoned along with it.

Words not otherwise connotative may, in the mode just adverted to, acquire

a special or technical connotation. Thus the word whiteness, as we have so

often remarked, connotes nothing; it merely denotes the attribute

corresponding to a certain sensation: but if we are making a

classification of colors, and desire to justify, or even merely to point

out, the particular place assigned to whiteness in our arrangement, we may

define it “the color produced by the mixture of all the simple rays;” and

this fact, though by no means implied in the meaning of the word whiteness

as ordinarily used, but only known by subsequent scientific investigation,

is part of its meaning in the particular essay or treatise, and becomes

the differentia of the species.(42)

The differentia, therefore, of a species may be defined to be, that part

of the connotation of the specific name, whether ordinary or special and

technical, which distinguishes the species in question from all other

species of the genus to which on the particular occasion we are referring

it.

§ 7. Having disposed of Genus, Species, and Differentia, we shall not find

much difficulty in attaining a clear conception of the distinction between

the other two predicables, as well as between them and the first three.

In the Aristotelian phraseology, Genus and Differentia are of the

_essence_ of the subject; by which, as we have seen, is really meant that

the properties signified by the genus and those signified by the

differentia, form part of the connotation of the name denoting the

species. Proprium and Accidens, on the other hand, form no part of the

essence, but are predicated of the species only _accidentally_. Both are

Accidents, in the wider sense in which the accidents of a thing are

opposed to its essence; though, in the doctrine of the Predicables,

Accidens is used for one sort of accident only, Proprium being another

sort. Proprium, continue the schoolmen, is predicated _accidentally_,

indeed, but _necessarily_; or, as they further explain it, signifies an

attribute which is not indeed part of the essence, but which flows from,

or is a consequence of, the essence, and is, therefore, inseparably

attached to the species; _e.g._, the various properties of a triangle,

which, though no part of its definition, must necessarily be possessed by

whatever comes under that definition. Accidens, on the contrary, has no

connection whatever with the essence, but may come and go, and the species

still remain what it was before. If a species could exist without its

Propria, it must be capable of existing without that on which its Propria

are necessarily consequent, and therefore without its essence, without

that which constitutes it a species. But an Accidens, whether separable or

inseparable from the species in actual experience, may be supposed

separated, without the necessity of supposing any other alteration; or at

least, without supposing any of the essential properties of the species to

be altered, since with them an Accidens has no connection.

A Proprium, therefore, of the species, may be defined, any attribute which

belongs to all the individuals included in the species, and which, though

not connoted by the specific name (either ordinarily if the classification

we are considering be for ordinary purposes, or specially if it be for a

special purpose), yet follows from some attribute which the name either

ordinarily or specially connotes.

One attribute may follow from another in two ways; and there are

consequently two kinds of Proprium. It may follow as a conclusion follows

premises, or it may follow as an effect follows a cause. Thus, the

attribute of having the opposite sides equal, which is not one of those

connoted by the word Parallelogram, nevertheless follows from those

connoted by it, namely, from having the opposite sides straight lines and

parallel, and the number of sides four. The attribute, therefore, of

having the opposite sides equal, is a Proprium of the class parallelogram;

and a Proprium of the first kind, which follows from the connoted

attributes by way of _demonstration_. The attribute of being capable of

understanding language, is a Proprium of the species man, since without

being connoted by the word, it follows from an attribute which the word

does connote, viz., from the attribute of rationality. But this is a

Proprium of the second kind, which follows by way of _causation_. How it

is that one property of a thing follows, or can be inferred, from another;

under what conditions this is possible, and what is the exact meaning of

the phrase; are among the questions which will occupy us in the two

succeeding Books. At present it needs only be said, that whether a

Proprium follows by demonstration or by causation, it follows

_necessarily_; that is to say, its not following would be inconsistent

with some law which we regard as a part of the constitution either of our

thinking faculty or of the universe.

§ 8. Under the remaining predicable, Accidens, are included all attributes

of a thing which are neither involved in the signification of the name

(whether ordinarily or as a term of art), nor have, so far as we know, any

necessary connection with attributes which are so involved. They are

commonly divided into Separable and Inseparable Accidents. Inseparable

accidents are those which—although we know of no connection between them

and the attributes constitutive of the species, and although, therefore,

so far as we are aware, they might be absent without making the name

inapplicable and the species a different species—are yet never in fact

known to be absent. A concise mode of expressing the same meaning is, that

inseparable accidents are properties which are universal to the species,

but not necessary to it. Thus, blackness is an attribute of a crow, and,

as far as we know, a universal one. But if we were to discover a race of

white birds, in other respects resembling crows, we should not say, These

are not crows; we should say, These are white crows. Crow, therefore, does

not connote blackness; nor, from any of the attributes which it does

connote, whether as a word in popular use or as a term of art, could

blackness be inferred. Not only, therefore, can we conceive a white crow,

but we know of no reason why such an animal should not exist. Since,

however, none but black crows are known to exist, blackness, in the

present state of our knowledge, ranks as an accident, but an inseparable

accident, of the species crow.

Separable Accidents are those which are found, in point of fact, to be

sometimes absent from the species; which are not only not necessary, but

not even universal. They are such as do not belong to every individual of

the species, but only to some individuals; or if to all, not at all times.

Thus the color of a European is one of the separable accidents of the

species man, because it is not an attribute of all human creatures. Being

born, is also (speaking in the logical sense) a separable accident of the

species man, because, though an attribute of all human beings, it is so

only at one particular time. _A fortiori_ those attributes which are not

constant even in the same individual, as, to be in one or in another

place, to be hot or cold, sitting or walking, must be ranked as separable

accidents.

Chapter VIII.

Of Definition.

§ 1. One necessary part of the theory of Names and of Propositions remains

to be treated of in this place: the theory of Definitions. As being the

most important of the class of propositions which we have characterized as

purely verbal, they have already received some notice in the chapter

preceding the last. But their fuller treatment was at that time postponed,

because definition is so closely connected with classification, that,

until the nature of the latter process is in some measure understood, the

former can not be discussed to much purpose.

The simplest and most correct notion of a Definition is, a proposition

declaratory of the meaning of a word; namely, either the meaning which it

bears in common acceptation, or that which the speaker or writer, for the

particular purposes of his discourse, intends to annex to it.

The definition of a word being the proposition which enunciates its

meaning, words which have no meaning are unsusceptible of definition.

Proper names, therefore, can not be defined. A proper name being a mere

mark put upon an individual, and of which it is the characteristic

property to be destitute of meaning, its meaning can not of course be

declared; though we may indicate by language, as we might indicate still

more conveniently by pointing with the finger, upon what individual that

particular mark has been, or is intended to be, put. It is no definition

of “John Thomson” to say he is “the son of General Thomson;” for the name

John Thomson does not express this. Neither is it any definition of “John

Thomson” to say he is “the man now crossing the street.” These

propositions may serve to make known who is the particular man to whom the

name belongs, but that may be done still more unambiguously by pointing to

him, which, however, has not been esteemed one of the modes of definition.

In the case of connotative names, the meaning, as has been so often

observed, is the connotation; and the definition of a connotative name, is

the proposition which declares its connotation. This might be done either

directly or indirectly. The direct mode would be by a proposition in this

form: “Man” (or whatsoever the word may be) “is a name connoting such and

such attributes,” or “is a name which, when predicated of any thing,

signifies the possession of such and such attributes by that thing.” Or

thus: Man is every thing which possesses such and such attributes: Man is

every thing which possesses corporeity, organization, life, rationality,

and certain peculiarities of external form.

This form of definition is the most precise and least equivocal of any;

but it is not brief enough, and is besides too technical for common

discourse. The more usual mode of declaring the connotation of a name, is

to predicate of it another name or names of known signification, which

connote the same aggregation of attributes. This may be done either by

predicating of the name intended to be defined, another connotative name

exactly synonymous, as, “Man is a human being,” which is not commonly

accounted a definition at all; or by predicating two or more connotative

names, which make up among them the whole connotation of the name to be

defined. In this last case, again, we may either compose our definition of

as many connotative names as there are attributes, each attribute being

connoted by one, as, Man is a corporeal, organized, animated, rational

being, shaped so and so; or we employ names which connote several of the

attributes at once, as, Man is a rational _animal_, shaped so and so.

The definition of a name, according to this view of it, is the sum total

of all the _essential_ propositions which can be framed with that name for

their subject. All propositions the truth of which is implied in the name,

all those which we are made aware of by merely hearing the name, are

included in the definition, if complete, and may be evolved from it

without the aid of any other premises; whether the definition expresses

them in two or three words, or in a larger number. It is, therefore, not

without reason that Condillac and other writers have affirmed a definition

to be an _analysis_. To resolve any complex whole into the elements of

which it is compounded, is the meaning of analysis: and this we do when we

replace one word which connotes a set of attributes collectively, by two

or more which connote the same attributes singly, or in smaller groups.

§ 2. From this, however, the question naturally arises, in what manner are

we to define a name which connotes only a single attribute: for instance,

“white,” which connotes nothing but whiteness; “rational,” which connotes

nothing but the possession of reason. It might seem that the meaning of

such names could only be declared in two ways; by a synonymous term, if

any such can be found; or in the direct way already alluded to: “White is

a name connoting the attribute whiteness.” Let us see, however, whether

the analysis of the meaning of the name, that is, the breaking down of

that meaning into several parts, admits of being carried farther. Without

at present deciding this question as to the word _white_, it is obvious

that in the case of _rational_ some further explanation may be given of

its meaning than is contained in the proposition, “Rational is that which

possesses the attribute of reason;” since the attribute reason itself

admits of being defined. And here we must turn our attention to the

definitions of attributes, or rather of the names of attributes, that is,

of abstract names.

In regard to such names of attributes as are connotative, and express

attributes of those attributes, there is no difficulty: like other

connotative names, they are defined by declaring their connotation. Thus

the word _fault_ may be defined, “a quality productive of evil or

inconvenience.” Sometimes, again, the attribute to be defined is not one

attribute, but a union of several: we have only, therefore, to put

together the names of all the attributes taken separately, and we obtain

the definition of the name which belongs to them all taken together; a

definition which will correspond exactly to that of the corresponding

concrete name. For, as we define a concrete name by enumerating the

attributes which it connotes, and as the attributes connoted by a concrete

name form the entire signification of the corresponding abstract name, the

same enumeration will serve for the definition of both. Thus, if the

definition of a _human being_ be this, “a being, corporeal, animated,

rational, shaped so and so,” the definition of _humanity_ will be

corporeity and animal life, combined with rationality, and with such and

such a shape.

When, on the other hand, the abstract name does not express a complication

of attributes, but a single attribute, we must remember that every

attribute is grounded on some fact or phenomenon, from which, and which

alone, it derives its meaning. To that fact or phenomenon, called in a

former chapter the foundation of the attribute, we must, therefore, have

recourse for its definition. Now, the foundation of the attribute may be a

phenomenon of any degree of complexity, consisting of many different

parts, either co-existent or in succession. To obtain a definition of the

attribute, we must analyze the phenomenon into these parts. Eloquence, for

example, is the name of one attribute only; but this attribute is grounded

on external effects of a complicated nature, flowing from acts of the

person to whom we ascribe the attribute; and by resolving this phenomenon

of causation into its two parts, the cause and the effect, we obtain a

definition of eloquence, viz. the power of influencing the feelings by

speech or writing.

A name, therefore, whether concrete or abstract, admits of definition,

provided we are able to analyze, that is, to distinguish into parts, the

attribute or set of attributes which constitute the meaning both of the

concrete name and of the corresponding abstract: if a set of attributes,

by enumerating them; if a single attribute, by dissecting the fact or

phenomenon (whether of perception or of internal consciousness) which is

the foundation of the attribute. But, further, even when the fact is one

of our simple feelings or states of consciousness, and therefore

unsusceptible of analysis, the names both of the object and of the

attribute still admit of definition; or rather, would do so if all our

simple feelings had names. Whiteness may be defined, the property or power

of exciting the sensation of white. A white object may be defined, an

object which excites the sensation of white. The only names which are

unsusceptible of definition, because their meaning is unsusceptible of

analysis, are the names of the simple feelings themselves. These are in

the same condition as proper names. They are not indeed, like proper

names, unmeaning; for the words _sensation of white_ signify, that the

sensation which I so denominate resembles other sensations which I

remember to have had before, and to have called by that name. But as we

have no words by which to recall those former sensations, except the very

word which we seek to define, or some other which, being exactly

synonymous with it, requires definition as much, words can not unfold the

signification of this class of names; and we are obliged to make a direct

appeal to the personal experience of the individual whom we address.

§ 3. Having stated what seems to be the true idea of a Definition, I

proceed to examine some opinions of philosophers, and some popular

conceptions on the subject, which conflict more or less with that idea.

The only adequate definition of a name is, as already remarked, one which

declares the facts, and the whole of the facts, which the name involves in

its signification. But with most persons the object of a definition does

not embrace so much; they look for nothing more, in a definition, than a

guide to the correct use of the term—a protection against applying it in a

manner inconsistent with custom and convention. Any thing, therefore, is

to them a sufficient definition of a term, which will serve as a correct

index to what the term _de_notes; though not embracing the whole, and

sometimes, perhaps, not even any part, of what it connotes. This gives

rise to two sorts of imperfect, or unscientific definition; Essential but

incomplete Definitions, and Accidental Definitions, or Descriptions. In

the former, a connotative name is defined by a part only of its

connotation; in the latter, by something which forms no part of the

connotation at all.

An example of the first kind of imperfect definitions is the following:

Man is a rational animal. It is impossible to consider this as a complete

definition of the word Man, since (as before remarked) if we adhered to it

we should be obliged to call the Houyhnhnms men; but as there happen to be

no Houyhnhnms, this imperfect definition is sufficient to mark out and

distinguish from all other things, the objects at present denoted by

“man;” all the beings actually known to exist, of whom the name is

predicable. Though the word is defined by some only among the attributes

which it connotes, not by all, it happens that all known objects which

possess the enumerated attributes, possess also those which are omitted;

so that the field of predication which the word covers, and the employment

of it which is conformable to usage, are as well indicated by the

inadequate definition as by an adequate one. Such definitions, however,

are always liable to be overthrown by the discovery of new objects in

nature.

Definitions of this kind are what logicians have had in view, when they

laid down the rule, that the definition of a species should be _per genus

et differentiam_. Differentia being seldom taken to mean the whole of the

peculiarities constitutive of the species, but some one of those

peculiarities only, a complete definition would be _per genus et

differentias_, rather than _differentiam_. It would include, with the name

of the superior genus, not merely _some_ attribute which distinguishes the

species intended to be defined from all other species of the same genus,

but _all_ the attributes implied in the name of the species, which the

name of the superior genus has not already implied. The assertion,

however, that a definition must of necessity consist of a genus and

differentiæ, is not tenable. It was early remarked by logicians, that the

_summum genus_ in any classification, having no genus superior to itself,

could not be defined in this manner. Yet we have seen that all names,

except those of our elementary feelings, are susceptible of definition in

the strictest sense; by setting forth in words the constituent parts of

the fact or phenomenon, of which the connotation of every word is

ultimately composed.

§ 4. Although the first kind of imperfect definition (which defines a

connotative term by a part only of what it connotes, but a part sufficient

to mark out correctly the boundaries of its denotation), has been

considered by the ancients, and by logicians in general, as a complete

definition; it has always been deemed necessary that the attributes

employed should really form part of the connotation; for the rule was that

the definition must be drawn from the _essence_ of the class; and this

would not have been the case if it had been in any degree made up of

attributes not connoted by the name. The second kind of imperfect

definition, therefore, in which the name of a class is defined by any of

its accidents—that is, by attributes which are not included in its

connotation—has been rejected from the rank of genuine Definition by all

logicians, and has been termed Description.

This kind of imperfect definition, however, takes its rise from the same

cause as the other, namely, the willingness to accept as a definition any

thing which, whether it expounds the meaning of the name or not, enables

us to discriminate the things denoted by the name from all other things,

and consequently to employ the term in predication without deviating from

established usage. This purpose is duly answered by stating any (no matter

what) of the attributes which are common to the whole of the class, and

peculiar to it; or any combination of attributes which happens to be

peculiar to it, though separately each of those attributes may be common

to it with some other things. It is only necessary that the definition (or

description) thus formed, should be _convertible_ with the name which it

professes to define; that is, should be exactly co-extensive with it,

being predicable of every thing of which it is predicable, and of nothing

of which it is not predicable; though the attributes specified may have no

connection with those which mankind had in view when they formed or

recognized the class, and gave it a name. The following are correct

definitions of Man, according to this test: Man is a mammiferous animal,

having (by nature) two hands (for the human species answers to this

description, and no other animal does): Man is an animal who cooks his

food: Man is a featherless biped.

What would otherwise be a mere description, may be raised to the rank of a

real definition by the peculiar purpose which the speaker or writer has in

view. As was seen in the preceding chapter, it may, for the ends of a

particular art or science, or for the more convenient statement of an

author’s particular doctrines, be advisable to give to some general name,

without altering its denotation, a special connotation, different from its

ordinary one. When this is done, a definition of the name by means of the

attributes which make up the special connotation, though in general a mere

accidental definition or description, becomes on the particular occasion

and for the particular purpose a complete and genuine definition. This

actually occurs with respect to one of the preceding examples, “Man is a

mammiferous animal having two hands,” which is the scientific definition

of man, considered as one of the species in Cuvier’s distribution of the

animal kingdom.

In cases of this sort, though the definition is still a declaration of the

meaning which in the particular instance the name is appointed to convey,

it can not be said that to state the meaning of the word is the purpose of

the definition. The purpose is not to expound a name, but a

classification. The special meaning which Cuvier assigned to the word Man

(quite foreign to its ordinary meaning, though involving no change in the

denotation of the word), was incidental to a plan of arranging animals

into classes on a certain principle, that is, according to a certain set

of distinctions. And since the definition of Man according to the ordinary

connotation of the word, though it would have answered every other purpose

of a definition, would not have pointed out the place which the species

ought to occupy in that particular classification; he gave the word a

special connotation, that he might be able to define it by the kind of

attributes on which, for reasons of scientific convenience, he had

resolved to found his division of animated nature.

Scientific definitions, whether they are definitions of scientific terms,

or of common terms used in a scientific sense, are almost always of the

kind last spoken of: their main purpose is to serve as the landmarks of

scientific classification. And since the classifications in any science

are continually modified as scientific knowledge advances, the definitions

in the sciences are also constantly varying. A striking instance is

afforded by the words Acid and Alkali, especially the former. As

experimental discovery advanced, the substances classed with acids have

been constantly multiplying, and by a natural consequence the attributes

connoted by the word have receded and become fewer. At first it connoted

the attributes, of combining with an alkali to form a neutral substance

(called a salt); being compounded of a base and oxygen; causticity to the

taste and touch; fluidity, etc. The true analysis of muriatic acid, into

chlorine and hydrogen, caused the second property, composition from a base

and oxygen, to be excluded from the connotation. The same discovery fixed

the attention of chemists upon hydrogen as an important element in acids;

and more recent discoveries having led to the recognition of its presence

in sulphuric, nitric, and many other acids, where its existence was not

previously suspected, there is now a tendency to include the presence of

this element in the connotation of the word. But carbonic acid, silica,

sulphurous acid, have no hydrogen in their composition; that property can

not, therefore, be connoted by the term, unless those substances are no

longer to be considered acids. Causticity and fluidity have long since

been excluded from the characteristics of the class, by the inclusion of

silica and many other substances in it; and the formation of neutral

bodies by combination with alkalis, together with such electro-chemical

peculiarities as this is supposed to imply, are now the only _differentiæ_

which form the fixed connotation of the word Acid, as a term of chemical

science.

What is true of the definition of any term of science, is of course true

of the definition of a science itself; and accordingly (as observed in the

Introductory Chapter of this work), the definition of a science must

necessarily be progressive and provisional. Any extension of knowledge or

alteration in the current opinions respecting the subject-matter, may lead

to a change more or less extensive in the particulars included in the

science; and its composition being thus altered, it may easily happen that

a different set of characteristics will be found better adapted as

differentiæ for defining its name.

In the same manner in which a special or technical definition has for its

object to expound the artificial classification out of which it grows; the

Aristotelian logicians seem to have imagined that it was also the business

of ordinary definition to expound the ordinary, and what they deemed the

natural, classification of things, namely, the division of them into

Kinds; and to show the place which each Kind occupies, as superior,

collateral, or subordinate, among other Kinds. This notion would account

for the rule that all definition must necessarily be _per genus et

differentiam_, and would also explain why a single differentia was deemed

sufficient. But to expound, or express in words, a distinction of Kind,

has already been shown to be an impossibility: the very meaning of a Kind

is, that the properties which distinguish it do not grow out of one

another, and can not therefore be set forth in words, even by implication,

otherwise than by enumerating them all: and all are not known, nor are

ever likely to be so. It is idle, therefore, to look to this as one of the

purposes of a definition: while, if it be only required that the

definition of a Kind should indicate what kinds include it or are included

by it, any definitions which expound the connotation of the names will do

this: for the name of each class must necessarily connote enough of its

properties to fix the boundaries of the class. If the definition,

therefore, be a full statement of the connotation, it is all that a

definition can be required to be.(43)

§ 5. Of the two incomplete and popular modes of definition, and in what

they differ from the complete or philosophical mode, enough has now been

said. We shall next examine an ancient doctrine, once generally prevalent

and still by no means exploded, which I regard as the source of a great

part of the obscurity hanging over some of the most important processes of

the understanding in the pursuit of truth. According to this, the

definitions of which we have now treated are only one of two sorts into

which definitions may be divided, viz., definitions of names, and

definitions of things. The former are intended to explain the meaning of a

term; the latter, the nature of a thing; the last being incomparably the

most important.

This opinion was held by the ancient philosophers, and by their followers,

with the exception of the Nominalists; but as the spirit of modern

metaphysics, until a recent period, has been on the whole a Nominalist

spirit, the notion of definitions of things has been to a certain extent

in abeyance, still continuing, however, to breed confusion in logic, by

its consequences indeed rather than by itself. Yet the doctrine in its own

proper form now and then breaks out, and has appeared (among other places)

where it was scarcely to be expected, in a justly admired word, Archbishop

Whately’s _Logic_.(44) In a review of that work published by me in the

_Westminster __ Review_ for January, 1828, and containing some opinions

which I no longer entertain, I find the following observations on the

question now before us; observations with which my present view of that

question is still sufficiently in accordance.

“The distinction between nominal and real definitions, between definitions

of words and what are called definitions of things, though conformable to

the ideas of most of the Aristotelian logicians, can not, as it appears to

us, be maintained. We apprehend that no definition is ever intended to

‘explain and unfold the nature of a thing.’ It is some confirmation of our

opinion, that none of those writers who have thought that there were

definitions of things, have ever succeeded in discovering any criterion by

which the definition of a thing can be distinguished from any other

proposition relating to the thing. The definition, they say, unfolds the

nature of the thing: but no definition can unfold its whole nature; and

every proposition in which any quality whatever is predicated of the

thing, unfolds some part of its nature. The true state of the case we take

to be this. All definitions are of names, and of names only; but, in some

definitions, it is clearly apparent, that nothing is intended except to

explain the meaning of the word; while in others, besides explaining the

meaning of the word, it is intended to be implied that there exists a

thing, corresponding to the word. Whether this be or be not implied in any

given case, can not be collected from the mere form of the expression. ‘A

centaur is an animal with the upper parts of a man and the lower parts of

a horse,’ and ‘A triangle is a rectilineal figure with three sides,’ are,

in form, expressions precisely similar; although in the former it is not

implied that any _thing_, conformable to the term, really exists, while in

the latter it is; as may be seen by substituting in both definitions, the

word _means_ for _is_. In the first expression, ‘A centaur means an

animal,’ etc., the sense would remain unchanged: in the second, ‘A

triangle means,’ etc., the meaning would be altered, since it would be

obviously impossible to deduce any of the truths of geometry from a

proposition expressive only of the manner in which we intend to employ a

particular sign.

“There are, therefore, expressions, commonly passing for definitions,

which include in themselves more than the mere explanation of the meaning

of a term. But it is not correct to call an expression of this sort a

peculiar kind of definition. Its difference from the other kind consists

in this, that it is not a definition, but a definition and something more.

The definition above given of a triangle, obviously comprises not one, but

two propositions, perfectly distinguishable. The one is, ‘There may exist

a figure, bounded by three straight lines;’ the other, ‘And this figure

may be termed a triangle.’ The former of these propositions is not a

definition at all: the latter is a mere nominal definition, or explanation

of the use and application of a term. The first is susceptible of truth or

falsehood, and may therefore be made the foundation of a train of

reasoning. The latter can neither be true nor false; the only character it

is susceptible of is that of conformity or disconformity to the ordinary

usage of language.”

There is a real distinction, then, between definitions of names, and what

are erroneously called definitions of things; but it is, that the latter,

along with the meaning of a name, covertly asserts a matter of fact. This

covert assertion is not a definition, but a postulate. The definition is a

mere identical proposition, which gives information only about the use of

language, and from which no conclusions affecting matters of fact can

possibly be drawn. The accompanying postulate, on the other hand, affirms

a fact, which may lead to consequences of every degree of importance. It

affirms the actual or possible existence of Things possessing the

combination of attributes set forth in the definition; and this, if true,

may be foundation sufficient on which to build a whole fabric of

scientific truth.

We have already made, and shall often have to repeat, the remark, that the

philosophers who overthrew Realism by no means got rid of the consequences

of Realism, but retained long afterward, in their own philosophy, numerous

propositions which could only have a rational meaning as part of a

Realistic system. It had been handed down from Aristotle, and probably

from earlier times, as an obvious truth, that the science of Geometry is

deduced from definitions. This, so long as a definition was considered to

be a proposition “unfolding the nature of the thing,” did well enough. But

Hobbes followed, and rejected utterly the notion that a definition

declares the nature of the thing, or does any thing but state the meaning

of a name; yet he continued to affirm as broadly as any of his

predecessors, that the ἀρχαὶ, _principia_, or original premises of

mathematics, and even of all science, are definitions; producing the

singular paradox, that systems of scientific truth, nay, all truths

whatever at which we arrive by reasoning, are deduced from the arbitrary

conventions of mankind concerning the signification of words.

To save the credit of the doctrine that definitions are the premises of

scientific knowledge, the proviso is sometimes added, that they are so

only under a certain condition, namely, that they be framed conformably to

the phenomena of nature; that is, that they ascribe such meanings to terms

as shall suit objects actually existing. But this is only an instance of

the attempt so often made, to escape from the necessity of abandoning old

language after the ideas which it expresses have been exchanged for

contrary ones. From the meaning of a name (we are told) it is possible to

infer physical facts, provided the name has corresponding to it an

existing thing. But if this proviso be necessary, from which of the two is

the inference really drawn? From the existence of a thing having the

properties, or from the existence of a name meaning them?

Take, for instance, any of the definitions laid down as premises in

Euclid’s Elements; the definition, let us say, of a circle. This, being

analyzed, consists of two propositions; the one an assumption with respect

to a matter of fact, the other a genuine definition. “A figure may exist,

having all the points in the line which bounds it equally distant from a

single point within it:” “Any figure possessing this property is called a

circle.” Let us look at one of the demonstrations which are said to depend

on this definition, and observe to which of the two propositions contained

in it the demonstration really appeals. “About the centre A, describe the

circle B C D.”

Here is an assumption that a figure, such as the definition expresses,

_may_ be described; which is no other than the postulate, or covert

assumption, involved in the so-called definition. But whether that figure

be called a circle or not is quite immaterial. The purpose would be as

well answered, in all respects except brevity, were we to say, “Through

the point B, draw a line returning into itself, of which every point shall

be at an equal distance from the point A.” By this the definition of a

circle would be got rid of, and rendered needless; but not the postulate

implied in it; without that the demonstration could not stand. The circle

being now described, let us proceed to the consequence. “Since B C D is a

circle, the radius B A is equal to the radius C A.” B A is equal to C A,

not because B C D is a circle, but because B C D is a figure with the

radii equal. Our warrant for assuming that such a figure about the centre

A, with the radius B A, may be made to exist, is the postulate. Whether

the admissibility of these postulates rests on intuition, or on proof, may

be a matter of dispute; but in either case they are the premises on which

the theorems depend; and while these are retained it would make no

difference in the certainty of geometrical truths, though every definition

in Euclid, and every technical term therein defined, were laid aside.

It is, perhaps, superfluous to dwell at so much length on what is so

nearly self-evident; but when a distinction, obvious as it may appear, has

been confounded, and by powerful intellects, it is better to say too much

than too little for the purpose of rendering such mistakes impossible in

future. I will, therefore detain the reader while I point out one of the

absurd consequences flowing from the supposition that definitions, as

such, are the premises in any of our reasonings, except such as relate to

words only. If this supposition were true, we might argue correctly from

true premises, and arrive at a false conclusion. We should only have to

assume as a premise the definition of a nonentity; or rather of a name

which has no entity corresponding to it. Let this, for instance, be our

definition:

A dragon is a serpent breathing flame.

This proposition, considered only as a definition, is indisputably

correct. A dragon _is_ a serpent breathing flame: the word _means_ that.

The tacit assumption, indeed (if there were any such understood

assertion), of the existence of an object with properties corresponding to

the definition, would, in the present instance, be false. Out of this

definition we may carve the premises of the following syllogism:

A dragon is a thing which breathes flame:

A dragon is a serpent:

From which the conclusion is,

Therefore some serpent or serpents breathe flame:

an unexceptionable syllogism in the first mode of the third figure, in

which both premises are true and yet the conclusion false; which every

logician knows to be an absurdity. The conclusion being false and the

syllogism correct, the premises can not be true. But the premises,

considered as parts of a definition, are true. Therefore, the premises

considered as parts of a definition can not be the real ones. The real

premises must be—

A dragon is a _really existing_ thing which breathes flame:

A dragon is a _really existing_ serpent:

which implied premises being false, the falsity of the conclusion presents

no absurdity.

If we would determine what conclusion follows from the same ostensible

premises when the tacit assumption of real existence is left out, let us,

according to the recommendation in a previous page, substitute _means_ for

_is_. We then have—

Dragon is _a word meaning_ a thing which breathes flame:

Dragon is _a word meaning_ a serpent:

From which the conclusion is,

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

breathes flame:

where the conclusion (as well as the premises) is true, and is the only

kind of conclusion which can ever follow from a definition, namely, a

proposition relating to the meaning of words.

There is still another shape into which we may transform this syllogism.

We may suppose the middle term to be the designation neither of a thing

nor of a name, but of an idea. We then have—

The _idea of_ a dragon is _an idea of_ a thing which breathes

flame:

The _idea of_ a dragon is _an idea of_ a serpent:

Therefore, there is _an idea of_ a serpent, which is _an idea of_

a thing breathing flame.

Here the conclusion is true, and also the premises; but the premises are

not definitions. They are propositions affirming that an idea existing in

the mind, includes certain ideal elements. The truth of the conclusion

follows from the existence of the psychological phenomenon called the idea

of a dragon; and therefore still from the tacit assumption of a matter of

fact.(45)

When, as in this last syllogism, the conclusion is a proposition

respecting an idea, the assumption on which it depends may be merely that

of the existence of an idea. But when the conclusion is a proposition

concerning a Thing, the postulate involved in the definition which stands

as the apparent premise, is the existence of a thing conformable to the

definition, and not merely of an idea conformable to it. This assumption

of real existence we always convey the impression that we intend to make,

when we profess to define any name which is already known to be a name of

really existing objects. On this account it is, that the assumption was

not necessarily implied in the definition of a dragon, while there was no

doubt of its being included in the definition of a circle.

§ 6. One of the circumstances which have contributed to keep up the

notion, that demonstrative truths follow from definitions rather than from

the postulates implied in those definitions, is, that the postulates, even

in those sciences which are considered to surpass all others in

demonstrative certainty, are not always exactly true. It is not true that

a circle exists, or can be described, which has all its radii _exactly_

equal. Such accuracy is ideal only; it is not found in nature, still less

can it be realized by art. People had a difficulty, therefore, in

conceiving that the most certain of all conclusions could rest on premises

which, instead of being certainly true, are certainly not true to the full

extent asserted. This apparent paradox will be examined when we come to

treat of Demonstration; where we shall be able to show that as much of the

postulate is true, as is required to support as much as is true of the

conclusion. Philosophers, however, to whom this view had not occurred, or

whom it did not satisfy, have thought it indispensable that there should

be found in definitions something _more_ certain, or at least more

accurately true, than the implied postulate of the real existence of a

corresponding object. And this something they flattered themselves they

had found, when they laid it down that a definition is a statement and

analysis not of the mere meaning of a word, nor yet of the nature of a

thing, but of an idea. Thus, the proposition, “A circle is a plane figure

bounded by a line all the points of which are at an equal distance from a

given point within it,” was considered by them, not as an assertion that

any real circle has that property (which would not be exactly true), but

that we _conceive_ a circle as having it; that our abstract idea of a

circle is an idea of a figure with its radii exactly equal.

Conformably to this it is said, that the subject-matter of mathematics,

and of every other demonstrative science, is not things as they really

exist, but abstractions of the mind. A geometrical line is a line without

breadth; but no such line exists in nature; it is a notion merely

suggested to the mind by its experience of nature. The definition (it is

said) is a definition of this mental line, not of any actual line: and it

is only of the mental line, not of any line existing in nature, that the

theorems of geometry are accurately true.

Allowing this doctrine respecting the nature of demonstrative truth to be

correct (which, in a subsequent place, I shall endeavor to prove that it

is not); even on that supposition, the conclusions which seem to follow

from a definition, do not follow from the definition as such, but from an

implied postulate. Even if it be true that there is no object in nature

answering to the definition of a line, and that the geometrical properties

of lines are not true of any lines in nature, but only of the idea of a

line; the definition, at all events, postulates the real existence of such

an idea: it assumes that the mind can frame, or rather has framed, the

notion of length without breadth, and without any other sensible property

whatever. To me, indeed, it appears that the mind can not form any such

notion; it can not conceive length without breadth; it can only, in

contemplating objects, attend to their length, exclusively of their other

sensible qualities, and so determine what properties may be predicated of

them in virtue of their length alone. If this be true, the postulate

involved in the geometrical definition of a line, is the real existence,

not of length without breadth, but merely of length, that is, of long

objects. This is quite enough to support all the truths of geometry, since

every property of a geometrical line is really a property of all physical

objects in so far as possessing length. But even what I hold to be the

false doctrine on the subject, leaves the conclusion that our reasonings

are grounded on the matters of fact postulated in definitions, and not on

the definitions themselves, entirely unaffected; and accordingly this

conclusion is one which I have in common with Dr. Whewell, in his

_Philosophy of the Inductive Sciences_: though, on the nature of

demonstrative truth, Dr. Whewell’s opinions are greatly at variance with

mine. And here, as in many other instances, I gladly acknowledge that his

writings are eminently serviceable in clearing from confusion the initial

steps in the analysis of the mental processes, even where his views

respecting the ultimate analysis are such as (though with unfeigned

respect) I can not but regard as fundamentally erroneous.

§ 7. Although, according to the opinion here presented, Definitions are

properly of names only, and not of things, it does not follow from this

that definitions are arbitrary. How to define a name, may not only be an

inquiry of considerable difficulty and intricacy, but may involve

considerations going deep into the nature of the things which are denoted

by the name. Such, for instance, are the inquiries which form the subjects

of the most important of Plato’s Dialogues; as, “What is rhetoric?” the

topic of the Gorgias, or, “What is justice?” that of the Republic. Such,

also, is the question scornfully asked by Pilate, “What is truth?” and the

fundamental question with speculative moralists in all ages, “What is

virtue?”

It would be a mistake to represent these difficult and noble inquiries as

having nothing in view beyond ascertaining the conventional meaning of a

name. They are inquiries not so much to determine what is, as what should

be, the meaning of a name; which, like other practical questions of

terminology, requires for its solution that we should enter, and sometimes

enter very deeply, into the properties not merely of names but of the

things named.

Although the meaning of every concrete general name resides in the

attributes which it connotes, the objects were named before the

attributes; as appears from the fact that in all languages, abstract names

are mostly compounds or other derivatives of the concrete names which

correspond to them. Connotative names, therefore, were, after proper

names, the first which were used: and in the simpler cases, no doubt, a

distinct connotation was present to the minds of those who first used the

name, and was distinctly intended by them to be conveyed by it. The first

person who used the word white, as applied to snow or to any other object,

knew, no doubt, very well what quality he intended to predicate, and had a

perfectly distinct conception in his mind of the attribute signified by

the name.

But where the resemblances and differences on which our classifications

are founded are not of this palpable and easily determinable kind;

especially where they consist not in any one quality but in a number of

qualities, the effects of which, being blended together, are not very

easily discriminated, and referred each to its true source; it often

happens that names are applied to namable objects, with no distinct

connotation present to the minds of those who apply them. They are only

influenced by a general resemblance between the new object and all or some

of the old familiar objects which they have been accustomed to call by

that name. This, as we have seen, is the law which even the mind of the

philosopher must follow, in giving names to the simple elementary feelings

of our nature: but, where the things to be named are complex wholes, a

philosopher is not content with noticing a general resemblance; he

examines what the resemblance consists in: and he only gives the same name

to things which resemble one another in the same definite particulars. The

philosopher, therefore, habitually employs his general names with a

definite connotation. But language was not made, and can only in some

small degree be mended, by philosophers. In the minds of the real arbiters

of language, general names, especially where the classes they denote can

not be brought before the tribunal of the outward senses to be identified

and discriminated, connote little more than a vague gross resemblance to

the things which they were earliest, or have been most, accustomed to call

by those names. When, for instance, ordinary persons predicate the words

_just_ or _unjust_ of any action, _noble_ or _mean_ of any sentiment,

expression, or demeanor, _statesman_ or _charlatan_ of any personage

figuring in politics, do they mean to affirm of those various subjects any

determinate attributes, of whatever kind? No: they merely recognize, as

they think, some likeness, more or less vague and loose, between these and

some other things which they have been accustomed to denominate or to hear

denominated by those appellations.

Language, as Sir James Mackintosh used to say of governments, “is not

made, but grows.” A name is not imposed at once and by previous purpose

upon a _class_ of objects, but is first applied to one thing, and then

extended by a series of transitions to another and another. By this

process (as has been remarked by several writers, and illustrated with

great force and clearness by Dugald Stewart in his Philosophical Essays) a

name not unfrequently passes by successive links of resemblance from one

object to another, until it becomes applied to things having nothing in

common with the first things to which the name was given; which, however,

do not, for that reason, drop the name; so that it at last denotes a

confused huddle of objects, having nothing whatever in common; and

connotes nothing, not even a vague and general resemblance. When a name

has fallen into this state, in which by predicating it of any object we

assert literally nothing about the object, it has become unfit for the

purposes either of thought or of the communication of thought; and can

only be made serviceable by stripping it of some part of its multifarious

denotation, and confining it to objects possessed of some attributes in

common, which it may be made to connote. Such are the inconveniences of a

language which “is not made, but grows.” Like the governments which are in

a similar case, it may be compared to a road which is not made but has

made itself: it requires continual mending in order to be passable.

From this it is already evident, why the question respecting the

definition of an abstract name is often one of so much difficulty. The

question, What is justice? is, in other words, What is the attribute which

mankind mean to predicate when they call an action just? To which the

first answer is, that having come to no precise agreement on the point,

they do not mean to predicate distinctly any attribute at all.

Nevertheless, all believe that there is some common attribute belonging to

all the actions which they are in the habit of calling just. The question

then must be, whether there is any such common attribute? and, in the

first place, whether mankind agree sufficiently with one another as to the

particular actions which they do or do not call just, to render the

inquiry, what quality those actions have in common, a possible one: if so,

whether the actions really have any quality in common; and if they have,

what it is. Of these three, the first alone is an inquiry into usage and

convention; the other two are inquiries into matters of fact. And if the

second question (whether the actions form a class at all) has been

answered negatively, there remains a fourth, often more arduous than all

the rest, namely, how best to form a class artificially, which the name

may denote.

And here it is fitting to remark, that the study of the spontaneous growth

of languages is of the utmost importance to those who would logically

remodel them. The classifications rudely made by established language,

when retouched, as they almost all require to be, by the hands of the

logician, are often themselves excellently suited to his purposes. As

compared with the classifications of a philosopher, they are like the

customary law of a country, which has grown up as it were spontaneously,

compared with laws methodized and digested into a code: the former are a

far less perfect instrument than the latter; but being the result of a

long, though unscientific, course of experience, they contain a mass of

materials which may be made very usefully available in the formation of

the systematic body of written law. In like manner, the established

grouping of objects under a common name, even when founded only on a gross

and general resemblance, is evidence, in the first place, that the

resemblance is obvious, and therefore considerable; and, in the next

place, that it is a resemblance which has struck great numbers of persons

during a series of years and ages. Even when a name, by successive

extensions, has come to be applied to things among which there does not

exist this gross resemblance common to them all, still at every step in

its progress we shall find such a resemblance. And these transitions of

the meaning of words are often an index to real connections between the

things denoted by them, which might otherwise escape the notice of

thinkers; of those at least who, from using a different language, or from

any difference in their habitual associations, have fixed their attention

in preference on some other aspect of the things. The history of

philosophy abounds in examples of such oversights, committed for want of

perceiving the hidden link that connected together the seemingly disparate

meanings of some ambiguous word.(46)

Whenever the inquiry into the definition of the name of any real object

consists of any thing else than a mere comparison of authorities, we

tacitly assume that a meaning must be found for the name, compatible with

its continuing to denote, if possible all, but at any rate the greater or

the more important part, of the things of which it is commonly predicated.

The inquiry, therefore, into the definition, is an inquiry into the

resemblances and differences among those things: whether there be any

resemblance running through them all; if not, through what portion of them

such a general resemblance can be traced: and finally, what are the common

attributes, the possession of which gives to them all, or to that portion

of them, the character of resemblance which has led to their being classed

together. When these common attributes have been ascertained and

specified, the name which belongs in common to the resembling objects

acquires a distinct instead of a vague connotation; and by possessing this

distinct connotation, becomes susceptible of definition.

In giving a distinct connotation to the general name, the philosopher will

endeavor to fix upon such attributes as, while they are common to all the

things usually denoted by the name, are also of greatest importance in

themselves; either directly, or from the number, the conspicuousness, or

the interesting character, of the consequences to which they lead. He will

select, as far as possible, such _differentiæ_ as lead to the greatest

number of interesting _propria_. For these, rather than the more obscure

and recondite qualities on which they often depend, give that general

character and aspect to a set of objects, which determine the groups into

which they naturally fall. But to penetrate to the more hidden agreement

on which these obvious and superficial agreements depend, is often one of

the most difficult of scientific problems. As it is among the most

difficult, so it seldom fails to be among the most important. And since

upon the result of this inquiry respecting the causes of the properties of

a class of things, there incidentally depends the question what shall be

the meaning of a word; some of the most profound and most valuable

investigations which philosophy presents to us, have been introduced by,

and have offered themselves under the guise of, inquiries into the

definition of a name.

Book II.

OF REASONING.

Διωρισμένων δε τούτων λέγωμεν ἤδη, διά τίνων, καὶ πότε, καὶ πῶς

γίνεται πᾶς συλλογισμός ὕστερον δὲ λεκτέον περὶ ἀποδείξεως.

Πρότερον γὰρ περὶ συλλογισμοῦ λεκτέον, ἥ περὶ ἀποδείξεως, διὰ τὸ

καθόλου μᾶλλον εἰναὶ τὸν συλλογισμόν. Ἡ μέν γὰρ ἀπόδειξις,

συλλογισμός τις; ὁ συλλογισμός δὲ ού πᾶς, ἀπόδειξις.—ARIST.,

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

Chapter I.

Of Inference, Or Reasoning, In General.

§ 1. In the preceding Book, we have been occupied not with the nature of

Proof, but with the nature of Assertion: the import conveyed by a

Proposition, whether that Proposition be true or false; not the means by

which to discriminate true from false Propositions. The proper subject,

however, of Logic is Proof. Before we could understand what Proof is, it

was necessary to understand what that is to which proof is applicable;

what that is which can be a subject of belief or disbelief, of affirmation

or denial; what, in short, the different kinds of Propositions assert.

This preliminary inquiry we have prosecuted to a definite result.

Assertion, in the first place, relates either to the meaning of words, or

to some property of the things which words signify. Assertions respecting

the meaning of words, among which definitions are the most important, hold

a place, and an indispensable one, in philosophy; but as the meaning of

words is essentially arbitrary, this class of assertions are not

susceptible of truth or falsity, nor therefore of proof or disproof.

Assertions respecting Things, or what may be called Real Propositions, in

contradistinction to verbal ones, are of various sorts. We have analyzed

the import of each sort, and have ascertained the nature of the things

they relate to, and the nature of what they severally assert respecting

those things. We found that whatever be the form of the proposition, and

whatever its nominal subject or predicate, the real subject of every

proposition is some one or more facts or phenomena of consciousness, or

some one or more of the hidden causes or powers to which we ascribe those

facts; and that what is predicated or asserted, either in the affirmative

or negative, of those phenomena or those powers, is always either

Existence, Order in Place, Order in Time, Causation, or Resemblance. This,

then, is the theory of the Import of Propositions, reduced to its ultimate

elements: but there is another and a less abstruse expression for it,

which, though stopping short in an earlier stage of the analysis, is

sufficiently scientific for many of the purposes for which such a general

expression is required. This expression recognizes the commonly received

distinction between Subject and Attribute, and gives the following as the

analysis of the meaning of propositions:—Every Proposition asserts, that

some given subject does or does not possess some attribute; or that some

attribute is or is not (either in all or in some portion of the subjects

in which it is met with) conjoined with some other attribute.

We shall now for the present take our leave of this portion of our

inquiry, and proceed to the peculiar problem of the Science of Logic,

namely, how the assertions, of which we have analyzed the import, are

proved or disproved; such of them, at least, as, not being amenable to

direct consciousness or intuition, are appropriate subjects of proof.

We say of a fact or statement, that it is proved, when we believe its

truth by reason of some other fact or statement from which it is said to

_follow_. Most of the propositions, whether affirmative or negative,

universal, particular, or singular, which we believe, are not believed on

their own evidence, but on the ground of something previously assented to,

from which they are said to be _inferred_. To infer a proposition from a

previous proposition or propositions; to give credence to it, or claim

credence for it, as a conclusion from something else; is to _reason_, in

the most extensive sense of the term. There is a narrower sense, in which

the name reasoning is confined to the form of inference which is termed

ratiocination, and of which the syllogism is the general type. The reasons

for not conforming to this restricted use of the term were stated in an

earlier stage of our inquiry, and additional motives will be suggested by

the considerations on which we are now about to enter.

§ 2. In proceeding to take into consideration the cases in which

inferences can legitimately be drawn, we shall first mention some cases in

which the inference is apparent, not real; and which require notice

chiefly that they may not be confounded with cases of inference properly

so called. This occurs when the proposition ostensibly inferred from

another, appears on analysis to be merely a repetition of the same, or

part of the same, assertion, which was contained in the first. All the

cases mentioned in books of Logic as examples of equipollency or

equivalence of propositions, are of this nature. Thus, if we were to

argue, No man is incapable of reason, for every man is rational; or, All

men are mortal, for no man is exempt from death; it would be plain that we

were not proving the proposition, but only appealing to another mode of

wording it, which may or may not be more readily comprehensible by the

hearer, or better adapted to suggest the real proof, but which contains in

itself no shadow of proof.

Another case is where, from a universal proposition, we affect to infer

another which differs from it only in being particular: as All A is B,

therefore Some A is B: No A is B, therefore Some A is not B. This, too, is

not to conclude one proposition from another, but to repeat a second time

something which had been asserted at first; with the difference, that we

do not here repeat the whole of the previous assertion, but only an

indefinite part of it.

A third case is where, the antecedent having affirmed a predicate of a

given subject, the consequent affirms of the same subject something

already connoted by the former predicate: as, Socrates is a man, therefore

Socrates is a living creature; where all that is connoted by living

creature was affirmed of Socrates when he was asserted to be a man. If the

propositions are negative, we must invert their order, thus: Socrates is

not a living creature, therefore he is not a man; for if we deny the less,

the greater, which includes it, is already denied by implication. These,

therefore, are not really cases of inference; and yet the trivial examples

by which, in manuals of Logic, the rules of the syllogism are illustrated,

are often of this ill-chosen kind; formal demonstrations of conclusions to

which whoever understands the terms used in the statement of the data, has

already, and consciously, assented.(47)

The most complex case of this sort of apparent inference is what is called

the Conversion of propositions; which consists in turning the predicate

into a subject, and the subject into a predicate, and framing out of the

same terms thus reversed, another proposition, which must be true if the

former is true. Thus, from the particular affirmative proposition, Some A

is B, we may infer that Some B is A. From the universal negative, No A is

B, we may conclude that No B is A. From the universal affirmative

proposition, All A is B, it can not be inferred that all B is A; though

all water is liquid, it is not implied that all liquid is water; but it is

implied that some liquid is so; and hence the proposition, All A is B, is

legitimately convertible into Some B is A. This process, which converts a

universal proposition into a particular, is termed conversion _per

accidens_. From the proposition, Some A is not B, we can not even infer

that some B is not A; though some men are not Englishmen, it does not

follow that some Englishmen are not men. The only mode usually recognized

of converting a particular negative proposition, is in the form, Some A is

not B, therefore something which is not B is A; and this is termed

conversion by contraposition. In this case, however, the predicate and

subject are not merely reversed, but one of them is changed. Instead of

[A] and [B], the terms of the new proposition are [a thing which is not

B], and [A]. The original proposition, Some A _is not_ B, is first changed

into a proposition equipollent with it, Some A _is_ “a thing which is not

B;” and the proposition, being now no longer a particular negative, but a

particular affirmative, admits of conversion in the first mode, or as it

is called, _simple_ conversion.(48)

In all these cases there is not really any inference; there is in the

conclusion no new truth, nothing but what was already asserted in the

premises, and obvious to whoever apprehends them. The fact asserted in the

conclusion is either the very same fact, or part of the fact, asserted in

the original proposition. This follows from our previous analysis of the

Import of Propositions. When we say, for example, that some lawful

sovereigns are tyrants, what is the meaning of the assertion? That the

attributes connoted by the term “lawful sovereign,” and the attributes

connoted by the term “tyrant,” sometimes co-exist in the same individual.

Now this is also precisely what we mean, when we say that some tyrants are

lawful sovereigns; which, therefore, is not a second proposition inferred

from the first, any more than the English translation of Euclid’s Elements

is a collection of theorems different from and consequences of, those

contained in the Greek original. Again, if we assert that no great general

is a rash man, we mean that the attributes connoted by “great general,”

and those connoted by “rash,” never co-exist in the same subject; which is

also the exact meaning which would be expressed by saying, that no rash

man is a great general. When we say that all quadrupeds are warm-blooded,

we assert, not only that the attributes connoted by “quadruped” and those

connoted by “warm-blooded” sometimes co-exist, but that the former never

exist without the latter: now the proposition, Some warm-blooded creatures

are quadrupeds, expresses the first half of this meaning, dropping the

latter half; and therefore has been already affirmed in the antecedent

proposition, All quadrupeds are warm-blooded. But that _all_ warm-blooded

creatures are quadrupeds, or, in other words, that the attributes connoted

by “warm-blooded” never exist without those connoted by “quadruped,” has

not been asserted, and can not be inferred. In order to re-assert, in an

inverted form, the whole of what was affirmed in the proposition, All

quadrupeds are warm-blooded, we must convert it by contraposition, thus,

Nothing which is not warm-blooded is a quadruped. This proposition, and

the one from which it is derived, are exactly equivalent, and either of

them may be substituted for the other; for, to say that when the

attributes of a quadruped are present, those of a warm-blooded creature

are present, is to say that when the latter are absent the former are

absent.

In a manual for young students, it would be proper to dwell at greater

length on the conversion and equipollency of propositions. For though that

can not be called reasoning or inference which is a mere re-assertion in

different words of what had been asserted before, there is no more

important intellectual habit, nor any the cultivation of which falls more

strictly within the province of the art of logic, than that of discerning

rapidly and surely the identity of an assertion when disguised under

diversity of language. That important chapter in logical treatises which

relates to the Opposition of Propositions, and the excellent technical

language which logic provides for distinguishing the different kinds or

modes of opposition, are of use chiefly for this purpose. Such

considerations as these, that contrary propositions may both be false, but

can not both be true; that subcontrary propositions may both be true, but

can not both be false; that of two contradictory propositions one must be

true and the other false; that of two subalternate propositions the truth

of the universal proves the truth of the particular, and the falsity of

the particular proves the falsity of the universal, but not _vicè

versa_;(49) are apt to appear, at first sight, very technical and

mysterious, but when explained, seem almost too obvious to require so

formal a statement, since the same amount of explanation which is

necessary to make the principles intelligible, would enable the truths

which they convey to be apprehended in any particular case which can

occur. In this respect, however, these axioms of logic are on a level with

those of mathematics. That things which are equal to the same thing are

equal to one another, is as obvious in any particular case as it is in the

general statement: and if no such general maxim had ever been laid down,

the demonstrations in Euclid would never have halted for any difficulty in

stepping across the gap which this axiom at present serves to bridge over.

Yet no one has ever censured writers on geometry, for placing a list of

these elementary generalizations at the head of their treatises, as a

first exercise to the learner of the faculty which will be required in him

at every step, that of apprehending a _general_ truth. And the student of

logic, in the discussion even of such truths as we have cited above,

acquires habits of circumspect interpretation of words, and of exactly

measuring the length and breadth of his assertions, which are among the

most indispensable conditions of any considerable mental attainment, and

which it is one of the primary objects of logical discipline to cultivate.

§ 3. Having noticed, in order to exclude from the province of Reasoning or

Inference properly so called, the cases in which the progression from one

truth to another is only apparent, the logical consequent being a mere

repetition of the logical antecedent; we now pass to those which are cases

of inference in the proper acceptation of the term, those in which we set

out from known truths, to arrive at others really distinct from them.

Reasoning, in the extended sense in which I use the term, and in which it

is synonymous with Inference, is popularly said to be of two kinds:

reasoning from particulars to generals, and reasoning from generals to

particulars; the former being called Induction, the latter Ratiocination

or Syllogism. It will presently be shown that there is a third species of

reasoning, which falls under neither of these descriptions, and which,

nevertheless, is not only valid, but is the foundation of both the others.

It is necessary to observe, that the expressions, reasoning from

particulars to generals, and reasoning from generals to particulars, are

recommended by brevity rather than by precision, and do not adequately

mark, without the aid of a commentary, the distinction between Induction

(in the sense now adverted to) and Ratiocination. The meaning intended by

these expressions is, that Induction is inferring a proposition from

propositions _less general_ than itself, and Ratiocination is inferring a

proposition from propositions _equally_ or _more_ general. When, from the

observation of a number of individual instances, we ascend to a general

proposition, or when, by combining a number of general propositions, we

conclude from them another proposition still more general, the process,

which is substantially the same in both instances, is called Induction.

When from a general proposition, not alone (for from a single proposition

nothing can be concluded which is not involved in the terms), but by

combining it with other propositions, we infer a proposition of the same

degree of generality with itself, or a less general proposition, or a

proposition merely individual, the process is Ratiocination. When, in

short, the conclusion is more general than the largest of the premises,

the argument is commonly called Induction; when less general, or equally

general, it is Ratiocination.

As all experience begins with individual cases, and proceeds from them to

generals, it might seem most conformable to the natural order of thought

that Induction should be treated of before we touch upon Ratiocination. It

will, however, be advantageous, in a science which aims at tracing our

acquired knowledge to its sources, that the inquirer should commence with

the latter rather than with the earlier stages of the process of

constructing our knowledge; and should trace derivative truths backward to

the truths from which they are deduced, and on which they depend for their

evidence, before attempting to point out the original spring from which

both ultimately take their rise. The advantages of this order of

proceeding in the present instance will manifest themselves as we advance,

in a manner superseding the necessity of any further justification or

explanation.

Of Induction, therefore, we shall say no more at present, than that it at

least is, without doubt, a process of real inference. The conclusion in an

induction embraces more than is contained in the premises. The principle

or law collected from particular instances, the general proposition in

which we embody the result of our experience, covers a much larger extent

of ground than the individual experiments which form its basis. A

principle ascertained by experience, is more than a mere summing up of

what has been specifically observed in the individual cases which have

been examined; it is a generalization grounded on those cases, and

expressive of our belief, that what we there found true is true in an

indefinite number of cases which we have not examined, and are never

likely to examine. The nature and grounds of this inference, and the

conditions necessary to make it legitimate, will be the subject of

discussion in the Third Book: but that such inference really takes place

is not susceptible of question. In every induction we proceed from truths

which we knew, to truths which we did not know; from facts certified by

observation, to facts which we have not observed, and even to facts not

capable of being now observed; future facts, for example; but which we do

not hesitate to believe on the sole evidence of the induction itself.

Induction, then, is a real process of Reasoning or Inference. Whether, and

in what sense, as much can be said of the Syllogism, remains to be

determined by the examination into which we are about to enter.

Chapter II.

Of Ratiocination, Or Syllogism.

§ 1. The analysis of the Syllogism has been so accurately and fully

performed in the common manuals of Logic, that in the present work, which

is not designed as a manual, it is sufficient to recapitulate, _memoriæ

causâ_, the leading results of that analysis, as a foundation for the

remarks to be afterward made on the functions of the Syllogism, and the

place which it holds in science.

To a legitimate syllogism it is essential that there should be three, and

no more than three, propositions, namely, the conclusion, or proposition

to be proved, and two other propositions which together prove it, and

which are called the premises. It is essential that there should be three,

and no more than three, terms, namely, the subject and predicate of the

conclusion, and another called the middle term, which must be found in

both premises, since it is by means of it that the other two terms are to

be connected together. The predicate of the conclusion is called the major

term of the syllogism; the subject of the conclusion is called the minor

term. As there can be but three terms, the major and minor terms must each

be found in one, and only one, of the premises, together with the middle

term which is in them both. The premise which contains the middle term and

the major term is called the major premise; that which contains the middle

term and the minor term is called the minor premise.

Syllogisms are divided by some logicians into three _figures_, by others

into four, according to the position of the middle term, which may either

be the subject in both premises, the predicate in both, or the subject in

one and the predicate in the other. The most common case is that in which

the middle term is the subject of the major premise and the predicate of

the minor. This is reckoned as the first figure. When the middle term is

the predicate in both premises, the syllogism belongs to the second

figure; when it is the subject in both, to the third. In the fourth figure

the middle term is the subject of the minor premise and the predicate of

the major. Those writers who reckon no more than three figures, include

this case in the first.

Each figure is divided into _moods_, according to what are called the

_quantity_ and _quality_ of the propositions, that is, according as they

are universal or particular, affirmative or negative. The following are

examples of all the legitimate moods, that is, all those in which the

conclusion correctly follows from the premises. A is the minor term, C the

major, B the middle term.

FIRST FIGURE.

All B is C No B is C All B is C No B is C

All A is B All A is B Some A is B Some A is B

therefore therefore therefore therefore

All A is C No A is C Some A is C Some A is not C

SECOND FIGURE.

No C is B All C is B No C is B All C is B

All A is B No A is B Some A is B Some A is not B

therefore therefore therefore therefore

No A is C No A is C Some A is not C Some A is not C

THIRD FIGURE.

All B is No B is C Some B is All B is Some B is No B is C

C C C not C

All B is All B is All B is Some B is All B is Some B is

A A A A A A

therefore therefore therefore therefore therefore therefore

Some A is Some A is Some A is Some A is Some A is Some A is

C not C C C not C not C

FOURTH FIGURE.

All C is B All C is B Some C is B No C is B No C is B

All B is A No B is A All B is A All B is A Some B is A

therefore therefore therefore therefore therefore

Some A is C Some A is Some A is C Some A is Some A is

not C not C not C

In these exemplars, or blank forms for making syllogisms, no place is

assigned to _singular_ propositions; not, of course, because such

propositions are not used in ratiocination, but because, their predicate

being affirmed or denied of the whole of the subject, they are ranked, for

the purposes of the syllogism, with universal propositions. Thus, these

two syllogisms—

All men are mortal, All men are mortal,

All kings are men, Socrates is a man,

therefore therefore

All kings are mortal, Socrates is mortal,

are arguments precisely similar, and are both ranked in the first mood of

the first figure.(50)

The reasons why syllogisms in any of the above forms are legitimate, that

is, why, if the premises are true, the conclusion must inevitably be so,

and why this is not the case in any other possible mood (that is, in any

other combination of universal and particular, affirmative and negative

propositions), any person taking interest in these inquiries may be

presumed to have either learned from the common-school books of the

syllogistic logic, or to be capable of discovering for himself. The reader

may, however, be referred, for every needful explanation, to Archbishop

Whately’s _Elements of Logic_, where he will find stated with

philosophical precision, and explained with remarkable perspicuity, the

whole of the common doctrine of the syllogism.

All valid ratiocination; all reasoning by which, from general propositions

previously admitted, other propositions equally or less general are

inferred; may be exhibited in some of the above forms. The whole of

Euclid, for example, might be thrown without difficulty into a series of

syllogisms, regular in mood and figure.

Though a syllogism framed according to any of these formulæ is a valid

argument, all correct ratiocination admits of being stated in syllogisms

of the first figure alone. The rules for throwing an argument in any of

the other figures into the first figure, are called rules for the

_reduction_ of syllogisms. It is done by the _conversion_ of one or other,

or both, of the premises. Thus an argument in the first mood of the second

figure, as—

No C is B

All A is B

therefore

No A is C,

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

negative, admits of simple conversion, and may be changed into No B is C,

which, as we showed, is the very same assertion in other words—the same

fact differently expressed. This transformation having been effected, the

argument assumes the following form:

No B is C

All A is B

therefore

No A is C,

which is a good syllogism in the second mood of the first figure. Again,

an argument in the first mood of the third figure must resemble the

following:

All B is C

All B is A

therefore

Some A is C,

where the minor premise, All B is A, conformably to what was laid down in

the last chapter respecting universal affirmatives, does not admit of

simple conversion, but may be converted _per accidens_, thus, Some A is B;

which, though it does not express the whole of what is asserted in the

proposition All B is A, expresses, as was formerly shown, part of it, and

must therefore be true if the whole is true. We have, then, as the result

of the reduction, the following syllogism in the third mood of the first

figure:

All B is C

Some A is B,

from which it obviously follows, that

Some A is C.

In the same manner, or in a manner on which after these examples it is not

necessary to enlarge, every mood of the second, third, and fourth figures

may be reduced to some one of the four moods of the first. In other words,

every conclusion which can be proved in any of the last three figures, may

be proved in the first figure from the same premises, with a slight

alteration in the mere manner of expressing them. Every valid

ratiocination, therefore, may be stated in the first figure, that is, in

one of the following forms:

Every B is C No B is C

All A is B, All A is B,

Some A is B, Some A is B,

therefore therefore

All A is C. No A is C.

Some A is C. Some A is not C.

Or, if more significant symbols are preferred:

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

form:

All animals are mortal;

All men/Some men/Socrates are animals;

therefore

All men/Some men/Socrates are mortal.

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

this form:

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

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

All negroes/Some negroes/Mr. A’s negro are capable of self-control;

therefore

No negroes are/Some negroes are not/Mr. A’s negro is not necessarily

vicious.

Though all ratiocination admits of being thrown into one or the other of

these forms, and sometimes gains considerably by the transformation, both

in clearness and in the obviousness of its consequence; there are, no

doubt, cases in which the argument falls more naturally into one of the

other three figures, and in which its conclusiveness is more apparent at

the first glance in those figures, than when reduced to the first. Thus,

if the proposition were that pagans may be virtuous, and the evidence to

prove it were the example of Aristides; a syllogism in the third figure,

Aristides was virtuous,

Aristides was a pagan,

therefore

Some pagan was virtuous,

would be a more natural mode of stating the argument, and would carry

conviction more instantly home, than the same ratiocination strained into

the first figure, thus—

Aristides was virtuous,

Some pagan was Aristides,

therefore

Some pagan was virtuous.

A German philosopher, Lambert, whose _Neues Organon_ (published in the

year 1764) contains among other things one of the most elaborate and

complete expositions which had ever been made of the syllogistic doctrine,

has expressly examined what sort of arguments fall most naturally and

suitably into each of the four figures; and his investigation is

characterized by great ingenuity and clearness of thought.(51) The

argument, however, is one and the same, in whichever figure it is

expressed; since, as we have already seen, the premises of a syllogism in

the second, third, or fourth figure, and those of the syllogism in the

first figure to which it may be reduced, are the same premises in every

thing except language, or, at least, as much of them as contributes to the

proof of the conclusion is the same. We are therefore at liberty, in

conformity with the general opinion of logicians, to consider the two

elementary forms of the first figure as the universal types of all correct

ratiocination; the one, when the conclusion to be proved is affirmative,

the other, when it is negative; even though certain arguments may have a

tendency to clothe themselves in the forms of the second, third, and

fourth figures; which, however, can not possibly happen with the only

class of arguments which are of first-rate scientific importance, those in

which the conclusion is a universal affirmative, such conclusions being

susceptible of proof in the first figure alone.(52)

§ 2. On examining, then, these two general formulæ, we find that in both

of them, one premise, the major, is a universal proposition; and according

as this is affirmative or negative, the conclusion is so too. All

ratiocination, therefore, starts from a _general_ proposition, principle,

or assumption: a proposition in which a predicate is affirmed or denied of

an entire class; that is, in which some attribute, or the negation of some

attribute, is asserted of an indefinite number of objects distinguished by

a common characteristic, and designated, in consequence, by a common name.

The other premise is always affirmative, and asserts that something (which

may be either an individual, a class, or part of a class) belongs to, or

is included in, the class respecting which something was affirmed or

denied in the major premise. It follows that the attribute affirmed or

denied of the entire class may (if that affirmation or denial was correct)

be affirmed or denied of the object or objects alleged to be included in

the class: and this is precisely the assertion made in the conclusion.

Whether or not the foregoing is an adequate account of the constituent

parts of the syllogism, will be presently considered; but as far as it

goes it is a true account. It has accordingly been generalized, and

erected into a logical maxim, on which all ratiocination is said to be

founded, insomuch that to reason, and to apply the maxim, are supposed to

be one and the same thing. The maxim is, That whatever can be affirmed (or

denied) of a class, may be affirmed (or denied) of every thing included in

the class. This axiom, supposed to be the basis of the syllogistic theory,

is termed by logicians the _dictum de omni et nullo_.

This maxim, however, when considered as a principle of reasoning, appears

suited to a system of metaphysics once indeed generally received, but

which for the last two centuries has been considered as finally abandoned,

though there have not been wanting in our own day attempts at its revival.

So long as what are termed Universals were regarded as a peculiar kind of

substances, having an objective existence distinct from the individual

objects classed under them, the _dictum de omni_ conveyed an important

meaning; because it expressed the intercommunity of nature, which it was

necessary on that theory that we should suppose to exist between those

general substances and the particular substances which were subordinated

to them. That every thing predicable of the universal was predicable of

the various individuals contained under it, was then no identical

proposition, but a statement of what was conceived as a fundamental law of

the universe. The assertion that the entire nature and properties of the

_substantia secunda_ formed part of the nature and properties of each of

the individual substances called by the same name; that the properties of

Man, for example, were properties of all men; was a proposition of real

significance when man did not _mean_ all men, but something inherent in

men, and vastly superior to them in dignity. Now, however, when it is

known that a class, a universal, a genus or species, is not an entity _per

se_, but neither more nor less than the individual substances themselves

which are placed in the class, and that there is nothing real in the

matter except those objects, a common name given to them, and common

attributes indicated by the name; what, I should be glad to know, do we

learn by being told, that whatever can be affirmed of a class, may be

affirmed of every object contained in the class? The class _is_ nothing

but the objects contained in it: and the _dictum de omni_ merely amounts

to the identical proposition, that whatever is true of certain objects, is

true of each of those objects. If all ratiocination were no more than the

application of this maxim to particular cases, the syllogism would indeed

be, what it has so often been declared to be, solemn trifling. The _dictum

de omni_ is on a par with another truth, which in its time was also

reckoned of great importance, “Whatever is, is.” To give any real meaning

to the _dictum de omni_, we must consider it not as an axiom, but as a

definition; we must look upon it as intended to explain, in a circuitous

and paraphrastic manner, the meaning of the word _class_.

An error which seemed finally refuted and dislodged from thought, often

needs only put on a new suit of phrases, to be welcomed back to its old

quarters, and allowed to repose unquestioned for another cycle of ages.

Modern philosophers have not been sparing in their contempt for the

scholastic dogma that genera and species are a peculiar kind of

substances, which general substances being the only permanent things,

while the individual substances comprehended under them are in a perpetual

flux, knowledge, which necessarily imports stability, can only have

relation to those general substances or universals, and not to the facts

or particulars included under them. Yet, though nominally rejected, this

very doctrine, whether disguised under the Abstract Ideas of Locke (whose

speculations, however, it has less vitiated than those of perhaps any

other writer who has been infected with it), under the ultra-nominalism of

Hobbes and Condillac, or the ontology of the later German schools, has

never ceased to poison philosophy. Once accustomed to consider scientific

investigation as essentially consisting in the study of universals, men

did not drop this habit of thought when they ceased to regard universals

as possessing an independent existence: and even those who went the length

of considering them as mere names, could not free themselves from the

notion that the investigation of truth consisted entirely or partly in

some kind of conjuration or juggle with those names. When a philosopher

adopted fully the Nominalist view of the signification of general

language, retaining along with it the _dictum de omni_ as the foundation

of all reasoning, two such premises fairly put together were likely, if he

was a consistent thinker, to land him in rather startling conclusions.

Accordingly it has been seriously held, by writers of deserved celebrity,

that the process of arriving at new truths by reasoning consists in the

mere substitution of one set of arbitrary signs for another; a doctrine

which they suppose to derive irresistible confirmation from the example of

algebra. If there were any process in sorcery or necromancy more

preternatural than this, I should be much surprised. The culminating point

of this philosophy is the noted aphorism of Condillac, that a science is

nothing, or scarcely any thing, but _une langue bien faite_; in other

words, that the one sufficient rule for discovering the nature and

properties of objects is to name them properly: as if the reverse were not

the truth, that it is impossible to name them properly except in

proportion as we are already acquainted with their nature and properties.

Can it be necessary to say, that none, not even the most trivial knowledge

with respect to Things, ever was or could be originally got at by any

conceivable manipulation of mere names, as such; and that what can be

learned from names, is only what somebody who used the names knew before?

Philosophical analysis confirms the indication of common sense, that the

function of names is but that of enabling us to _remember_ and to

_communicate_ our thoughts. That they also strengthen, even to an

incalculable extent, the power of thought itself, is most true: but they

do this by no intrinsic and peculiar virtue; they do it by the power

inherent in an artificial memory, an instrument of which few have

adequately considered the immense potency. As an artificial memory,

language truly is, what it has so often been called, an instrument of

thought; but it is one thing to be the instrument, and another to be the

exclusive subject upon which the instrument is exercised. We think,

indeed, to a considerable extent, by means of names, but what we think of,

are the things called by those names; and there can not be a greater error

than to imagine that thought can be carried on with nothing in our mind

but names, or that we can make the names think for us.

§ 3. Those who considered the _dictum de omni_ as the foundation of the

syllogism, looked upon arguments in a manner corresponding to the

erroneous view which Hobbes took of propositions. Because there are some

propositions which are merely verbal, Hobbes, in order apparently that his

definition might be rigorously universal, defined a proposition as if no

propositions declared any thing except the meaning of words. If Hobbes was

right; if no further account than this could be given of the import of

propositions; no theory could be given but the commonly received one, of

the combination of propositions in a syllogism. If the minor premise

asserted nothing more than that something belongs to a class, and if the

major premise asserted nothing of that class except that it is included in

another class, the conclusion would only be that what was included in the

lower class is included in the higher, and the result, therefore, nothing

except that the classification is consistent with itself. But we have seen

that it is no sufficient account of the meaning of a proposition, to say

that it refers something to, or excludes something from, a class. Every

proposition which conveys real information asserts a matter of fact,

dependent on the laws of nature, and not on classification. It asserts

that a given object does or does not possess a given attribute; or it

asserts that two attributes, or sets of attributes, do or do not

(constantly or occasionally) co-exist. Since such is the purport of all

propositions which convey any real knowledge, and since ratiocination is a

mode of acquiring real knowledge, any theory of ratiocination which does

not recognize this import of propositions, can not, we may be sure, be the

true one.

Applying this view of propositions to the two premises of a syllogism, we

obtain the following results. The major premise, which, as already

remarked, is always universal, asserts, that all things which have a

certain attribute (or attributes) have or have not along with it, a

certain other attribute (or attributes). The minor premise asserts that

the thing or set of things which are the subject of that premise, have the

first-mentioned attribute; and the conclusion is, that they have (or that

they have not), the second. Thus in our former example,

All men are mortal,

Socrates is a man,

therefore

Socrates is mortal,

the subject and predicate of the major premise are connotative terms,

denoting objects and connoting attributes. The assertion in the major

premise is, that along with one of the two sets of attributes, we always

find the other: that the attributes connoted by “man” never exist unless

conjoined with the attribute called mortality. The assertion in the minor

premise is that the individual named Socrates possesses the former

attributes; and it is concluded that he possesses also the attribute

mortality. Or, if both the premises are general propositions, as

All men are mortal,

All kings are men,

therefore

All kings are mortal,

the minor premise asserts that the attributes denoted by kingship only

exist in conjunction with those signified by the word man. The major

asserts as before, that the last-mentioned attributes are never found

without the attribute of mortality. The conclusion is, that wherever the

attributes of kingship are found, that of mortality is found also.

If the major premise were negative, as, No men are omnipotent, it would

assert, not that the attributes connoted by “man” never exist without, but

that they never exist with, those connoted by “omnipotent:” from which,

together with the minor premise, it is concluded, that the same

incompatibility exists between the attribute omnipotence and those

constituting a king. In a similar manner we might analyze any other

example of the syllogism.

If we generalize this process, and look out for the principle or law

involved in every such inference, and presupposed in every syllogism, the

propositions of which are any thing more than merely verbal; we find, not

the unmeaning _dictum de omni et nullo_, but a fundamental principle, or

rather two principles, strikingly resembling the axioms of mathematics.

The first, which is the principle of affirmative syllogisms, is, that

things which co-exist with the same thing, co-exist with one another: or

(still more precisely) a thing which co-exists with another thing, which

other co-exists with a third thing, also co-exists with that third thing.

The second is the principle of negative syllogisms, and is to this effect:

that a thing which co-exists with another thing, with which other a third

thing does not co-exist, is not co-existent with that third thing. These

axioms manifestly relate to facts, and not to conventions; and one or

other of them is the ground of the legitimacy of every argument in which

facts and not conventions are the matter treated of.(53)

§ 4. It remains to translate this exposition of the syllogism from the one

into the other of the two languages in which we formerly remarked(54) that

all propositions, and of course therefore all combinations of

propositions, might be expressed. We observed that a proposition might be

considered in two different lights; as a portion of our knowledge of

nature, or as a memorandum for our guidance. Under the former, or

speculative aspect, an affirmative general proposition is an assertion of

a speculative truth, viz., that whatever has a certain attribute has a

certain other attribute. Under the other aspect, it is to be regarded not

as a part of our knowledge, but as an aid for our practical exigencies, by

enabling us, when we see or learn that an object possesses one of the two

attributes, to infer that it possesses the other; thus employing the first

attribute as a mark or evidence of the second. Thus regarded, every

syllogism comes within the following general formula:

Attribute A is a mark of attribute B,

The given object has the mark A,

therefore

The given object has the attribute B.

Referred to this type, the arguments which we have lately cited as

specimens of the syllogism, will express themselves in the following

manner:

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

Socrates has the attributes of man,

therefore

Socrates has the attribute mortality.

And again,

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

The attributes of a king are a mark of the attributes of man,

therefore

The attributes of a king are a mark of the attribute mortality.

And, lastly,

The attributes of man are a mark of the absence of the attribute

omnipotence,

The attributes of a king are a mark of the attributes of man,

therefore

The attributes of a king are a mark of the absence of the attribute

signified by the word omnipotent (or, are evidence of the absence of that

attribute).

To correspond with this alteration in the form of the syllogisms, the

axioms on which the syllogistic process is founded must undergo a

corresponding transformation. In this altered phraseology, both those

axioms may be brought under one general expression; namely, that whatever

has any mark, has that which it is a mark of. Or, when the minor premise

as well as the major is universal, we may state it thus: Whatever is a

mark of any mark, is a mark of that which this last is a mark of. To trace

the identity of these axioms with those previously laid down, may be left

to the intelligent reader. We shall find, as we proceed, the great

convenience of the phraseology into which we have last thrown them, and

which is better adapted than any I am acquainted with, to express with

precision and force what is aimed at, and actually accomplished, in every

case of the ascertainment of a truth by ratiocination.(55)

Chapter III.

Of The Functions And Logical Value Of The Syllogism.

§ 1. We have shown what is the real nature of the truths with which the

Syllogism is conversant, in contradistinction to the more superficial

manner in which their import is conceived in the common theory; and what

are the fundamental axioms on which its probative force or conclusiveness

depends. We have now to inquire, whether the syllogistic process, that of

reasoning from generals to particulars, is, or is not, a process of

inference; a progress from the known to the unknown: a means of coming to

a knowledge of something which we did not know before.

Logicians have been remarkably unanimous in their mode of answering this

question. It is universally allowed that a syllogism is vicious if there

be any thing more in the conclusion than was assumed in the premises. But

this is, in fact, to say, that nothing ever was, or can be, proved by

syllogism, which was not known, or assumed to be known, before. Is

ratiocination, then, not a process of inference? And is the syllogism, to

which the word reasoning has so often been represented to be exclusively

appropriate, not really entitled to be called reasoning at all? This seems

an inevitable consequence of the doctrine, admitted by all writers on the

subject, that a syllogism can prove no more than is involved in the

premises. Yet the acknowledgment so explicitly made, has not prevented one

set of writers from continuing to represent the syllogism as the correct

analysis of what the mind actually performs in discovering and proving the

larger half of the truths, whether of science or of daily life, which we

believe; while those who have avoided this inconsistency, and followed out

the general theorem respecting the logical value of the syllogism to its

legitimate corollary, have been led to impute uselessness and frivolity to

the syllogistic theory itself, on the ground of the _petitio principii_

which they allege to be inherent in every syllogism. As I believe both

these opinions to be fundamentally erroneous, I must request the attention

of the reader to certain considerations, without which any just

appreciation of the true character of the syllogism, and the functions it

performs in philosophy, appears to me impossible; but which seem to have

been either overlooked, or insufficiently adverted to, both by the

defenders of the syllogistic theory and by its assailants.

§ 2. It must be granted that in every syllogism, considered as an argument

to prove the conclusion, there is a _petitio principii_. When we say,

All men are mortal,

Socrates is a man,

therefore

Socrates is mortal;

it is unanswerably urged by the adversaries of the syllogistic theory,

that the proposition, Socrates is mortal, is presupposed in the more

general assumption, All men are mortal: that we can not be assured of the

mortality of all men, unless we are already certain of the mortality of

every individual man: that if it be still doubtful whether Socrates, or

any other individual we choose to name, be mortal or not, the same degree

of uncertainty must hang over the assertion, All men are mortal: that the

general principle, instead of being given as evidence of the particular

case, can not itself be taken for true without exception, until every

shadow of doubt which could affect any case comprised with it, is

dispelled by evidence _aliundè_; and then what remains for the syllogism

to prove? That, in short, no reasoning from generals to particulars can,

as such, prove any thing: since from a general principle we can not infer

any particulars, but those which the principle itself assumes as known.

This doctrine appears to me irrefragable; and if logicians, though unable

to dispute it, have usually exhibited a strong disposition to explain it

away, this was not because they could discover any flaw in the argument

itself, but because the contrary opinion seemed to rest on arguments

equally indisputable. In the syllogism last referred to, for example, or

in any of those which we previously constructed, is it not evident that

the conclusion may, to the person to whom the syllogism is presented, be

actually and _bona fide_ a new truth? Is it not matter of daily experience

that truths previously unthought of, facts which have not been, and can

not be, directly observed, are arrived at by way of general reasoning? We

believe that the Duke of Wellington is mortal. We do not know this by

direct observation, so long as he is not yet dead. If we were asked how,

this being the case, we know the duke to be mortal, we should probably

answer, Because all men are so. Here, therefore, we arrive at the

knowledge of a truth not (as yet) susceptible of observation, by a

reasoning which admits of being exhibited in the following syllogism:

All men are mortal,

The Duke of Wellington is a man,

therefore

The Duke of Wellington is mortal.

And since a large portion of our knowledge is thus acquired, logicians

have persisted in representing the syllogism as a process of inference or

proof; though none of them has cleared up the difficulty which arises from

the inconsistency between that assertion, and the principle, that if there

be any thing in the conclusion which was not already asserted in the

premises, the argument is vicious. For it is impossible to attach any

serious scientific value to such a mere salvo, as the distinction drawn

between being involved _by implication_ in the premises, and being

directly asserted in them. When Archbishop Whately says(56) that the

object of reasoning is “merely to expand and unfold the assertions wrapped

up, as it were, and implied in those with which we set out, and to bring a

person to perceive and acknowledge the full force of that which he has

admitted,” he does not, I think, meet the real difficulty requiring to be

explained, namely, how it happens that a science, like geometry, _can_ be

all “wrapped up” in a few definitions and axioms. Nor does this defense of

the syllogism differ much from what its assailants urge against it as an

accusation, when they charge it with being of no use except to those who

seek to press the consequences of an admission into which a person has

been entrapped without having considered and understood its full force.

When you admitted the major premise, you asserted the conclusion; but,

says Archbishop Whately, you asserted it by implication merely: this,

however, can here only mean that you asserted it unconsciously; that you

did not know you were asserting it; but, if so, the difficulty revives in

this shape—Ought you not to have known? Were you warranted in asserting

the general proposition without having satisfied yourself of the truth of

every thing which it fairly includes? And if not, is not the syllogistic

art _prima facie_ what its assailants affirm it to be, a contrivance for

catching you in a trap, and holding you fast in it?(57)

§ 3. From this difficulty there appears to be but one issue. The

proposition that the Duke of Wellington is mortal, is evidently an

inference; it is got at as a conclusion from something else; but do we, in

reality, conclude it from the proposition, All men are mortal? I answer,

no.

The error committed is, I conceive, that of overlooking the distinction

between two parts of the process of philosophizing, the inferring part,

and the registering part; and ascribing to the latter the functions of the

former. The mistake is that of referring a person to his own notes for the

origin of his knowledge. If a person is asked a question, and is at the

moment unable to answer it, he may refresh his memory by turning to a

memorandum which he carries about with him. But if he were asked, how the

fact came to his knowledge, he would scarcely answer, because it was set

down in his note-book: unless the book was written, like the Koran, with a

quill from the wing of the angel Gabriel.

Assuming that the proposition, The Duke of Wellington is mortal, is

immediately an inference from the proposition, All men are mortal; whence

do we derive our knowledge of that general truth? Of course from

observation. Now, all which man can observe are individual cases. From

these all general truths must be drawn, and into these they may be again

resolved; for a general truth is but an aggregate of particular truths; a

comprehensive expression, by which an indefinite number of individual

facts are affirmed or denied at once. But a general proposition is not

merely a compendious form for recording and preserving in the memory a

number of particular facts, all of which have been observed.

Generalization is not a process of mere naming, it is also a process of

inference. From instances which we have observed, we feel warranted in

concluding, that what we found true in those instances, holds in all

similar ones, past, present, and future, however numerous they may be. We

then, by that valuable contrivance of language which enables us to speak

of many as if they were one, record all that we have observed, together

with all that we infer from our observations, in one concise expression;

and have thus only one proposition, instead of an endless number, to

remember or to communicate. The results of many observations and

inferences, and instructions for making innumerable inferences in

unforeseen cases, are compressed into one short sentence.

When, therefore, we conclude from the death of John and Thomas, and every

other person we ever heard of in whose case the experiment had been fairly

tried, that the Duke of Wellington is mortal like the rest; we may,

indeed, pass through the generalization, All men are mortal, as an

intermediate stage; but it is not in the latter half of the process, the

descent from all men to the Duke of Wellington, that the _inference_

resides. The inference is finished when we have asserted that all men are

mortal. What remains to be performed afterward is merely deciphering our

own notes.

Archbishop Whately has contended that syllogizing, or reasoning from

generals to particulars, is not, agreeably to the vulgar idea, a peculiar

_mode_ of reasoning, but the philosophical analysis of _the_ mode in which

all men reason, and must do so if they reason at all. With the deference

due to so high an authority, I can not help thinking that the vulgar

notion is, in this case, the more correct. If, from our experience of

John, Thomas, etc., who once were living, but are now dead, we are

entitled to conclude that all human beings are mortal, we might surely

without any logical inconsequence have concluded at once from those

instances, that the Duke of Wellington is mortal. The mortality of John,

Thomas, and others is, after all, the whole evidence we have for the

mortality of the Duke of Wellington. Not one iota is added to the proof by

interpolating a general proposition. Since the individual cases are all

the evidence we can possess, evidence which no logical form into which we

choose to throw it can make greater than it is; and since that evidence is

either sufficient in itself, or, if insufficient for the one purpose, can

not be sufficient for the other; I am unable to see why we should be

forbidden to take the shortest cut from these sufficient premises to the

conclusion, and constrained to travel the “high priori road,” by the

arbitrary fiat of logicians. I can not perceive why it should be

impossible to journey from one place to another unless we “march up a

hill, and then march down again.” It may be the safest road, and there may

be a resting-place at the top of the hill, affording a commanding view of

the surrounding country; but for the mere purpose of arriving at our

journey’s end, our taking that road is perfectly optional; it is a

question of time, trouble, and danger.

Not only _may_ we reason from particulars to particulars without passing

through generals, but we perpetually do so reason. All our earliest

inferences are of this nature. From the first dawn of intelligence we draw

inferences, but years elapse before we learn the use of general language.

The child, who, having burned his fingers, avoids to thrust them again

into the fire, has reasoned or inferred, though he has never thought of

the general maxim, Fire burns. He knows from memory that he has been

burned, and on this evidence believes, when he sees a candle, that if he

puts his finger into the flame of it, he will be burned again. He believes

this in every case which happens to arise; but without looking, in each

instance, beyond the present case. He is not generalizing; he is inferring

a particular from particulars. In the same way, also, brutes reason. There

is no ground for attributing to any of the lower animals the use of signs,

of such a nature as to render general propositions possible. But those

animals profit by experience, and avoid what they have found to cause them

pain, in the same manner, though not always with the same skill, as a

human creature. Not only the burned child, but the burned dog, dreads the

fire.

I believe that, in point of fact, when drawing inferences from our

personal experience, and not from maxims handed down to us by books or

tradition, we much oftener conclude from particulars to particulars

directly, than through the intermediate agency of any general proposition.

We are constantly reasoning from ourselves to other people, or from one

person to another, without giving ourselves the trouble to erect our

observations into general maxims of human or external nature. When we

conclude that some person will, on some given occasion, feel or act so and

so, we sometimes judge from an enlarged consideration of the manner in

which human beings in general, or persons of some particular character,

are accustomed to feel and act; but much oftener from merely recollecting

the feelings and conduct of the same person in some previous instance, or

from considering how we should feel or act ourselves. It is not only the

village matron, who, when called to a consultation upon the case of a

neighbor’s child, pronounces on the evil and its remedy simply on the

recollection and authority of what she accounts the similar case of her

Lucy. We all, where we have no definite maxims to steer by, guide

ourselves in the same way: and if we have an extensive experience, and

retain its impressions strongly, we may acquire in this manner a very

considerable power of accurate judgment, which we may be utterly incapable

of justifying or of communicating to others. Among the higher order of

practical intellects there have been many of whom it was remarked how

admirably they suited their means to their ends, without being able to

give any sufficient reasons for what they did; and applied, or seemed to

apply, recondite principles which they were wholly unable to state. This

is a natural consequence of having a mind stored with appropriate

particulars, and having been long accustomed to reason at once from these

to fresh particulars, without practicing the habit of stating to one’s

self or to others the corresponding general propositions. An old warrior,

on a rapid glance at the outlines of the ground, is able at once to give

the necessary orders for a skillful arrangement of his troops; though if

he has received little theoretical instruction, and has seldom been called

upon to answer to other people for his conduct, he may never have had in

his mind a single general theorem respecting the relation between ground

and array. But his experience of encampments, in circumstances more or

less similar, has left a number of vivid, unexpressed, ungeneralized

analogies in his mind, the most appropriate of which, instantly suggesting

itself, determines him to a judicious arrangement.

The skill of an uneducated person in the use of weapons, or of tools, is

of a precisely similar nature. The savage who executes unerringly the

exact throw which brings down his game, or his enemy, in the manner most

suited to his purpose, under the operation of all the conditions

necessarily involved, the weight and form of the weapon, the direction and

distance of the object, the action of the wind, etc., owes this power to a

long series of previous experiments, the results of which he certainly

never framed into any verbal theorems or rules. The same thing may

generally be said of any other extraordinary manual dexterity. Not long

ago a Scotch manufacturer procured from England, at a high rate of wages,

a working dyer, famous for producing very fine colors, with the view of

teaching to his other workmen the same skill. The workman came; but his

mode of proportioning the ingredients, in which lay the secret of the

effects he produced, was by taking them up in handfuls, while the common

method was to weigh them. The manufacturer sought to make him turn his

handling system into an equivalent weighing system, that the general

principle of his peculiar mode of proceeding might be ascertained. This,

however, the man found himself quite unable to do, and therefore could

impart his skill to nobody. He had, from the individual cases of his own

experience, established a connection in his mind between fine effects of

color, and tactual perceptions in handling his dyeing materials; and from

these perceptions he could, in any particular case, infer the means to be

employed, and the effects which would be produced, but could not put

others in possession of the grounds on which he proceeded, from having

never generalized them in his own mind, or expressed them in language.

Almost every one knows Lord Mansfield’s advice to a man of practical good

sense, who, being appointed governor of a colony, had to preside in its

courts of justice, without previous judicial practice or legal education.

The advice was to give his decision boldly, for it would probably be

right; but never to venture on assigning reasons, for they would almost

infallibly be wrong. In cases like this, which are of no uncommon

occurrence, it would be absurd to suppose that the bad reason was the

source of the good decision. Lord Mansfield knew that if any reason were

assigned it would be necessarily an afterthought, the judge being _in

fact_ guided by impressions from past experience, without the circuitous

process of framing general principles from them, and that if he attempted

to frame any such he would assuredly fail. Lord Mansfield, however, would

not have doubted that a man of equal experience who had also a mind stored

with general propositions derived by legitimate induction from that

experience, would have been greatly preferable as a judge, to one, however

sagacious, who could not be trusted with the explanation and justification

of his own judgments. The cases of men of talent performing wonderful

things they know not how, are examples of the rudest and most spontaneous

form of the operations of superior minds. It is a defect in them, and

often a source of errors, not to have generalized as they went on; but

generalization, though a help, the most important indeed of all helps, is

not an essential.

Even the scientifically instructed, who possess, in the form of general

propositions, a systematic record of the results of the experience of

mankind, need not always revert to those general propositions in order to

apply that experience to a new case. It is justly remarked by Dugald

Stewart, that though the reasonings in mathematics depend entirely on the

axioms, it is by no means necessary to our seeing the conclusiveness of

the proof, that the axioms should be expressly adverted to. When it is

inferred that AB is equal to CD because each of them is equal to EF, the

most uncultivated understanding, as soon as the propositions were

understood, would assent to the inference, without having ever heard of

the general truth that “things which are equal to the same thing are equal

to one another.” This remark of Stewart, consistently followed out, goes

to the root, as I conceive, of the philosophy of ratiocination; and it is

to be regretted that he himself stopped short at a much more limited

application of it. He saw that the general propositions on which a

reasoning is said to depend, may, in certain cases, be altogether omitted,

without impairing its probative force. But he imagined this to be a

peculiarity belonging to axioms; and argued from it, that axioms are not

the foundations or first principles of geometry, from which all the other

truths of the science are synthetically deduced (as the laws of motion and

of the composition of forces in dynamics, the equal mobility of fluids in

hydrostatics, the laws of reflection and refraction in optics, are the

first principles of those sciences); but are merely necessary assumptions,

self-evident indeed, and the denial of which would annihilate all

demonstration, but from which, as premises, nothing can be demonstrated.

In the present, as in many other instances, this thoughtful and elegant

writer has perceived an important truth, but only by halves. Finding, in

the case of geometrical axioms, that general names have not any talismanic

virtue for conjuring new truths out of the well where they lie hid, and

not seeing that this is equally true in every other case of

generalization, he contended that axioms are in their nature barren of

consequences, and that the really fruitful truths, the real first

principles of geometry, are the definitions; that the definition, for

example, of the circle is to the properties of the circle, what the laws

of equilibrium and of the pressure of the atmosphere are to the rise of

the mercury in the Torricellian tube. Yet all that he had asserted

respecting the function to which the axioms are confined in the

demonstrations of geometry, holds equally true of the definitions. Every

demonstration in Euclid might be carried on without them. This is apparent

from the ordinary process of proving a proposition of geometry by means of

a diagram. What assumption, in fact, do we set out from, to demonstrate by

a diagram any of the properties of the circle? Not that in all circles the

radii are equal, but only that they are so in the circle ABC. As our

warrant for assuming this, we appeal, it is true, to the definition of a

circle in general; but it is only necessary that the assumption be granted

in the case of the particular circle supposed. From this, which is not a

general but a singular proposition, combined with other propositions of a

similar kind, some of which _when generalized_ are called definitions, and

other axioms, we prove that a certain conclusion is true, not of all

circles, but of the particular circle ABC; or at least would be so, if the

facts precisely accorded with our assumptions. The enunciation, as it is

called, that is, the general theorem which stands at the head of the

demonstration, is not the proposition actually demonstrated. One instance

only is demonstrated: but the process by which this is done, is a process

which, when we consider its nature, we perceive might be exactly copied in

an indefinite number of other instances; in every instance which conforms

to certain conditions. The contrivance of general language furnishing us

with terms which connote these conditions, we are able to assert this

indefinite multitude of truths in a single expression, and this expression

is the general theorem. By dropping the use of diagrams, and substituting,

in the demonstrations, general phrases for the letters of the alphabet, we

might prove the general theorem directly, that is, we might demonstrate

all the cases at once; and to do this we must, of course, employ as our

premises, the axioms and definitions in their general form. But this only

means, that if we can prove an individual conclusion by assuming an

individual fact, then in whatever case we are warranted in making an

exactly similar assumption, we may draw an exactly similar conclusion. The

definition is a sort of notice to ourselves and others, what assumptions

we think ourselves entitled to make. And so in all cases, the general

propositions, whether called definitions, axioms, or laws of nature, which

we lay down at the beginning of our reasonings, are merely abridged

statements, in a kind of short-hand, of the particular facts, which, as

occasion arises, we either think we may proceed on as proved, or intend to

assume. In any one demonstration it is enough if we assume for a

particular case suitably selected, what by the statement of the definition

or principle we announce that we intend to assume in all cases which may

arise. The definition of the circle, therefore, is to one of Euclid’s

demonstrations, exactly what, according to Stewart, the axioms are; that

is, the demonstration does not depend on it, but yet if we deny it the

demonstration fails. The proof does not rest on the general assumption,

but on a similar assumption confined to the particular case: that case,

however, being chosen as a specimen or paradigm of the whole class of

cases included in the theorem, there can be no ground for making the

assumption in that case which does not exist in every other; and to deny

the assumption as a general truth, is to deny the right of making it in

the particular instance.

There are, undoubtedly, the most ample reasons for stating both the

principles and the theorems in their general form, and these will be

explained presently, so far as explanation is requisite. But, that

unpracticed learners, even in making use of one theorem to demonstrate

another, reason rather from particular to particular than from the general

proposition, is manifest from the difficulty they find in applying a

theorem to a case in which the configuration of the diagram is extremely

unlike that of the diagram by which the original theorem was demonstrated.

A difficulty which, except in cases of unusual mental power, long practice

can alone remove, and removes chiefly by rendering us familiar with all

the configurations consistent with the general conditions of the theorem.

§ 4. From the considerations now adduced, the following conclusions seem

to be established. All inference is from particulars to particulars:

General propositions are merely registers of such inferences already made,

and short formulæ for making more: The major premise of a syllogism,

consequently, is a formula of this description: and the conclusion is not

an inference drawn _from_ the formula, but an inference drawn _according_

to the formula: the real logical antecedent, or premise, being the

particular facts from which the general proposition was collected by

induction. Those facts, and the individual instances which supplied them,

may have been forgotten: but a record remains, not indeed descriptive of

the facts themselves, but showing how those cases may be distinguished,

respecting which, the facts, when known, were considered to warrant a

given inference. According to the indications of this record we draw our

conclusion: which is, to all intents and purposes, a conclusion from the

forgotten facts. For this it is essential that we should read the record

correctly: and the rules of the syllogism are a set of precautions to

insure our doing so.

This view of the functions of the syllogism is confirmed by the

consideration of precisely those cases which might be expected to be least

favorable to it, namely, those in which ratiocination is independent of

any previous induction. We have already observed that the syllogism, in

the ordinary course of our reasoning, is only the latter half of the

process of traveling from premises to a conclusion. There are, however,

some peculiar cases in which it is the whole process. Particulars alone

are capable of being subjected to observation; and all knowledge which is

derived from observation, begins, therefore, of necessity, in particulars;

but our knowledge may, in cases of certain descriptions, be conceived as

coming to us from other sources than observation. It may present itself as

coming from testimony, which, on the occasion and for the purpose in hand,

is accepted as of an authoritative character: and the information thus

communicated, may be conceived to comprise not only particular facts but

general propositions, as when a scientific doctrine is accepted without

examination on the authority of writers, or a theological doctrine on that

of Scripture. Or the generalization may not be, in the ordinary sense, an

assertion at all, but a command; a law, not in the philosophical, but in

the moral and political sense of the term: an expression of the desire of

a superior, that we, or any number of other persons, shall conform our

conduct to certain general instructions. So far as this asserts a fact,

namely, a volition of the legislator, that fact is an individual fact, and

the proposition, therefore, is not a general proposition. But the

description therein contained of the conduct which it is the will of the

legislator that his subjects should observe, is general. The proposition

asserts, not that all men _are_ any thing, but that all men _shall_ do

something.

In both these cases the generalities are the original data, and the

particulars are elicited from them by a process which correctly resolves

itself into a series of syllogisms. The real nature, however, of the

supposed deductive process, is evident enough. The only point to be

determined is, whether the authority which declared the general

proposition, intended to include this case in it; and whether the

legislator intended his command to apply to the present case among others,

or not. This is ascertained by examining whether the case possesses the

marks by which, as those authorities have signified, the cases which they

meant to certify or to influence may be known. The object of the inquiry

is to make out the witness’s or the legislator’s intention, through the

indication given by their words. This is a question, as the Germans

express it, of hermeneutics. The operation is not a process of inference,

but a process of interpretation.

In this last phrase we have obtained an expression which appears to me to

characterize, more aptly than any other, the functions of the syllogism in

all cases. When the premises are given by authority, the function of

Reasoning is to ascertain the testimony of a witness, or the will of a

legislator, by interpreting the signs in which the one has intimated his

assertion and the other his command. In like manner, when the premises are

derived from observation, the function of Reasoning is to ascertain what

we (or our predecessors) formerly thought might be inferred from the

observed facts, and to do this by interpreting a memorandum of ours, or of

theirs. The memorandum reminds us, that from evidence, more or less

carefully weighed, it formerly appeared that a certain attribute might be

inferred wherever we perceive a certain mark. The proposition, All men are

mortal (for instance) shows that we have had experience from which we

thought it followed that the attributes connoted by the term man, are a

mark of mortality. But when we conclude that the Duke of Wellington is

mortal, we do not infer this from the memorandum, but from the former

experience. All that we infer from the memorandum is our own previous

belief, (or that of those who transmitted to us the proposition),

concerning the inferences which that former experience would warrant.

This view of the nature of the syllogism renders consistent and

intelligible what otherwise remains obscure and confused in the theory of

Archbishop Whately and other enlightened defenders of the syllogistic

doctrine, respecting the limits to which its functions are confined. They

affirm in as explicit terms as can be used, that the sole office of

general reasoning is to prevent inconsistency in our opinions; to prevent

us from assenting to any thing, the truth of which would contradict

something to which we had previously on good grounds given our assent. And

they tell us, that the sole ground which a syllogism affords for assenting

to the conclusion, is that the supposition of its being false, combined

with the supposition that the premises are true, would lead to a

contradiction in terms. Now this would be but a lame account of the real

grounds which we have for believing the facts which we learn from

reasoning, in contradistinction to observation. The true reason why we

believe that the Duke of Wellington will die, is that his fathers, and our

fathers, and all other persons who were contemporary with them, have died.

Those facts are the real premises of the reasoning. But we are not led to

infer the conclusion from those premises, by the necessity of avoiding any

verbal inconsistency. There is no contradiction in supposing that all

those persons have died, and that the Duke of Wellington may,

notwithstanding, live forever. But there would be a contradiction if we

first, on the ground of those same premises, made a general assertion

including and covering the case of the Duke of Wellington, and then

refused to stand to it in the individual case. There is an inconsistency

to be avoided between the memorandum we make of the inferences which may

be justly drawn in future cases, and the inferences we actually draw in

those cases when they arise. With this view we interpret our own formula,

precisely as a judge interprets a law: in order that we may avoid drawing

any inferences not conformable to our former intention, as a judge avoids

giving any decision not conformable to the legislator’s intention. The

rules for this interpretation are the rules of the syllogism: and its sole

purpose is to maintain consistency between the conclusions we draw in

every particular case, and the previous general directions for drawing

them; whether those general directions were framed by ourselves as the

result of induction, or were received by us from an authority competent to

give them.

§ 5. In the above observations it has, I think, been shown, that, though

there is always a process of reasoning or inference where a syllogism is

used, the syllogism is not a correct analysis of that process of reasoning

or inference; which is, on the contrary (when not a mere inference from

testimony), an inference from particulars to particulars; authorized by a

previous inference from particulars to generals, and substantially the

same with it; of the nature, therefore, of Induction. But while these

conclusions appear to me undeniable, I must yet enter a protest, as strong

as that of Archbishop Whately himself, against the doctrine that the

syllogistic art is useless for the purposes of reasoning. The reasoning

lies in the act of generalization, not in interpreting the record of that

act; but the syllogistic form is an indispensable collateral security for

the correctness of the generalization itself.

It has already been seen, that if we have a collection of particulars

sufficient for grounding an induction, we need not frame a general

proposition; we may reason at once from those particulars to other

particulars. But it is to be remarked withal, that whenever, from a set of

particular cases, we can legitimately draw any inference, we may

legitimately make our inference a general one. If, from observation and

experiment, we can conclude to one new case, so may we to an indefinite

number. If that which has held true in our past experience will therefore

hold in time to come, it will hold not merely in some individual case, but

in all cases of some given description. Every induction, therefore, which

suffices to prove one fact, proves an indefinite multitude of facts: the

experience which justifies a single prediction must be such as will

suffice to bear out a general theorem. This theorem it is extremely

important to ascertain and declare, in its broadest form of generality;

and thus to place before our minds, in its full extent, the whole of what

our evidence must prove if it proves any thing.

This throwing of the whole body of possible inferences from a given set of

particulars, into one general expression, operates as a security for their

being just inferences, in more ways than one. First, the general principle

presents a larger object to the imagination than any of the singular

propositions which it contains. A process of thought which leads to a

comprehensive generality, is felt as of greater importance than one which

terminates in an insulated fact; and the mind is, even unconsciously, led

to bestow greater attention upon the process, and to weigh more carefully

the sufficiency of the experience appealed to, for supporting the

inference grounded upon it. There is another, and a more important,

advantage. In reasoning from a course of individual observations to some

new and unobserved case, which we are but imperfectly acquainted with (or

we should not be inquiring into it), and in which, since we are inquiring

into it, we probably feel a peculiar interest; there is very little to

prevent us from giving way to negligence, or to any bias which may affect

our wishes or our imagination, and, under that influence, accepting

insufficient evidence as sufficient. But if, instead of concluding

straight to the particular case, we place before ourselves an entire class

of facts—the whole contents of a general proposition, every tittle of

which is legitimately inferable from our premises, if that one particular

conclusion is so; there is then a considerable likelihood that if the

premises are insufficient, and the general inference therefore,

groundless, it will comprise within it some fact or facts the reverse of

which we already know to be true; and we shall thus discover the error in

our generalization by a _reductio ad impossibile_.

Thus if, during the reign of Marcus Aurelius, a subject of the Roman

empire, under the bias naturally given to the imagination and expectations

by the lives and characters of the Antonines, had been disposed to expect

that Commodus would be a just ruler; supposing him to stop there, he might

only have been undeceived by sad experience. But if he reflected that this

expectation could not be justifiable unless from the same evidence he was

warranted in concluding some general proposition, as, for instance, that

all Roman emperors are just rulers; he would immediately have thought of

Nero, Domitian, and other instances, which, showing the falsity of the

general conclusion, and therefore the insufficiency of the premises, would

have warned him that those premises could not prove in the instance of

Commodus, what they were inadequate to prove in any collection of cases in

which his was included.

The advantage, in judging whether any controverted inference is

legitimate, of referring to a parallel case, is universally acknowledged.

But by ascending to the general proposition, we bring under our view not

one parallel case only, but all possible parallel cases at once; all cases

to which the same set of evidentiary considerations are applicable.

When, therefore, we argue from a number of known cases to another case

supposed to be analogous, it is always possible, and generally

advantageous, to divert our argument into the circuitous channel of an

induction from those known cases to a general proposition, and a

subsequent application of that general proposition to the unknown case.

This second part of the operation, which, as before observed, is

essentially a process of interpretation, will be resolvable into a

syllogism or a series of syllogisms, the majors of which will be general

propositions embracing whole classes of cases; every one of which

propositions must be true in all its extent, if the argument is

maintainable. If, therefore, any fact fairly coming within the range of

one of these general propositions, and consequently asserted by it, is

known or suspected to be other than the proposition asserts it to be, this

mode of stating the argument causes us to know or to suspect that the

original observations, which are the real grounds of our conclusion, are

not sufficient to support it. And in proportion to the greater chance of

our detecting the inconclusiveness of our evidence, will be the increased

reliance we are entitled to place in it if no such evidence of defect

shall appear.

The value, therefore, of the syllogistic form, and of the rules for using

it correctly, does not consist in their being the form and the rules

according to which our reasonings are necessarily, or even usually, made;

but in their furnishing us with a mode in which those reasonings may

always be represented, and which is admirably calculated, if they are

inconclusive, to bring their inconclusiveness to light. An induction from

particulars to generals, followed by a syllogistic process from those

generals to other particulars, is a form in which we may always state our

reasonings if we please. It is not a form in which we _must_ reason, but

it is a form in which we _may_ reason, and into which it is indispensable

to throw our reasoning, when there is any doubt of its validity: though

when the case is familiar and little complicated, and there is no

suspicion of error, we may, and do, reason at once from the known

particular cases to unknown ones.(58)

These are the uses of syllogism, as a mode of verifying any given

argument. Its ulterior uses, as respects the general course of our

intellectual operations, hardly require illustration, being in fact the

acknowledged uses of general language. They amount substantially to this,

that the inductions may be made once for all: a single careful

interrogation of experience may suffice, and the result may be registered

in the form of a general proposition, which is committed to memory or to

writing, and from which afterward we have only to syllogize. The

particulars of our experiments may then be dismissed from the memory, in

which it would be impossible to retain so great a multitude of details;

while the knowledge which those details afforded for future use, and which

would otherwise be lost as soon as the observations were forgotten, or as

their record became too bulky for reference, is retained in a commodious

and immediately available shape by means of general language.

Against this advantage is to be set the countervailing inconvenience, that

inferences originally made on insufficient evidence become consecrated,

and, as it were, hardened into general maxims; and the mind cleaves to

them from habit, after it has outgrown any liability to be misled by

similar fallacious appearances if they were now for the first time

presented; but having forgotten the particulars, it does not think of

revising its own former decision. An inevitable drawback, which, however

considerable in itself, forms evidently but a small set-off against the

immense benefits of general language.

The use of the syllogism is in truth no other than the use of general

propositions in reasoning. We _can_ reason without them; in simple and

obvious cases we habitually do so; minds of great sagacity can do it in

cases not simple and obvious, provided their experience supplies them with

instances essentially similar to every combination of circumstances likely

to arise. But other minds, and the same minds where they have not the same

pre-eminent advantages of personal experience, are quite helpless without

the aid of general propositions, wherever the case presents the smallest

complication; and if we made no general propositions, few persons would

get much beyond those simple inferences which are drawn by the more

intelligent of the brutes. Though not necessary to reasoning, general

propositions are necessary to any considerable progress in reasoning. It

is, therefore, natural and indispensable to separate the process of

investigation into two parts; and obtain general formulæ for determining

what inferences may be drawn, before the occasion arises for drawing the

inferences. The work of drawing them is then that of applying the formulæ;

and the rules of syllogism are a system of securities for the correctness

of the application.

§ 6. To complete the series of considerations connected with the

philosophical character of the syllogism, it is requisite to consider,

since the syllogism is not the universal type of the reasoning process,

what is the real type. This resolves itself into the question, what is the

nature of the minor premise, and in what manner it contributes to

establish the conclusion: for as to the major, we now fully understand,

that the place which it nominally occupies in our reasonings, properly

belongs to the individual facts or observations of which it expresses the

general result; the major itself being no real part of the argument, but

an intermediate halting-place for the mind, interposed by an artifice of

language between the real premises and the conclusion, by way of a

security, which it is in a most material degree, for the correctness of

the process. The minor, however, being an indispensable part of the

syllogistic expression of an argument, without doubt either is, or

corresponds to, an equally indispensable part of the argument itself, and

we have only to inquire what part.

It is perhaps worth while to notice here a speculation of a philosopher to

whom mental science is much indebted, but who, though a very penetrating,

was a very hasty thinker, and whose want of due circumspection rendered

him fully as remarkable for what he did not see, as for what he saw. I

allude to Dr. Thomas Brown, whose theory of ratiocination is peculiar. He

saw the _petitio principii_ which is inherent in every syllogism, if we

consider the major to be itself the evidence by which the conclusion is

proved, instead of being, what in fact it is, an assertion of the

existence of evidence sufficient to prove any conclusion of a given

description. Seeing this, Dr. Brown not only failed to see the immense

advantage, in point of security for correctness, which is gained by

interposing this step between the real evidence and the conclusion; but he

thought it incumbent on him to strike out the major altogether from the

reasoning process, without substituting any thing else, and maintained

that our reasonings consist only of the minor premise and the conclusion,

Socrates is a man, therefore Socrates is mortal: thus actually

suppressing, as an unnecessary step in the argument, the appeal to former

experience. The absurdity of this was disguised from him by the opinion he

adopted, that reasoning is merely analyzing our own general notions, or

abstract ideas; and that the proposition, Socrates is mortal, is evolved

from the proposition, Socrates is a man, simply by recognizing the notion

of mortality as already contained in the notion we form of a man.

After the explanations so fully entered into on the subject of

propositions, much further discussion can not be necessary to make the

radical error of this view of ratiocination apparent. If the word man

connoted mortality; if the meaning of “mortal” were involved in the

meaning of “man;” we might, undoubtedly, evolve the conclusion from the

minor alone, because the minor would have already asserted it. But if, as

is in fact the case, the word man does not connote mortality, how does it

appear that in the mind of every person who admits Socrates to be a man,

the idea of man must include the idea of mortality? Dr. Brown could not

help seeing this difficulty, and in order to avoid it, was led, contrary

to his intention, to re-establish, under another name, that step in the

argument which corresponds to the major, by affirming the necessity of

_previously perceiving_ the relation between the idea of man and the idea

of mortal. If the reasoner has not previously perceived this relation, he

will not, says Dr. Brown, infer because Socrates is a man, that Socrates

is mortal. But even this admission, though amounting to a surrender of the

doctrine that an argument consists of the minor and the conclusion alone,

will not save the remainder of Dr. Brown’s theory. The failure of assent

to the argument does not take place merely because the reasoner, for want

of due analysis, does not perceive that his idea of man includes the idea

of mortality; it takes place, much more commonly, because in his mind that

relation between the two ideas has never existed. And in truth it never

does exist, except as the result of experience. Consenting, for the sake

of the argument, to discuss the question on a supposition of which we have

recognized the radical incorrectness, namely, that the meaning of a

proposition relates to the ideas of the things spoken of, and not to the

things themselves; I must yet observe, that the idea of man, as a

universal idea, the common property of all rational creatures, can not

involve any thing but what is strictly implied in the name. If any one

includes in his own private idea of man, as no doubt is always the case,

some other attributes, such for instance as mortality, he does so only as

the consequence of experience, after having satisfied himself that all men

possess that attribute: so that whatever the idea contains, in any

person’s mind, beyond what is included in the conventional signification

of the word, has been added to it as the result of assent to a

proposition; while Dr. Brown’s theory requires us to suppose, on the

contrary, that assent to the proposition is produced by evolving, through

an analytic process, this very element out of the idea. This theory,

therefore, may be considered as sufficiently refuted; and the minor

premise must be regarded as totally insufficient to prove the conclusion,

except with the assistance of the major, or of that which the major

represents, namely, the various singular propositions expressive of the

series of observations, of which the generalization called the major

premise is the result.

In the argument, then, which proves that Socrates is mortal, one

indispensable part of the premises will be as follows: “My father, and my

father’s father, A, B, C, and an indefinite number of other persons, were

mortal;” which is only an expression in different words of the observed

fact that they have died. This is the major premise divested of the

_petitio principii_, and cut down to as much as is really known by direct

evidence.

In order to connect this proposition with the conclusion Socrates is

mortal, the additional link necessary is such a proposition as the

following: “Socrates resembles my father, and my father’s father, and the

other individuals specified.” This proposition we assert when we say that

Socrates is a man. By saying so we likewise assert in what respect he

resembles them, namely, in the attributes connoted by the word man. And we

conclude that he further resembles them in the attribute mortality.

§ 7. We have thus obtained what we were seeking, a universal type of the

reasoning process. We find it resolvable in all cases into the following

elements: Certain individuals have a given attribute; an individual or

individuals resemble the former in certain other attributes; therefore

they resemble them also in the given attribute. This type of ratiocination

does not claim, like the syllogism, to be conclusive from the mere form of

the expression; nor can it possibly be so. That one proposition does or

does not assert the very fact which was already asserted in another, may

appear from the form of the expression, that is, from a comparison of the

language; but when the two propositions assert facts which are _bona fide_

different, whether the one fact proves the other or not can never appear

from the language, but must depend on other considerations. Whether, from

the attributes in which Socrates resembles those men who have heretofore

died, it is allowable to infer that he resembles them also in being

mortal, is a question of Induction; and is to be decided by the principles

or canons which we shall hereafter recognize as tests of the correct

performance of that great mental operation.

Meanwhile, however, it is certain, as before remarked, that if this

inference can be drawn as to Socrates, it can be drawn as to all others

who resemble the observed individuals in the same attributes in which he

resembles them; that is (to express the thing concisely) of all mankind.

If, therefore, the argument be admissible in the case of Socrates, we are

at liberty, once for all, to treat the possession of the attributes of man

as a mark, or satisfactory evidence, of the attribute of mortality. This

we do by laying down the universal proposition, All men are mortal, and

interpreting this, as occasion arises, in its application to Socrates and

others. By this means we establish a very convenient division of the

entire logical operation into two steps; first, that of ascertaining what

attributes are marks of mortality; and, secondly, whether any given

individuals possess those marks. And it will generally be advisable, in

our speculations on the reasoning process, to consider this double

operation as in fact taking place, and all reasoning as carried on in the

form into which it must necessarily be thrown to enable us to apply to it

any test of its correct performance.

Although, therefore, all processes of thought in which the ultimate

premises are particulars, whether we conclude from particulars to a

general formula, or from particulars to other particulars according to

that formula, are equally Induction; we shall yet, conformably to usage,

consider the name Induction as more peculiarly belonging to the process of

establishing the general proposition, and the remaining operation, which

is substantially that of interpreting the general proposition, we shall

call by its usual name, Deduction. And we shall consider every process by

which any thing is inferred respecting an unobserved case, as consisting

of an Induction followed by a Deduction; because, although the process

needs not necessarily be carried on in this form, it is always susceptible

of the form, and must be thrown into it when assurance of scientific

accuracy is needed and desired.

§ 8. The theory of the syllogism laid down in the preceding pages, has

obtained, among other important adhesions, three of peculiar value: those

of Sir John Herschel,(59) Dr. Whewell,(60) and Mr. Bailey;(61) Sir John

Herschel considering the doctrine, though not strictly “a discovery,”

having been anticipated by Berkeley,(62) to be “one of the greatest steps

which have yet been made in the philosophy of Logic.” “When we consider”

(to quote the further words of the same authority) “the inveteracy of the

habits and prejudices which it has cast to the winds,” there is no cause

for misgiving in the fact that other thinkers, no less entitled to

consideration, have formed a very different estimate of it. Their

principal objection can not be better or more succinctly stated than by

borrowing a sentence from Archbishop Whately.(63) “In every case where an

inference is drawn from Induction (unless that name is to be given to a

mere random guess without any grounds at all) we must form a judgment that

the instance or instances adduced are _sufficient_ to authorize the

conclusion; that it is _allowable_ to take these instances as a sample

warranting an inference respecting the whole class;” and the expression of

this judgment in words (it has been said by several of my critics) _is_

the major premise.

I quite admit that the major is an affirmation of the sufficiency of the

evidence on which the conclusion rests. That it is so, is the very essence

of my own theory. And whoever admits that the major premise is _only_

this, adopts the theory in its essentials.

But I can not concede that this recognition of the sufficiency of the

evidence—that is, of the correctness of the induction—is a part of the

induction itself; unless we ought to say that it is a part of every thing

we do, to satisfy ourselves that it has been done rightly. We conclude

from known instances to unknown by the impulse of the generalizing

propensity; and (until after a considerable amount of practice and mental

discipline) the question of the sufficiency of the evidence is only raised

by a retrospective act, turning back upon our own footsteps, and examining

whether we were warranted in doing what we have provisionally done. To

speak of this reflex operation as part of the original one, requiring to

be expressed in words in order that the verbal formula may correctly

represent the psychological process, appears to me false psychology.(64)

We review our syllogistic as well as our inductive processes, and

recognize that they have been correctly performed; but logicians do not

add a third premise to the syllogism, to express this act of recognition.

A careful copyist verifies his transcript by collating it with the

original; and if no error appears, he recognizes that the transcript has

been correctly made. But we do not call the examination of the copy a part

of the act of copying.

The conclusion in an induction is inferred from the evidence itself, and

not from a recognition of the sufficiency of the evidence; as I infer that

my friend is walking toward me because I see him, and not because I

recognize that my eyes are open, and that eyesight is a means of

knowledge. In all operations which require care, it is good to assure

ourselves that the process has been performed accurately; but the testing

of the process is not the process itself; and, besides, may have been

omitted altogether, and yet the process be correct. It is precisely

because that operation is omitted in ordinary unscientific reasoning, that

there is any thing gained in certainty by throwing reasoning into the

syllogistic form. To make sure, as far as possible, that it shall not be

omitted, we make the testing operation a part of the reasoning process

itself. We insist that the inference from particulars to particulars shall

pass through a general proposition. But this is a security for good

reasoning, not a condition of all reasoning; and in some cases not even a

security. Our most familiar inferences are all made before we learn the

use of general propositions; and a person of untutored sagacity will

skillfully apply his acquired experience to adjacent cases, though he

would bungle grievously in fixing the limits of the appropriate general

theorem. But though he may conclude rightly, he never, properly speaking,

knows whether he has done so or not; he has not tested his reasoning. Now,

this is precisely what forms of reasoning do for us. We do not need them

to enable us to reason, but to enable us to know whether we reason

correctly.

In still further answer to the objection, it may be added that—even when

the test has been applied, and the sufficiency of the evidence

recognized—if it is sufficient to support the general proposition, it is

sufficient also to support an inference from particulars to particulars

without passing through the general proposition. The inquirer who has

logically satisfied himself that the conditions of legitimate induction

were realized in the cases A, B, C, would be as much justified in

concluding directly to the Duke of Wellington as in concluding to all men.

The general conclusion is never legitimate, unless the particular one

would be so too; and in no sense, intelligible to me, can the particular

conclusion be said to be drawn from the general one. Whenever there is

ground for drawing any conclusion at all from particular instances, there

is ground for a general conclusion; but that this general conclusion

should be actually drawn, however useful, can not be an indispensable

condition of the validity of the inference in the particular case. A man

gives away sixpence by the same power by which he disposes of his whole

fortune; but it is not necessary to the legality of the smaller act, that

he should make a formal assertion of his right to the greater one.

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

§ 9. The preceding considerations enable us to understand the true nature

of what is termed, by recent writers, Formal Logic, and the relation

between it and Logic in the widest sense. Logic, as I conceive it, is the

entire theory of the ascertainment of reasoned or inferred truth. Formal

Logic, therefore, which Sir William Hamilton from his own point of view,

and Archbishop Whately from his, have represented as the whole of Logic

properly so called, is really a very subordinate part of it, not being

directly concerned with the process of Reasoning or Inference in the sense

in which that process is a part of the Investigation of Truth. What, then,

is Formal Logic? The name seems to be properly applied to all that portion

of doctrine which relates to the equivalence of different modes of

expression; the rules for determining when assertions in a given form

imply or suppose the truth or falsity of other assertions. This includes

the theory of the Import of Propositions, and of their Conversion,

Æquipollence, and Opposition; of those falsely called Inductions (to be

hereafter spoken of)(66), in which the apparent generalization is a mere

abridged statement of cases known individually; and finally, of the

syllogism: while the theory of Naming, and of (what is inseparably

connected with it) Definition, though belonging still more to the other

and larger kind of logic than to this, is a necessary preliminary to this.

The end aimed at by Formal Logic, and attained by the observance of its

precepts, is not truth, but consistency. It has been seen that this is the

only direct purpose of the rules of the syllogism; the intention and

effect of which is simply to keep our inferences or conclusions in

complete consistency with our general formulæ or directions for drawing

them. The Logic of Consistency is a necessary auxiliary to the logic of

truth, not only because what is inconsistent with itself or with other

truths can not be true, but also because truth can only be successfully

pursued by drawing inferences from experience, which, if warrantable at

all, admit of being generalized, and, to test their warrantableness,

require to be exhibited in a generalized form; after which the correctness

of their application to particular cases is a question which specially

concerns the Logic of Consistency. This Logic, not requiring any

preliminary knowledge of the processes or conclusions of the various

sciences, may be studied with benefit in a much earlier stage of education

than the Logic of Truth: and the practice which has empirically obtained

of teaching it apart, through elementary treatises which do not attempt to

include any thing else, though the reasons assigned for the practice are

in general very far from philosophical, admits of philosophical

justification.

Chapter IV.

Of Trains Of Reasoning, And Deductive Sciences.

§ 1. In our analysis of the syllogism, it appeared that the minor premise

always affirms a resemblance between a new case and some cases previously

known; while the major premise asserts something which, having been found

true of those known cases, we consider ourselves warranted in holding true

of any other case resembling the former in certain given particulars.

If all ratiocinations resembled, as to the minor premise, the examples

which were exclusively employed in the preceding chapter; if the

resemblance, which that premise asserts, were obvious to the senses, as in

the proposition “Socrates is a man,” or were at once ascertainable by

direct observation; there would be no necessity for trains of reasoning,

and Deductive or Ratiocinative Sciences would not exist. Trains of

reasoning exist only for the sake of extending an induction founded, as

all inductions must be, on observed cases, to other cases in which we not

only can not directly observe the fact which is to be proved, but can not

directly observe even the mark which is to prove it.

§ 2. Suppose the syllogism to be, All cows ruminate, the animal which is

before me is a cow, therefore it ruminates. The minor, if true at all, is

obviously so: the only premise the establishment of which requires any

anterior process of inquiry, is the major; and provided the induction of

which that premise is the expression was correctly performed, the

conclusion respecting the animal now present will be instantly drawn;

because, as soon as she is compared with the formula, she will be

identified as being included in it. But suppose the syllogism to be the

following: All arsenic is poisonous, the substance which is before me is

arsenic, therefore it is poisonous. The truth of the minor may not here be

obvious at first sight; it may not be intuitively evident, but may itself

be known only by inference. It may be the conclusion of another argument,

which, thrown into the syllogistic form, would stand thus: Whatever when

lighted produces a dark spot on a piece of white porcelain held in the

flame, which spot is soluble in hypochloride of calcium, is arsenic; the

substance before me conforms to this condition; therefore it is arsenic.

To establish, therefore, the ultimate conclusion, The substance before me

is poisonous, requires a process, which, in order to be syllogistically

expressed, stands in need of two syllogisms; and we have a Train of

Reasoning.

When, however, we thus add syllogism to syllogism, we are really adding

induction to induction. Two separate inductions must have taken place to

render this chain of inference possible; inductions founded, probably, on

different sets of individual instances, but which converge in their

results, so that the instance which is the subject of inquiry comes within

the range of them both. The record of these inductions is contained in the

majors of the two syllogisms. First, we, or others for us, have examined

various objects which yielded under the given circumstances a dark spot

with the given property, and found that they possessed the properties

connoted by the word arsenic; they were metallic, volatile, their vapor

had a smell of garlic, and so forth. Next, we, or others for us, have

examined various specimens which possessed this metallic and volatile

character, whose vapor had this smell, etc., and have invariably found

that they were poisonous. The first observation we judge that we may

extend to all substances whatever which yield that particular kind of dark

spot; the second, to all metallic and volatile substances resembling those

we examined; and consequently, not to those only which are seen to be

such, but to those which are concluded to be such by the prior induction.

The substance before us is only seen to come within one of these

inductions; but by means of this one, it is brought within the other. We

are still, as before, concluding from particulars to particulars; but we

are now concluding from particulars observed, to other particulars which

are not, as in the simple case, _seen_ to resemble them in material

points, but _inferred_ to do so, because resembling them in something

else, which we have been led by quite a different set of instances to

consider as a mark of the former resemblance.

This first example of a train of reasoning is still extremely simple, the

series consisting of only two syllogisms. The following is somewhat more

complicated: No government, which earnestly seeks the good of its

subjects, is likely to be overthrown; some particular government earnestly

seeks the good of its subjects, therefore it is not likely to be

overthrown. The major premise in this argument we shall suppose not to be

derived from considerations _a priori_, but to be a generalization from

history, which, whether correct or erroneous, must have been founded on

observation of governments concerning whose desire of the good of their

subjects there was no doubt. It has been found, or thought to be found,

that these were not easily overthrown, and it has been deemed that those

instances warranted an extension of the same predicate to any and every

government which resembles them in the attribute of desiring earnestly the

good of its subjects. But _does_ the government in question thus resemble

them? This may be debated _pro_ and _con_ by many arguments, and must, in

any case, be proved by another induction; for we can not directly observe

the sentiments and desires of the persons who carry on the government. To

prove the minor, therefore, we require an argument in this form: Every

government which acts in a certain manner, desires the good of its

subjects; the supposed government acts in that particular manner,

therefore it desires the good of its subjects. But is it true that the

government acts in the manner supposed? This minor also may require proof;

still another induction, as thus: What is asserted by intelligent and

disinterested witnesses, may be believed to be true; that the government

acts in this manner, is asserted by such witnesses, therefore it may be

believed to be true. The argument hence consists of three steps. Having

the evidence of our senses that the case of the government under

consideration resembles a number of former cases, in the circumstance of

having something asserted respecting it by intelligent and disinterested

witnesses, we infer, first, that, as in those former instances, so in this

instance, the assertion is true. Secondly, what was asserted of the

government being that it acts in a particular manner, and other

governments or persons having been observed to act in the same manner, the

government in question is brought into known resemblance with those other

governments or persons; and since they were known to desire the good of

the people, it is thereupon, by a second induction, inferred that the

particular government spoken of, desires the good of the people. This

brings that government into known resemblance with the other governments

which were thought likely to escape revolution, and thence, by a third

induction, it is concluded that this particular government is also likely

to escape. This is still reasoning from particulars to particulars, but we

now reason to the new instance from three distinct sets of former

instances: to one only of those sets of instances do we directly perceive

the new one to be similar; but from that similarity we inductively infer

that it has the attribute by which it is assimilated to the next set, and

brought within the corresponding induction; after which by a repetition of

the same operation we infer it to be similar to the third set, and hence a

third induction conducts us to the ultimate conclusion.

§ 3. Notwithstanding the superior complication of these examples, compared

with those by which in the preceding chapter we illustrated the general

theory of reasoning, every doctrine which we then laid down holds equally

true in these more intricate cases. The successive general propositions

are not steps in the reasoning, are not intermediate links in the chain of

inference, between the particulars observed and those to which we apply

the observation. If we had sufficiently capacious memories, and a

sufficient power of maintaining order among a huge mass of details, the

reasoning could go on without any general propositions; they are mere

formulæ for inferring particulars from particulars. The principle of

general reasoning is (as before explained), that if, from observation of

certain known particulars, what was seen to be true of them can be

inferred to be true of any others, it may be inferred of all others which

are of a certain description. And in order that we may never fail to draw

this conclusion in a new case when it can be drawn correctly, and may

avoid drawing it when it can not, we determine once for all what are the

distinguishing marks by which such cases may be recognized. The subsequent

process is merely that of identifying an object, and ascertaining it to

have those marks; whether we identify it by the very marks themselves, or

by others which we have ascertained (through another and a similar

process) to be marks of those marks. The real inference is always from

particulars to particulars, from the observed instances to an unobserved

one: but in drawing this inference, we conform to a formula which we have

adopted for our guidance in such operations, and which is a record of the

criteria by which we thought we had ascertained that we might distinguish

when the inference could, and when it could not, be drawn. The real

premises are the individual observations, even though they may have been

forgotten, or, being the observations of others and not of ourselves, may,

to us, never have been known: but we have before us proof that we or

others once thought them sufficient for an induction, and we have marks to

show whether any new case is one of those to which, if then known, the

induction would have been deemed to extend. These marks we either

recognize at once, or by the aid of other marks, which by another previous

induction we collected to be marks of the first. Even these marks of marks

may only be recognized through a third set of marks; and we may have a

train of reasoning, of any length, to bring a new case within the scope of

an induction grounded on particulars its similarity to which is only

ascertained in this indirect manner.

Thus, in the preceding example, the ultimate inductive inference was, that

a certain government was not likely to be overthrown; this inference was

drawn according to a formula in which desire of the public good was set

down as a mark of not being likely to be overthrown; a mark of this mark

was, acting in a particular manner; and a mark of acting in that manner

was, being asserted to do so by intelligent and disinterested witnesses:

this mark, the government under discussion was recognized by the senses as

possessing. Hence that government fell within the last induction, and by

it was brought within all the others. The perceived resemblance of the

case to one set of observed particular cases, brought it into known

resemblance with another set, and that with a third.

In the more complex branches of knowledge, the deductions seldom consist,

as in the examples hitherto exhibited, of a single chain, _a_ a mark of

_b, b_ of _c, c_ of _d_, therefore _a_ a mark of _d_. They consist (to

carry on the same metaphor) of several chains united at the extremity, as

thus: _a_ a mark of _d, b_ of _e, c_ of _f, d e f_ of _n_, therefore _a b

c_ a mark of _n_. Suppose, for example, the following combination of

circumstances: 1st, rays of light impinging on a reflecting surface; 2d,

that surface parabolic; 3d, those rays parallel to each other and to the

axis of the surface. It is to be proved that the concourse of these three

circumstances is a mark that the reflected rays will pass through the

focus of the parabolic surface. Now, each of the three circumstances is

singly a mark of something material to the case. Rays of light impinging

on a reflecting surface are a mark that those rays will be reflected at an

angle equal to the angle of incidence. The parabolic form of the surface,

is a mark that, from any point of it, a line drawn to the focus and a line

parallel to the axis will make equal angles with the surface. And finally,

the parallelism of the rays to the axis is a mark that their angle of

incidence coincides with one of these equal angles. The three marks taken

together are therefore a mark of all these three things united. But the

three united are evidently a mark that the angle of reflection must

coincide with the other of the two equal angles, that formed by a line

drawn to the focus; and this again, by the fundamental axiom concerning

straight lines, is a mark that the reflected rays pass through the focus.

Most chains of physical deduction are of this more complicated type; and

even in mathematics such are abundant, as in all propositions where the

hypothesis includes numerous conditions: “_If_ a circle be taken, and _if_

within that circle a point be taken, not the centre, and _if_ straight

lines be drawn from that point to the circumference, then,” etc.

§ 4. The considerations now stated remove a serious difficulty from the

view we have taken of reasoning; which view might otherwise have seemed

not easily reconcilable with the fact that there are Deductive or

Ratiocinative Sciences. It might seem to follow, if all reasoning be

induction, that the difficulties of philosophical investigation must lie

in the inductions exclusively, and that when these were easy, and

susceptible of no doubt or hesitation, there could be no science, or, at

least, no difficulties in science. The existence, for example, of an

extensive Science of Mathematics, requiring the highest scientific genius

in those who contributed to its creation, and calling for a most continued

and vigorous exertion of intellect in order to appropriate it when

created, may seem hard to be accounted for on the foregoing theory. But

the considerations more recently adduced remove the mystery, by showing,

that even when the inductions themselves are obvious, there may be much

difficulty in finding whether the particular case which is the subject of

inquiry comes within them; and ample room for scientific ingenuity in so

combining various inductions, as, by means of one within which the case

evidently falls, to bring it within others in which it can not be directly

seen to be included.

When the more obvious of the inductions which can be made in any science

from direct observations, have been made, and general formulas have been

framed, determining the limits within which these inductions are

applicable; as often as a new case can be at once seen to come within one

of the formulas, the induction is applied to the new case, and the

business is ended. But new cases are continually arising, which do not

obviously come within any formula whereby the question we want solved in

respect of them could be answered. Let us take an instance from geometry:

and as it is taken only for illustration, let the reader concede to us for

the present, what we shall endeavor to prove in the next chapter, that the

first principles of geometry are results of induction. Our example shall

be the fifth proposition of the first book of Euclid. The inquiry is, Are

the angles at the base of an isosceles triangle equal or unequal? The

first thing to be considered is, what inductions we have, from which we

can infer equality or inequality. For inferring equality we have the

following formulæ: Things which being applied to each other coincide, are

equals. Things which are equal to the same thing are equals. A whole and

the sum of its parts are equals. The sums of equal things are equals. The

differences of equal things are equals. There are no other original

formulæ to prove equality. For inferring inequality we have the following:

A whole and its parts are unequals. The sums of equal things and unequal

things are unequals. The differences of equal things and unequal things

are unequals. In all, eight formulæ. The angles at the base of an

isosceles triangle do not obviously come within any of these. The formulæ

specify certain marks of equality and of inequality, but the angles can

not be perceived intuitively to have any of those marks. On examination it

appears that they have; and we ultimately succeed in bringing them within

the formula, “The differences of equal things are equal.” Whence comes the

difficulty of recognizing these angles as the differences of equal things?

Because each of them is the difference not of one pair only, but of

innumerable pairs of angles; and out of these we had to imagine and select

two, which could either be intuitively perceived to be equals, or

possessed some of the marks of equality set down in the various formulæ.

By an exercise of ingenuity, which, on the part of the first inventor,

deserves to be regarded as considerable, two pairs of angles were hit

upon, which united these requisites. First, it could be perceived

intuitively that their differences were the angles at the base; and,

secondly, they possessed one of the marks of equality, namely, coincidence

when applied to one another. This coincidence, however, was not perceived

intuitively, but inferred, in conformity to another formula.

For greater clearness, I subjoin an analysis of the demonstration. Euclid,

it will be remembered, demonstrates his fifth proposition by means of the

fourth. This it is not allowable for us to do, because we are undertaking

to trace deductive truths not to prior deductions, but to their original

inductive foundation. We must, therefore, use the premises of the fourth

proposition instead of its conclusion, and prove the fifth directly from

first principles. To do so requires six formulas. (We presuppose an

equilateral triangle, whose vertices are A, D, E, with point B on the side

AD, and point C on the side AE, such that BC is parallel to DE. We must

begin, as in Euclid, by prolonging the equal sides AB, AC, to equal

distances, and joining the extremities BE, DC.)

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

AD and AE are sums of equals by the supposition. Having that mark of

equality, they are concluded by this formula to be equal.

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

another, coincide._

AC, AB, are within this formula by supposition; AD, AE, have been brought

within it by the preceding step. The angle at A considered as an angle of

the triangle ABE, and the same angle considered as an angle of the

triangle ACD, are of course within the formula. All these pairs,

therefore, possess the property which, according to the second formula, is

a mark that when applied to one another they will coincide. Conceive them,

then, applied to one another, by turning over the triangle ABE, and laying

it on the triangle ACD in such a manner that AB of the one shall lie upon

AC of the other. Then, by the equality of the angles, AE will lie on AD.

But AB and AC, AE and AD are equals; therefore they will coincide

altogether, and of course at their extremities, D, E, and B, C.

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

coincide._

BE and CD have been brought within this formula by the preceding

induction; they will, therefore, coincide.

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

The third induction having shown that BE and CD coincide, and the second

that AB, AC, coincide, the angles ABE and ACD are thereby brought within

the fourth formula, and accordingly coincide.

FIFTH FORMULA.—_Things which coincide are equal._

The angles ABE and ACD are brought within this formula by the induction

immediately preceding. This train of reasoning being also applicable,

_mutatis mutandis_, to the angles EBC, DCB, these also are brought within

the fifth formula. And, finally,

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

The angle ABC being the difference of ABE, CBE, and the angle ACB being

the difference of ACD, DCB; which have been proved to be equals; ABC and

ACB are brought within the last formula by the whole of the previous

process.

The difficulty here encountered is chiefly that of figuring to ourselves

the two angles at the base of the triangle ABC as remainders made by

cutting one pair of angles out of another, while each pair shall be

corresponding angles of triangles which have two sides and the intervening

angle equal. It is by this happy contrivance that so many different

inductions are brought to bear upon the same particular case. And this not

being at all an obvious thought, it may be seen from an example so near

the threshold of mathematics, how much scope there may well be for

scientific dexterity in the higher branches of that and other sciences, in

order so to combine a few simple inductions, as to bring within each of

them innumerable cases which are not obviously included in it; and how

long, and numerous, and complicated may be the processes necessary for

bringing the inductions together, even when each induction may itself be

very easy and simple. All the inductions involved in all geometry are

comprised in those simple ones, the formulæ of which are the Axioms, and a

few of the so-called Definitions. The remainder of the science is made up

of the processes employed for bringing unforeseen cases within these

inductions; or (in syllogistic language) for proving the minors necessary

to complete the syllogisms; the majors being the definitions and axioms.

In those definitions and axioms are laid down the whole of the marks, by

an artful combination of which it has been found possible to discover and

prove all that is proved in geometry. The marks being so few, and the

inductions which furnish them being so obvious and familiar; the

connecting of several of them together, which constitutes Deductions, or

Trains of Reasoning, forms the whole difficulty of the science, and, with

a trifling exception, its whole bulk; and hence Geometry is a Deductive

Science.

§ 5. It will be seen hereafter(67) that there are weighty scientific

reasons for giving to every science as much of the character of a

Deductive Science as possible; for endeavoring to construct the science

from the fewest and the simplest possible inductions, and to make these,

by any combinations however complicated, suffice for proving even such

truths, relating to complex cases, as could be proved, if we chose, by

inductions from specific experience. Every branch of natural philosophy

was originally experimental; each generalization rested on a special

induction, and was derived from its own distinct set of observations and

experiments. From being sciences of pure experiment, as the phrase is, or,

to speak more correctly, sciences in which the reasonings mostly consist

of no more than one step, and are expressed by single syllogisms, all

these sciences have become to some extent, and some of them in nearly the

whole of their extent, sciences of pure reasoning; whereby multitudes of

truths, already known by induction from as many different sets of

experiments, have come to be exhibited as deductions or corollaries from

inductive propositions of a simpler and more universal character. Thus

mechanics, hydrostatics, optics, acoustics, thermology, have successively

been rendered mathematical; and astronomy was brought by Newton within the

laws of general mechanics. Why it is that the substitution of this

circuitous mode of proceeding for a process apparently much easier and

more natural, is held, and justly, to be the greatest triumph of the

investigation of nature, we are not, in this stage of our inquiry,

prepared to examine. But it is necessary to remark, that although, by this

progressive transformation, all sciences tend to become more and more

Deductive, they are not, therefore, the less Inductive; every step in the

Deduction is still an Induction. The opposition is not between the terms

Deductive and Inductive, but between Deductive and Experimental. A science

is experimental, in proportion as every new case, which presents any

peculiar features, stands in need of a new set of observations and

experiments—a fresh induction. It is deductive, in proportion as it can

draw conclusions, respecting cases of a new kind, by processes which bring

those cases under old inductions; by ascertaining that cases which can not

be observed to have the requisite marks, have, however, marks of those

marks.

We can now, therefore, perceive what is the generic distinction between

sciences which can be made Deductive, and those which must as yet remain

Experimental. The difference consists in our having been able, or not yet

able, to discover marks of marks. If by our various inductions we have

been able to proceed no further than to such propositions as these, _a_ a

mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of _d_, or c

and _d_ marks of one another, without any thing to connect _a_ or _b_ with

_c_ or _d_; we have a science of detached and mutually independent

generalizations, such as these, that acids redden vegetable blues, and

that alkalies color them green; from neither of which propositions could

we, directly or indirectly, infer the other: and a science, so far as it

is composed of such propositions, is purely experimental. Chemistry, in

the present state of our knowledge, has not yet thrown off this character.

There are other sciences, however, of which the propositions are of this

kind: _a_ a mark of _b, b_ a mark of _c, c_ of _d, d_ of _e_, etc. In

these sciences we can mount the ladder from _a_ to _e_ by a process of

ratiocination; we can conclude that _a_ is a mark of _e_, and that every

object which has the mark _a_ has the property _e_, although, perhaps, we

never were able to observe _a_ and _e_ together, and although even _d_,

our only direct mark of _e_, may not be perceptible in those objects, but

only inferable. Or, varying the first metaphor, we may be said to get from

_a_ to _e_ underground: the marks _b_, _c_, _d_, which indicate the route,

must all be possessed somewhere by the objects concerning which we are

inquiring; but they are below the surface: _a_ is the only mark that is

visible, and by it we are able to trace in succession all the rest.

§ 6. We can now understand how an experimental may transform itself into a

deductive science by the mere progress of experiment. In an experimental

science, the inductions, as we have said, lie detached, as, _a_ a mark of

_b, c_ a mark of _d_, _e_ a mark of _f_, and so on: now, a new set of

instances, and a consequent new induction, may at any time bridge over the

interval between two of these unconnected arches; _b_, for example, may be

ascertained to be a mark of _c_, which enables us thenceforth to prove

deductively that _a_ is a mark of _c_. Or, as sometimes happens, some

comprehensive induction may raise an arch high in the air, which bridges

over hosts of them at once; _b_, _d_, _f_, and all the rest, turning out

to be marks of some one thing, or of things between which a connection has

already been traced. As when Newton discovered that the motions, whether

regular or apparently anomalous, of all the bodies of the solar system

(each of which motions had been inferred by a separate logical operation,

from separate marks), were all marks of moving round a common centre, with

a centripetal force varying directly as the mass, and inversely as the

square of the distance from that centre. This is the greatest example

which has yet occurred of the transformation, at one stroke, of a science

which was still to a great degree merely experimental, into a deductive

science.

Transformations of the same nature, but on a smaller scale, continually

take place in the less advanced branches of physical knowledge, without

enabling them to throw off the character of experimental sciences. Thus

with regard to the two unconnected propositions before cited, namely,

Acids redden vegetable blues, Alkalies make them green; it is remarked by

Liebig, that all blue coloring matters which are reddened by acids (as

well as, reciprocally, all red coloring matters which are rendered blue by

alkalies) contain nitrogen: and it is quite possible that this

circumstance may one day furnish a bond of connection between the two

propositions in question, by showing that the antagonistic action of acids

and alkalies in producing or destroying the color blue, is the result of

some one, more general, law. Although this connecting of detached

generalizations is so much gain, it tends but little to give a deductive

character to any science as a whole; because the new courses of

observation and experiment, which thus enable us to connect together a few

general truths, usually make known to us a still greater number of

unconnected new ones. Hence chemistry, though similar extensions and

simplifications of its generalizations are continually taking place, is

still in the main an experimental science; and is likely so to continue

unless some comprehensive induction should be hereafter arrived at, which,

like Newton’s, shall connect a vast number of the smaller known inductions

together, and change the whole method of the science at once. Chemistry

has already one great generalization, which, though relating to one of the

subordinate aspects of chemical phenomena, possesses within its limited

sphere this comprehensive character; the principle of Dalton, called the

atomic theory, or the doctrine of chemical equivalents: which by enabling

us to a certain extent to foresee the proportions in which two substances

will combine, before the experiment has been tried, constitutes

undoubtedly a source of new chemical truths obtainable by deduction, as

well as a connecting principle for all truths of the same description

previously obtained by experiment.

§ 7. The discoveries which change the method of a science from

experimental to deductive, mostly consist in establishing, either by

deduction or by direct experiment, that the varieties of a particular

phenomenon uniformly accompany the varieties of some other phenomenon

better known. Thus the science of sound, which previously stood in the

lowest rank of merely experimental science, became deductive when it was

proved by experiment that every variety of sound was consequent on, and

therefore a mark of, a distinct and definable variety of oscillatory

motion among the particles of the transmitting medium. When this was

ascertained, it followed that every relation of succession or co-existence

which obtained between phenomena of the more known class, obtained also

between the phenomena which correspond to them in the other class. Every

sound, being a mark of a particular oscillatory motion, became a mark of

every thing which, by the laws of dynamics, was known to be inferable from

that motion; and every thing which by those same laws was a mark of any

oscillatory motion among the particles of an elastic medium, became a mark

of the corresponding sound. And thus many truths, not before suspected,

concerning sound, become deducible from the known laws of the propagation

of motion through an elastic medium; while facts already empirically known

respecting sound, become an indication of corresponding properties of

vibrating bodies, previously undiscovered.

But the grand agent for transforming experimental into deductive sciences,

is the science of number. The properties of number, alone among all known

phenomena, are, in the most rigorous sense, properties of all things

whatever. All things are not colored, or ponderable, or even extended; but

all things are numerable. And if we consider this science in its whole

extent, from common arithmetic up to the calculus of variations, the

truths already ascertained seem all but infinite, and admit of indefinite

extension.

These truths, though affirmable of all things whatever, of course apply to

them only in respect of their quantity. But if it comes to be discovered

that variations of quality in any class of phenomena, correspond regularly

to variations of quantity either in those same or in some other phenomena;

every formula of mathematics applicable to quantities which vary in that

particular manner, becomes a mark of a corresponding general truth,

respecting the variations in quality which accompany them: and the science

of quantity being (as far as any science can be) altogether deductive, the

theory of that particular kind of qualities becomes, to this extent,

deductive likewise.

The most striking instance in point which history affords (though not an

example of an experimental science rendered deductive, but of an

unparalleled extension given to the deductive process in a science which

was deductive already), is the revolution in geometry which originated

with Descartes, and was completed by Clairaut. These great mathematicians

pointed out the importance of the fact, that to every variety of position

in points, direction in lines, or form in curves or surfaces (all of which

are Qualities), there corresponds a peculiar relation of quantity between

either two or three rectilineal co-ordinates; insomuch that if the law

were known according to which those co-ordinates vary relatively to one

another, every other geometrical property of the line or surface in

question, whether relating to quantity or quality, would be capable of

being inferred. Hence it followed that every geometrical question could be

solved, if the corresponding algebraical one could; and geometry received

an accession (actual or potential) of new truths, corresponding to every

property of numbers which the progress of the calculus had brought, or

might in future bring, to light. In the same general manner, mechanics,

astronomy, and in a less degree, every branch of natural philosophy

commonly so called, have been made algebraical. The varieties of physical

phenomena with which those sciences are conversant, have been found to

answer to determinable varieties in the quantity of some circumstance or

other; or at least to varieties of form or position, for which

corresponding equations of quantity had already been, or were susceptible

of being, discovered by geometers.

In these various transformations, the propositions of the science of

number do but fulfill the function proper to all propositions forming a

train of reasoning, viz., that of enabling us to arrive in an indirect

method, by marks of marks, at such of the properties of objects as we can

not directly ascertain (or not so conveniently) by experiment. We travel

from a given visible or tangible fact, through the truths of numbers, to

the facts sought. The given fact is a mark that a certain relation

subsists between the quantities of some of the elements concerned; while

the fact sought presupposes a certain relation between the quantities of

some other elements: now, if these last quantities are dependent in some

known manner upon the former, or _vicè versa_, we can argue from the

numerical relation between the one set of quantities, to determine that

which subsists between the other set; the theorems of the calculus

affording the intermediate links. And thus one of the two physical facts

becomes a mark of the other, by being a mark of a mark of a mark of it.

Chapter V.

Of Demonstration, And Necessary Truths.

§ 1. If, as laid down in the two preceding chapters, the foundation of all

sciences, even deductive or demonstrative sciences, is Induction; if every

step in the ratiocinations even of geometry is an act of induction; and if

a train of reasoning is but bringing many inductions to bear upon the same

subject of inquiry, and drawing a case within one induction by means of

another; wherein lies the peculiar certainty always ascribed to the

sciences which are entirely, or almost entirely, deductive? Why are they

called the Exact Sciences? Why are mathematical certainty, and the

evidence of demonstration, common phrases to express the very highest

degree of assurance attainable by reason? Why are mathematics by almost

all philosophers, and (by some) even those branches of natural philosophy

which, through the medium of mathematics, have been converted into

deductive sciences, considered to be independent of the evidence of

experience and observation, and characterized as systems of Necessary

Truth?

The answer I conceive to be, that this character of necessity, ascribed to

the truths of mathematics, and (even with some reservations to be

hereafter made) the peculiar certainty attributed to them, is an illusion;

in order to sustain which, it is necessary to suppose that those truths

relate to, and express the properties of, purely imaginary objects. It is

acknowledged that the conclusions of geometry are deduced, partly at

least, from the so-called Definitions, and that those definitions are

assumed to be correct representations, as far as they go, of the objects

with which geometry is conversant. Now we have pointed out that, from a

definition as such, no proposition, unless it be one concerning the

meaning of a word, can ever follow; and that what apparently follows from

a definition, follows in reality from an implied assumption that there

exists a real thing conformable thereto. This assumption, in the case of

the definitions of geometry, is not strictly true: there exist no real

things exactly conformable to the definitions. There exist no points

without magnitude; no lines without breadth, nor perfectly straight; no

circles with all their radii exactly equal, nor squares with all their

angles perfectly right. It will perhaps be said that the assumption does

not extend to the actual, but only to the possible, existence of such

things. I answer that, according to any test we have of possibility, they

are not even possible. Their existence, so far as we can form any

judgment, would seem to be inconsistent with the physical constitution of

our planet at least, if not of the universe. To get rid of this

difficulty, and at the same time to save the credit of the supposed system

of necessary truth, it is customary to say that the points, lines,

circles, and squares which are the subject of geometry, exist in our

conceptions merely, and are part of our minds; which minds, by working on

their own materials, construct an _a priori_ science, the evidence of

which is purely mental, and has nothing whatever to do with outward

experience. By howsoever high authorities this doctrine may have been

sanctioned, it appears to me psychologically incorrect. The points, lines,

circles, and squares which any one has in his mind, are (I apprehend)

simply copies of the points, lines, circles, and squares which he has

known in his experience. Our idea of a point, I apprehend to be simply our

idea of the _minimum visibile_, the smallest portion of surface which we

can see. A line, as defined by geometers, is wholly inconceivable. We can

reason about a line as if it had no breadth; because we have a power,

which is the foundation of all the control we can exercise over the

operations of our minds; the power, when a perception is present to our

senses, or a conception to our intellects, of _attending_ to a part only

of that perception or conception, instead of the whole. But we can not

_conceive_ a line without breadth; we can form no mental picture of such a

line: all the lines which we have in our minds are lines possessing

breadth. If any one doubts this, we may refer him to his own experience. I

much question if any one who fancies that he can conceive what is called a

mathematical line, thinks so from the evidence of his consciousness: I

suspect it is rather because he supposes that unless such a conception

were possible, mathematics could not exist as a science: a supposition

which there will be no difficulty in showing to be entirely groundless.

Since, then, neither in nature, nor in the human mind, do there exist any

objects exactly corresponding to the definitions of geometry, while yet

that science can not be supposed to be conversant about nonentities;

nothing remains but to consider geometry as conversant with such lines,

angles, and figures, as really exist; and the definitions, as they are

called, must be regarded as some of our first and most obvious

generalizations concerning those natural objects. The correctness of those

generalizations, as generalizations, is without a flaw: the equality of

all the radii of a circle is true of all circles, so far as it is true of

any one: but it is not exactly true of any circle; it is only nearly true;

so nearly that no error of any importance in practice will be incurred by

feigning it to be exactly true. When we have occasion to extend these

inductions, or their consequences, to cases in which the error would be

appreciable—to lines of perceptible breadth or thickness, parallels which

deviate sensibly from equidistance, and the like—we correct our

conclusions, by combining with them a fresh set of propositions relating

to the aberration; just as we also take in propositions relating to the

physical or chemical properties of the material, if those properties

happen to introduce any modification into the result; which they easily

may, even with respect to figure and magnitude, as in the case, for

instance, of expansion by heat. So long, however, as there exists no

practical necessity for attending to any of the properties of the object

except its geometrical properties, or to any of the natural irregularities

in those, it is convenient to neglect the consideration of the other

properties and of the irregularities, and to reason as if these did not

exist: accordingly, we formally announce in the definitions, that we

intend to proceed on this plan. But it is an error to suppose, because we

resolve to confine our attention to a certain number of the properties of

an object, that we therefore conceive, or have an idea of, the object,

denuded of its other properties. We are thinking, all the time, of

precisely such objects as we have seen and touched, and with all the

properties which naturally belong to them; but, for scientific

convenience, we feign them to be divested of all properties, except those

which are material to our purpose, and in regard to which we design to

consider them.

The peculiar accuracy, supposed to be characteristic of the first

principles of geometry, thus appears to be fictitious. The assertions on

which the reasonings of the science are founded, do not, any more than in

other sciences, exactly correspond with the fact; but we suppose that they

do so, for the sake of tracing the consequences which follow from the

supposition. The opinion of Dugald Stewart respecting the foundations of

geometry, is, I conceive, substantially correct; that it is built on

hypotheses; that it owes to this alone the peculiar certainty supposed to

distinguish it; and that in any science whatever, by reasoning from a set

of hypotheses, we may obtain a body of conclusions as certain as those of

geometry, that is, as strictly in accordance with the hypotheses, and as

irresistibly compelling assent, _on condition_ that those hypotheses are

true.(68)

When, therefore, it is affirmed that the conclusions of geometry are

necessary truths, the necessity consists in reality only in this, that

they correctly follow from the suppositions from which they are deduced.

Those suppositions are so far from being necessary, that they are not even

true; they purposely depart, more or less widely, from the truth. The only

sense in which necessity can be ascribed to the conclusions of any

scientific investigation, is that of legitimately following from some

assumption, which, by the conditions of the inquiry, is not to be

questioned. In this relation, of course, the derivative truths of every

deductive science must stand to the inductions, or assumptions, on which

the science is founded, and which, whether true or untrue, certain or

doubtful in themselves, are always supposed certain for the purposes of

the particular science. And therefore the conclusions of all deductive

sciences were said by the ancients to be necessary propositions. We have

observed already that to be predicated necessarily was characteristic of

the predicable Proprium, and that a proprium was any property of a thing

which could be deduced from its essence, that is, from the properties

included in its definition.

§ 2. The important doctrine of Dugald Stewart, which I have endeavored to

enforce, has been contested by Dr. Whewell, both in the dissertation

appended to his excellent _Mechanical Euclid_, and in his elaborate work

on the _Philosophy of the Inductive Sciences_; in which last he also

replies to an article in the Edinburgh Review (ascribed to a writer of

great scientific eminence), in which Stewart’s opinion was defended

against his former strictures. The supposed refutation of Stewart consists

in proving against him (as has also been done in this work) that the

premises of geometry are not definitions, but assumptions of the real

existence of things corresponding to those definitions. This, however, is

doing little for Dr. Whewell’s purpose; for it is these very assumptions

which are asserted to be hypotheses, and which he, if he denies that

geometry is founded on hypotheses, must show to be absolute truths. All he

does, however, is to observe, that they, at any rate, are not _arbitrary_

hypotheses; that we should not be at liberty to substitute other

hypotheses for them; that not only “a definition, to be admissible, must

necessarily refer to and agree with some conception which we can

distinctly frame in our thoughts,” but that the straight lines, for

instance, which we define, must be “those by which angles are contained,

those by which triangles are bounded, those of which parallelism may be

predicated, and the like.”(69) And this is true; but this has never been

contradicted. Those who say that the premises of geometry are hypotheses,

are not bound to maintain them to be hypotheses which have no relation

whatever to fact. Since an hypothesis framed for the purpose of scientific

inquiry must relate to something which has real existence (for there can

be no science respecting nonentities), it follows that any hypothesis we

make respecting an object, to facilitate our study of it, must not involve

any thing which is distinctly false, and repugnant to its real nature: we

must not ascribe to the thing any property which it has not; our liberty

extends only to slightly exaggerating some of those which it has (by

assuming it to be completely what it really is very nearly), and

suppressing others, under the indispensable obligation of restoring them

whenever, and in as far as, their presence or absence would make any

material difference in the truth of our conclusions. Of this nature,

accordingly, are the first principles involved in the definitions of

geometry. That the hypotheses should be of this particular character, is,

however, no further necessary, than inasmuch as no others could enable us

to deduce conclusions which, with due corrections, would be true of real

objects: and in fact, when our aim is only to illustrate truths, and not

to investigate them, we are not under any such restriction. We might

suppose an imaginary animal, and work out by deduction, from the known

laws of physiology, its natural history; or an imaginary commonwealth, and

from the elements composing it, might argue what would be its fate. And

the conclusions which we might thus draw from purely arbitrary hypotheses,

might form a highly useful intellectual exercise: but as they could only

teach us what _would_ be the properties of objects which do not really

exist, they would not constitute any addition to our knowledge of nature:

while, on the contrary, if the hypothesis merely divests a real object of

some portion of its properties, without clothing it in false ones, the

conclusions will always express, under known liability to correction,

actual truth.

§ 3. But though Dr. Whewell has not shaken Stewart’s doctrine as to the

hypothetical character of that portion of the first principles of geometry

which are involved in the so-called definitions, he has, I conceive,

greatly the advantage of Stewart on another important point in the theory

of geometrical reasoning; the necessity of admitting, among those first

principles, axioms as well as definitions. Some of the axioms of Euclid

might, no doubt, be exhibited in the form of definitions, or might be

deduced, by reasoning, from propositions similar to what are so called.

Thus, if instead of the axiom, Magnitudes which can be made to coincide

are equal, we introduce a definition, “Equal magnitudes are those which

may be so applied to one another as to coincide;” the three axioms which

follow (Magnitudes which are equal to the same are equal to one another—If

equals are added to equals, the sums are equal—If equals are taken from

equals, the remainders are equal), may be proved by an imaginary

superposition, resembling that by which the fourth proposition of the

first book of Euclid is demonstrated. But though these and several others

may be struck out of the list of first principles, because, though not

requiring demonstration, they are susceptible of it; there will be found

in the list of axioms two or three fundamental truths, not capable of

being demonstrated: among which must be reckoned the proposition that two

straight lines can not inclose a space (or its equivalent, Straight lines

which coincide in two points coincide altogether), and some property of

parallel lines, other than that which constitutes their definition: one of

the most suitable for the purpose being that selected by Professor

Playfair: “Two straight lines which intersect each other can not both of

them be parallel to a third straight line.”(70)

The axioms, as well those which are indemonstrable as those which admit of

being demonstrated, differ from that other class of fundamental principles

which are involved in the definitions, in this, that they are true without

any mixture of hypothesis. That things which are equal to the same thing

are equal to one another, is as true of the lines and figures in nature,

as it would be of the imaginary ones assumed in the definitions. In this

respect, however, mathematics are only on a par with most other sciences.

In almost all sciences there are some general propositions which are

exactly true, while the greater part are only more or less distant

approximations to the truth. Thus in mechanics, the first law of motion

(the continuance of a movement once impressed, until stopped or slackened

by some resisting force) is true without qualification or error. The

rotation of the earth in twenty-four hours, of the same length as in our

time, has gone on since the first accurate observations, without the

increase or diminution of one second in all that period. These are

inductions which require no fiction to make them be received as accurately

true: but along with them there are others, as for instance the

propositions respecting the figure of the earth, which are but

approximations to the truth; and in order to use them for the further

advancement of our knowledge, we must feign that they are exactly true,

though they really want something of being so.

§ 4. It remains to inquire, what is the ground of our belief in

axioms—what is the evidence on which they rest? I answer, they are

experimental truths; generalizations from observation. The proposition,

Two straight lines can not inclose a space—or, in other words, Two

straight lines which have once met, do not meet again, but continue to

diverge—is an induction from the evidence of our senses.

This opinion runs counter to a scientific prejudice of long standing and

great strength, and there is probably no proposition enunciated in this

work for which a more unfavorable reception is to be expected. It is,

however, no new opinion; and even if it were so, would be entitled to be

judged, not by its novelty, but by the strength of the arguments by which

it can be supported. I consider it very fortunate that so eminent a

champion of the contrary opinion as Dr. Whewell has found occasion for a

most elaborate treatment of the whole theory of axioms, in attempting to

construct the philosophy of the mathematical and physical sciences on the

basis of the doctrine against which I now contend. Whoever is anxious that

a discussion should go to the bottom of the subject, must rejoice to see

the opposite side of the question worthily represented. If what is said by

Dr. Whewell, in support of an opinion which he has made the foundation of

a systematic work, can be shown not to be conclusive, enough will have

been done, without going elsewhere in quest of stronger arguments and a

more powerful adversary.

It is not necessary to show that the truths which we call axioms are

originally _suggested_ by observation, and that we should never have known

that two straight lines can not inclose a space if we had never seen a

straight line: thus much being admitted by Dr. Whewell, and by all, in

recent times, who have taken his view of the subject. But they contend,

that it is not experience which _proves_ the axiom; but that its truth is

perceived _a priori_, by the constitution of the mind itself, from the

first moment when the meaning of the proposition is apprehended; and

without any necessity for verifying it by repeated trials, as is requisite

in the case of truths really ascertained by observation.

They can not, however, but allow that the truth of the axiom, Two straight

lines can not inclose a space, even if evident independently of

experience, is also evident from experience. Whether the axiom needs

confirmation or not, it receives confirmation in almost every instant of

our lives; since we can not look at any two straight lines which intersect

one another, without seeing that from that point they continue to diverge

more and more. Experimental proof crowds in upon us in such endless

profusion, and without one instance in which there can be even a suspicion

of an exception to the rule, that we should soon have stronger ground for

believing the axiom, even as an experimental truth, than we have for

almost any of the general truths which we confessedly learn from the

evidence of our senses. Independently of _a priori_ evidence, we should

certainly believe it with an intensity of conviction far greater than we

accord to any ordinary physical truth: and this too at a time of life much

earlier than that from which we date almost any part of our acquired

knowledge, and much too early to admit of our retaining any recollection

of the history of our intellectual operations at that period. Where then

is the necessity for assuming that our recognition of these truths has a

different origin from the rest of our knowledge, when its existence is

perfectly accounted for by supposing its origin to be the same? when the

causes which produce belief in all other instances, exist in this

instance, and in a degree of strength as much superior to what exists in

other cases, as the intensity of the belief itself is superior? The burden

of proof lies on the advocates of the contrary opinion: it is for them to

point out some fact, inconsistent with the supposition that this part of

our knowledge of nature is derived from the same sources as every other

part.(71)

This, for instance, they would be able to do, if they could prove

chronologically that we had the conviction (at least practically) so early

in infancy as to be anterior to those impressions on the senses, upon

which, on the other theory, the conviction is founded. This, however, can

not be proved: the point being too far back to be within the reach of

memory, and too obscure for external observation. The advocates of the _a

priori_ theory are obliged to have recourse to other arguments. These are

reducible to two, which I shall endeavor to state as clearly and as

forcibly as possible.

§ 5. In the first place it is said, that if our assent to the proposition

that two straight lines can not inclose a space, were derived from the

senses, we could only be convinced of its truth by actual trial, that is,

by seeing or feeling the straight lines; whereas, in fact, it is seen to

be true by merely thinking of them. That a stone thrown into water goes to

the bottom, may be perceived by our senses, but mere thinking of a stone

thrown into the water would never have led us to that conclusion: not so,

however, with the axioms relating to straight lines: if I could be made to

conceive what a straight line is, without having seen one, I should at

once recognize that two such lines can not inclose a space. Intuition is

“imaginary looking;”(72) but experience must be real looking: if we see a

property of straight lines to be true by merely fancying ourselves to be

looking at them, the ground of our belief can not be the senses, or

experience; it must be something mental.

To this argument it might be added in the case of this particular axiom

(for the assertion would not be true of all axioms), that the evidence of

it from actual ocular inspection is not only unnecessary, but

unattainable. What says the axiom? That two straight lines _can not_

inclose a space; that after having once intersected, if they are prolonged

to infinity they do not meet, but continue to diverge from one another.

How can this, in any single case, be proved by actual observation? We may

follow the lines to any distance we please; but we can not follow them to

infinity: for aught our senses can testify, they may, immediately beyond

the farthest point to which we have traced them, begin to approach, and at

last meet. Unless, therefore, we had some other proof of the impossibility

than observation affords us, we should have no ground for believing the

axiom at all.

To these arguments, which I trust I can not be accused of understating, a

satisfactory answer will, I conceive, be found, if we advert to one of the

characteristic properties of geometrical forms—their capacity of being

painted in the imagination with a distinctness equal to reality: in other

words, the exact resemblance of our ideas of form to the sensations which

suggest them. This, in the first place, enables us to make (at least with

a little practice) mental pictures of all possible combinations of lines

and angles, which resemble the realities quite as well as any which we

could make on paper; and in the next place, make those pictures just as

fit subjects of geometrical experimentation as the realities themselves;

inasmuch as pictures, if sufficiently accurate, exhibit of course all the

properties which would be manifested by the realities at one given

instant, and on simple inspection: and in geometry we are concerned only

with such properties, and not with that which pictures could not exhibit,

the mutual action of bodies one upon another. The foundations of geometry

would therefore be laid in direct experience, even if the experiments

(which in this case consist merely in attentive contemplation) were

practiced solely upon what we call our ideas, that is, upon the diagrams

in our minds, and not upon outward objects. For in all systems of

experimentation we take some objects to serve as representatives of all

which resemble them; and in the present case the conditions which qualify

a real object to be the representative of its class, are completely

fulfilled by an object existing only in our fancy. Without denying,

therefore, the possibility of satisfying ourselves that two straight lines

can not inclose a space, by merely thinking of straight lines without

actually looking at them; I contend, that we do not believe this truth on

the ground of the imaginary intuition simply, but because we know that the

imaginary lines exactly resemble real ones, and that we may conclude from

them to real ones with quite as much certainty as we could conclude from

one real line to another. The conclusion, therefore, is still an induction

from observation. And we should not be authorized to substitute

observation of the image in our mind, for observation of the reality, if

we had not learned by long-continued experience that the properties of the

reality are faithfully represented in the image; just as we should be

scientifically warranted in describing an animal which we have never seen,

from a picture made of it with a daguerreotype; but not until we had

learned by ample experience, that observation of such a picture is

precisely equivalent to observation of the original.

These considerations also remove the objection arising from the

impossibility of ocularly following the lines in their prolongation to

infinity. For though, in order actually to see that two given lines never

meet, it would be necessary to follow them to infinity; yet without doing

so we may know that if they ever do meet, or if, after diverging from one

another, they begin again to approach, this must take place not at an

infinite, but at a finite distance. Supposing, therefore, such to be the

case, we can transport ourselves thither in imagination, and can frame a

mental image of the appearance which one or both of the lines must present

at that point, which we may rely on as being precisely similar to the

reality. Now, whether we fix our contemplation upon this imaginary

picture, or call to mind the generalizations we have had occasion to make

from former ocular observation, we learn by the evidence of experience,

that a line which, after diverging from another straight line, begins to

approach to it, produces the impression on our senses which we describe by

the expression, “a bent line,” not by the expression, “a straight

line.”(73)

The preceding argument, which is, to my mind unanswerable, merges,

however, in a still more comprehensive one, which is stated most clearly

and conclusively by Professor Bain. The psychological reason why axioms,

and indeed many propositions not ordinarily classed as such, may be

learned from the idea only without referring to the fact, is that in the

process of acquiring the idea we have learned the fact. The proposition is

assented to as soon as the terms are understood, because in learning to

understand the terms we have acquired the experience which proves the

proposition to be true. “We required,” says Mr. Bain,(74) “concrete

experience in the first instance, to attain to the notion of whole and

part; but the notion, once arrived at, implies that the whole is greater.

In fact, we could not have the notion without an experience tantamount to

this conclusion.... When we have mastered the notion of straightness, we

have also mastered that aspect of it expressed by the affirmation that two

straight lines can not inclose a space. No intuitive or innate powers or

perceptions are needed in such case.... We can not have the full meaning

of Straightness, without going through a comparison of straight objects

among themselves, and with their opposites, bent or crooked objects. The

result of this comparison is, _inter alia_, that straightness in two lines

is seen to be incompatible with inclosing a space; the inclosure of space

involves crookedness in at least one of the lines.” And similarly, in the

case of every first principle,(75) “the same knowledge that makes it

understood, suffices to verify it.” The more this observation is

considered the more (I am convinced) it will be felt to go to the very

root of the controversy.

§ 6. The first of the two arguments in support of the theory that axioms

are _a priori_ truths, having, I think, been sufficiently answered; I

proceed to the second, which is usually the most relied on. Axioms (it is

asserted) are conceived by us not only as true, but as universally and

necessarily true. Now, experience can not possibly give to any proposition

this character. I may have seen snow a hundred times, and may have seen

that it was white, but this can not give me entire assurance even that all

snow is white; much less that snow _must_ be white. “However many

instances we may have observed of the truth of a proposition, there is

nothing to assure us that the next case shall not be an exception to the

rule. If it be strictly true that every ruminant animal yet known has

cloven hoofs, we still can not be sure that some creature will not

hereafter be discovered which has the first of these attributes, without

having the other.... Experience must always consist of a limited number of

observations; and, however numerous these may be, they can show nothing

with regard to the infinite number of cases in which the experiment has

not been made.” Besides, Axioms are not only universal, they are also

necessary. Now “experience can not offer the smallest ground for the

necessity of a proposition. She can observe and record what has happened;

but she can not find, in any case, or in any accumulation of cases, any

reason for what _must_ happen. She may see objects side by side; but she

can not see a reason why they must ever be side by side. She finds certain

events to occur in succession; but the succession supplies, in its

occurrence, no reason for its recurrence. She contemplates external

objects; but she can not detect any internal bond, which indissolubly

connects the future with the past, the possible with the real. To learn a

proposition by experience, and to see it to be necessarily true, are two

altogether different processes of thought.”(76) And Dr. Whewell adds, “If

any one does not clearly comprehend this distinction of necessary and

contingent truths, he will not be able to go along with us in our

researches into the foundations of human knowledge; nor, indeed, to pursue

with success any speculation on the subject.”(77)

In the following passage, we are told what the distinction is, the

non-recognition of which incurs this denunciation. “Necessary truths are

those in which we not only learn that the proposition _is_ true, but see

that it _must be_ true; in which the negation of the truth is not only

false, but impossible; in which we can not, even by an effort of

imagination, or in a supposition, conceive the reverse of that which is

asserted. That there are such truths can not be doubted. We may take, for

example, all relations of number. Three and Two added together make Five.

We can not conceive it to be otherwise. We can not, by any freak of

thought, imagine Three and Two to make Seven.”(78)

Although Dr. Whewell has naturally and properly employed a variety of

phrases to bring his meaning more forcibly home, he would, I presume,

allow that they are all equivalent; and that what he means by a necessary

truth, would be sufficiently defined, a proposition the negation of which

is not only false but inconceivable. I am unable to find in any of his

expressions, turn them what way you will, a meaning beyond this, and I do

not believe he would contend that they mean any thing more.

This, therefore, is the principle asserted: that propositions, the

negation of which is inconceivable, or in other words, which we can not

figure to ourselves as being false, must rest on evidence of a higher and

more cogent description than any which experience can afford.

Now I can not but wonder that so much stress should be laid on the

circumstance of inconceivableness, when there is such ample experience to

show, that our capacity or incapacity of conceiving a thing has very

little to do with the possibility of the thing in itself; but is in truth

very much an affair of accident, and depends on the past history and

habits of our own minds. There is no more generally acknowledged fact in

human nature, than the extreme difficulty at first felt in conceiving any

thing as possible, which is in contradiction to long established and

familiar experience; or even to old familiar habits of thought. And this

difficulty is a necessary result of the fundamental laws of the human

mind. When we have often seen and thought of two things together, and have

never in any one instance either seen or thought of them separately, there

is by the primary law of association an increasing difficulty, which may

in the end become insuperable, of conceiving the two things apart. This is

most of all conspicuous in uneducated persons, who are in general utterly

unable to separate any two ideas which have once become firmly associated

in their minds; and if persons of cultivated intellect have any advantage

on the point, it is only because, having seen and heard and read more, and

being more accustomed to exercise their imagination, they have experienced

their sensations and thoughts in more varied combinations, and have been

prevented from forming many of these inseparable associations. But this

advantage has necessarily its limits. The most practiced intellect is not

exempt from the universal laws of our conceptive faculty. If daily habit

presents to any one for a long period two facts in combination, and if he

is not led during that period either by accident or by his voluntary

mental operations to think of them apart, he will probably in time become

incapable of doing so even by the strongest effort; and the supposition

that the two facts can be separated in nature, will at last present itself

to his mind with all the characters of an inconceivable phenomenon.(79)

There are remarkable instances of this in the history of science:

instances in which the most instructed men rejected as impossible, because

inconceivable, things which their posterity, by earlier practice and

longer perseverance in the attempt, found it quite easy to conceive, and

which every body now knows to be true. There was a time when men of the

most cultivated intellects, and the most emancipated from the dominion of

early prejudice, could not credit the existence of antipodes; were unable

to conceive, in opposition to old association, the force of gravity acting

upward instead of downward. The Cartesians long rejected the Newtonian

doctrine of the gravitation of all bodies toward one another, on the faith

of a general proposition, the reverse of which seemed to them to be

inconceivable—the proposition that a body can not act where it is not. All

the cumbrous machinery of imaginary vortices, assumed without the smallest

particle of evidence, appeared to these philosophers a more rational mode

of explaining the heavenly motions, than one which involved what seemed to

them so great an absurdity.(80)

And they no doubt found it as impossible to conceive that a body should

act upon the earth from the distance of the sun or moon, as we find it to

conceive an end to space or time, or two straight lines inclosing a space.

Newton himself had not been able to realize the conception, or we should

not have had his hypothesis of a subtle ether, the occult cause of

gravitation; and his writings prove, that though he deemed the particular

nature of the intermediate agency a matter of conjecture, the necessity of

_some_ such agency appeared to him indubitable.

If, then, it be so natural to the human mind, even in a high state of

culture, to be incapable of conceiving, and on that ground to believe

impossible, what is afterward not only found to be conceivable but proved

to be true; what wonder if in cases where the association is still older,

more confirmed, and more familiar, and in which nothing ever occurs to

shake our conviction, or even suggest to us any conception at variance

with the association, the acquired incapacity should continue, and be

mistaken for a natural incapacity? It is true, our experience of the

varieties in nature enables us, within certain limits, to conceive other

varieties analogous to them. We can conceive the sun or moon falling; for

though we never saw them fall, nor ever, perhaps, imagined them falling,

we have seen so many other things fall, that we have innumerable familiar

analogies to assist the conception; which, after all, we should probably

have some difficulty in framing, were we not well accustomed to see the

sun and moon move (or appear to move), so that we are only called upon to

conceive a slight change in the direction of motion, a circumstance

familiar to our experience. But when experience affords no model on which

to shape the new conception, how is it possible for us to form it? How,

for example, can we imagine an end to space or time? We never saw any

object without something beyond it, nor experienced any feeling without

something following it. When, therefore, we attempt to conceive the last

point of space, we have the idea irresistibly raised of other points

beyond it. When we try to imagine the last instant of time, we can not

help conceiving another instant after it. Nor is there any necessity to

assume, as is done by a modern school of metaphysicians, a peculiar

fundamental law of the mind to account for the feeling of infinity

inherent in our conceptions of space and time; that apparent infinity is

sufficiently accounted for by simpler and universally acknowledged laws.

Now, in the case of a geometrical axiom, such, for example, as that two

straight lines can not inclose a space—a truth which is testified to us by

our very earliest impressions of the external world—how is it possible

(whether those external impressions be or be not the ground of our belief)

that the reverse of the proposition _could_ be otherwise than

inconceivable to us? What analogy have we, what similar order of facts in

any other branch of our experience, to facilitate to us the conception of

two straight lines inclosing a space? Nor is even this all. I have already

called attention to the peculiar property of our impressions of form, that

the ideas or mental images exactly resemble their prototypes, and

adequately represent them for the purposes of scientific observation. From

this, and from the intuitive character of the observation, which in this

case reduces itself to simple inspection, we can not so much as call up in

our imagination two straight lines, in order to attempt to conceive them

inclosing a space, without by that very act repeating the scientific

experiment which establishes the contrary. Will it really be contended

that the inconceivableness of the thing, in such circumstances, proves any

thing against the experimental origin of the conviction? Is it not clear

that in whichever mode our belief in the proposition may have originated,

the impossibility of our conceiving the negative of it must, on either

hypothesis, be the same? As, then, Dr. Whewell exhorts those who have any

difficulty in recognizing the distinction held by him between necessary

and contingent truths, to study geometry—a condition which I can assure

him I have conscientiously fulfilled—I, in return, with equal confidence,

exhort those who agree with him, to study the general laws of association;

being convinced that nothing more is requisite than a moderate familiarity

with those laws, to dispel the illusion which ascribes a peculiar

necessity to our earliest inductions from experience, and measures the

possibility of things in themselves, by the human capacity of conceiving

them.

I hope to be pardoned for adding, that Dr. Whewell himself has both

confirmed by his testimony the effect of habitual association in giving to

an experimental truth the appearance of a necessary one, and afforded a

striking instance of that remarkable law in his own person. In his

_Philosophy of the Inductive Sciences_ he continually asserts, that

propositions which not only are not self-evident, but which we know to

have been discovered gradually, and by great efforts of genius and

patience, have, when once established, appeared so self-evident that, but

for historical proof, it would have been impossible to conceive that they

had not been recognized from the first by all persons in a sound state of

their faculties. “We now despise those who, in the Copernican controversy,

could not conceive the apparent motion of the sun on the heliocentric

hypothesis; or those who, in opposition to Galileo, thought that a uniform

force might be that which generated a velocity proportional to the space;

or those who held there was something absurd in Newton’s doctrine of the

different refrangibility of differently colored rays; or those who

imagined that when elements combine, their sensible qualities must be

manifest in the compound; or those who were reluctant to give up the

distinction of vegetables into herbs, shrubs, and trees. We can not help

thinking that men must have been singularly dull of comprehension, to find

a difficulty in admitting what is to us so plain and simple. We have a

latent persuasion that we in their place should have been wiser and more

clear-sighted; that we should have taken the right side, and given our

assent at once to the truth. Yet in reality such a persuasion is a mere

delusion. The persons who, in such instances as the above, were on the

losing side, were very far, in most cases, from being persons more

prejudiced, or stupid, or narrow-minded, than the greater part of mankind

now are; and the cause for which they fought was far from being a

manifestly bad one, till it had been so decided by the result of the

war.... So complete has been the victory of truth in most of these

instances, that at present we can hardly imagine the struggle to have been

necessary. _The very essence of these triumphs is, that they lead us to

regard the views we reject as not only false but inconceivable._”(81)

This last proposition is precisely what I contend for; and I ask no more,

in order to overthrow the whole theory of its author on the nature of the

evidence of axioms. For what is that theory? That the truth of axioms can

not have been learned from experience, because their falsity is

inconceivable. But Dr. Whewell himself says, that we are continually led,