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.
In Two Volumes.
Vol. I.
Third Edition.
London:
John Parker, West Strand.
M DCCC LI.
CONTENTS
PREFACE TO THE FIRST EDITION.
PREFACE TO THE THIRD EDITION.
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.
I. Feelings, or States of Consciousness.
II. Substances.
III. Attributes: and, first, Qualities.
IV. Relations.
V. Quantity.
VI. Attributes Concluded.
VII. General Results.
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. OF 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.
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. OF THE COMPOSITION OF CAUSES.
CHAPTER VII. OF 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.
Footnotes
PREFACE TO THE FIRST EDITION.
This book makes no pretence of giving to the world a new theory of the
intellectual operations. Its claim to attention, if it possess any, is
grounded on the fact that it is an attempt not to supersede, but to embody
and systematize, the best ideas which have been either promulgated on its
subject by speculative writers, or conformed to by accurate thinkers in
their scientific inquiries.
To cement together the detached fragments of a subject, never yet treated
as a whole; to harmonize the true portions of discordant theories, by
supplying the links of thought necessary to connect them, and by
disentangling them from the errors with which they are always more or less
interwoven; must necessarily require a considerable amount of original
speculation. To other originality than this, the present work lays no
claim. In the existing state of the cultivation of the sciences, there
would be a very strong presumption against any one who should imagine that
he had effected a revolution in the theory of the investigation of truth,
or added any fundamentally new process to the practice of it. The
improvement which remains to be effected in the methods of philosophizing
(and the author believes that they have much need of improvement) can only
consist in performing, more systematically and accurately, operations with
which, at least in their elementary form, the human intellect in some one
or other of its employments is already familiar.
In the portion of the work which treats of Ratiocination, the author has
not deemed it necessary to enter into technical details which may be
obtained in so perfect a shape from the existing treatises on what is
termed the Logic of the Schools. In the contempt entertained by many
modern philosophers for the syllogistic art, it will be seen that he by no
means participates; although the scientific theory on which its defence is
usually rested appears to him erroneous: and the view which he has
suggested of the nature and functions of the Syllogism may, perhaps,
afford the means of conciliating the principles of the art with as much as
is well grounded in the doctrines and objections of its assailants.
The same abstinence from details could not be observed in the First Book,
on Names and Propositions; because many useful principles and distinctions
which were contained in the old Logic, have been gradually omitted from
the writings of its later teachers; and it appeared desirable both to
revive these, and to reform and rationalize the philosophical foundation
on which they stood. The earlier chapters of this preliminary Book will
consequently appear, to some readers, needlessly elementary and
scholastic. But those who know in what darkness the nature of our
knowledge, and of the processes by which it is obtained, is often involved
by a confused apprehension of the import of the different classes of Words
and Assertions, will not regard these discussions as either frivolous, or
irrelevant to the topics considered in the later Books.
On the subject of Induction, the task to be performed was that of
generalizing the modes of investigating truth and estimating evidence, by
which so many important and recondite laws of nature have, in the various
sciences, been aggregated to the stock of human knowledge. That this is
not a task free from difficulty may be presumed from the fact, that even
at a very recent period, eminent writers (among whom it is sufficient to
name Archbishop Whately, and the author of a celebrated article on Bacon
in the _Edinburgh Review_) have not scrupled to pronounce it
impossible.(1) The author has endeavoured to combat their theory in the
manner in which Diogenes confuted the sceptical reasonings against the
possibility of motion; remembering that Diogenes’ argument would have been
equally conclusive, though his individual perambulations might not have
extended beyond the circuit of his own tub.
Whatever may be the value of what the author has succeeded in effecting on
this branch of his subject, it is a duty to acknowledge that for much of
it he has been indebted to several important treatises, partly historical
and partly philosophical, on the generalities and processes of physical
science, which have been published within the last few years. To these
treatises, and to their authors, he has endeavoured to do justice in the
body of the work. But as with one of these writers, Dr. Whewell, he has
occasion frequently to express differences of opinion, it is more
particularly incumbent on him in this place to declare, that without the
aid derived from the facts and ideas contained in that gentleman’s
_History of the Inductive Sciences_, the corresponding portion of this
work would probably not have been written.
The concluding Book is an attempt to contribute towards the solution of a
question, which the decay of old opinions, and the agitation that disturbs
European society to its inmost depths, render as important in the present
day to the practical interests of human life, as it must at all times be
to the completeness of our speculative knowledge: viz. Whether moral and
social phenomena are really exceptions to the general certainty and
uniformity of the course of nature; and how far the methods, by which so
many of the laws of the physical world have been numbered among truths
irrevocably acquired and universally assented to, can be made instrumental
to the formation of a similar body of received doctrine in moral and
political science.
PREFACE TO THE THIRD EDITION.
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.
I have carefully reconsidered all the points on which my conclusions have
been assailed. But I have not to announce a change of opinion on any
matter of importance. Such minor oversights as have been detected, either
by myself or by my critics, I have, in general silently, corrected: but it
is not to be inferred that I agree with the objections which have been
made to a passage, in every instance in which I have altered or cancelled
it. I have often done so, merely that it might not remain a
stumbling-block, when the amount of discussion necessary to place the
matter in its true light would have exceeded what was suitable to the
occasion.
To several of the arguments which have been urged against me, I have
thought it useful to reply with some degree of minuteness; not from any
taste for controversy, but because the opportunity was favourable for
placing my own conclusions, and the grounds of them, more clearly and
completely before the reader. Truth, on these subjects, is militant, and
can only establish itself by means of conflict. The most opposite opinions
can make a plausible show of evidence while each has the statement of its
own case; and it is only possible to ascertain which of them is in the
right, after hearing and comparing what each can say against the other,
and what the other can urge in its defence.
Even the criticisms from which I most dissent have been of great service
to me, by showing in what places the exposition most needed to be
improved, or the arguments 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.
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 favour.
This diversity is not so much an evil to be complained of, as an
inevitable and in some degree a proper result of the imperfect state of
those sciences. It is not to be expected that there should be agreement
about the definition of a thing, until there is agreement about the thing
itself. To define a thing, is to select from among the whole of its
properties those which shall be understood to be designated and declared
by its name; and the properties must be well known to us before we can be
competent to determine which of them are fittest to be chosen for this
purpose. Accordingly, in the case of so complex an aggregation of
particulars as are comprehended in anything which can be called a science,
the definition we set out with is seldom that which a more extensive
knowledge of the subject shows to be the most appropriate. Until we know
the particulars themselves, we cannot fix upon the most correct and
compact mode of circumscribing them by a general description. It was not
till 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 imperfections; and if the
former are progressive, the latter ought to be so too. As much, therefore,
as is to be expected from a definition placed at the commencement of a
subject, is that it should define the scope of our inquiries: and the
definition which I am about to offer of the science of logic, pretends to
nothing more, than to be a statement of the question which I have put to
myself, and which this book is an attempt to resolve. The reader is at
liberty to object to it as a definition of logic; but it is at all events
a correct definition of the subject of these volumes.
§ 2. Logic has often been called the Art of Reasoning. A writer(2) who has
done more than any other living 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 the
science on which it rests, it is only because several sciences are often
necessary to form the groundwork of a single art. Such is the complication
of human affairs, 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.
Professedly, indeed, these previous topics were introduced only on account
of their connexion with reasoning, and as a preparation for the doctrine
and rules of the syllogism. Yet they were treated with greater minuteness,
and dwelt on at greater length, than was required for that purpose alone.
More recent writers on logic have generally understood the term as it was
employed by the able author of the Port Royal Logic; viz. as equivalent to
the Art of Thinking. Nor is this acceptation confined to books, and
scientific inquirers. 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 premisses. 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 premisses; 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; the latter, of Inference. The
truths known by intuition are the original premisses from which all others
are inferred. Our assent to the conclusion being grounded on the truth of
the premisses, 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 premisses 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 premisses of our knowledge; with their
number or nature, the mode in which they are obtained, or the tests by
which they may be distinguished; logic, in a direct way at least, has, in
the sense in which I conceive the science, nothing to do. These questions
are partly not a subject of science at all, partly that of a very
different science.
Whatever is known to us by consciousness, is known beyond possibility of
question. What one sees or feels, whether bodily or mentally, one cannot
but be sure that one sees or feels. No science is required for the purpose
of establishing such truths; no rules of art can render our knowledge of
them more certain than it is in itself. There is no logic for this portion
of our knowledge.
But we may fancy that we see or feel what we in reality infer. Newton saw
the truth of many propositions of geometry without reading the
demonstrations, but not, we may be sure, without their flashing through
his mind. A truth, or supposed truth, which is really the result of a very
rapid inference, may seem to be apprehended intuitively. It has long been
agreed by thinkers of the most opposite schools, that this mistake is
actually made in so familiar an instance as that of the eyesight. There is
nothing of which we appear to ourselves to be more directly conscious,
than the distance of an object from us. Yet it has long been ascertained,
that what is perceived by the eye, is at most nothing more than a
variously coloured surface; that when we fancy we see distance, all we
really see is certain variations of apparent size, and degrees of
faintness of colour; and that our estimate of the object’s distance from
us is the result of a comparison (made with so much rapidity that we are
unconscious of making it) between the size and colour of the object as
they appear at the time, and the size and colour of the same or of similar
objects as they appeared when close at hand, or when their degree of
remoteness was known by other evidence. The perception of distance by the
eye, which seems so like intuition, is thus, in reality, an inference
grounded on experience; an inference, too, which we learn to make; and
which we make with more and more correctness as our experience increases;
though in familiar cases it takes place, so rapidly as to appear exactly
on a par with those perceptions of sight which are really intuitive, our
perceptions of colour.(3)
Of the science, therefore, which expounds the operations of the human
understanding in the pursuit of truth, one essential part is the inquiry:
What are the facts which are the objects of intuition or consciousness,
and what are those which we merely infer? But this inquiry has never been
considered a portion of logic. Its place is in another and a perfectly
distinct department of science, to which the name metaphysics more
particularly belongs: that portion of mental philosophy which attempts to
determine what part of the furniture of the mind belongs to it originally,
and what part is constructed out of materials furnished to it from
without. To this science appertain the great and much debated questions of
the existence of matter; the existence of spirit, and of a distinction
between it and matter; the reality of time and space, as things without
the mind, and distinguishable from the objects which are said to exist
_in_ them. For in the present state of the discussion on these topics, it
is almost universally allowed that the existence of matter or of spirit,
of space or of time, is, in its nature, unsusceptible of being proved; and
that if anything is known of them, it must be by immediate intuition. To
the same science belong the inquiries into the nature of Conception,
Perception, Memory, and Belief; all of which are operations of the
understanding in the pursuit of truth; but with which, as phenomena of the
mind, or with the possibility which may or may not exist of analysing any
of them into simpler phenomena, the logician as such has no concern. To
this science must also be referred the following, and all analogous
questions: To what extent our intellectual faculties and our emotions are
innate—to what extent the result of association: Whether God, and duty,
are realities, the existence of which is manifest to us à priori by the
constitution of our rational faculty; or whether our ideas of them are
acquired notions, the origin of which we are able to trace and explain;
and the reality of the objects themselves a question not of consciousness
or intuition, but of evidence and reasoning.
The province of logic must be restricted to that portion of our knowledge
which consists of inferences from truths previously known; whether those
antecedent data be general propositions, or particular observations and
perceptions. Logic is not the science of Belief, but the science of Proof,
or Evidence. In so far as belief professes to be founded on proof, the
office of logic is to supply a test for ascertaining whether or not the
belief is well grounded. With the claims which any proposition has to
belief on the evidence of consciousness, that is, without evidence in the
proper sense of the word, logic has nothing to do.
§ 5. By far the greatest portion of our knowledge, whether of general
truths or of particular facts, being avowedly matter of inference, nearly
the whole, not only of science, but of human conduct, is amenable to the
authority of logic. To draw inferences has been said to be the great
business of life. Every one has daily, hourly, and momentary need of
ascertaining facts which he has not directly observed; not from any
general purpose of adding to his stock of knowledge, but because the facts
themselves are of importance to his interests or to his occupations. The
business of the magistrate, of the military commander, of the navigator,
of the physician, of the agriculturist, is merely to judge of evidence,
and to act accordingly. They all have to ascertain certain facts, in order
that they may afterwards apply certain rules, either devised by
themselves, or prescribed for their guidance by others; and as they do
this well or ill, so they discharge well or ill the duties of their
several callings. It is the only occupation in which the mind never ceases
to be engaged; and is the subject, not of logic, but of knowledge in
general.
Logic, however, is not the same thing with knowledge, though the field of
logic is coextensive with the field of knowledge. Logic is the common
judge and arbiter of all particular investigations. It does not undertake
to find evidence, but to determine whether it has been found. Logic
neither observes, nor invents, nor discovers; but judges. It is no part of
the business of logic to inform the surgeon what appearances are found to
accompany a violent death. This he must learn from his own experience and
observation, or from that of others, his predecessors in his peculiar
pursuit. But logic sits in judgment on the sufficiency of that observation
and experience to justify his rules, and on the sufficiency of his rules
to justify his conduct. It does not give him proofs, but teaches him what
makes them proofs, and how he is to judge of them. It does not teach that
any particular fact proves any other, but points out to what conditions
all facts must conform, in order that they may prove other facts. To
decide whether any given fact fulfils these conditions, or whether facts
can be found which fulfil them in a given case, belongs exclusively to the
particular art or science, or to our knowledge of the particular subject.
It is in this sense that logic is, what Bacon so expressively called it,
_ars artium_; the science of science itself. All science consists of data
and conclusions from those data, of proofs and what they prove: now logic
points out what relations must subsist between data and whatever can be
concluded from them, between proof and everything which it can prove. If
there be any such indispensable relations, and if these can be precisely
determined, every particular branch of science, as well as every
individual in the guidance of his conduct, is bound to conform to those
relations, under the penalty of making false inferences, of drawing
conclusions which are not grounded in the realities of things. Whatever
has at any time been concluded justly, whatever knowledge has been
acquired otherwise than by immediate intuition, depended on the observance
of the laws which it is the province of logic to investigate. If the
conclusions are just, and the knowledge real, those laws, whether known or
not, have been observed.
§ 6. We need not, therefore, seek any farther for a solution of the
question, so often agitated, respecting the utility of logic. If a science
of logic exists, or is capable of existing, it must be useful. If there be
rules to which every mind consciously or unconsciously conforms in every
instance in which it infers rightly, there seems little necessity for
discussing whether a person is more likely to observe those rules, when he
knows the rules, than when he is unacquainted with them.
A science may undoubtedly be brought to a certain, not inconsiderable,
stage of advancement, without the application of any other logic to it
than what all persons, who are said to have a sound understanding, acquire
empirically in the course of their studies. Mankind judged of evidence,
and often correctly, before logic was a science, or they never could have
made it one. And they executed great mechanical works before they
understood the laws of mechanics. But there are limits both to what
mechanicians can do without principles of mechanics, and to what thinkers
can do without principles of logic. A few individuals may, by
extraordinary genius, anticipate the results of science; 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 proceeding from known truths to unknown, and all other
intellectual operations in so far as auxiliary to this. It includes,
therefore, the operation of Naming; for language is an instrument of
thought, as well as a means of communicating our thoughts. It includes,
also, Definition, and Classification. For, the use of these operations
(putting all other minds than one’s own out of consideration) is to serve
not only for keeping our evidences and the conclusions from them permanent
and readily accessible in the memory, but for so marshalling the facts
which we may at any time be engaged in investigating, as to enable us to
perceive more clearly what evidence there is, and to judge with fewer
chances of error whether it be sufficient. These, therefore, are
operations specially instrumental to the estimation of evidence, and as
such are within the province of Logic. There are other more elementary
processes, concerned in all thinking, such as Conception, Memory, and the
like; but of these it is not necessary that Logic should take any peculiar
cognizance, since they have no special connexion with the problem of
Evidence, further than that, like all other problems addressed to the
understanding, it presupposes them.
Our object, then, will be to attempt a correct analysis of the
intellectual process called Reasoning or Inference, and of such other
mental operations as are intended to facilitate this: as well as, on the
foundation of this analysis, and _pari __ passu_ with it, to bring
together or frame a set of rules or canons for testing the sufficiency of
any given evidence to prove any given proposition.
With respect to the first part of this undertaking, I do not attempt to
decompose the mental operations in question into their ultimate elements.
It is enough if the analysis as far as it goes is correct, and if it goes
far enough for the practical purposes of logic considered as an art. The
separation of a complicated phenomenon into its component parts, is not
like a connected and interdependent chain of proof. If one link of an
argument breaks, the whole drops to the ground; but one step towards an
analysis holds good and has an independent value, though we should never
be able to make a second. The results of analytical chemistry are not the
less valuable, though it should be discovered that all which we now call
simple substances are really compounds. All other things are at any rate
compounded of those elements: whether the elements themselves admit of
decomposition, is an important inquiry, but does not affect the certainty
of the science up to that point.
I shall, accordingly, attempt to analyse the process of inference, and the
processes subordinate to inference, so far only as may be requisite for
ascertaining the difference between a correct and an incorrect performance
of those processes. The reason for thus limiting our design, is evident.
It has been said by objectors to logic, that we do not learn to use our
muscles by studying their anatomy. The fact is not quite fairly stated;
for if the action of any of our muscles were vitiated by local weakness,
or other physical defect, a knowledge of their anatomy might be very
necessary for effecting a cure. But we should be justly liable to the
criticism involved in this objection, were we, in a treatise on logic, to
carry the analysis of the reasoning process beyond the point at which any
inaccuracy which may have crept into it must become visible. In learning
bodily exercises (to carry on the same illustration) we do, and must,
analyse the bodily motions so far as is necessary for distinguishing those
which ought to be performed from those which ought not. To a similar
extent, and no further, it is necessary that the logician should analyse
the mental processes with which Logic is concerned. Any ulterior and
minuter analysis must be left to metaphysics; which in this, as in other
parts of our mental nature, decides what are ultimate facts, and what are
resolvable into other facts. And I believe it will be found that the
conclusions arrived at in this work have no necessary connexion with any
particular views respecting the ulterior analysis. Logic is common ground
on which the partisans of Hartley and of Reid, of Locke and of Kant, may
meet and join hands. Particular and detached opinions of all these
thinkers will no doubt occasionally be controverted, since all of them
were logicians as well as metaphysicians; but the field on which their
principal battles have been fought, lies beyond the boundaries of our
science.
It cannot, indeed, be pretended that logical principles can be altogether
irrelevant to those more abstruse discussions; nor is it possible but that
the view we are led to take of the problem which logic proposes, must have
a tendency favourable to the adoption of some one opinion on these
controverted subjects rather than another. For metaphysics, in
endeavouring to solve its own peculiar problem, must employ means, the
validity of which falls under the cognizance of logic. It proceeds, no
doubt, as far as possible, merely by a closer and more attentive
interrogation of our consciousness, or more properly speaking, of our
memory; and so far is not amenable to logic. But wherever this method is
insufficient to attain the end of its inquiries, it must proceed, like
other sciences, by means of evidence. Now, the moment this science begins
to draw inferences from evidence, logic becomes the sovereign judge
whether its inferences are well-grounded, or what other inferences would
be so.
This, however, constitutes no nearer or other relation between logic and
metaphysics than that which exists between logic and all the other
sciences. 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.
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_.
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 make himself 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 fertile source of error; unless they taught
their pupil to put away the glasses which distort the object, and to use
those which are adapted to his purpose in such a manner as to assist, not
perplex his vision; he would not be in a condition to practise the
remaining part of their discipline with any prospect of advantage.
Therefore it is that an inquiry into language, so far as is needful to
guard against the errors to which it gives rise, has at all times been
deemed a necessary preliminary to the study of logic.
But there is another reason, of a still more fundamental nature, why the
import of words should be the earliest subject of the logician’s
consideration: because without it he cannot examine into the import of
Propositions. Now this is a subject which stands on the very threshold of
the science of logic.
The object of logic, as defined in the Introductory Chapter, is to
ascertain how we come by that portion of our knowledge (much the greatest
portion) which is not intuitive: and by what criterion we can, in matters
not self-evident, distinguish between things proved and things not proved,
between what is worthy and what is unworthy of belief. Of the various
questions which present themselves to our inquiring faculties, some
receive an answer from direct consciousness, others, if resolved at all,
can only be resolved by means of evidence. Logic is concerned with these
last. But before inquiring into the mode of resolving questions, it is
necessary to inquire, what are those which offer themselves? what
questions are conceivable? what inquiries are there, to which mankind have
either obtained, or been able to imagine it possible that they should
obtain, an answer? This point is best ascertained by a survey and analysis
of Propositions.
§ 2. The answer to every question which it is possible to frame, is
contained in a Proposition, or Assertion. Whatever can be an object of
belief, or even of disbelief, must, when put into words, assume the form
of a proposition. All truth and all error lie in propositions. What, by a
convenient misapplication of an abstract term, we call a Truth, means
simply a True Proposition; and errors are false propositions. To know the
import of all possible propositions, would be to know all questions which
can be raised, all matters which are susceptible of being either believed
or disbelieved. How many kinds of inquiries can be propounded; how many
kinds of judgments can be made; and how many kinds of propositions it is
possible to frame with a meaning; are but different forms of one and the
same question. Since, then, the objects of all Belief and of all Inquiry
express themselves in propositions; a sufficient scrutiny of Propositions
and of their varieties will apprize us what questions mankind have
actually asked of themselves, and what, in the nature of answers to those
questions, they have actually thought they had grounds to believe.
Now the first glance at a proposition shows that it is formed by putting
together two names. A proposition, according to the common simple
definition, which is sufficient for our purpose, is, _discourse_, _in
which something is affirmed or denied of something_. Thus, in the
proposition, Gold is yellow, the quality _yellow_ is affirmed of the
substance _gold_. In the proposition, Franklin was not born in England,
the fact expressed by the words _born in England_ is denied of the man
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
towards what we are in quest of. It appears from this, that for an act of
belief, _one_ object is not sufficient; the simplest act of belief
supposes, and has something to do with, _two_ objects: two names, to say
the least; and (since the names must be names of something) two _nameable
things_. A large class of thinkers would cut the matter short by saying,
two _ideas_. They would say, that the subject and predicate are both of
them names of ideas; the idea of gold, for instance, and the idea of
yellow; and that what takes place (or a part of what takes place) in the
act of belief, consists in bringing (as it is often expressed) one of
these ideas under the other. But this we are not yet in a condition to
say: whether such be the correct mode of describing the phenomenon, is an
after consideration. The result with which for the present we must be
contented, is, that in every act of belief _two_ objects are in some
manner taken cognizance of; that there can be no belief claimed, or
question propounded, which does not embrace two distinct (either material
or intellectual) subjects of thought; each of them capable or not of being
conceived by itself, but incapable of being believed by itself.
I may say, for instance, “the sun.” The word has a meaning, and suggests
that meaning to the mind of any one who is listening to me. But suppose I
ask him, Whether it is true: whether he believes it? He can give no
answer. There is as yet nothing to believe, or to disbelieve. Now,
however, let me make, of all possible assertions respecting the sun, the
one which involves the least of reference to any object besides itself;
let me say, “the sun exists.” Here, at once, is something which a person
can say he believes. But here, instead of only one, we find two distinct
objects of conception: the sun is one object; existence is another. Let it
not be said, that this second conception, existence, is involved in the
first; for the sun may be conceived as no longer existing. “The sun” does
not convey all the meaning that is conveyed by “the sun exists:” “my
father” does not include all the meaning of “my father exists,” for he may
be dead; “a round square” does not include the meaning of “a round square
exists,” for it does not and cannot exist. When I say, “the sun,” “my
father,” or a “round square,” I call upon the hearer for no belief or
disbelief, nor can either the one or the other be afforded me; but if I
say, “the sun exists,” “my father exists,” or “a round square exists,” I
call for belief; and should, in the first of the three instances, meet
with it; in the second, with belief or disbelief, as the case might be; in
the third, with disbelief.
§ 3. This first step in the analysis of the object of belief, which,
though so obvious, will be found to be not unimportant, is the only one
which we shall find it practicable to make without a preliminary survey of
language. If we attempt to proceed further in the same path, that is, to
analyse any further the import of Propositions; we find forced upon us, as
a subject of previous consideration, the import of Names. For every
proposition consists of two names; and every proposition affirms or denies
one of these names, of the other. Now what we do, what passes in our mind,
when we affirm or deny two names of one another, must depend on what they
are names of; since it is with reference to that, and not to the mere
names themselves, that we make the affirmation or denial. Here, therefore,
we find a new reason why the signification of names, and the relation
generally between names and the things signified by them, must occupy the
preliminary stage of the inquiry we are engaged 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
labours of his predecessors, and conduct himself as if he were the first
person who had ever turned an inquiring eye upon nature. What does any
one’s personal knowledge of Things amount to, after subtracting all which
he has acquired by means of the words of other people? Even after he has
learned as much as people usually do learn from others, will the notions
of things contained in his individual mind afford as sufficient a basis
for a _catalogue raisonné_ as the notions which are in the minds of all
mankind?
In any enumeration and classification of Things, which does not set out
from their names, no varieties of things will of course be comprehended
but those recognised by the particular inquirer; and it will still remain
to be established, by a subsequent examination of names, that the
enumeration has omitted nothing which ought to have been included. But if
we begin with names, and use them as our clue to the things, we bring at
once before us all the distinctions which have been recognised, not by a
single inquirer, but by all inquirers taken together. It doubtless may,
and I believe it will, be found, that mankind have multiplied the
varieties unnecessarily, and have imagined distinctions among things where
there were only distinctions in the manner of naming them. But we are not
entitled to assume this in the commencement. We must begin by recognising
the distinctions made by ordinary language. If some of these appear, on a
close examination, not to be fundamental, the enumeration of the different
kinds of realities may be abridged accordingly. But to impose upon the
facts in the first instance the yoke of a theory, while the grounds of the
theory are reserved for discussion in a subsequent stage, is not a course
which a logician can reasonably adopt.
CHAPTER II. OF NAMES.
§ 1. “A name,” says Hobbes,(4) “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(5) before in his mind.” This simple
definition of a name, as a word (or set of words) serving the double
purpose of a mark to recall to ourselves the likeness of a former thought,
and a sign to make it known to others, appears unexceptionable. Names,
indeed, do much more than this; but whatever else they do, grows out of,
and is the result of this: as will appear in its proper place.
Are names more properly said to be the names of things, or of our ideas of
things? The first is the expression in common use; the last is that of
some metaphysicians, who conceived that in adopting it they were
introducing a highly important distinction. The eminent thinker, just
quoted, seems to countenance the latter opinion. “But seeing,” he
continues, “names ordered in speech (as is defined) are signs of our
conceptions, it is manifest they are not signs of the things themselves;
for that the sound of this word _stone_ should be the sign of a stone,
cannot be understood in any sense but this, that he that hears it collects
that he that pronounces it thinks of a stone.”
If it be merely meant that the conception alone, and not the thing itself,
is recalled by the name, or imparted to the hearer, this of course cannot
be denied. Nevertheless, there seems good reason for adhering to the
common usage, and calling the word _sun_ the name of the sun, and not the
name of our idea of the sun. For names are not intended only to make the
hearer conceive what we conceive, but also to inform him what we believe.
Now, when I use a name for the purpose of expressing a belief, it is a
belief concerning the thing itself, not concerning my idea of it. When I
say, “the sun is the cause of day,” I do not mean that my idea of the sun
causes or excites in me the idea of day; or in other words, that thinking
of the sun makes me think of day. I mean, that a certain physical fact,
which is called the sun’s presence (and which, in the ultimate analysis,
resolves itself into sensations, not ideas) causes another physical fact,
which is called day. It seems proper to consider a word as the _name_ of
that which we intend to be understood by it when we use it; of that which
any fact that we assert of it is to be understood of; that, in short,
concerning which, when we employ the word, we intend to give information.
Names, therefore, shall always be spoken of in this work as the names of
things themselves, and not merely of our ideas of things.
But the question now arises, of what things? and to answer this it is
necessary to take into consideration the different kinds of names.
§ 2. It is usual, before examining the various classes into which names
are commonly divided, to begin by distinguishing from names of every
description, those words which are not names, but only parts of names.
Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the
inflected cases of nouns substantive, as _me_, _him_, _John’s_;(6) and
even adjectives, as _large_, _heavy_. These words do not express things of
which anything can be affirmed or denied. We cannot say, Heavy fell, or A
heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the
room. Unless, indeed, we are speaking of the mere words themselves, as
when we say, Truly is an English word, or, Heavy is an adjective. In that
case they are complete names, viz. names of those particular sounds, or of
those particular collections of written characters. This employment of a
word to denote the mere letters and syllables of which it is composed, was
termed by the schoolmen the _suppositio materialis_ of the word. In any
other sense we cannot introduce one of these words into the subject of a
proposition, unless in combination with other words; as, A heavy _body_
fell, A truly _important fact_ was asserted, A _member_ of _parliament_
was in the room.
An adjective, however, is capable of standing by itself as the predicate
of a proposition; as when we say, Snow is white; and occasionally even as
the subject, for we may say, White is an agreeable colour. The adjective
is often said to be so used by a grammatical ellipsis: Snow is white,
instead of Snow is a white object; White is an agreeable colour, instead
of, A white colour, or, The colour white, is agreeable. The Greeks and
Romans were allowed, by the rules of their language, to employ this
ellipsis universally in the subject as well as in the predicate of a
proposition. In English this cannot, generally speaking, be done. We may
say, The earth is round; but we cannot say, Round is easily moved; we must
say, A round object. This distinction, however, is rather grammatical than
logical. Since there is no difference of meaning between _round_, and _a
round object_, it is only custom which prescribes that on any given
occasion one shall be used, and not the other. We shall therefore, without
scruple, speak of adjectives as names, whether in their own right, or as
representative of the more circuitous forms of expression above
exemplified. The other classes of subsidiary words have no title whatever
to be considered as names. An adverb, or an accusative case, cannot under
any circumstances (except when their mere letters and syllables are spoken
of) figure as one of the terms of a proposition.
Words which are not capable of being used as names, but only as parts of
names, were called by some of the schoolmen Syncategorematic terms: from
σὺν, with, and κατηγορέω, to predicate, because it was only _with_ some
other word that they could be predicated. A word which could be used
either as the subject or predicate of a proposition without being
accompanied by any other word, was termed by the same authorities a
Categorematic term. A combination of one or more Categorematic, and one or
more Syncategorematic words, as, A heavy body, or A court of justice, they
sometimes called a _mixed_ term; but this seems a needless multiplication
of technical expressions. A mixed term is, in the only useful sense of the
word, Categorematic. It belongs to the class of what have been called
many-worded names.
For, as one word is frequently not a name, but only part of a name, so a
number of words often compose one single name, and no more. These words,
“the place which the wisdom or policy of antiquity had destined for the
residence of the Abyssinian princes,” form in the estimation of the
logician only one name; one Categorematic term. A mode of determining
whether any set of words makes only one name, or more than one, is by
predicating something of it, and observing whether, by this predication,
we make only one assertion or several. Thus, when we say, John Nokes, who
was the mayor of the town, died yesterday,—by this predication we make but
one assertion; whence it appears that “John Nokes, who was the mayor of
the town,” is no more than one name. It is true that in this proposition,
besides the assertion that John Nokes died yesterday, there is included
another assertion, namely, that John Nokes was mayor of the town. But this
last assertion was already made: we did not make it by adding the
predicate, “died yesterday.” Suppose, however, that the words had been,
John Nokes _and_ the mayor of the town, they would have formed two names
instead of one. For when we say, John Nokes and the mayor of the town died
yesterday, we make two assertions; one, that John Nokes died yesterday;
the other, that the mayor of the town died yesterday.
It being needless to illustrate at any greater length the subject of
many-worded names, we proceed to the distinctions which have been
established among names, not according to the words they are composed of,
but according to their signification.
§ 3. All names are names of something, real or imaginary; but all things
have not names appropriated to them individually. For some individual
objects we require, and consequently have, separate distinguishing names;
there is a name for every person, and for every remarkable place. Other
objects, of which we have not occasion to speak so frequently, we do not
designate by a name of their own; but when the necessity arises for naming
them, we do so by putting together several words, each of which, by
itself, might be and is used for an indefinite number of other objects; as
when I say, _this stone_: “this” and “stone” being, each of them, names
that may be used of many other objects besides the particular one meant,
although 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, Peter, 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 although
there are many persons who bear that name, it is not conferred upon them
to indicate any qualities, or anything which belongs to them in common;
and cannot be said to be affirmed of them in any _sense_ at all,
consequently not in the same sense. “The present queen of England” is also
an individual name. For, that there never can be more than one person at a
time of whom it can be truly affirmed, is implied in the meaning of the
words.
It is not unusual, by way of explaining what is meant by a general name,
to say that it is the name of a _class_. But this, though a convenient
mode of expression for some purposes, is objectionable as a definition,
since it explains the clearer of two things by the more obscure. It would
be more logical to reverse the proposition, and turn it into a definition
of the word _class_: “A class is the indefinite multitude of individuals
denoted by a general name.”
It is necessary to distinguish _general_ from _collective_ names. A
general name is one which can be predicated of _each_ individual of a
multitude; a collective name cannot be predicated of each separately, but
only of all taken together. “The 76th regiment of foot,” which is a
collective name, is not a general but an individual name; for although it
can be predicated of a multitude of individual soldiers taken jointly, it
cannot be predicated of them severally. We may say, Jones is a soldier,
and Thompson is a soldier, and Smith is a soldier, but we cannot say,
Jones is the 76th regiment, and Thompson is the 76th regiment, and Smith
is the 76th regiment. We can only say, Jones, and Thompson, and Smith, and
Brown, and so forth, (enumerating all the soldiers,) are the 76th
regiment.
“The 76th regiment” is a collective name, but not a general one: “a
regiment” is both a collective and a general name. General with respect to
all individual regiments, of each of which separately it can be affirmed;
collective with respect to the individual soldiers, of whom any regiment
is composed.
§ 4. The second general division of names is into _concrete_ and
_abstract_. A concrete name is a name which stands for a thing; an
abstract name is a name which stands for an attribute of a thing. Thus,
_John_, _the sea_, _this table_, are names of things. _White_, also, is a
name of a thing, or rather of things. Whiteness, again, is the name of a
quality or attribute of those things. Man is a name of many things;
humanity is a name of an attribute of those things. _Old_ is a name of
things; _old age_ is a name of one of their attributes.
I have used the words concrete and abstract in the sense annexed to them
by the schoolmen, who, notwithstanding the imperfections of their
philosophy, were unrivalled in the construction of technical language, and
whose definitions, in logic at least, though they never went more than a
little way into the subject, have seldom, I think, been altered but to be
spoiled. A practice, however, has grown up in more modern times, which, if
not introduced by Locke, has gained currency chiefly from his example, of
applying the expression “abstract name” to all names which are the result
of abstraction or generalization, and consequently to all general names,
instead of confining it to the names of attributes. The metaphysicians of
the Condillac school,—whose admiration of Locke, passing over the
profoundest speculations of that truly original genius, usually fastens
with peculiar eagerness upon his weakest points,—have gone on imitating
him in this abuse of language, until there is now some difficulty in
restoring the word to its original signification. A more wanton alteration
in the meaning of a word is rarely to be met with; for the expression
_general name_, the exact equivalent of which exists in all languages I am
acquainted with, was already available for the purpose to which _abstract_
has been misappropriated, while the misappropriation leaves that important
class of words, the names of attributes, without any compact distinctive
appellation. The old acceptation, however, has not gone so completely out
of use, as to deprive those who still adhere to it of all chance of being
understood. By _abstract_, then, I shall always mean the opposite of
_concrete_: by an abstract name, the name of an attribute; by a concrete
name, the name of an object.
Do abstract names belong to the class of general, or to that of singular
names? Some of them are certainly general. I mean those which are names
not of one single and definite attribute, but of a class of attributes.
Such is the word _colour_, which is a name common to whiteness, redness,
&c. Such is even the word whiteness, in respect of the different shades of
whiteness to which it is applied in common; the word magnitude, in respect
of the various degrees of magnitude and the various dimensions of space;
the word weight, in respect of the various degrees of weight. Such also is
the word _attribute_ itself, the common name of all particular attributes.
But when only one attribute, neither variable in degree nor in kind, is
designated by the name; as visibleness; tangibleness; equality;
squareness; milkwhiteness; then the name can hardly be considered general;
for though it denotes an attribute of many different objects, the
attribute itself is always conceived as one, not many. The question is,
however, of no moment, and perhaps the best way of deciding it would be to
consider these names as neither general nor individual, but to place them
in a class apart.
It may be objected to our definition of an abstract name, that not only
the names which we have called abstract, but adjectives, which we have
placed in the concrete class, are names of attributes; that _white_, for
example, is as much the name of the colour, as _whiteness_ is. But (as
before remarked) a word ought to be considered as the name of that which
we intend to be understood by it when we put it to its principal use, that
is, when we employ it in predication. When we say snow is white, milk is
white, linen is white, we do not mean it to be understood that snow, or
linen, or milk, is a colour. We mean that they are things having the
colour. The reverse is the case with the word whiteness; what we affirm to
_be_ whiteness is not snow but the colour of snow. Whiteness, therefore,
is the name of the colour exclusively: white is a name of all things
whatever having the colour; a name, not of the quality whiteness, but of
every white object. It is true, this name was given to all those various
objects on account of the quality; and we may therefore say, without
impropriety, that the quality forms part of its signification; but a name
can only be said to stand for, or to be a name of, the things of which it
can be predicated. We shall presently see that all names which can be said
to have any signification, all names by applying which to an individual we
give any information respecting that individual, may be said to _imply_ an
attribute of some sort; but they are not names of the attribute; it has
its own proper abstract name.
§ 5. This leads to the consideration of a third great division of names,
into _connotative_ and _non-connotative_, the latter sometimes, but
improperly, called _absolute_. This is one of the most important
distinctions which we shall have occasion to point out, and one of those
which go deepest into the nature of language.
A non-connotative term is one which signifies a subject only, or an
attribute only. A connotative term is one which denotes a subject, and
implies an attribute. By a subject is here meant anything which possesses
attributes. Thus John, or London, or England, are names which signify a
subject only. Whiteness, length, virtue, signify an attribute only. None
of these names, therefore, are connotative. But _white_, _long_,
_virtuous_, are connotative. The word white, denotes all white things, as
snow, paper, the foam of the sea, &c., and implies, or as it was termed by
the schoolmen, _connotes_,(7) the attribute _whiteness_. The word white is
not predicated of the attribute, but of the subjects, snow, &c.; but when
we predicate it of them, we imply, or connote, that the attribute
whiteness belongs to them. The same may be said of the other words above
cited. Virtuous, for example, is the name of a class, which includes
Socrates, Howard, the man of Ross, and an undefined number of other
individuals, past, present, and to come. These individuals, collectively
and severally, can alone be said with propriety to be denoted by the word:
of them alone can it properly be said to be a name. But it is a name
applied to all of them in consequence of an attribute which they are
supposed to possess in common, the attribute which has received the name
of virtue. It is applied to all beings that are considered to possess this
attribute; and to none which are not so considered.
All concrete general names are connotative. The word _man_, for example,
denotes Peter, Jane, John, and an indefinite number of other individuals,
of whom, taken as a class, it is the name. But it is applied to them,
because they possess, and to signify that they possess, certain
attributes. These seem to be, corporeity, animal life, rationality, and a
certain external form, which for distinction we call the human. Every
existing thing, which possessed all these attributes, would be called a
man; and anything which possessed none of them, or only one, or two, or
even three of them without the fourth, would not be so called. For
example, if in the interior of Africa there were to be discovered a race
of animals possessing reason equal to that of human beings, but with the
form of an elephant, they would not be called men. Swift’s Houyhnhms were
not 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;
James, Mary, 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.(8)
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. It is thus, for example, with
such a word as _fault_; equivalent to _bad_ or _hurtful quality_. This
word is a name common to many attributes, and connotes hurtfulness, an
attribute of those various attributes. When, for example, we say that
slowness, in a horse, is a fault, we do not mean that the slow movement,
the actual change of place of the slow horse, is a thing to be avoided,
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, becomes 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 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, although we may give to an individual a name utterly unmeaning, which
we call a proper name,—a word which answers the purpose of showing what
thing it is we are talking about, but not of telling anything about it;
yet a name peculiar to an individual is not necessarily of this
description. It may be significant of some attribute, or some union of
attributes, which being possessed by no object but one, determines the
name exclusively to that individual. “The sun” is a name of this
description; “God,” when used by a monotheist, is another. These, however,
are scarcely examples of what we are now attempting to illustrate, being,
in strictness of language, general, and 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 exists but one individual possessing
the attribute which it connotes; as, for instance, “the _only_ son of John
Stiles;” “the _first_ emperor of Rome.” Or the attribute connoted may be a
connexion with some determinate event, and the connexion may be of such a
kind as only one individual could have; or may at least be such as only
one individual actually had; and this may be implied in the form of the
expression. “The father of Socrates,” is an example of the one kind (since
Socrates could not have had two fathers); “the author of the Iliad,” “the
murderer of Henri Quatre,” of the second. For, although 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 word
itself imports (among other things) that there can be only one such person
at a time. This being the case, and the application of the name being
afterwards limited by the 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.
If, like the robber in the Arabian Nights, we make a mark with chalk on a
house to enable us to know it again, the mark has a purpose, but it has
not properly any meaning. The chalk does not declare anything about the
house; it does not mean, This is such a person’s house, or This is a house
which contains booty. The object of making the mark is merely distinction.
I say to myself, All these houses are so nearly alike, that if I lose
sight of them I shall not again be able to distinguish that which I am now
looking at, from any of the others; I must therefore contrive to make the
appearance of this one house unlike that of the others, that I may
hereafter know, when I see the mark—not indeed any attribute of the
house—but simply that it is the same house which I am now looking at.
Morgiana chalked all the other houses in a similar manner, and defeated
the scheme: how? simply by obliterating the difference of appearance
between that house and the others. The chalk was still there, but it no
longer served the purpose of a distinctive 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 anything its proper name; when we say, pointing to a
man, this is Brown or Smith, or pointing to a city, that it is York, we do
not, merely by so doing, convey to the hearer any information about them,
except that those are their names. By enabling him to identify the
individuals, we may connect them with information previously possessed by
him; by saying, This is York, we may tell him that it contains the
Minster. But this is in virtue of what he has previously heard concerning
York; not by anything implied in the name. It is otherwise when objects
are spoken of by connotative names. When we say, The town is built of
marble, we give the hearer what may be entirely new information, and this
merely by the signification of the many-worded connotative name, “built of
marble.” Such names are not signs of the mere objects, invented because we
have occasion to think and speak of those objects individually; but signs
which accompany an attribute: a kind of livery in which the attribute
clothes all objects which are 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 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 conceivable 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 of which he is but imperfectly
conscious, 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.(9) 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 small 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 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 reflected
on the present condition of those branches of knowledge. Since, however,
the introduction of a new technical language as the vehicle of
speculations on subjects belonging to the domain of daily discussion, is
extremely difficult to effect, and would not be free from inconvenience
even if effected, the problem for the philosopher, and one of the most
difficult which he has to resolve, is, in retaining the existing
phraseology, how best to alleviate its imperfections. This can only be
accomplished by giving to every general concrete name which there is
frequent occasion to predicate, a definite and fixed connotation; in order
that it may be known what attributes, when we call an object by that name,
we really mean to predicate of the object. And the question of most nicety
is, how to give this fixed connotation to a name, with the least possible
change in the objects which the name is habitually employed to denote;
with the least possible disarrangement, either by adding or subtraction,
of the group of objects which, in however imperfect a manner, it serves to
circumscribe and hold together; and with the least vitiation of the truth
of any propositions which are commonly received as true.
This desirable purpose, of giving a fixed connotation where it is wanting,
is the end aimed at whenever any one attempts to give a definition of a
general name already in use; every definition of a connotative name being
an attempt either merely to declare, or to declare and analyse, the
connotation of the name. And the fact, that no questions which have arisen
in the moral sciences have been subjects of keener controversy than the
definitions of almost all the leading expressions, is a proof how great an
extent the evil to which we have adverted has attained.
Names with indeterminate connotation are not to be confounded with names
which have more than one connotation, that is to say, ambiguous words. A
word may have several meanings, but all of them fixed and recognised ones;
as the word _post_, for example, or the word _box_, the various senses of
which it would be endless to enumerate. And the paucity of existing names,
in comparison with the demand for them, may often render it advisable and
even necessary to retain a name in this multiplicity of acceptations,
distinguishing these so clearly as to prevent their being confounded with
one another. Such a word may be considered as two or more names,
accidentally written and spoken alike.(10)
§ 6. The fourth principal division of names, is into _positive_ and
_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-many_,
_not-tree_, _not-good_. To every positive concrete name, a corresponding
negative one might be framed. After giving a name to any one thing, or to
any plurality of things, we might create a second name which should be a
name of all things whatever except that particular thing or things. These
negative names are employed whenever we have occasion to speak
collectively of all things other than some thing or class of things. When
the positive name is connotative, the corresponding negative name is
connotative likewise; but in a peculiar way, connoting not the presence
but the absence of an attribute. Thus, _not-white_ denotes all things
whatever except white things; and connotes the attribute of not possessing
whiteness. For the non-possession of any given attribute is also an
attribute, and may receive a name as such; and thus negative concrete
names may obtain negative abstract names to correspond to them.
Names which are positive in form are often negative in reality, and others
are really positive though their form is negative. The word
_inconvenient_, for example, does not express the mere absence of
convenience; it expresses a positive attribute, that of being the cause of
discomfort or annoyance. So the word _unpleasant_, notwithstanding its
negative form, does not connote the mere absence of pleasantness, but a
less degree of what is signified by the word _painful_, which, it is
hardly necessary to say, is positive. _Idle_, on the other hand, is a word
which, though positive in form, expresses nothing but what would be
signified either by the phrase _not working_, or by the phrase _not
disposed to work_; and _sober_, either by _not drunk_ or by _not 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 filiation. The
concrete name connotes an attribute, and the abstract name which answers
to it denotes that attribute. But of what nature is the attribute? Wherein
consists the peculiarity in the connotation of a relative name?
The attribute signified by a relative name, say some, is a relation; and
this they give, if not as a sufficient explanation, at least as the only
one attainable. If they are asked, What then is a relation? they do not
profess to be able to tell. It is generally regarded as something
peculiarly recondite and mysterious. I cannot, however, perceive in what
respect it is more so than any other attribute; indeed, it appears to me
to be so in a somewhat less degree. I conceive, rather, that it is by
examining into the signification of relative names, or in other words,
into the nature of the attribute which they connote, that a clear insight
may best be obtained into the nature of all attributes; of all that is
meant by an attribute.
It is obvious, in fact, that if we take any two correlative names,
_father_ and _son_, for instance, although the objects _de_noted by the
names are different, they both, in a certain sense, connote the same
thing. They cannot, indeed, be said to connote the same _attribute_; to be
a father, is not the same thing as to be a son. But when we call one man a
father, another his 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
cannot be explained but by mentioning another. Or we may state it
thus—when the name cannot be employed in discourse, so as to have a
meaning, unless the name of some other thing than what it is itself the
name of, be either expressed or understood. These definitions are all, at
bottom, equivalent, being modes of variously expressing this one
distinctive circumstance—that every other attribute of an object might,
without any contradiction, be conceived still to exist if all objects
besides that one were annihilated;(11) 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_;
but 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_
standing for an iron instrument, and _file_ standing for 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 everything which 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 the kinds of Things which are capable of
being made predicates, or of having anything predicated of them: after
which to determine the import of Predication, that is, of Propositions,
can be no arduous task.
The necessity of an enumeration of Existences, as the basis of Logic, did
not escape the attention of the schoolmen, and of their master, Aristotle,
the most comprehensive, if not the most sagacious, of the ancient
philosophers. The Categories, or Predicaments—the former a Greek word, the
latter its literal translation in the Latin language—were intended by him
and his followers as an enumeration of all things capable of being named;
an enumeration by the _summa genera_, _i.e._ the most extensive classes
into which things could be distributed; which, therefore, were so many
highest Predicates, one or other of which was supposed capable of being
affirmed with truth of every nameable thing whatsoever. The following are
the classes into which, according to this school of philosophy, Things in
general might be reduced:—
Οὐσία, Substantia.
Ποσὸν, Quantitas.
Ποιόν, Qualitas.
Πρός τι, Relatio.
Ποιεῖν, Actio.
Πάσχειν, Passio.
Ποῦ, Ubi.
Πότε, Quando.
Κεῖσθαι, Situs.
Εχειν, Habitus.
The imperfections of this classification are too obvious to require, and
its merits are not sufficient to reward, a minute examination. It is a
mere catalogue of the distinctions rudely marked out by the language of
familiar life, with little or no attempt to penetrate, by philosophic
analysis, to the _rationale_ even of those common distinctions. Such an
analysis, however superficially conducted, would have shown the
enumeration to be both redundant and defective. Some objects are omitted,
and others repeated several times under different heads. It is like a
division of animals into men, quadrupeds, horses, asses, and ponies. That,
for instance, could not be a very comprehensive view of the nature of
Relation which could exclude action, passivity, and local situation from
that category. The same observation applies to the categories Quando (or
position in time), and Ubi (or position in space); while the distinction
between the latter and Situs is merely verbal. The incongruity of erecting
into a _summum genus_ the class which forms the tenth category is
manifest. On the other hand, the enumeration takes no notice of anything
besides substances and attributes. In what category are we to place
sensations, or any other feelings, and states of mind; as hope, joy, fear;
sound, smell, taste; pain, pleasure; thought, judgment, conception, and
the like? Probably all these would have been placed by the Aristotelian
school in the categories of _actio_ and _passio_; and the relation of such
of them as are active, to their objects, and of such of them as are
passive, to their causes, would rightly be so placed; but the things
themselves, the feelings or states of mind, wrongly. Feelings, or states
of consciousness, are assuredly to be counted among realities, but they
cannot be reckoned either among substances or attributes.
§ 2. Before recommencing, under better auspices, the attempt made with
such imperfect success by the great founder of the science of logic, we
must take notice of an unfortunate ambiguity in all the concrete names
which correspond to the most general of all abstract terms, the word
Existence. When we have occasion for a name which shall be capable of
denoting whatever exists, as contradistinguished from non-entity or
Nothing, there is hardly a word applicable to the purpose which is not
also, and even more familiarly, taken in a sense in which it denotes only
substances. But substances are not all that exist; attributes, if such
things are to be spoken of, must be said to exist; feelings also exist.
Yet when we speak of an _object_, or of a _thing_, we are almost always
supposed to mean a substance. There seems a kind of contradiction in using
such an expression as that one _thing_ is merely an attribute of another
thing. And the announcement of a Classification of Things would, I
believe, prepare most readers for an enumeration like those in natural
history, beginning with the great divisions of animal, vegetable, and
mineral, and subdividing them into classes and orders. If, rejecting the
word Thing, we endeavour to find another of a more general import, or at
least more exclusively confined to that general import, a word denoting
all that exists, and connoting only simple existence; no word might be
presumed fitter for such a purpose than _being_: originally the present
participle of a verb which in one of its meanings is exactly equivalent to
the verb _exist_; and therefore suitable, even by its grammatical
formation, to be the concrete of the abstract _existence_. But this word,
strange as the fact may appear, is still more completely spoiled for the
purpose which it seemed expressly made for, than the word Thing. _Being_
is, by custom, exactly synonymous with substance; except that it is free
from a slight taint of a second ambiguity; being applied impartially to
matter and to mind, while substance, though originally and in strictness
applicable to both, is apt to suggest in preference the idea of matter.
Attributes are never called Beings; nor are Feelings. A Being is that
which excites feelings, and which possesses attributes. The soul is called
a Being; God and angels are called Beings; but if we were to say,
extension, colour, wisdom, virtue are beings, we should perhaps be
suspected of thinking with some of the ancients, that the cardinal virtues
are animals; or, at the least, of holding with the Platonic school the
doctrine of self-existent Ideas, or with the followers of Epicurus that of
Sensible Forms, which detach themselves in every direction from bodies,
and by coming in contact with our organs, cause our perceptions. We should
be supposed, in short, to believe that Attributes are Substances.
In consequence of this perversion of the word Being, philosophers looking
about for something to supply its place, laid their hands upon the word
Entity, a piece of barbarous Latin, invented by the schoolmen to be used
as an abstract name, in which class its grammatical form would seem to
place it; but being seized by logicians in distress to stop a leak in
their terminology, it has ever since been used as a concrete name. The
kindred word _essence_, born at the same time and of the same parents,
scarcely underwent a more complete transformation when, from being the
abstract of the verb _to be_, it came to denote something sufficiently
concrete to be enclosed in a glass bottle. The word Entity, since it
settled down into a concrete name, has retained its universality of
signification somewhat less impaired than any of the names before
mentioned. Yet the same gradual decay to which, after a certain age, all
the language of psychology seems liable, has been at work even here. If
you call virtue an _entity_, you are indeed somewhat less strongly
suspected of believing it to be a substance than if you called it a
_being_; but you are by no means free from the suspicion. Every word which
was originally intended to connote mere existence, seems, after a 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 very names which, for want of
better, I am necessitated to employ. It must now be the writer’s endeavour
so to employ them as in no case to leave the meaning doubtful or obscure.
No one of the above terms being altogether unambiguous, I shall not
confine myself to any one, but shall employ on each occasion the word
which seems least likely in the particular case to lead to
misunderstanding; nor do I pretend to use either these or any other words
with a rigorous adherence to one single sense. To do so would often leave
us without a word to express what is signified by a known word in some one
or other of its senses: unless authors had an unlimited licence to coin
new words, together with (what it would be more difficult to assume)
unlimited power of making their readers adopt them. Nor would it be wise
in a writer, on a subject involving so much of abstraction, to deny
himself the advantage derived from even an improper use of a term, when,
by means of it, some familiar association is called up which brings the
meaning home to the mind, as it were by a flash.
The difficulty both to the writer and reader, of the attempt which must be
made to use vague words so as to convey a precise meaning, is not wholly a
matter of regret. It is not unfitting that logical treatises should afford
an example of that, to facilitate which is among the most important uses
of logic. Philosophical language will for a long time, and popular
language still longer, retain so much of vagueness and ambiguity, that
logic would be of little value if it did not, among its other advantages,
exercise the understanding in doing its work neatly and correctly with
these imperfect tools.
After this preamble it is time to proceed to our enumeration. We shall
commence with Feelings, the simplest class of nameable things; the term
Feeling being of course understood in its most enlarged sense.
I. Feelings, or States of Consciousness.
§ 3. A Feeling and a State of Consciousness are, in the language of
philosophy, equivalent expressions: everything is a feeling of which the
mind is conscious; everything which it _feels_, or, in other words, which
forms a part of its own sentient existence. In popular language Feeling is
not always synonymous with State of Consciousness; being often taken more
peculiarly for those states which are conceived as belonging to the
sensitive, or to the emotional, phasis of our nature, and sometimes, with
a still narrower restriction, to the emotional alone: as distinguished
from what are conceived as belonging to the percipient or to the
intellectual phasis. But this is an admitted departure from correctness of
language; just as, by a popular perversion the exact converse of this, the
word Mind is withdrawn from its rightful generality of signification, and
restricted to the intellect. The still greater perversion by which Feeling
is sometimes confined not only to bodily sensations, but to the sensations
of a single sense, that of touch, needs not be more particularly adverted
to.
Feeling, in the proper sense of the term, is a genus, of which Sensation,
Emotion, and Thought, are subordinate species. Under the word Thought is
here to be included whatever we are internally conscious of when we are
said to think; from the consciousness we have when we think of a red
colour without having it before our eyes, to the most recondite thoughts
of a philosopher or poet. Be it remembered, however, that by a thought is
to be understood what passes in the mind itself, and not any object
external to the mind, which the person is commonly said to be thinking of.
He may be thinking of the sun, or of God, but the sun and God are not
thoughts; his mental image, however, of the sun, and his idea of God, are
thoughts; states of his mind, not of the objects themselves: and so also
is his belief of the existence of the sun, or of God; or his disbelief, if
the case be so. Even imaginary objects, (which are said to exist only in
our ideas,) are to be distinguished from our ideas of them. I may think of
a hobgoblin, as I may think of the loaf which was eaten yesterday, or of
the flower which will bloom to-morrow. But the hobgoblin which never
existed is not the same thing with my idea of a hobgoblin, any more than
the loaf which once existed is the same thing with my idea of a loaf, or
the flower which does not yet exist, but which will exist, is the same
with my idea of a flower. They are all, not thoughts, but objects of
thought; though at the present time all the objects are alike
non-existent.
In like manner, a Sensation is to be carefully distinguished from the
object which causes the sensation; our sensation of white from a white
object; nor is it less to be distinguished from the attribute whiteness,
which we ascribe to the object in consequence of its exciting the
sensation. Unfortunately for clearness and due discrimination in
considering these subjects, our sensations seldom receive separate names.
We have a name for the objects which produce in us a certain sensation;
the word _white_. We have a name for the quality in those objects, to
which we ascribe the sensation; the name _whiteness_. But when we speak of
the sensation itself, (as we have not occasion to do this often except in
our scientific speculations,) language, which adapts itself for the most
part only to the common uses of life, has provided us with no
single-worded or immediate designation; we must employ a circumlocution,
and say, The sensation of white, or The sensation of whiteness; we must
denominate the sensation either from the object, or from the attribute, by
which it is excited. Yet the sensation, though it never _does_, might very
well be _conceived_ to exist, without anything whatever to excite it. We
can conceive it as arising spontaneously in the mind. But if it so arose,
we should have no name to denote it which would not be a misnomer. In the
case of our sensations of hearing we are better provided; we have the word
Sound, and a whole vocabulary of words to denote the various kinds of
sounds. For as we are often conscious of these sensations in the absence
of any _perceptible_ object, we can more easily conceive having them in
the absence of any object whatever. We need only shut our eyes and listen
to music, to have a conception of an universe with nothing in it except
sounds, and ourselves hearing them: and what is easily conceived
separately, easily obtains a separate name. But in general our names of
sensations denote indiscriminately the sensation and the attribute. Thus,
_colour_ stands for the sensations of white, red, &c., but also for the
quality in the coloured object. We talk of the colours of things as among
their _properties_.
§ 4. In the case of sensations, another distinction has also to be kept in
view, which is often confounded, and never without mischievous
consequences. This is, the distinction between the sensation itself, and
the state of the bodily organs which precedes the sensation, and which
constitutes the physical agency by which it is produced. One of the
sources of confusion on this subject is the division commonly made of
feelings into Bodily and Mental. Philosophically speaking, there is no
foundation at all for this distinction: even sensations are states of the
sentient mind, not states of the body, as distinguished from it. What I am
conscious of when I see the colour blue, is a feeling of blue colour,
which is one thing; the picture on my retina, or the phenomenon of
hitherto mysterious nature which takes place in my optic nerve or in my
brain, is another thing, of which I am not at all conscious, and which
scientific investigation alone could have apprised me of. These are states
of my body; but the sensation of blue, which is the consequence of these
states of body, is not a state of body: that which perceives and is
conscious is called Mind. When sensations are called bodily feelings, it
is only as being the class of feelings which are immediately occasioned by
bodily states; whereas the other kinds of feelings, thoughts, for
instance, or emotions, are immediately excited not by anything acting upon
the bodily organs, but by sensations, or by previous thoughts. This,
however, is a distinction not in our feelings, but in the agency which
produces our feelings: all of them when actually produced are states of
mind.
Besides the affection of our bodily organs from without, and the sensation
thereby produced in our minds, many writers admit a third link in the
chain of phenomena, which they call a Perception, and which consists in
the recognition of an external object as the exciting cause of the
sensation. This perception, they say, is an _act_ of the mind, proceeding
from its own spontaneous activity; while in 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 recognised.
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(12)) 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 when I say that these sensations come to me from an external
object which I _perceive_, the meaning of these words is, that receiving
the sensations, I intuitively _believe_ that an external cause of those
sensations exists. The laws of intuitive belief, and the conditions under
which it is legitimate, are a subject which, as we have already so often
remarked, belongs not to logic, but to the science of the ultimate laws of
the human mind.
To the same region of speculation belongs all that can be said respecting
the distinction which the German metaphysicians and their French and
English followers so elaborately draw between the _acts_ of the mind and
its merely passive _states_; between what it receives from, and what it
gives to, the crude materials of its experience. I am aware that with
reference to the view which those writers take of the primary elements of
thought and knowledge, this distinction is fundamental. But for the
present purpose, which is to examine, not the original groundwork of our
knowledge, but how we come by that portion of it which is not original;
the difference between active and passive states of mind is of secondary
importance. For us, they all are states of mind, they all are feelings; by
which, let it be said once more, I mean to imply nothing of passivity, but
simply that they are psychological facts, facts which take place in the
mind, and are to be carefully distinguished from the external or physical
facts with which they may be connected, either as effects or as causes.
§ 5. Among active states of mind, there is however one species which
merits particular attention, because it forms a principal part of the
connotation of some important classes of names. I mean _volitions_, or
acts of the will. When we speak of sentient beings by relative names, a
large portion of the connotation of the name usually consists of the
_actions_ of those beings; actions past, present, and possible or probable
future. Take, for instance, the words Sovereign and Subject. What meaning
do these words convey, but that of innumerable actions, done or to be done
by the sovereign and the subjects, to or in regard to one another
reciprocally? So with the words physician and patient, leader and
follower, tutor and pupil. In many cases the words also connote actions
which would be done under certain contingencies by persons other than
those denoted: as the words mortgagor and mortgagee, obligor and obligee,
and many other words expressive of legal relation, which connote what a
court of justice would do to enforce the legal obligation if not
fulfilled. There are also words which connote actions previously done by
persons other than those denoted either by the name itself or by its
correlative; as the word brother. From these instances, it may be seen how
large a portion of the connotation of names consists of actions. Now what
is an action? Not one thing, but a series of two things: the state of mind
called a volition, followed by an effect. The volition or intention to
produce the effect, is one thing; the effect produced in consequence of
the intention, is another thing; the two together constitute the action. I
form the purpose of instantly moving my arm; that is a state of my mind:
my arm (not being tied or paralytic) moves in obedience to my purpose;
that is a physical fact, consequent on a state of mind. The intention,
followed by the fact, or, (if we prefer the expression,) the fact when
preceded and caused by the intention, is called the action of moving my
arm.
§ 6. Of the first leading division of nameable things, viz. Feelings or
States of Consciousness, we began by recognising three sub-divisions;
Sensations, Thoughts, and Emotions. The first two of these we have
illustrated at considerable length; the third, Emotions, not being
perplexed by similar ambiguities, does not require similar
exemplification. And, finally, we have found it necessary to add to these
three a fourth species, commonly known by the name Volitions. Without
seeking to prejudge the metaphysical question whether any mental state or
phenomenon can be found which is not included in one or other of these
four species, it appears to me that the amount of illustration bestowed
upon these may, so far as we are concerned, suffice for the whole genus.
We shall, therefore, proceed to the two remaining classes of nameable
things; all things which are external to the mind being considered as
belonging either to the class of Substances or to that of Attributes.
II. Substances.
Logicians have endeavoured to define Substance and Attribute; but their
definitions are not so much attempts to draw a distinction between the
things themselves, as instructions what difference it is customary to make
in the grammatical structure of the sentence, according as we are speaking
of substances or of attributes. Such definitions are rather lessons of
English, or of Greek, Latin, or German, than of mental philosophy. An
attribute, say the school logicians, must be the attribute _of_ something:
colour, for example, must be the colour _of_ something; goodness must be
the goodness _of_ something: and if this something should cease to exist,
or should cease to be connected with the attribute, the existence of the
attribute would be at an end. A substance, on the contrary, is
self-existent; in speaking about it, we need not put _of_ after its name.
A stone is not the stone _of_ anything; the moon is not the moon _of_
anything, but simply the moon. Unless, indeed, the name which we choose to
give to the substance be a relative name; if so, it must be followed
either by _of_ or by some other particle, implying, as that preposition
does, a reference to something else: but then the other characteristic
peculiarity of an attribute would fail; the _something_ might be
destroyed, and the substance might still subsist. Thus, a father must be
the father _of_ something, and so far resembles an attribute, in being
referred to something besides himself: if there were no child, there would
be no father: but this, when we look into the matter, only means that we
should not call him father. The man called father might still exist though
there were no child, as he existed before there was a child: and there
would be no contradiction in supposing him to exist, although the whole
universe except himself were destroyed. But destroy all white substances,
and where would be the attribute whiteness? Whiteness, without any white
thing, is a contradiction in terms.
This is the nearest approach to a solution of the difficulty, that will be
found in the common treatises on logic. It will scarcely be thought to be
a satisfactory one. If an attribute is distinguished from a substance by
being the attribute _of_ something, it seems highly necessary to
understand what is meant by _of_: a particle which needs explanation too
much itself to be placed in front of the explanation of anything else. And
as for the self-existence of substances, it is very true that a substance
may be conceived to exist without any other substance, but so also may an
attribute without any other attribute: and we can no more imagine a
substance without attributes than we can imagine attributes without a
substance.
Metaphysicians, however, have probed the question deeper, and given an
account of Substance considerably more satisfactory than this. Substances
are usually distinguished as Bodies or Minds. Of each of these,
philosophers have at length provided us with a definition which seems
unexceptionable.
§ 7. A Body, according to the received doctrine of modern metaphysicians,
may be defined the external cause to which we ascribe our sensations. When
I see and touch a piece of gold, I am conscious of a sensation of yellow
colour, and sensations of hardness and weight; and by varying the mode of
handling, I may add to these sensations many others completely distinct
from them. The sensations are all of which I am directly conscious; but I
consider them as produced by something not only existing independently of
my will, but external to my bodily organs and to my mind. This external
something I call a body.
It may be asked, how come we to ascribe our sensations to any external
cause? And is there sufficient ground for so ascribing them? It is known,
that there are metaphysicians who have raised a controversy on the point;
maintaining that we are not warranted in referring our sensations to a
cause, such as we understand by the word Body, or to any cause whatever,
unless, indeed, a First Cause. Though we have no concern here with this
controversy, nor with the metaphysical niceties on which it turns, one of
the best ways of showing what is meant by Substance is, to consider what
position it is necessary to take up, in order to maintain its existence
against opponents.
It is certain, then, that a part of our notion of a body consists of the
notion of a number of sensations of our own, or of other sentient beings,
habitually occurring simultaneously. My conception of the table at which I
am writing is compounded of its visible form and size, which are complex
sensations of sight; its tangible form and size, which are complex
sensations of our organs of touch and of our muscles; its weight, which is
also a sensation of touch and of the muscles; its colour, which is a
sensation of sight; its hardness, which is a sensation of the muscles; its
composition, which is another word for all the varieties of sensation
which we receive under various circumstances from the wood of which it is
made; and so forth. All or most of these various sensations frequently
are, and, as we learn by experience, always might be, experienced
simultaneously, or in many different orders of succession, at our own
choice: and hence the thought of any one of them makes us think of the
others, and the whole becomes mentally amalgamated into one mixed state of
consciousness, which, in the language of the school of Locke and Hartley,
is termed a Complex Idea.
Now, there are philosophers who have argued as follows. If we take an
orange, and conceive it to be divested of its natural colour without
acquiring any new one; to lose its softness without becoming hard, its
roundness without becoming square or pentagonal, or of any other regular
or irregular figure whatever; to be deprived of size, of weight, of taste,
of smell; to lose all its mechanical and all its chemical properties, and
acquire no new ones; to become, in short, invisible, intangible,
imperceptible not only by all our senses, but by the senses of all other
sentient beings, real or possible; nothing, say these thinkers, would
remain. For of what nature, they ask, could be the residuum? and by what
token could it manifest its presence? To the unreflecting its existence
seems to rest on the evidence of the senses. But to the senses nothing is
apparent except the sensations. We know, indeed, that these sensations are
bound together by some law; they do not come together at random, but
according to a systematic order, which is part of the order established in
the universe. When we experience one of these sensations, we usually
experience the others also, or know that we have it in our power to
experience them. But a fixed law of connexion, making the sensations occur
together, does not, say these philosophers, necessarily require what is
called a substratum to support them. The conception of a substratum is but
one of many possible forms in which that connexion presents itself to our
imagination; a mode of, as it were, realizing the idea. If there be such a
substratum, suppose it this instant miraculously annihilated, and let the
sensations continue to occur in the same order, and how would the
substratum be missed? By what signs should we be able to discover that its
existence had terminated? should we not have as much reason to believe
that it still existed as we now have? and if we should not then be
warranted in believing it, how can we be so now? A body, therefore,
according to these metaphysicians, is not anything intrinsically different
from the sensations which the body is said to produce in us; it is, in
short, a set of sensations joined together according to a fixed law.
The controversies to which these speculations have given rise, and the
doctrines which have been developed in the attempt to find a conclusive
answer to them, have been fruitful of important consequences to the
Science of Mind. The sensations (it was answered) which we are conscious
of, and which we receive not at random, but joined together in a certain
uniform manner, imply not only a law or laws of connexion, but a cause
external to our mind, which cause, by its own laws, determines the laws
according to which the sensations are connected and experienced. The
schoolmen used to call this external cause by the name we have already
employed, a _substratum_; and its attributes (as they expressed
themselves) _inhered_, literally _stuck_, in it. To this substratum the
name Matter is usually given in philosophical discussions. It was soon,
however, acknowledged by all who reflected on the subject, that the
existence of matter could 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
an universe of “Things in themselves,” totally distinct from the universe
of phenomena, or of things as they appear to our senses; and even when
bringing into use a technical expression (_Noumenon_) to denote what the
thing is in itself, as contrasted with the _representation_ of it in our
minds; he allows that this representation (the matter of which, he says,
consists of our sensations, though the form is given by the laws of the
mind itself) is all we know of the object: and that the real nature of the
Thing is, and by the constitution of our faculties ever must remain, at
least in the present state of existence, an impenetrable mystery to
us.(13) There is not the slightest reason for believing that what we call
the sensible qualities of the object are a type of anything inherent in
itself, or bear any affinity to its own nature. A cause does not, as such,
resemble its effects; an east wind is not like the feeling of cold, nor
heat like the steam of boiling water: why then should matter resemble our
sensations? why should the inmost nature of fire or water resemble the
impressions made by these objects upon our senses?(14) And if not on the
principle of resemblance, on what other principle can the manner in which
objects affect us through our senses afford us any insight into the
inherent nature of those objects? 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. Those, however, who still look upon Ontology as a possible
science, and think, not only that bodies have an essential constitution of
their own, lying deeper than our perceptions, but that this essence or
nature is accessible to human investigation, cannot expect to find their
refutation here. The question depends on the nature and laws of Intuitive
Knowledge, and is not within the province of logic.
§ 8. Body having now been defined the external cause, and (according to
the more reasonable opinion) the _hidden_ 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 the
mysterious something which excites the mind to feel, so mind is the
mysterious something which feels, and thinks. It is unnecessary to give in
the case of mind, as we gave in the case of matter, a particular statement
of the sceptical system by which its existence as a Thing in itself,
distinct from the series of what are denominated its states, is called in
question. But it is necessary to remark, that on the inmost nature of the
thinking principle, as well as on the inmost nature of matter, we are, and
with our faculties must always remain, entirely in the dark. All which we
are aware of, even in our own minds, is (in the words of Mr. Mill) a
certain “thread of consciousness;” a series of feelings, that is, of
sensations, thoughts, emotions, and volitions, more or less numerous and
complicated. There is a something I call Myself, or, by another form of
expression, my mind, which I consider as distinct from these sensations,
thoughts, &c.; a something which I conceive to be not the thoughts, but
the being that has the thoughts, and which I can conceive as existing for
ever in a state of quiescence, without any thoughts at all. But what this
being is, although it is myself, I have no knowledge, other than the
series of its states of consciousness. As bodies manifest themselves to me
only through the sensations of which I regard them as the causes, so the
thinking principle, or mind, in my own nature, makes itself known to me
only by the feelings of which it is conscious. I know nothing about
myself, save my capacities of feeling or being conscious (including, of
course, thinking and willing): and were I to learn anything new concerning
my own nature, I cannot with my present faculties conceive this new
information to be anything else, than that I have some additional
capacities, as yet unknown to me, of feeling, thinking, or willing.
Thus, then, as body is the unsentient cause to which we are naturally
prompted to refer a certain portion of our feelings, so mind may be
described as the sentient _subject_ (in the German sense of the term) of
all feelings; that which has or feels them. But of the nature of either
body or mind, further than the feelings which the former excites, and
which the latter experiences, we do not, according to the best existing
doctrine, know anything; and if anything, logic has nothing to do with it,
or with the manner in which the knowledge is acquired. With this result we
may conclude this portion of our subject, and pass to the third and only
remaining class or division of Nameable 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 cannot know,
anything of bodies but the sensations which they excite in us or 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 denoted by the terms.
Attributes are usually distributed under the three heads of Quality,
Quantity, and Relation. We shall come to the two latter presently: in the
first place we shall confine ourselves to the former.
Let us take, then, as our example, one of what are termed the sensible
qualities of objects, and let that example be whiteness. When we ascribe
whiteness to any substance, as, for instance, snow; when we say that snow
has the quality whiteness, what do we really assert? Simply, that when
snow is present to our organs, we have a particular sensation, which we
are accustomed to call the sensation of white. But how do I know that snow
is present? Obviously by the sensations which I derive from it, and not
otherwise. I infer that the object is present, because it gives me a
certain assemblage or series of sensations. And when I ascribe to it the
attribute whiteness, my meaning is only, that, of the sensations composing
this group or series, that which I call the sensation of white colour is
one.
This is one view which may be taken of the subject. But there is also
another, and a different view. It may be said, that it is true we _know_
nothing of sensible objects, except the sensations they excite in us; that
the fact of our receiving from snow the particular sensation which is
called a sensation of white, is the _ground_ on which we ascribe to that
substance the quality whiteness; the sole proof of its possessing that
quality. But because one thing may be the sole evidence of the existence
of another thing, it does not follow that the two are one and the same.
The attribute whiteness (it may be said) is not the fact of our 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, which is as much as to say under
different suppositions as to surrounding circumstances. Because _quality_
and _sensation_ cannot be put indiscriminately one for the other, it is
supposed that they cannot both signify the same thing, namely, the
impression or feeling with which we are affected through our senses by the
presence of an object; although 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 regarded as
emanating from any one of the numerous objects, the presence of which to
our organs excites in our minds that among various other sensations or
feelings. And if this be admissible as a supposition, it rests with those
who contend for an entity _per se_ called a quality, to show that their
opinion is preferable, or is anything in fact but a lingering remnant of
the scholastic doctrine of occult causes; the very absurdity which Molière
so happily ridiculed when he made one of his pedantic physicians account
for the fact that “l’opium endormit,” by the maxim “parcequ’il a une vertu
soporifique.”
It is evident that when the physician stated that opium had “une vertu
soporifique,” he did not account for, but merely asserted over again, the
fact that it _endormit_. In like manner, when we say that snow is white
because it has the quality of whiteness, we are only re-asserting in more
technical language the fact that it excites in us the sensation of white.
If it be said that the sensation must have some cause, I answer, its cause
is the presence of the assemblage of phenomena which is termed the object.
When we have asserted that as often as the object is present, and our
organs in their normal state, the sensation takes place, we have stated
all that we know about the matter. There is no need, after assigning a
certain and intelligible cause, to suppose an occult cause besides, for
the purpose of enabling the real cause to produce its effect. If I am
asked, why does the presence of the object cause this sensation in me, I
cannot tell: I can only say that such is my nature, and the nature of the
object; that the fact forms a part of the constitution of things. And to
this we must at last come, even after interpolating the imaginary entity.
Whatever number of links the chain of causes and effects may consist of,
how any one link produces the one which is next to it remains equally
inexplicable to us. It is as easy to comprehend that the object should
produce the sensation directly and at once, as that it should produce the
same sensation by the aid of something else called the _power_ of
producing it.
But as the difficulties which may be felt in adopting this view of the
subject cannot be removed without discussions transcending the bounds of
our science, I content myself with a passing indication, and shall, for
the purposes of logic, adopt a language compatible with either view of the
nature of qualities. I shall say,—what at least admits of no dispute,—that
the quality of whiteness ascribed to the object snow, is _grounded_ on its
exciting in us the sensation of white; and adopting the language already
used by the school logicians in the case of the kind of attributes called
Relations, I shall term the sensation of white the _foundation_ of the
quality whiteness. For logical purposes the sensation is the only
essential part of what is meant by the word; the only part which we ever
can be concerned in proving. When that is proved, the quality is proved;
if an object excites a sensation it has, of course, the power of exciting
it.
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 oneself or to
somebody else. There is no part of what the names expressive of the
relation imply, that is not resolvable into states of consciousness;
outward objects being, no doubt, supposed throughout as the causes by
which some of those states of consciousness are excited, and minds as the
subjects by which all of them are experienced, but neither the external
objects nor the minds making their existence known otherwise than by the
states of consciousness.
Cases of relation are not always so complicated as those to which we last
alluded. The simplest of all cases of relation are those expressed by the
words antecedent and consequent, and by the word simultaneous. If we say,
for instance, that dawn preceded sunrise, the fact in which the two
things, dawn and sunrise, were jointly concerned, consisted only of the
two things themselves; no third thing entered into the fact or phenomenon
at all; unless, indeed, we choose to call the succession of the two
objects a third thing; but their succession is not something added to the
things themselves; it is something involved in them. Dawn and sunrise
announce themselves to our consciousness by two successive sensations; our
consciousness of the succession of these sensations is not a third
sensation or feeling added to them; we have not first the two feelings,
and then a feeling of their succession. To have two feelings at all,
implies having them either successively, or else simultaneously.
Sensations, or other feelings, being given, succession and
simultaneousness are the two conditions, to the alternative of which they
are subjected by the nature of our faculties; and no one has been able, or
needs expect, to analyse the matter any farther.
§ 11. In a somewhat similar position are two other sorts of relation,
Likeness and Unlikeness. I have two sensations; we will suppose them to be
simple ones; two sensations of white, or one sensation of white and
another of black. I call the first two sensations _like_; the last two
_unlike_. What is the fact or phenomenon constituting the _fundamentum_ of
this relation? The two sensations first, and then what we call a feeling
of resemblance, or of want of resemblance. Let us confine ourselves to the
former case. Resemblance is evidently a feeling; a state of the
consciousness of the observer. Whether the feeling of the resemblance of
the two colours be a third state of consciousness, which I have _after_
having the two sensations of colour, or whether (like the feeling of their
succession) it is involved in the sensations themselves, may be a matter
of discussion. But in either case, these feelings of resemblance, and of
its opposite, dissimilarity, are parts of our nature; and parts so far
from being capable of analysis, that they are presupposed in every attempt
to analyse any of our other feelings. Likeness and unlikeness, therefore,
as well as antecedence, sequence, and simultaneousness, must stand apart
among relations, as things _sui generis_. They are attributes grounded on
facts, that is, on states of consciousness, but on states which are
peculiar, unresolvable, and inexplicable.
But, although likeness or unlikeness cannot be resolved into anything
else, complex cases of likeness or unlikeness can be resolved into simpler
ones. When we say of two things which consist of parts, that they are like
one another, the likeness of the wholes does admit of analysis; it is
compounded of likenesses between the various parts respectively. 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 portion at least of these sensations. If we say
that two attributes are like one another, (since we know nothing of
attributes except the sensations or states of feeling on which they are
grounded,) we mean really that those sensations, or states of feeling,
resemble each other. We may also say that two relations are alike. The
fact of resemblance between relations is sometimes called _analogy_,
forming one of the numerous meanings of that word. The relation in which
Priam stood to Hector, namely, that of father and son, resembles the
relation in which Philip stood to Alexander; resembles it so closely that
they are called the same relation. The relation in which Cromwell stood to
England resembles the relation in which Napoleon stood to France, though
not so closely as to be called the same relation. The meaning in both
these instances must be, that a resemblance existed between the facts
which constituted the _fundamentum relationis_.
This resemblance may exist in all conceivable gradations, from perfect
undistinguishableness to something extremely slight. When we say, that a
thought suggested to the mind of a person of genius is like a seed cast
into the ground, because the former produces a multitude of other
thoughts, and the latter a multitude of other seeds, this is saying that
between the relation of an inventive mind to a thought contained in it,
and the relation of a fertile soil to a seed contained in it, there exists
a resemblance: the real resemblance being in the two _fundamenta
relationis_, in each of which there occurs a germ, producing by its
development a multitude of other things similar to itself. And as,
whenever two objects are jointly concerned in a phenomenon, this
constitutes a relation between those objects, so, if we suppose a second
pair of objects concerned in a second phenomenon, the slightest
resemblance between the two phenomena is sufficient to admit of its being
said that the two relations resemble; provided, of course, the points of
resemblance are found in those portions of the two phenomena respectively
which are connoted by the relative names.
While speaking of resemblance, it is necessary to take notice of an
ambiguity of language, against which scarcely any one is sufficiently on
his guard. Resemblance, when it exists in the highest degree of all,
amounting to undistinguishableness, is often called identity, and the two
similar things are said to be the same. I say often, not always; for we do
not say that two visible objects, two persons for instance, are the same,
because they are so much alike that one might be mistaken for the other:
but we constantly use this mode of expression when speaking of feelings;
as when I say that the sight of any object gives me the _same_ sensation
or emotion to-day that it did yesterday, or the _same_ which it gives to
some other person. This is evidently an incorrect application of the word
_same_; for the feeling which I had yesterday is gone, never to return;
what I have to-day is another feeling, exactly like the former perhaps,
but distinct from it; and it is evident that two different persons cannot
be experiencing the same feeling, in the sense in which we say that they
are both sitting at the same table. By a similar ambiguity we say, that
two persons are ill of the _same_ disease; that two persons hold the
_same_ office; not in the sense in which we say that they are engaged in
the same adventure, or sailing in the same ship, but in the sense that
they fill offices exactly similar, though, perhaps, in distant places.
Great confusion of ideas is often produced, and many fallacies engendered,
in otherwise enlightened understandings, by not being sufficiently alive
to the fact (in itself not always to be avoided,) that they use the same
name to express ideas so different as those of identity and
undistinguishable resemblance. Among modern writers, Archbishop Whately
stands almost alone in having drawn attention to this distinction, and to
the ambiguity connected with 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 the province of Logic to
analyse it; nor to decide whether it is susceptible of analysis or not.
For us the following considerations are sufficient. It is evident that the
sensations I receive from the gallon of water, and those I receive from
the gallon of wine, are not the same, that is, not precisely alike;
neither are they altogether unlike: they are partly similar, partly
dissimilar; and that in which they resemble is precisely that in which
alone the gallon of water and the ten gallons do not resemble. That in
which the gallon of water and the gallon of wine are like each other, and
in which the gallon and the ten gallons of water are unlike each other, is
called their quantity. This likeness and unlikeness I do not pretend to
explain, no more than any other kind of likeness or unlikeness. But my
object is to show, that when we say of two things that they differ in
quantity, just as when we say that they differ in quality, the assertion
is always grounded on a difference in the sensations which they excite.
Nobody, I presume, will say, that to see, or to lift, or to drink, ten
gallons of water, does not include in itself a different set of sensations
from those of seeing, lifting, or drinking one gallon; or that to see or
handle a foot rule, and to see or handle a yard-measure made exactly like
it, are the same sensations. I do not undertake to say what the difference
in the sensations is. Everybody knows, and nobody can tell; no more than
any one could tell what white is, to a person who had never had the
sensation. But the difference, so far as cognizable by our faculties, lies
in the sensations. Whatever difference we say there is in the things
themselves, is, in this as in all other cases, grounded, and grounded
exclusively, on a difference in the sensations excited by them.
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
recognise a somewhat different character in certain peculiar relations,
those of succession and simultaneity, of likeness and unlikeness. These,
not being grounded on any fact or phenomenon distinct from the related
objects themselves, do not admit of the same kind of analysis. But these
relations, though not, like other relations, grounded on states of
consciousness, are themselves states of consciousness: resemblance is
nothing but our feeling of resemblance; succession is nothing but our
feeling of succession. Or, if this be disputed, (and we cannot, without
transgressing the bounds of our science, discuss it here,) at least our
knowledge of these relations, and even our possibility of knowledge, is
confined to those which subsist between sensations, or other states of
consciousness; for, though we ascribe resemblance, or succession, or
simultaneity, to objects and to attributes, it is always in virtue of
resemblance or succession or simultaneity in the sensations or states of
consciousness which those objects excite, and on which those attributes
are grounded.
§ 14. In the preceding investigation we have, for the sake of simplicity,
considered bodies only, and omitted minds. But what we have said, is
applicable, _mutatis mutandis_, to the latter. The attributes of minds, as
well as those of bodies, are grounded on states of feeling or
consciousness. But in the case of a mind, we have to consider its own
states, as well as those which it produces in other minds. Every attribute
of a mind consists either in being itself affected in a certain way, or
affecting other minds in a certain way. Considered in itself, we can
predicate nothing of it but the series of its own feelings. When we say of
any mind, that it is devout, or superstitious, or meditative, or cheerful,
we mean that the ideas, emotions, or volitions implied in those words,
form a frequently recurring part of the series of feelings, or states of
consciousness, which fill up the sentient existence of that mind.
In addition, however, to those attributes of a mind which are grounded on
its own states of feeling, attributes may also be ascribed to it, in the
same manner as to a body, grounded on the feelings which it excites in
other minds. A mind does not, indeed, like a body, excite sensations, but
it may excite thoughts or emotions. The most important example of
attributes ascribed on this ground, is the employment of terms expressive
of approbation or blame. When, for example, we say of any character, or
(in other words) of any mind, that it is admirable, we mean that the
contemplation of it excites the sentiment of admiration; and indeed
somewhat more, for the word implies that we not only feel admiration, but
approve that sentiment in ourselves. In some cases, under the semblance of
a single attribute, two are really predicated: one of them, a state of the
mind itself; the other, a state with which other minds are affected by
thinking of it. As when we say of any one that he is generous. The word
generosity expresses a certain state of mind, but being a term of praise,
it also expresses that this state of mind excites in us another mental
state, called approbation. The assertion made, therefore, is twofold, and
of the following purport: Certain feelings form habitually a part of this
person’s sentient existence; and the idea of those feelings of his,
excites the sentiment of approbation in ourselves or others.
As we thus ascribe attributes to minds on the ground of ideas and
emotions, so may we to bodies on similar grounds, and not solely on the
ground of sensations: as in speaking of the beauty of a statue; since this
attribute is grounded on the peculiar feeling of pleasure which the statue
produces in our minds; which is not a sensation, but an emotion.
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 made themselves the subject of
predications—is now concluded.
Our enumeration commenced with Feelings. These we scrupulously
distinguished from the objects which excite them, and from the organs by
which they are, or may be supposed to be, conveyed. Feelings are of four
sorts: Sensations, Thoughts, Emotions, and Volitions. What are called
perceptions are merely a particular case of Belief, and belief is a kind
of thought. Actions are merely volitions followed by an effect. If there
be any other kind of mental state not included under these subdivisions,
we did not think it necessary or proper in this place to discuss its
existence, or the rank which ought to be assigned to it.
After Feelings we proceeded to Substances. These are either Bodies or
Minds. Without entering into the grounds of the metaphysical doubts which
have been raised concerning the existence of Matter and Mind as objective
realities, we stated as sufficient for us the conclusion in which the best
thinkers are now very generally 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 Nameable Things is Attributes; and these are
of three kinds, Quality, Relation, and Quantity. Qualities, like
substances, are known to us no otherwise than by the sensations or other
states of consciousness which they excite: and while, in compliance with
common usage, we have continued to speak of them as a distinct class of
Things, we showed that in predicating them no one means to predicate
anything but those sensations or states of consciousness, on which they
may be said to be grounded, and by which alone they can be defined or
described. Relations, except the simple cases of likeness and unlikeness,
succession and simultaneity, are similarly grounded on some fact or
phenomenon, that is, on some series of sensations or states of
consciousness, more or less complicated. The third species of attribute,
Quantity, is also manifestly grounded on something in our sensations or
states of feeling, since there is an indubitable difference in the
sensations excited by a larger and a smaller bulk, or by a greater or a
less degree of intensity, in any object of sense or of consciousness. All
attributes, therefore, are to us nothing but either our sensations and
other states of feeling, or something inextricably involved therein; and
to this even the peculiar and simple relations just adverted to are not
exceptions. Those peculiar relations, however, are so important, and, even
if they might in strictness be classed among states of consciousness, are
so fundamentally distinct from any other of those states, that it would be
a vain subtlety to confound them under that common head, and it is
necessary that they should be classed apart.
As the result, therefore, of our analysis, we obtain the following as an
enumeration and classification of all Nameable Things:—
1st. Feelings, or States of Consciousness.
2nd. The Minds which experience those feelings.
3rd. The Bodies, or external objects, which excite certain of those
feelings, together with the powers or properties whereby they excite them;
these being included rather in compliance with common opinion, and because
their existence is taken for granted in the common language from which I
cannot prudently deviate, than because the recognition of such powers or
properties as real existences appears to me warranted by a sound
philosophy.
4th, and last. The Successions and Co-existences, the Likenesses and
Unlikenesses, between feelings or states of consciousness. Those
relations, when considered as subsisting between other things, exist in
reality only between the states of consciousness which those things, if
bodies, excite, if minds, either excite or experience.
This, until a better can be suggested, may serve as a substitute for the
abortive Classification of Existences, termed the Categories of Aristotle.
The practical application of it will appear when we commence the inquiry
into the Import of Propositions; in other words, when we inquire what it
is which the mind actually believes, when it gives what is called its
assent to a proposition.
These four classes comprising, if the classification be correct, all
Nameable Things, these or some of them must of course compose the
signification of all names; and of these, or some of them, is made up
whatever we call a fact.
For distinction’s sake, every fact which is solely composed of feelings or
states of consciousness considered as such, is often called a
Psychological or Subjective fact; while every fact which is composed,
either wholly or in part, of something different from these, that is, of
substances and attributes, is called an Objective fact. We may say, then,
that every objective fact is grounded on a corresponding subjective one;
and has no meaning to us, (apart from the subjective fact which
corresponds to it,) except as a name for the unknown and inscrutable
process by which that subjective or psychological fact is brought to pass.
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
cannot conclude from merely seeing two names put together, that they are a
predicate and a subject, that is, that one of them is intended to be
affirmed or denied of the other, it is necessary that there should be some
mode or form of indicating that such is the intention; some sign to
distinguish a predication from any other kind of discourse. This is
sometimes done by a slight alteration of one of the words, called an
_inflection_; as when we say, Fire burns; the change of the second word
from _burn_ to _burns_ showing that we mean to affirm the predicate burn
of the subject fire. But this function is more commonly fulfilled by the
word _is_, when an affirmation is intended, _is not_, when a negation; or
by some other part of the verb _to be_. The word which thus serves the
purpose of a sign of predication is called, as we formerly observed, the
_copula_. It is important that there should be no indistinctness in our
conception of the nature and office of the copula; for confused notions
respecting it are among the causes which have spread mysticism over the
field of logic, and perverted its speculations into 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 cannot possibly be implied that a centaur
exists, since the proposition itself expressly asserts that the thing has
no real existence.
Many volumes might be filled with the frivolous speculations concerning
the nature of Being, (το ὄν, οὐσία, Ens, Entitas, Essentia, and the like,)
which have arisen from overlooking this double meaning of the words _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
non-entity, it must still, at bottom, answer to the same idea; and that a
meaning must be found for it which shall suit all these cases. The fog
which rose from this narrow spot diffused itself at an early period over
the whole surface of metaphysics. Yet it becomes us not to triumph over
the great intellects of Plato and Aristotle because we are now able to
preserve ourselves from many errors into which they, perhaps inevitably,
fell. The fire-teazer of a modern steam-engine produces by his exertions
far greater effects than Milo of Crotona could, but he is not therefore a
stronger man. The Greeks seldom knew any language but their own. This
rendered it far more difficult for them than it is for us, to acquire a
readiness in detecting ambiguities. One of the advantages of having
accurately studied a plurality of languages, especially of those languages
which eminent thinkers have used as the vehicle of their thoughts, is the
practical lesson we learn respecting the ambiguities of words, by finding
that the same word in one language corresponds, on different occasions, to
different words in another. When not thus exercised, even the strongest
understandings find it difficult to believe that things which have a
common name, have not in some respect or other a common nature; and often
expend much labour not only unprofitably but mischievously, (as was
frequently done by the two philosophers just mentioned,) on 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. Mill(15)
was, I believe, the first who distinctly characterized the ambiguity, and
pointed out how many errors in the received systems of philosophy it has
had to answer for. It has indeed misled the moderns scarcely less than the
ancients, though their mistakes, because our understandings are not yet so
completely emancipated from their influence, do not appear equally
irrational.
We shall now briefly review the principal distinctions which exist among
propositions, and the technical terms most commonly in use to express
those distinctions.
§ 2. A proposition being a portion of discourse in which something is
affirmed or denied of something, the first division of propositions is
into affirmative and negative. An affirmative proposition is that in which
the predicate is _affirmed_ of the subject; as, Cæsar is dead. A negative
proposition is that in which the predicate is _denied_ of the subject; as,
Cæsar is not dead. The copula, in this last species of proposition,
consists of the words _is not_, which are the sign of negation; _is_ being
the sign of affirmation.
Some logicians, among whom may be mentioned Hobbes, state this distinction
differently; they recognise only one form of copula, _is_, and attach the
negative sign to the predicate. “Cæsar is dead,” and “Cæsar is not dead,”
according to these writers, are propositions agreeing not in the subject
and predicate, but in the subject only. They do not consider “dead,” but
“not dead,” to be the predicate of the second proposition, and they
accordingly define a negative proposition to be one in which the predicate
is a negative name. The point, though not of much practical moment,
deserves notice as an example (not unfrequent in logic) where by means of
an apparent simplification, but which is merely verbal, matters are made
more complex than before. The notion of these writers was, that they could
get rid of the distinction between affirming and denying, by treating
every case of denying as the affirming of a negative name. But what is
meant by a negative name? A name expressive of the _absence_ of an
attribute. So that when we affirm a negative name, what we are really
predicating is absence and not presence; we are asserting not that
anything _is_, but that something is _not_; to express which operation no
word seems so proper as the word denying. The fundamental distinction is
between a fact and the non-existence of that fact; between seeing
something and not seeing it, between Cæsar’s being dead and his not being
dead; and if this were a merely verbal distinction, the generalization
which brings both within the same form of assertion would be a real
simplification: the distinction, however, being real, and in the facts, it
is the generalization confounding the distinction that is merely verbal;
and tends to obscure the subject, by treating the difference between two
kinds of truth 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
the designations belonging to the event asserted, to the _sun’s_ rising
to-day. They affect, not the predicate, but the applicability of the
predicate to the particular subject. That which we affirm to be past,
present, or future, is not what the subject signifies, nor what the
predicate signifies, but specifically and expressly what the predication
signifies; what is expressed only by the proposition as such, and not by
either or both of the terms. Therefore the circumstance of time is
properly considered as attaching to the copula, which is the sign of
predication, and not to the predicate. If the same cannot be said of such
modifications as these, Cæsar _may_ be dead; Cæsar is _perhaps_ dead; it
is _possible_ that Cæsar is dead; it is only because these fall altogether
under another head, being properly assertions not of anything relating to
the fact itself, but of the state of our own mind in regard to it; namely,
our absence of disbelief of it. Thus “Cæsar may be dead” means “I am not
sure that Cæsar is alive.”
§ 3. The next division of propositions is into Simple and Complex. A
simple proposition is that in which one predicate is affirmed or denied of
one subject. A complex proposition is that in which there is more than one
predicate, or more than one subject, or both.
At first sight this division has the air of an absurdity; a solemn
distinction of things into one and more than one; as if we were to divide
horses into single horses and teams of horses. And it is true that what is
called a complex proposition is often not a proposition at all, but
several propositions, held together by a conjunction. Such, for example,
is this: Cæsar is dead, and Brutus is alive: or even this, Cæsar is dead,
_but_ Brutus is alive. There are here two distinct assertions; and we
might as well call a street a complex house, as these two propositions a
complex proposition. It is true that the syncategorematic words _and_ and
_but_ have a meaning; but that meaning is so far from making the two
propositions one, that it adds a third proposition to them. All particles
are abbreviations, and generally abbreviations of propositions; a kind of
short-hand, whereby that which, to be expressed fully, would have required
a proposition or a series of propositions, is suggested to the mind at
once. Thus the words, Cæsar is dead and Brutus is alive, are equivalent to
these: Cæsar is dead; Brutus is alive; it is desired that the two
preceding propositions should be thought of together. If the words were,
Cæsar is dead _but_ Brutus is alive, the sense would be equivalent to the
same three propositions together with a fourth; “between the two preceding
propositions there exists a contrast:” viz., either between the two facts
themselves, or between the feelings with which it is desired that they
should be regarded.
In the instances cited, the two propositions are kept visibly distinct,
each subject having its separate predicate, and each predicate its
separate subject. For brevity, however, and to avoid repetition, the
propositions are often blended together: as in this, “Peter and James
preached at Jerusalem and in Galilee,” which contains four propositions:
Peter preached at Jerusalem, Peter preached in Galilee, James preached at
Jerusalem, James preached in Galilee.
We have seen that when the two or more propositions comprised in what is
called a complex proposition, are stated absolutely, and not under any
condition or proviso, it is not a proposition at all, but a plurality of
propositions; since what it expresses is not a single assertion, but
several assertions, which, if true when joined, are true also when
separated. But there is a kind of proposition which, though it contains a
plurality of subjects and of predicates, and may be said in one sense of
the word to consist of several propositions, contains but one assertion;
and its truth does not at all imply that of the simple propositions which
compose it. An example of this is, when the simple propositions are
connected by the particle _or_; as, Either A is B _or_ C is D; or by the
particle _if_; as, A is B _if_ C is D. In the former case, the proposition
is called _disjunctive_, in the latter _conditional_: the name
_hypothetical_ was originally common to both. As has been well remarked by
Archbishop Whately and others, the disjunctive form is resolvable into the
conditional; every disjunctive proposition being equivalent to two or more
conditional ones. “Either A is B or C is D,” means, “if A is not B, C is
D; and if C is not D, A is B.” All hypothetical propositions, therefore,
though disjunctive in form, are conditional in meaning; and the words
hypothetical and conditional may be, as indeed they generally are, used
synonymously. Propositions in which the assertion is not dependent on a
condition, are said, in the language of logicians, to be _categorical_.
An hypothetical proposition is not, like the pretended complex
propositions which we previously considered, a mere aggregation of simple
propositions. The simple propositions which form part of the words in
which it is couched, form no part of the assertion which it conveys. When
we say, If the Koran comes from God, Mahomet is the prophet of God, we do
not intend to affirm either that the Koran does come from God, or that
Mahomet is really his prophet. Neither of these simple propositions may be
true, and yet the truth of the hypothetical proposition may be
indisputable. What is asserted is not the truth of either of the
propositions, but the inferribility of the one from the other. What, then,
is the subject, and what the predicate, of the hypothetical proposition?
“The Koran” is not the subject of it, nor is “Mahomet:” for nothing is
affirmed or denied either of the Koran or of Mahomet. The real subject of
the predication is the entire proposition, “Mahomet is the prophet of
God;” and the affirmation is, that this is a legitimate inference from the
proposition, “The Koran comes from God.” The subject and predicate,
therefore, of an hypothetical proposition are names of propositions. The
subject is some one proposition. The predicate is a general relative name
applicable to propositions; of this form—“an inference from so and so.” A
fresh instance is here afforded of the remark, that all particles are
abbreviations; since “_If_ A is B, C is D,” is found to be an abbreviation
of the following: “The proposition C is D, is a legitimate inference from
the proposition A is B.”
The distinction, therefore, between hypothetical and categorical
propositions, is not so great as it at first appears. In the conditional,
as well as in the categorical form, one predicate is affirmed of one
subject, and no more: but a conditional proposition is a proposition
concerning a proposition; the subject of the assertion is itself an
assertion. Nor is this a property peculiar to hypothetical propositions.
There are other classes of assertions concerning propositions. Like other
things, a proposition has attributes which may be predicated of it. The
attribute predicated of it in an hypothetical proposition, is that of
being an inference from a certain other proposition. But this is only one
of many attributes that might be predicated. We may say, That the whole is
greater than its part, is an axiom in mathematics: That the Holy Ghost
proceeds from the Father alone, is a tenet of the Greek Church: The
doctrine of the divine right of kings was renounced by Parliament at the
Revolution: The infallibility of the Pope has no countenance from
Scripture. In all these cases the subject of the predication is an entire
proposition. That which these different predicates are affirmed of, is
_the proposition_, “the whole is greater than its part;” _the
proposition_, “the Holy Ghost proceeds from the Father alone;” _the
proposition_, “kings have a divine right;” _the proposition_, “the Pope is
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 non-assignable portion of them
only, it is particular. Thus, All men are mortal; Every man is mortal; are
universal propositions. No man is immortal, is also an universal
proposition, since the predicate, immortal, is denied of each and every
individual denoted by the term man; the negative proposition being exactly
equivalent to the following, Every man is not-immortal. But “some men are
wise,” “some men are not wise,” are particular propositions; the predicate
_wise_ being in the one case affirmed and in the other denied not of each
and every individual denoted by the term man, but only of each and every
one of some portion of those individuals, without specifying what portion;
for if this were specified, the proposition would be changed either into a
singular proposition, or into an universal proposition with a different
subject; as, for instance, “all _properly instructed_ men are wise.” There
are other forms of particular propositions: as, “_Most_ men are
imperfectly educated:” it being immaterial how large a portion of the
subject the predicate is asserted of, as long as it is left uncertain how
that portion is to be distinguished from the rest.
When the form of the expression does not clearly show whether the general
name which is the subject of the proposition is meant to stand for all the
individuals denoted by it, or only for some of them, the proposition is
commonly called Indefinite; but this, as Archbishop Whately observes, is a
solecism, of the same nature as that committed by some grammarians when in
their list of genders they enumerate the _doubtful_ gender. The speaker
must mean to assert the proposition either as an universal or as a
particular proposition, though he has failed to declare which: and it
often happens that though the words do not show which of the two he
intends, the context, or the custom of speech, supplies the deficiency.
Thus, when it is affirmed that “Man is mortal,” nobody doubts that the
assertion is intended of all human beings, and the word indicative of
universality is commonly omitted, only because the meaning is evident
without it. In the proposition, “Wine is good,” it is understood with
equal readiness, though for somewhat different reasons, that the assertion
is not intended to be universal, but particular.
When a general name stands for each and every individual which it is a
name of, or in other words, which it denotes, it is said by logicians to
be _distributed_, or taken distributively. Thus, in the proposition, All
men are mortal, the subject, Man, is distributed, because mortality is
affirmed of each and every man. The predicate, Mortal, is not distributed,
because the only mortals who are spoken of in the proposition are those
who happen to be men; while the word may, for aught that appears, (and in
fact does,) comprehend within it an indefinite number of objects besides
men. In the proposition, Some men are mortal, both the predicate and the
subject are undistributed. In the following, No men have wings, both the
predicate and the subject are distributed. Not only is the attribute of
having wings denied of the entire class Man, but that class is severed and
cast out from the whole of the class Winged, and not merely from some part
of that class.
This phraseology, which is of great service in stating and demonstrating
the rules of the syllogism, enables us to express very concisely the
definitions of an universal and a particular proposition. An universal
proposition is that of which the subject is distributed; a particular
proposition is that of which the subject is undistributed.
There are many more distinctions among propositions than those we have
here stated, some of them of considerable importance. But, for explaining
and illustrating these, more suitable opportunities will occur in the
sequel.
CHAPTER V. OF THE IMPORT OF PROPOSITIONS.
§ 1. An inquiry into the nature of propositions must have one of two
objects: to analyse the state of mind called Belief, or to analyse what is
believed. All language recognises a difference between a doctrine or
opinion, and the act of entertaining the opinion; between assent, and what
is assented to.
Logic, according to the conception here formed of it, has no concern with
the nature of the act of judging or believing; the consideration of that
act, as a phenomenon of the mind, belongs to another science.
Philosophers, however, from Descartes downwards, and especially from the
era of Leibnitz and Locke, have by no means observed this distinction; and
would have treated with great disrespect any attempt to analyse the import
of Propositions, unless founded on an analysis of the act of Judgment. A
proposition, they would have said, is but the expression in words of a
Judgment. The thing expressed, not the mere verbal expression, is the
important matter. When the mind assents to a proposition, it judges. Let
us find out what the mind does when it judges, and we shall know what
propositions mean, and not otherwise.
Conformably to these views, almost all the writers on Logic in the last
two centuries, whether English, German, or French, have made their theory
of Propositions, from one end to the other, a theory of Judgments. They
considered a Proposition, or a Judgment, for they used the two words
indiscriminately, to consist in affirming or denying one _idea_ of
another. To judge, was to put two ideas together, or to bring one idea
under another, or to compare two ideas, or to perceive the agreement or
disagreement between two ideas: and the whole doctrine of Propositions,
together with the theory of Reasoning, (always necessarily founded on the
theory of Propositions,) was stated as if Ideas, or Conceptions, or
whatever other term the writer preferred as a name for mental
representations generally, constituted essentially the subject matter and
substance of those operations.
It is, of course, true, that in any case of judgment, as for instance when
we judge that gold is yellow, a process takes place in our minds, of which
some one or other of these theories is a partially correct account. We
must have the idea of gold and the idea of yellow, and these two ideas
must be brought together in our mind. But in the first place, it is
evident that this is only a part of what takes place; for we may put two
ideas together without any act of belief; as when we merely imagine
something, such as a golden mountain; or when we actually disbelieve: for
in order even to disbelieve that Mahomet was an apostle of God, we must
put the idea of Mahomet and that of an apostle of God together. To
determine what it is that happens in the case of assent or dissent besides
putting two ideas together, is one of the most intricate of metaphysical
problems. But whatever the solution may be, we may venture to assert that
it can have nothing whatever to do with the import of propositions; for
this reason, that propositions (except where the mind itself is the
subject treated of) are not assertions respecting our ideas of things, but
assertions respecting the things themselves. In order to believe that gold
is yellow, I must, indeed, have the idea of gold, and the idea of yellow,
and something having reference to those ideas must take place in my mind;
but my belief has not reference to the ideas, it has reference to the
things. What I believe is a fact relating to the outward thing, gold, and
to the impression made by that outward thing upon the human organs; not a
fact relating to my conception of gold, which would be a fact in my mental
history, not a fact of external nature. It is true, that in order to
believe this fact in external nature, another fact must take place in my
mind, a process must be performed upon my ideas; but so it must in
everything else that I do. I cannot dig the ground unless I have the idea
of the ground, and of a spade, and of all the other things I am operating
upon, and unless I put those ideas together.(16) 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, although it cannot be performed unless I have in my
mind the ideas of them. And so, in like manner, believing is an act which
has for its subject the facts themselves, although a previous mental
conception of the facts is an indispensable condition. When I say that
fire causes heat, do I mean that my idea of fire causes my idea of heat?
No: I mean that the natural phenomenon, fire, causes the natural
phenomenon, heat. When I mean to assert anything respecting the ideas, I
give them their proper name, I call them ideas: as when I say, that a
child’s idea of a battle is unlike the reality, or that the ideas
entertained of the Deity have a great effect on the characters of mankind.
The notion that what is of primary importance to the logician in a
proposition, is the relation between the two _ideas_ corresponding to the
subject and predicate, (instead of the relation between the two
_phenomena_ which they respectively express,) seems to me one of the most
fatal errors ever introduced into the philosophy of Logic; and the
principal cause why the theory of the science has made such inconsiderable
progress during the last two centuries. The treatises on Logic, and on the
branches of Mental Philosophy connected with Logic, which have been
produced since the intrusion of this cardinal error, though sometimes
written by men of extraordinary abilities and attainments, almost always
tacitly imply a theory that the investigation of truth consists in
contemplating and handling our ideas, or conceptions of things, instead of
the things themselves: a doctrine tantamount to the assertion, that the
only mode of acquiring knowledge of nature is to study it at second hand,
as represented in our own minds. Meanwhile, inquiries into every kind of
natural phenomena were incessantly establishing great and fruitful truths
on the 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 come at, should deem a science futile,
which consisted chiefly of such speculations. What has been done for the
advancement of Logic since these doctrines came into vogue, has been done
not by professed logicians, but by discoverers in the other sciences; in
whose methods of investigation many principles of logic, not previously
thought of, have successively come forth into light, but who have
generally committed the error of supposing that nothing whatever was known
of the art of philosophizing by the old logicians, because their modern
interpreters have written to so little purpose respecting it.
We have to inquire, then, on the present occasion, not into Judgment, but
judgments; not into the act of believing, but into the thing believed.
What is the immediate object of belief in a Proposition? What is the
matter of fact signified by it? What is it to which, when I assert the
proposition, I give my assent, and call upon others to give theirs? What
is that which is expressed by the form of discourse called a Proposition,
and the conformity of which to fact constitutes the truth of the
proposition?
§ 2. One of the clearest and most consecutive thinkers whom this country
or the world has produced, I mean Hobbes, has given the following answer
to this question. In every proposition (says he) what is signified is, the
belief of the speaker that the predicate is a name of the same thing of
which the subject is a name; and if it really is so, the proposition is
true. Thus the proposition, All men are living beings (he would say) is
true, because _living being_ is a name of everything of which _man_ is a
name. All men are six feet high, is not true, because _six feet high_ is
not a name of everything (though it is of some things) of which _man_ is a
name.
What is stated in this theory as the definition of a true proposition,
must be allowed to be a property which all true propositions possess. The
subject and predicate being both of them names of things, if they were
names of quite different things the one name could not, consistently with
its signification, be predicated of the other. If it be true that some men
are copper-coloured, it must be true—and the proposition does really
assert—that among the individuals denoted by the name man, there are some
who are also among those denoted by the name copper-coloured. If it be
true that all oxen ruminate, it must be true that all the individuals
denoted by the name ox are also among those denoted by the name
ruminating; and whoever asserts that all oxen ruminate, undoubtedly does
assert that this relation subsists between the two names.
The assertion, therefore, which, according to Hobbes, is the only one made
in any proposition, really is made in every proposition: and his analysis
has consequently one of the requisites for being the true one. We may go a
step farther; it is the only analysis that is rigorously true of all
propositions without exception. What he gives as the meaning of
propositions, is part of the meaning of all propositions, and the whole
meaning of some. This, however, only shows what an extremely minute
fragment of meaning it is quite possible to include within the logical
formula of a proposition. It does not show that no proposition means more.
To warrant us in putting together two words with a copula between them, it
is really enough that the thing or things denoted by one of the names
should be capable, without violation of usage, of being called by the
other name also. If, then, this be all the meaning necessarily implied in
the form of discourse called a Proposition, why do I object to it as the
scientific definition of what a proposition means? Because, though the
mere collocation which makes the proposition a proposition, conveys no
more than this scanty amount of meaning, that same collocation combined
with other circumstances, that _form_ combined with other _matter_, does
convey more, and much more.
The only propositions of which Hobbes’ principle is a sufficient account,
are that limited and unimportant class in which both the predicate and the
subject are proper names. For, as has already been remarked, proper names
have strictly no meaning; they are mere marks for individual objects: and
when a proper name is predicated of another proper name, all the
signification conveyed is, that both the names are marks for the same
object. But this is precisely what Hobbes produces as a theory of
predication in general. His doctrine is a full explanation of such
predications as these: Hyde was Clarendon, or, Tully is Cicero. It
exhausts the meaning of those propositions. But it is a sadly inadequate
theory of any others. That it should ever have been thought of as such,
can be accounted for only by the fact, that Hobbes, in common with the
other Nominalists, bestowed little or no attention upon the _connotation_
of words; and sought for their meaning exclusively in what they _denote_:
as if all names had been (what none but proper names really are) marks put
upon individuals; and as if there were no difference between a proper and
a general name, except that the first denotes only one individual, and the
last a greater number.
It has been seen, however, that the meaning of all names, except proper
names and that portion of the class of abstract names which are not
connotative, resides in the connotation. When, therefore, we are analysing
the meaning of any proposition in which the predicate and the subject, or
either of them, are connotative names, it is to the connotation of those
terms that we must exclusively look, and not to what they _denote_, or in
the language of Hobbes, (language so far correct,) are names of.
In asserting that the truth of a proposition depends on the conformity of
import between its terms, as, for instance, that the proposition, Socrates
is wise, is a true proposition, because Socrates and wise are names
applicable to, or, as he expresses it, names of, the same person; it is
very remarkable that so powerful a thinker should not have asked himself
the question, But how came they to be names of the same person? Surely not
because such was the intention of those who invented the words. When
mankind fixed the meaning of the word wise, they were not thinking of
Socrates, nor, when his parents gave him the name 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 John, Jane, and the remainder of the individuals. The
word _mortal_, in like manner connotes a certain attribute or attributes;
and when we say, All men are mortal, the meaning of the proposition is,
that all beings which possess the one set of attributes, possess also the
other. If, in our experience, the attributes connoted by _man_ are always
accompanied by the attribute connoted by _mortal_, it will follow as a
consequence, that the class _man_ will be wholly included in the class
_mortal_, and that _mortal_ will be a name of all things of which _man_ is
a name: but why? Those objects are brought under the name, by possessing
the attributes connoted by it: but their possession of the attributes is
the real condition on which the truth of the proposition depends; not
their being called by the name. Connotative names do not precede, but
follow, the attributes which they connote. If one attribute happens to be
always found in conjunction with another attribute, the concrete names
which answer to those attributes will of course be predicable of the same
subjects, and may be said, in Hobbes’ language, (in the propriety of which
on this occasion I fully concur,) to be two names for the same things. But
the possibility of a concurrent application of the two names, is a mere
consequence of the conjunction between the two attributes, and was, in
most cases, never thought of when the names were invented and their
signification fixed. That the diamond is combustible, was a proposition
certainly not dreamt of when the words Diamond and Combustible first
received their meaning; and could not have been discovered by the most
ingenious and refined analysis of the signification of those words. It was
found out by a very different process, namely, by exerting the senses, and
learning from them, that the attribute of combustibility existed in all
those diamonds upon which the experiment was tried; the number and
character of the experiments being such, that what was true of those
individuals might be concluded to be true of all substances “called by the
name,” that is, of all substances possessing the attributes which the name
connotes. The assertion, therefore, when analysed, is, that wherever we
find certain attributes, there will be found a certain other attribute:
which is not a question of the signification of names, but of laws of
nature; the order existing among phenomena.
§ 3. Although Hobbes’ theory of Predication has not, in the terms in which
he stated it, met with a very favourable reception from subsequent
thinkers, a theory virtually identical with it, and not by any means so
perspicuously expressed, may almost be said to have taken the rank of an
established opinion. The most generally received notion of Predication
decidedly is that it consists in referring something to a _class_, _i.e._,
either placing an individual under a class, or placing one class under
another class. Thus, the proposition, Man is mortal, asserts, according to
this view of it, that the class man is included in the class mortal.
“Plato is a philosopher,” asserts that the individual Plato is one of
those who compose the class philosopher. If the proposition is negative,
then instead of placing something in a class, it is said to exclude
something from a class. Thus, if the following be the proposition, The
elephant is not carnivorous; what is asserted (according to this theory)
is, that the elephant is excluded from the class carnivorous, or is not
numbered among the things comprising that class. There is no real
difference, except in language, between this theory of Predication and the
theory of Hobbes. For a class _is_ absolutely nothing but an indefinite
number of individuals denoted by a general name. The name given to them in
common, is what makes them a class. To refer anything to a class,
therefore, is to look upon it as one of the things which are to be called
by that common name. To exclude it from a class, is to say that the common
name is not applicable to it.
How widely these views of predication have prevailed, is evident from
this, that they are the basis of the celebrated _dictum de omni et nullo_.
When the syllogism is resolved, by all who treat of it, into an inference
that what is true of a class is true of all things whatever that belong to
the class; and when this is laid down by almost all professed logicians as
the ultimate principle to which all reasoning owes its validity; it is
clear that in the general estimation of logicians, the propositions of
which reasonings are composed can be the expression of nothing but the
process of dividing things into classes, and referring everything to its
proper class.
This theory appears to me a signal example of a logical error very often
committed in logic, that of ὕστερον προτέρον, or explaining a thing by
something which presupposes it. When I say that snow is white, I may and
ought to be thinking of snow as a class, because I am asserting a
proposition as true of all snow: but I am certainly not thinking of white
objects as a class; I am thinking of no white object whatever except snow,
but only of that, and of the sensation of white which it gives me. When,
indeed, I have judged, or assented to the propositions, that snow is
white, and that several other things also are white, I gradually begin to
think of white objects as a class, including snow and those other things.
But this is a conception which followed, not preceded, those judgments,
and therefore cannot be given as an explanation of them. Instead of
explaining the effect by the cause, this doctrine explains the cause by
the effect, and is, I conceive, founded on a latent misconception of the
nature of classification.
There is a sort of language very generally prevalent in these discussions,
which seems to suppose that classification is an arrangement and grouping
of definite and known individuals: that when names were imposed, mankind
took into consideration all the individual objects in the universe, made
them up 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 will be composed; we may do so while believing
that no such individuals exist. If by the _meaning_ of a general name are
to be understood the things which it is the name of, no general name,
except by accident, has a fixed meaning at all, or ever long retains the
same meaning. The only mode in which any general name has a definite
meaning, is by being a name of an indefinite variety of things; namely, of
all things, known or unknown, past, present, or future, which possess
certain definite attributes. When, by studying not the meaning of words,
but the phenomena of nature, we discover that these attributes are
possessed by some object not previously known to possess them, (as when
chemists found that the diamond was combustible,) we include this new
object in the class; but it did not already belong to the class. We place
the individual in the class because the proposition is true; the
proposition is not true because the object is placed in the class.
It will appear hereafter in treating of reasoning, how much the theory of
that intellectual process has been vitiated by the influence of these
erroneous notions, and by the habit which they exemplify of assimilating
all the operations of the human understanding which have truth for their
object, to processes of mere classification and naming. Unfortunately, the
minds which have been entangled in this net are precisely those which have
escaped the other cardinal error commented upon in the beginning of the
present chapter. Since the revolution which dislodged Aristotle from the
schools, logicians may almost be divided into those who have looked upon
reasoning as essentially an affair of Ideas, and those who have looked
upon it as essentially an affair of Names.
Although, however, Hobbes’ theory of Predication, according to the
well-known remark of Leibnitz, and the avowal of Hobbes himself,(17)
renders truth and falsity completely arbitrary, with no standard but the
will of men, it must not be concluded that either Hobbes, or any of the
other thinkers who have in the main agreed with him, did in fact consider
the distinction between truth and error as less real, or attached less
importance to it, than other people. To suppose that they did so would
argue total unacquaintance with their other speculations. But this shows
how little hold their doctrine possessed over their own minds. No person
at bottom ever imagined that there was nothing more in truth than
propriety of expression; than using language in conformity to a previous
convention. When the inquiry was brought down from generals to a
particular case, it has always been acknowledged that there is a
distinction between verbal and real questions; that some false
propositions are uttered from ignorance of the meaning of words, but that
in others the source of the error is a misapprehension of things; that a
person who has not the use of language at all may form propositions
mentally, and that they may be untrue, that is, he may believe as matters
of fact what are not really so. This last admission cannot be made in
stronger terms than it is by Hobbes himself;(18) though he will not allow
such erroneous belief to be called falsity, but only error. And he has
himself laid down, in other places, doctrines in which the true theory of
predication is by implication contained. He distinctly says that general
names are given to things on account of their attributes, and that
abstract names are the names of those attributes. “Abstract is that which
in any subject denotes the cause of the concrete name.... And these causes
of names are the same with the causes of our conceptions, namely, some
power of action, or affection, of the thing conceived, which some call the
manner by which anything works upon our senses, but by most men they are
called _accidents_.”(19) It is strange that having gone so far, he should
not have gone one step farther, and seen that what he calls the cause of
the concrete name, is in reality the meaning of it; and that when we
predicate of any subject a name which is given _because_ of an attribute,
(or, as he calls it, an accident,) our object is not to affirm the name,
but, by means of the name, to affirm the attribute.
§ 4. Let the predicate be, as we have said, a connotative term; and to
take the simplest case first, let the subject be a proper name: “The
summit of Chimborazo is white.” The word white connotes an attribute which
is possessed by the individual object designated by the words, “summit of
Chimborazo,” which attribute consists in the physical fact, of its
exciting in human beings the sensation which we call a sensation of white.
It will be admitted that, by asserting the proposition, we wish to
communicate information of that physical fact, and are not thinking of the
names, except as the necessary means of making that communication. The
meaning of the proposition, therefore, is, that the individual thing
denoted by the subject, has the attributes connoted by the predicate.
If we now suppose the subject also to be a connotative name, the meaning
expressed by the proposition has advanced a step farther in complication.
Let us first suppose the proposition to be universal, as well as
affirmative: “All men are mortal.” In this case, as in the last, what the
proposition asserts, (or expresses a belief of,) is, of course, that the
objects denoted by the subject (man) possess the attributes connoted by
the predicate (mortal). But the characteristic of this case is, that the
objects are no longer _individually_ designated. They are pointed out only
by some of their attributes: they are the objects called men, that is,
possessing the attributes connoted by the name man; and the only thing
known of them may be those attributes: indeed, as the proposition is
general, and the objects denoted by the subject are therefore indefinite
in number, most of them are not known individually at all. The assertion,
therefore, is not, as before, that the attributes which the predicate
connotes are possessed by any given individual, or by any number of
individuals previously known as John, Thomas, &c., but that those
attributes are possessed by each and every individual possessing certain
other attributes; that whatever has the attributes connoted by the
subject, has also those connoted by the predicate; that the latter set of
attributes _constantly accompany_ the former set. Whatever has the
attributes of man has the attribute of mortality; mortality constantly
accompanies the attributes of man.
If it be remembered that every attribute is _grounded_ on some fact or
phenomenon, either of outward sense or of inward consciousness, and that
to _possess_ an attribute is another phrase for being the cause of, or
forming part of, the fact or phenomenon upon which the attribute is
grounded; we may add one more step to complete the analysis. The
proposition which asserts that one attribute always accompanies another
attribute, really asserts thereby no other thing than this, that one
phenomenon always accompanies another phenomenon; insomuch that where we
find the one, we have assurance of the existence of the other. Thus, in
the proposition, All men are mortal, the word man connotes the attributes
which we ascribe to a certain kind of living creatures, on the ground of
certain phenomena which they exhibit, and which are partly physical
phenomena, namely the impressions made on our senses by their bodily form
and structure, and partly mental phenomena, namely the sentient and
intellectual life which they have of their own. All this is understood
when we utter the word man, by any one to whom the meaning of the word is
known. Now, when we say, Man is mortal, we mean that wherever these
various physical and mental phenomena are all found, there we have
assurance that the other physical and mental phenomenon, called death,
will not fail to take place. The proposition does not affirm _when_; for
the connotation of the word _mortal_ goes no farther than to the
occurrence of the phenomenon at some time or other, leaving the precise
time undecided.
§ 5. We have already proceeded far enough not only to demonstrate the
error of Hobbes, but to ascertain the real import of by far the most
numerous class of propositions. The object of belief in a proposition,
when it asserts anything more than the meaning of words, is generally, as
in the cases which we have examined, either the coexistence 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 coexistence. And this case includes innumerable
instances which no one, previous to reflection, would think of referring
to it. Take the following example: A generous person is worthy of honour.
Who would expect to recognize here a case of coexistence between
phenomena? But so it is. The attribute which causes a person to be termed
generous, is ascribed to him on the ground of states of his mind, and
particulars of his conduct: both are phenomena; the former are facts of
internal consciousness, the latter, so far as distinct from the former,
are physical facts, or perceptions of the senses. Worthy of honour, admits
of a similar analysis. Honour, as here used, means a state of approving
and admiring emotion, followed on occasion by corresponding outward acts.
“Worthy of honour” connotes all this, together with our approval of the
act of showing honour. All these are phenomena; states of internal
consciousness, accompanied or followed by physical facts. When we say, A
generous person is worthy of honour, we affirm coexistence between the two
complicated phenomena connoted by the two terms respectively. We affirm,
that wherever and whenever the inward feelings and outward facts implied
in the word generosity, have place, then and there the existence and
manifestation of an inward feeling, honour, would be followed in our minds
by another inward feeling, approval.
After the analysis in a former chapter of the import of names, many
examples are not needed to illustrate the import of propositions. When
there is any obscurity or difficulty, it does not lie in the meaning of
the proposition, but in the meaning of the names which compose it; in the
very 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 coexistence of one such phenomenon with another; or the succession
of one such phenomenon to another: their _conjunction_, in short, so that
where the one is found, we may calculate on finding both.
This, however, though the most common, is not the only meaning which
propositions are ever intended to convey. In the first place, sequences
and coexistences are not only asserted respecting Phenomena; we make
propositions also respecting those hidden causes of phenomena, which are
named substances and attributes. A substance, however, being to us nothing
but either that which causes, or that which is conscious of, phenomena;
and the same being true, _mutatis mutandis_, of attributes; no assertion
can be made, at least with a meaning, concerning these unknown and
unknowable entities, except in virtue of the Phenomena by which alone they
manifest themselves to our faculties. When we say, Socrates was
cotemporary with the Peloponnesian war, the foundation of this assertion,
as of all assertions concerning substances, is an assertion concerning the
phenomena which they exhibit,—namely, that the series of facts by which
Socrates manifested himself to mankind, and the series of mental states
which constituted his sentient existence, went on simultaneously with the
series of facts known by the name of the Peloponnesian war. Still, the
proposition does not assert that alone; it asserts that the Thing in
itself, the _noumenon_ Socrates, was existing, and doing or experiencing
those various facts, during the same time. Coexistence and sequence,
therefore, may be affirmed or denied not only between phenomena, but
between noumena, or between a noumenon and phenomena. And both of noumena
and of phenomena we may affirm simple existence. But what is a noumenon?
An unknown cause. In affirming, therefore, the existence of a noumenon, we
affirm causation. Here, therefore, are two additional kinds of fact,
capable of being asserted in a proposition. Besides the propositions which
assert Sequence or Coexistence, there are some which assert simple
Existence; and others assert Causation, which, subject to the explanations
which will follow in the Third Book, must be considered provisionally as a
distinct and peculiar kind of assertion.
§ 6. To these four kinds of matter-of-fact or assertion, must be added a
fifth, Resemblance. This was a species of attribute which we found it
impossible to analyse; for which no _fundamentum_, distinct from the
objects themselves, could be assigned. Besides propositions which assert a
sequence or coexistence between two phenomena, there are therefore also
propositions which assert resemblance between them: as, This colour is
like that colour;—The heat of to-day is _equal_ to the heat of yesterday.
It is true that such an assertion might with some plausibility be brought
within the description of an affirmation of sequence, by considering it as
an assertion that the simultaneous contemplation of the two colours is
_followed_ by a specific feeling termed the feeling of resemblance. But
there would be nothing gained by encumbering ourselves, especially in this
place, with a generalization which may be looked upon as strained. Logic
does not undertake to analyse mental facts into their ultimate elements.
Resemblance between two phenomena is more intelligible in itself than any
explanation could make it, and under any classification must remain
specifically distinct from the ordinary cases of sequence and coexistence.
It is sometimes said that all propositions whatever, of which the
predicate is a general name, do, in point of fact, affirm or deny
resemblance. All such propositions affirm that a thing belongs to a class;
but things being classed together according to their resemblance,
everything is of course classed with the things which it is supposed to
resemble most; and thence, it may be said, when we affirm that Gold is a
metal, or that Socrates is a man, the affirmation intended is, that gold
resembles other metals, and Socrates other men, more nearly than they
resemble the objects contained in any other of the classes co-ordinate
with these.
There is some slight degree of foundation for this remark, but no more
than a slight degree. The arrangement of things into classes, such as the
class _metal_, or the class _man_, is grounded indeed on a resemblance
among the things which are placed in the same class, but not on a mere
general resemblance: the resemblance it is grounded on consists in the
possession by all those things, of certain common peculiarities; and those
peculiarities it is which the terms connote, and which the propositions
consequently assert; not the resemblance: for though when I say, Gold is a
metal, I say by implication that if there be any other metals it must
resemble them, yet if there were no other metals I might still assert the
proposition with the same meaning as at present, namely, that gold has the
various properties implied in the word metal; just as it might be said,
Christians are men, even if there were no men who were not Christians.
Propositions, therefore, in which objects are referred to a class because
they possess the attributes constituting the class, are so far from
asserting nothing but resemblance, that they do not, properly speaking,
assert resemblance at all.
But we remarked some time ago, (and the reasons of the remark will be more
fully entered into in a subsequent Book,(20)) 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. As, for instance, there are substances
called metals which have very few of the properties by which metals are
commonly recognised; and almost every great family of plants or animals
has a few anomalous genera or species on its borders, which are admitted
into it by a sort of courtesy, and concerning which it has been matter of
discussion to what family they properly belonged. Now when the class-name
is predicated of any object of this description, we do, by so predicating
it, affirm resemblance and nothing more. And in order to be scrupulously
correct it ought to be said, that in every case in which we predicate a
general name, we affirm, not absolutely that the object possesses the
properties designated by the name, but that it _either_ possesses those
properties, or if it does not, at any rate resembles the things which do
so, more than it resembles any other things. In most cases, however, it is
unnecessary to suppose any such alternative, the latter of the two grounds
being very seldom that on which the assertion is made: and when it is,
there is generally some slight difference in the form of the expression,
as, This species (or genus) is _considered_, or _may be ranked_, as
belonging to such and such a family: we should hardly say positively that
it does belong to it, unless it possessed unequivocally the properties of
which the class-name is scientifically significant.
There is still another exceptional case, in which, though the predicate is
a name of a class, yet in predicating it we affirm nothing but
resemblance, the class being founded not on resemblance in any given
particular, but on general unanalysable resemblance. The classes in
question are those into which our simple sensations, or other simple
feelings, are divided. Sensations of white, for instance, are classed
together, not because we can take them to pieces, and say they are alike
in this, and not alike in that, but because we feel them to be alike
altogether, though in different degrees. When, therefore, I say, The
colour I saw yesterday was a white colour, or, The sensation I feel is one
of tightness, in both cases the attribute I affirm of the colour or of the
other sensation is mere resemblance,—simple _likeness_ to sensations which
I have had before, and which have had those names bestowed upon them. The
names of feelings, like other concrete general names, are connotative; but
they connote a mere resemblance. When predicated of any individual
feeling, the information they convey is that of its likeness to the other
feelings which we have been accustomed to call by the same name. Thus much
may suffice in illustration of the kind of Propositions in which the
matter-of-fact asserted (or denied) is simple Resemblance.
Existence, Coexistence, Sequence, Causation, Resemblance: one or other of
these is asserted (or denied) in every proposition without exception. This
five-fold division is an exhaustive classification of matters-of-fact; of
all things that can be believed or tendered for belief; of all questions
that can be propounded, and all answers that can be returned to them.
Instead of Coexistence and Sequence, we shall sometimes say, for greater
particularity, Order in Place, and Order in Time: Order in Place being one
of the modes of coexistence, not necessary to be more particularly
analysed here; while the mere fact of coexistence, or simultaneousness,
may be classed, together with Sequence, under the head of Order in Time.
§ 7. In the foregoing inquiry into the import of Propositions, we have
thought it necessary to analyse _directly_ those alone, in which the terms
of the proposition (or the predicate at least) are concrete terms. But, in
doing so, we have indirectly analysed those in which the terms are
abstract. The distinction between an abstract term and its corresponding
concrete, does not turn upon any difference in what they are appointed to
signify; for the real signification of a concrete general name is, as we
have so often said, its connotation; and what the concrete term connotes,
forms the entire meaning of the abstract name. Since there is nothing in
the import of an abstract name which is not in the import of the
corresponding concrete, it is natural to suppose that neither can there be
anything in the import of a proposition of which the terms are abstract,
but what there is in some proposition which can be framed of concrete
terms.
And this presumption a closer examination will confirm. An abstract name
is the name of an attribute, or combination of attributes. The
corresponding concrete is a name given to things, because of, and in order
to express, their possessing that attribute, or that combination of
attributes. When, therefore, we predicate of anything a concrete name, the
attribute is what we in reality predicate of it. But it has now been shown
that in all propositions of which the predicate is a concrete name, what
is really predicated is one of five things: Existence, Coexistence,
Causation, Sequence, or Resemblance. An attribute, therefore, is
necessarily either an existence, a coexistence, a causation, a sequence,
or a resemblance. When a proposition consists of a subject and predicate
which are abstract terms, it consists of terms which must necessarily
signify one or other of these things. When we predicate of anything an
abstract name, we affirm of the thing that it is one or other of these
five things; that it is a case of Existence, or of Coexistence, or of
Causation, or of Sequence, or of Resemblance.
It is impossible to imagine any proposition expressed in abstract terms,
which cannot be transformed into a precisely equivalent proposition in
which the terms are concrete, namely, either the concrete names which
connote the attributes themselves, or the names of the _fundamenta_ of
those attributes, the facts or phenomena on which they are grounded. To
illustrate the latter case, let us take this proposition, of which the
subject only is an abstract name,—“Thoughtlessness is dangerous.”
Thoughtlessness is an attribute grounded on the facts which we call
thoughtless actions; and the proposition is equivalent to this,
Thoughtless actions are dangerous. In the next example the predicate as
well as the subject are abstract names: “Whiteness is a colour;” or “The
colour of snow is a whiteness.” These attributes being grounded on
sensations, the equivalent propositions in the concrete would be, The
sensation of white is one of the sensations called those of colour,—The
sensation of sight, caused by looking at snow, is one of the sensations
called sensations of white. In these propositions, as we have before seen,
the matter-of-fact asserted is a Resemblance. In the following examples,
the concrete terms are those which directly correspond to the abstract
names; connoting the attribute which these denote. “Prudence is a virtue:”
this may be rendered, “All prudent persons, _in so far as_ prudent, are
virtuous:” “Courage is deserving of honour,” thus, “All courageous persons
are deserving of honour _in so far_ as they are courageous;” which is
equivalent to this—“All courageous persons deserve an addition to the
honour, or a diminution of the disgrace, which would attach to them on
other grounds.”
In order to throw still further light upon the import of propositions of
which the terms are abstract, we will subject one of the examples given
above to a minuter analysis. The proposition we shall select is the
following:—“Prudence is a virtue.” Let us substitute for the word virtue
an equivalent but more definite expression, such as “a mental quality
beneficial to society,” or “a mental quality pleasing to God,” or whatever
else we adopt as the definition of virtue. What the proposition asserts is
a sequence, accompanied with causation, namely, that benefit to society,
or that the approval of God, is consequent on, and caused by, prudence.
Here is a sequence; but between what? We understand the consequent of the
sequence, but we have yet to analyse the antecedent. Prudence is an
attribute; and, in connexion with it, two things besides itself are to be
considered; prudent persons, who are the _subjects_ of the attribute, and
prudential conduct, which may be called the _foundation_ of it. Now is
either of these the antecedent? and, first, is it meant, that the approval
of God, or benefit to society, is attendant upon all prudent _persons_?
No; except _in so far_ as they are prudent; for prudent persons who are
scoundrels can seldom on the whole be beneficial to society, nor
acceptable to any good being. Is it upon prudential _conduct_, then, that
divine approbation and benefit to mankind are supposed to be invariably
consequent? Neither is this the assertion meant when it is said that
prudence is a virtue; except with the same reservation as before, and for
the same reason, namely, that prudential conduct, although in _so far as_
it is prudential it is beneficial to society, may yet, by reason of some
other of its qualities, be productive of an injury outweighing the
benefit, and deserve a displeasure exceeding the approbation which would
be due to the prudence. Neither the substance, therefore, (viz., the
person,) nor the phenomenon, (the conduct,) is an antecedent on which the
other term of the sequence is universally consequent. But the proposition,
“Prudence is a virtue,” is an universal proposition. What is it, then,
upon which the proposition affirms the effects in question to be
universally consequent? Upon that _in_ the person, and in the conduct,
which causes them to be called prudent, and which is equally in them when
the action, though prudent, is wicked; namely, a correct foresight of
consequences, a just estimation of their importance to the object in view,
and repression of any unreflecting impulse at variance with the deliberate
purpose. These, which are states of the person’s mind, are the real
antecedent in the sequence, the real cause in the causation, asserted by
the proposition. But these are also the real ground, or foundation, of the
attribute Prudence; since wherever these states of mind exist we may
predicate prudence, even before we know whether any conduct has followed.
And in this manner every assertion respecting an attribute may be
transformed into an assertion exactly equivalent respecting the fact or
phenomenon which is the ground of the attribute. And no case can be
assigned, where that which is predicated of the fact or phenomenon, does
not belong to one or other of the five species formerly enumerated: it is
either simple Existence, or it is some Sequence, Coexistence, Causation,
or Resemblance.
And as these five are the only things which can be affirmed, so are they
the only things which can be denied. “No horses are web-footed” denies
that the attributes of a horse ever coexist with web-feet. It is scarcely
necessary to apply the same analysis to Particular affirmations and
negations. “Some birds are web-footed,” affirms that, with the attributes
connoted by _bird_, the phenomenon web-feet is sometimes coexistent: “Some
birds are not web-footed,” asserts that there are other instances in which
this coexistence does not have place. Any further explanation of a thing
which, if the previous exposition has been assented to, is so obvious, may
here be spared.
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
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, although 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’ 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 were said to be of the _essence_ of the subject. The
essence of a thing, they said, was that without which the thing could
neither be, nor be conceived to be. Thus, rationality was of the essence
of man, because without rationality, man could not be conceived to exist.
The different attributes which made up the essence of the thing, were
called its essential properties; and a proposition in which any of these
were predicated of it, was called an Essential Proposition, and was
considered to go deeper into the nature of the thing, and to convey more
important information respecting it, than any other proposition could do.
All properties, not of the essence of the thing, were called its
accidents; were supposed to have nothing at all, or nothing comparatively,
to do with its inmost nature; and the propositions in which any of these
were predicated of it were called Accidental Propositions. A connexion may
be traced between this distinction, which originated with the schoolmen,
and the well known dogmas of _substantiæ secundæ_ or general substances,
and _substantial forms_, doctrines which under varieties of language
pervaded alike the Aristotelian and the Platonic schools, and of which
more of the spirit has come down to modern times than might be conjectured
from the disuse of the phraseology. The false views of the nature of
classification and generalization which prevailed among the schoolmen, and
of which these dogmas were the technical expression, afford the only
explanation which can be given of their having misunderstood the real
nature of those Essences which held so conspicuous a place in their
philosophy. They said, truly, that _man_ cannot be conceived without
rationality. But though _man_ cannot, a being may be conceived exactly
like a man in all points except that one quality, and those others which
are the conditions or consequences of it. All therefore which is really
true in the assertion that man cannot be conceived without rationality, is
only, that if he had not rationality, he would not be reputed a man. There
is no impossibility in conceiving the _thing_, nor, for aught we know, in
its existing: the impossibility is in the conventions of language, which
will not allow the thing, even if it exist, to be called by the name which
is reserved for rational beings. Rationality, in short, is involved in the
meaning of the word man; is one of the attributes connoted by the name.
The essence of man, simply means the whole of the attributes connoted by
the word; and any one of those attributes taken singly, is an essential
property of man.
The doctrines which prevented the real meaning of Essences from being
understood, not having assumed so settled a shape in the time of Aristotle
and his immediate followers as was afterwards given to them by the
Realists of the middle ages, we find a nearer approach to a rational view
of the subject in the writings of the ancient Aristotelians than in their
more modern followers. Porphyry, in his _Isagoge_, approached so near to
the true conception of essences, that only one step remained to be taken,
but this step, so easy in appearance, was reserved for the Nominalists of
modern times. By altering any property, not of the essence of the thing,
you merely, according to Porphyry, made a difference in it; you made it
ἀλλοῖον: but by altering any property which was of its essence, you made
it _another thing_, ἄλλο.(21) To a modern it is obvious that between the
change which only makes a thing different, and the change which makes it
_another thing_, the only distinction is that in the one case, though
changed, it is still called by the same name. Thus, pound ice in a mortar,
and being still called ice, it is only made ἀλλοῖον: melt it, and it
becomes ἄλλο, another thing, namely, water. Now it is really the same
thing, _i.e._ the same particles of matter, in both cases; and you cannot
so change anything that it shall cease to be the same thing in this sense.
The identity which it can be deprived of is merely that of the name: when
the thing ceases to be called ice, it becomes _another thing_; its
essence, what constituted it ice, is gone; while, as long as it continues
to be so called, nothing is gone except some of its accidents. But these
reflections, so easy to us, would have been difficult to persons who
thought, as most of the Aristotelians did, that objects were made what
they were called, that ice (for instance) was made ice, not by the
possession of certain properties to which mankind have chosen to attach
that name, but by participation in the nature of a certain _general
substance_, called _Ice in general_, which substance, together with all
the properties that belonged to it, _inhered_ in every individual piece of
ice. As they did not consider these universal substances to be attached to
all general names, but only to some, they thought that an object borrowed
only a part of its properties from an universal substance, and that the
rest belonged to it individually: the former they called its essence, and
the latter its accidents. The scholastic doctrine of essences long
survived the theory on which it rested, that of the existence of real
entities corresponding to general terms; and it was reserved for Locke, at
the end of the seventeenth century, to convince philosophers that the
supposed essences of classes were merely the signification of their names;
nor, among the signal services which his writings rendered to philosophy,
was there one more needful or more valuable.(22)
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
only 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 we have 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
object 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
retains a footing in some remote fastness after it has been driven from
the open country. The essences of individuals were an unmeaning figment
arising from a misapprehension of the essences of classes, yet even Locke,
when he extirpated the parent error, could not shake himself free from
that which was its fruit. He distinguished two sorts of essences, Real and
Nominal. His nominal essences were the essences of classes, explained
nearly as we have now explained them. Nor is anything wanting to render
the third book of Locke’s Essay a nearly unexceptionable treatise on the
connotation of names, except to free its language from the assumption of
what are called Abstract Ideas, which unfortunately is involved in the
phraseology, although not necessarily connected with the thoughts,
contained in that immortal Third Book.(23) 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.
Nothing has probably contributed more to the opinion so commonly 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 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
premisses 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 supposed 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 the 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 ordinary cases, come into view at all.
Although, however, Predication does not presuppose Classification, and
although the theory of Names and of Propositions is not cleared up, but
only encumbered, by intruding the idea of classification into it, there is
nevertheless a close connexion between Classification and the employment
of General Names. By every general name which we introduce, we create a
class, if there be any things, real or imaginary, to compose it; that is,
any Things corresponding to the signification of the name. Classes,
therefore, mostly owe their existence to general language. But general
language, also, though that is not the most common case, sometimes owes
its existence to classes. A general, which is as much as to say a
significant, name, is indeed mostly introduced because we have a
signification to express by it; because we need a word by means of which
to predicate the attributes which it connotes. But it is also true that a
name is sometimes introduced because we have found it convenient to create
a class; because we have thought it useful for the regulation of our
mental operations, that a certain group of objects should be thought of
together. A naturalist, for purposes connected with his particular
science, sees reason to distribute the animal or vegetable creation into
certain groups rather than into any others, and he requires a name to
bind, as it were, each of his groups together. It must not however be
supposed that such names, when introduced, differ in any respect, as to
their mode of signification, from other connotative names. The classes
which they denote are, as much as any other classes, constituted by
certain common attributes, and their names are significant of those
attributes, and of nothing else. The names of Cuvier’s classes and orders,
_Plantigrades_, _Digitigrades_, &c., are as much the expression of
attributes as if those names had preceded, instead of growing out of, his
classification of animals. The only peculiarity of the case is, that the
convenience of classification was here the primary motive for introducing
the names; while in other cases the name is introduced as a means of
predication, and the formation of a class denoted by it is only an
indirect consequence.
The principles which ought to regulate Classification as a logical process
subservient to the investigation of truth, cannot be discussed to any
purpose until a much later stage of our inquiry. But, of classification as
resulting from, and implied in, the fact of employing general language, we
cannot forbear to treat here, without leaving the theory of general names,
and of their employment in predication, mutilated and formless.
§ 2. This portion of the theory of general language is the subject of what
is termed the doctrine of the Predicables; a set of distinctions handed
down from Aristotle, and his follower Porphyry, many of which have taken a
firm root in scientific, and some of them even in popular, phraseology.
The predicables are a five-fold division of General Names, not grounded as
usual on a difference in their meaning, that is, in the attribute which
they connote, but on a difference in the kind of class which they denote.
We may predicate of a thing five different varieties of class-name:—
A _genus_ of the thing (γένος).
A _species_ (εἴδος).
A _differentia_ (διαφορὰ).
A _proprium_ (ἰδιόν).
An _accidens_ (συμβεβηκός).
It is to be remarked of these distinctions, that they express, not what
the predicate is in its own meaning, but what relation it bears to the
subject of which it happens on the particular occasion to be predicated.
There are not some names which are exclusively genera, and others which
are exclusively species, or differentiæ; but the same name is referred to
one or another Predicable, according to the subject of which it is
predicated on the particular occasion. _Animal_, for instance, is a genus
with respect to man, or John; a species with respect to Substance, or
Being. _Rectangular_ is one of the Differentiæ of a geometrical square; it
is merely one of the Accidentia of the table at which I am writing. The
words genus, species, &c., are therefore relative terms; they are names
applied to certain predicates, to express the relation between them and
some given subject: a relation grounded, as we shall see, not on what the
predicate connotes, but on the class which it _de_notes, and on the place
which, in some given classification, that class occupies relatively to the
particular subject.
§ 3. Of these five names, two, Genus and Species, are not only used by
naturalists in a technical acceptation not precisely agreeing with their
philosophical meaning, but have also acquired a popular acceptation, much
more general than either. In this popular sense any two classes, one of
which includes the whole of the other and more, may be called a Genus and
a Species. Such, for instance, are Animal and Man; Man and Mathematician.
Animal is a genus; Man and Brute are its two species; or we may divide it
into a greater number of species, as man, horse, dog, &c. _Biped_, or
_two-footed animal_, may also be considered a genus, of which man and bird
are two species. _Taste_ is a genus, of which sweet taste, sour taste,
salt taste, &c. are species. _Virtue_ is a genus; justice, prudence,
courage, fortitude, generosity, &c. are its species.
The same class which is a genus with reference to the sub-classes or
species included in it, may be itself a species with reference to a more
comprehensive, or, as it is often called, a superior, genus. Man is a
species with reference to animal, but a genus with reference to the
species mathematician. Animal is a genus, divided into two species, man
and brute; but animal is also a species, which, with another species,
vegetable, makes up the genus, organized being. Biped is a genus with
reference to man and bird, but a species with respect to the superior
genus, animal. Taste is a genus divided into species, but also a species
of the genus sensation. Virtue, a genus with reference to justice,
temperance, &c., is one of the species of the genus, mental quality.
In this popular sense the words Genus and Species have passed into common
discourse. And it should be observed that, in ordinary parlance, not the
name of the class, but the class itself, is said to be the genus or
species; not, of course, the class in the sense of each individual of that
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; and man and brute co-ordinate species under that genus: _biped_
would not have been admitted to be a genus with reference to man, but a
_proprium_ or _accidens_ only. It was requisite, according to their
theory, that genus and species should be of the _essence_ of the subject.
_Animal_ was of the essence of man; _biped_ was not. And in every
classification they considered some one class as the lowest or _infima_
species. Man, for instance, was a lowest species. Any further divisions
into which the class might be capable of being broken down, as man into
white, black, and red man, or into priest and layman, they did not admit
to be species.
It has been seen, however, in the preceding chapter, that the distinction
between the essence of a class, and the attributes or properties which are
not of its essence—a distinction which has given occasion to so much
abstruse speculation, and to which so mysterious a character was formerly,
and by many writers is still, attached,—amounts to nothing more than the
difference between those attributes of the class which are, and those
which are not, involved in the signification of the class-name. As applied
to individuals, the word Essence, we found, has no meaning, except in
connexion with the exploded tenets of the Realists; and what the schoolmen
chose to call the essence of an individual, was simply the essence of the
class to which that individual was most familiarly referred.
Is there no difference, then, save this merely verbal one, between the
classes which the schoolmen admitted to be genera or species, and those to
which they refused the title? Is it an error to regard some of the
differences which exist among objects as differences _in kind_ (_genere_
or _specie_), and others only as differences in the accidents? Were the
schoolmen right or wrong in giving to some of the classes into which
things may be divided, the name of _kinds_, and considering others as
secondary divisions, grounded on differences of a comparatively
superficial nature? Examination will show that the Aristotelians did mean
something by this distinction, and something important; but which, being
but indistinctly conceived, was inadequately expressed by the phraseology
of essences, and by 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 of 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 characterise them
by, except precisely what is connoted by the name: white things, for
example, are not distinguished by any common properties, except whiteness;
or if they are, it is only by such as are in some way dependent on, or
connected with, whiteness. But a hundred generations have not exhausted
the common properties of animals or of plants, of sulphur or of
phosphorus; nor do we suppose them to be exhaustible, but proceed to new
observations and experiments, in the full confidence of discovering new
properties which were by no means implied in those we previously knew.
While, if any one were to propose for investigation the common properties
of all things which are of the same colour, the same shape, or the same
specific gravity, the absurdity would be palpable. We have no ground to
believe that any such common properties exist, except such as may be shown
to be involved in the supposition itself, or to be derivable from it by
some law of causation. It appears, therefore, that the properties, on
which we ground our classes, sometimes exhaust all that the class has in
common, or contain it all by some mode of implication; but in other
instances we make a selection of a few properties from among not only a
greater number, but a number inexhaustible by us, and to which as we know
no bounds, they may, so far as we are concerned, be regarded as infinite.
There is no impropriety in saying that of these two classifications, the
one answers to a much more radical distinction in the things themselves,
than the other does. And if any one even chooses to say that the one
classification is made by nature, the other by us for our convenience, he
will be right; provided he means no more than this: Where a certain
apparent difference between things (although perhaps in itself of little
moment) answers to we know not what number of other differences, pervading
not only their known properties but properties yet undiscovered, it is not
optional but imperative to recognise this difference as the foundation of
a specific distinction: while, on the contrary, differences that are
merely finite and determinate, like those designated by the words white,
black, or red, may be disregarded if the purpose for which the
classification is made does not require attention to those particular
properties. The differences, however, are made by nature, in both cases;
while the recognition of those differences as grounds of classification
and of naming, is, equally in both cases, the act of man: only in the one
case, the ends of language and of classification would be subverted if no
notice were taken of the difference, while in the other case, the
necessity of taking notice of it depends on the importance or unimportance
of the particular qualities in which the difference happens to consist.
Now, these classes, distinguished by unknown multitudes of properties, and
not solely by a few determinate ones, 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 usual 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, Sir Isaac Newton would be said to be of the species man. There
are indeed numerous sub-classes included in the class man, to which Newton
also belongs; as, 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 cannot.
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, maybe differences
of kind, within our meaning of the term. I do not say that they are so.
For in the progress of physiology it may almost be said to be made out,
that the differences which really exist between different races, sexes,
&c., follow as consequences, under laws of nature, from a small number of
primary differences which can be precisely determined, and which, as the
phrase is, _account for_ all the rest. If this be so, these are not
distinctions in kind; no more than Christian, Jew, Mussulman, and Pagan, a
difference which also carries many consequences along with it. And in this
way classes are often mistaken for real kinds, which are afterwards proved
not to be so. But if it turned out, that the differences were not capable
of being thus accounted for, then Caucasian, Mongolian, Negro, &c., would
be really different Kinds of human beings, and entitled to be ranked as
species by the logician; though not by the naturalist. For (as already
noticed) the word species is used in a very different signification in
logic and in natural history. By the naturalist, organized beings are
never said to be of different species, if it is supposed that they could
possibly have descended from the same stock. That, however, is a sense
artificially given to the word, for the technical purposes of a particular
science. To the logician, if a negro and a white man differ in the same
manner (however less in degree) as a horse and a camel do, that is, if
their differences are inexhaustible, and not referrible to any common
cause, they are different species, whether they are descended from common
ancestors or not. But if their differences can all be traced to climate
and habits, or to some one special difference 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 any ascertainable law; then out of the
class man we might cut another class, flat-nosed man, which, according to
our definition, would be a Kind. But if we could do this, man would not
be, as it was assumed to be, the proximate Kind. Therefore, the properties
of the proximate Kind do comprehend those (whether known or unknown) of
all other Kinds to which the individual belongs; which was the point we
undertook to prove. And hence, every other Kind which is predicable of the
individual, will be to the proximate Kind in the relation of a genus,
according to even the popular acceptation of the terms genus and species;
that is, it will be a larger class, including it and more.
We are now able to fix the logical meaning of these terms. Every class
which is a real Kind, that is, which is distinguished from all other
classes by an indeterminate multitude of properties not derivable from one
another, is either a genus or a species. A Kind which is not divisible
into other Kinds, cannot be a genus, because it has no species under it;
but it is itself a species, both with reference to the individuals below
and to the genera above, (Species Prædicabilis and Species Subjicibilis.)
But every Kind which admits of division into real Kinds (as animal into
quadruped, bird, &c., or quadruped into various species of quadrupeds) 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
whether we use the concrete or the abstract form) is generally assigned by
logicians as the Differentia; and doubtless this attribute serves the
purpose of distinction: but it has also been remarked of man, that he is a
cooking animal; the only animal that dresses its food. This, therefore, is
another of the attributes by which the species man is distinguished from
other species of the same genus: would this attribute serve equally well
for a differentia? The Aristotelians say No; having laid it down that the
differentia must, like the genus and species, be of the _essence_ of the
subject.
And here we lose even that vestige of a meaning grounded in the nature of
the things themselves, which may be supposed to be attached to the word
essence when it is said that genus and species must be of the essence of
the thing. There can be no doubt that when the schoolmen talked of the
essences of things as opposed to their accidents, they had confusedly in
view the distinction between differences of kind, and the differences
which are not of kind; they meant to intimate that genera and species must
be Kinds. Their notion of the essence of a thing was a vague notion of a
something which makes it what it is, _i.e._, which makes it the Kind of
thing that it is—which causes it to have all that variety of properties
which distinguish its Kind. But when the matter came to be looked at more
closely, nobody could discover what caused the thing to have all those
properties, nor even that there was anything which caused it to have them.
Logicians, however, not liking to admit this, and being unable to detect
what made the thing to be what it was, satisfied themselves with what made
it to be what it was called. Of the innumerable properties, known and
unknown, that are common to the class man, a portion only, and of course a
very small portion, are connoted by its name; these few, however, will
naturally have been thus distinguished from the rest either for their
greater obviousness, or for greater supposed importance. These properties,
then, which were connoted by the name, logicians seized upon, and called
them the essence of the species; and not stopping there, they affirmed
them, in the case of the _infima species_, to be the essence of the
individual too; for it was their maxim, that the species contained the
“whole essence” of the thing. Metaphysics, that fertile field of delusion
propagated by language, does not afford a more signal instance of such
delusion. On this account it was that rationality, being connoted by the
name man, was allowed to be a differentia of the class; but the
peculiarity of cooking their food, not being connoted, was relegated to
the class of accidental properties.
The distinction, therefore, between Differentia, Proprium, and Accidens,
is not founded 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
Houyhnhms 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, although 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
thinks it desirable that our ideas should arrange themselves. 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
some of Cuvier’s families are founded. In doing this, the naturalist
creates so 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 those 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; although not commonly considered
as ambiguous, because it happens in both cases to _de_note the same
individual objects. But a case is conceivable in which the ambiguity would
become evident: we have only to imagine that some new kind of animal were
discovered, having Linnæus’s three characteristics of humanity, but not
rational, or not of the human form. In ordinary parlance these animals
would not be called men; but in natural history they must still be called
so by those, if any there be, who adhere to the Linnæan classification;
and the question would arise, whether the word should continue to be used
in two senses, or the classification be given up, and the technical sense
of the term be abandoned along with 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 colours, and desire to justify, or even merely to point
out, the particular place assigned to whiteness in our arrangement, we may
define it “the colour produced by the mixture of all the simple rays;” and
this fact, though by no means implied in the meaning of the word whiteness
as ordinarily used, but only known by subsequent scientific investigation,
is part of its meaning in the particular essay or treatise, and becomes
the differentia of the species.(24)
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
connexion whatever with the essence, but may come and go, and the species
still remain what it was before. If a species could exist without its
Propria, it must be capable of existing without that on which its Propria
are necessarily consequent, and therefore without its essence, without
that which constitutes it a species. But an Accidens, whether separable or
inseparable from the species in actual experience, may be supposed
separated, without the necessity of supposing any other alteration; or at
least, without supposing any of the essential properties of the species to
be altered, since with them an Accidens has no connexion.
A Proprium, therefore, of the species, may be defined, any attribute which
belongs to all the individuals included in the species, and which,
although 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
premisses, 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, it _cannot but_ follow, consistently with
some law which we regard as a part of the constitution either of our
thinking faculty or of the universe.
§ 8. Under the remaining predicable, Accidens, are included all attributes
of a thing which are neither involved in the signification of the name,
(whether ordinarily or as a term of art,) nor have, so far as we know, any
necessary connexion with attributes which are so involved. They are
commonly divided into Separable and Inseparable Accidents. Inseparable
accidents are those which—although we know of no connexion between them
and the attributes constitutive of the species, and although, therefore,
so far as we are aware, they might be absent without making the name
inapplicable and the species a different species—are yet never in fact
known to be absent. A concise mode of expressing the same meaning is, that
inseparable accidents are properties which are universal to the species,
but not necessary to it. Thus, blackness is an attribute of a crow, and,
as far as we know, 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 colour of an European is one of the separable accidents of the
species man, because it is not an attribute of all human creatures. Being
born, is also (speaking in the logical sense) a separable accident of the
species man, because, although 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 cannot be discussed to much purpose.
The simplest and most correct notion of a Definition is, a proposition
declaratory of the meaning of a word; namely, either the meaning which it
bears in common acceptation, or that which the speaker or writer, for the
particular purposes of his discourse, intends to annex to it.
The definition of a word being the proposition which enunciates its
meaning, words which have no meaning are unsusceptible of definition.
Proper names, therefore, cannot be defined. A proper name being a mere
mark put upon an individual, and of which it is the characteristic
property to be destitute of meaning, its meaning cannot of course be
declared; though we may indicate by language, as we might indicate still
more conveniently by pointing with the finger, upon what individual that
particular mark has been, or is intended to be, put. It is no definition
of “John Thomson” to say he is “the son of General Thomson;” for the name
John Thomson does not express this. Neither is it any definition of “John
Thomson” to say he is “the man now crossing the street.” These
propositions may serve to make known who is the particular man to whom the
name belongs; but that may be done still more unambiguously by pointing to
him, which, however, has not usually 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 may be done either
directly or indirectly. The direct mode would be by a proposition in this
form: “Man” (or whatsover the word may be) “is a name connoting such and
such attributes,” or “is a name which, when predicated of anything,
signifies the possession of such and such attributes by that thing.” Or
thus: Man is everything which possesses such and such attributes: Man is
everything which possesses corporeity, organization, life, rationality,
and certain peculiarities of external form.
This form of definition is the most precise and least equivocal of any;
but it is not brief enough, and is besides too technical and pedantic for
common discourse. The more usual mode of declaring the connotation of a
name, is to predicate of it another name or names of known signification,
which connote the same aggregation of attributes. This may be done either
by predicating of the name intended to be defined, another connotative
name exactly synonymous, as, “Man is a human being,” which is not commonly
accounted a definition at all; or by predicating two or more connotative
names, which make up among them the whole connotation of the name to be
defined. In this last case, again, we may either compose our definition of
as many connotative names as there are attributes, each attribute being
connoted by one; as, Man is a corporeal, organized, animated, rational
being, shaped so and so; or we may employ names which connote several of
the attributes at once, as, Man is a rational _animal_, shaped so and so.
The definition of a name, according to this view of it, is the sum total
of all the _essential_ propositions which can be framed with that name for
their subject. All propositions the truth of which is implied in the name,
all those which we are made aware of by merely hearing the name, are
included in the definition, if complete, and may be evolved from it
without the aid of any other premisses; whether the definition expresses
them in two or three words, or in a larger number. It is, therefore, not
without reason that Condillac and other writers have affirmed a definition
to be an _analysis_. To resolve any complex whole into the elements of
which it is compounded, is the meaning of analysis; and this we do when we
replace one word which connotes a set of attributes collectively, by two
or more which connote the same attributes singly, or in smaller groups.
§ 2. From this, however, the question naturally arises, in what manner are
we to define a name which connotes only a single attribute? for instance,
“white,” which connotes nothing but whiteness; “rational,” which connotes
nothing but the possession of reason. It might seem that the meaning of
such names could only be declared in two ways; by a synonymous term, if
any such can be found; or in the direct way already alluded to: “White is
a name connoting the attribute whiteness.” Let us see, however, whether
the analysis of the meaning of the name, that is, the breaking down of
that meaning into several parts, admits of being carried farther. Without
at present deciding this question as to the word _white_, it is obvious
that in the case of _rational_ some further explanation may be given of
its meaning than is contained in the proposition, “Rational is that which
possesses the attribute of reason;” since the attribute reason itself
admits of being defined. And here we must turn our attention to the
definitions of attributes, or rather of the names of attributes, that is,
of abstract names.
In regard to such names of attributes as are connotative, and express
attributes of those attributes, there is no difficulty: like other
connotative names, they are defined by declaring their connotation. Thus,
the word _fault_ may be defined, “a quality productive of evil or
inconvenience.” Sometimes, again, the attribute to be defined is not one
attribute, but an union of several: we have only, therefore, to put
together the names of all the attributes taken separately, and we obtain
the definition of the name which belongs to them all taken together; a
definition which will correspond exactly to that of the corresponding
concrete name. For, as we define a concrete name by enumerating the
attributes which it connotes, and as the attributes connoted by a concrete
name form the entire signification of the corresponding abstract one, 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, and shaped so and so,” the definition of _humanity_ will be,
corporeity and animal life, combined with rationality, and with such and
such a shape.
When, on the other hand, the abstract name does not express a complication
of attributes, but a single attribute, we must remember that every
attribute is grounded on some fact or phenomenon, from which, and which
alone, it derives its meaning. To that fact or phenomenon, called in a
former chapter the foundation of the attribute, we must, therefore, have
recourse for its definition. Now, the foundation of the attribute may be a
phenomenon of any degree of complexity, consisting of many different
parts, either coexistent or in succession. To obtain a definition of the
attribute, we must analyse the phenomenon into these parts. Eloquence, for
example, is the name of one attribute only; but this attribute is grounded
on external effects of a complicated nature, flowing from acts of the
person to whom we 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 analyse, that is, to distinguish into parts, the
attribute or set of attributes which constitute the meaning both of the
concrete name and of the corresponding abstract: if a set of attributes,
by enumerating them; if a single attribute, by dissecting the fact or
phenomenon (whether of perception or of internal consciousness) which is
the foundation of the attribute. But, further, even when the fact is one
of our simple feelings or states of consciousness, and therefore
unsusceptible of analysis, the names both of the object and of the
attribute still admit of definition; or, rather, would do so if all our
simple feelings had names. Whiteness may be defined, the property or power
of exciting the sensation of white. A white object may be defined an
object which excites the sensation of white. The only names which are
unsusceptible of definition, because their meaning is unsusceptible of
analysis, are the names of the simple feelings themselves. These are in
the same condition as proper names. They are not indeed, like proper
names, unmeaning; for the words _sensation of white_ signify, that the
sensation which I so denominate resembles other sensations which I
remember to have had before, and to have called by that name. But as we
have no words by which to 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 cannot unfold the
signification of this class of names; and we are obliged to make a direct
appeal to the personal experience of the individual whom we address.
§ 3. Having stated what seems to be the true idea of a Definition, we
proceed to examine some opinions of philosophers, and some popular
conceptions on the subject, which conflict more or less with that idea.
The only adequate definition of a name is, as already remarked, one which
declares the facts, and the whole of the facts, which the name involves in
its signification. But with most persons the object of a definition does
not embrace so much; they look for nothing more, in a definition, than a
guide to the correct use of the term—a protection against applying it in a
manner inconsistent with custom and convention. Anything, therefore, is to
them a sufficient definition of a term, which will serve as a correct
index to what the term _de_notes; although 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; namely,
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 Houyhnhms men; but as there
happen to be no Houyhnhms, this imperfect definition is sufficient to mark
out and distinguish from all other things, the objects at present denoted
by “man;” all the beings actually known to exist, of whom the name is
predicable. Though the word is defined by some only among the attributes
which it connotes, not by all, it happens that all known objects which
possess the enumerated attributes, possess also those which are omitted;
so that the field of predication which the word covers, and the employment
of it which is conformable to usage, are as well indicated by the
inadequate definition as by an adequate one. Such definitions, however,
are always liable to be overthrown by the discovery of new objects in
nature.
Definitions of this kind are what logicians have had in view, when they
laid down the rule, that the definition of a species should be _per genus
et differentiam_. Differentia being seldom taken to mean the whole of the
peculiarities constitutive of the species, but some one of those
peculiarities only, a complete definition would be _per genus et
differentias_, rather than _differentiam_. It would include, with the name
of the superior genus, not merely _some_ attribute which distinguishes the
species intended to be defined from all other species of the same genus,
but _all_ the attributes implied in the name of the species, which the
name of the superior genus has not already implied. The assertion,
however, that a definition must of necessity consist of a genus and
differentiæ, is not tenable. It was early remarked by logicians, that the
_summum genus_ in any classification, having no genus superior to itself,
could not be defined in this manner. Yet we have seen that all names,
except those of our elementary feelings, are susceptible of definition in
the strictest sense; by setting forth in words the constituent parts of
the fact or phenomenon, of which the connotation of every word is
ultimately composed.
§ 4. Although the first kind of imperfect definition, (which defines a
connotative term by a part only of what it connotes, but a part sufficient
to mark out correctly the boundaries of its denotation,) has been
considered by the ancients, and by logicians in general, as a complete
definition; it has always been deemed necessary that the attributes
employed should really form part of the connotation; for the rule was that
the definition must be drawn from the _essence_ of the class; and this
would not have been the case if it had been in any degree made up of
attributes not connoted by the name. The second kind of imperfect
definition, therefore, in which the name of a class is defined by any of
its accidents,—that is, by attributes which are not included in its
connotation,—has been rejected from the rank of genuine Definition by all
logicians, and has been termed Description.
This kind of imperfect definition, however, takes its rise from the same
cause as the other, namely, the willingness to accept as a definition
anything which, whether it expounds the meaning of the name or not,
enables us to discriminate the things denoted by the name from all other
things, and consequently to employ the term in predication without
deviating from established usage. This purpose is duly answered by stating
any (no matter what) of the attributes which are common to the whole of
the class, and peculiar to it; or any combination of attributes which may
happen to be peculiar to it, though separately each of those attributes
may be common to it with some other things. It is only necessary that the
definition (or description) thus formed, should be _convertible_ with the
name which it professes to define; that is, should be exactly co-extensive
with it, being predicable of everything of which it is predicable, and of
nothing of which it is not predicable; although the attributes specified
may have no connexion with those which mankind had in view when they
formed or recognised the class, and gave it a name. The following are
correct definitions of Man, according to this test: Man is a mammiferous
animal, having (by nature) two hands (for the human species answers to
this description, and no other animal does): Man is an animal who cooks
his food: Man is a featherless biped.
What would otherwise be a mere description, may be raised to the rank of a
real definition by the peculiar purpose which the speaker or writer has in
view. As was seen in the preceding chapter, it may, for the ends of a
particular art or science, or for the more convenient statement of an
author’s particular doctrines, be advisable to give to some general name,
without altering its denotation, a special connotation, different from its
ordinary one. When this is done, a definition of the name by means of the
attributes which make up the special connotation, though in general a mere
accidental definition or description, becomes on the particular occasion
and for the particular purpose a complete and genuine definition. This
actually occurs with respect to one of the preceding examples, “Man is a
mammiferous animal having two hands,” which is the scientific definition
of man considered as one of the species in Cuvier’s distribution of the
animal kingdom.
In cases of this sort, although the definition is still a declaration of
the meaning which in the particular instance the name is appointed to
convey, it cannot be said that to state the meaning of the word is the
purpose of the definition. The purpose is not to expound a name, but to
help to expound a classification. The special meaning which Cuvier
assigned to the word Man, (quite foreign to its ordinary meaning, though
involving no change in the denotation of the word,) was incidental to a
plan of arranging animals into classes on a certain principle, that is,
according to a certain set of distinctions. And since the definition of
Man according to the ordinary connotation of the word, though it would
have answered every other purpose of a definition, would not have pointed
out the place which the species ought to occupy in that particular
classification; he gave the word a special connotation, that he might be
able to define it by the kind of attributes on which, for reasons of
scientific convenience, he had resolved to found his division of animated
nature.
Scientific definitions, whether they are definitions of scientific terms
or of common terms used in a scientific sense, are almost always of the
kind last spoken of: their main purpose is to serve as the landmarks of
scientific classification. And since the classifications in any science
are continually modified as scientific knowledge advances, the definitions
in the sciences are also constantly varying. A striking instance is
afforded by the words Acid and Alkali, especially the former. As
experimental discovery advanced, the substances classed with acids have
been constantly multiplying, and by a natural consequence the attributes
connoted by the word have receded and become fewer. At first it connoted
the attributes, of combining with an alkali to form a neutral substance
(called a salt); being compounded of a base and oxygen; causticity to the
taste and touch; fluidity, &c. The true analysis of muriatic acid, into
chlorine and hydrogen, caused the second property, composition from a base
and oxygen, to be excluded from the connotation. The same discovery fixed
the attention of chemists upon hydrogen as an important element in acids;
and more recent discoveries having led to the recognition of its presence
in sulphuric, nitric, and many other acids, where its existence was not
previously suspected, there is now a tendency to include the presence of
this element in the connotation of the word. But carbonic acid, silica,
sulphurous acid, have no hydrogen in their composition; that property
cannot therefore be connoted by the term, unless those substances are no
longer to be considered acids. Causticity, and fluidity, have long since
been excluded from the characteristics of the class, by the inclusion of
silica and many other substances in it; and the formation of neutral
bodies by combination with alkalis, together with such electro-chemical
peculiarities as this is supposed to imply, are now the only _differentiæ_
which form the fixed connotation of the word Acid, as a term of chemical
science.
Scientific men are still seeking, and may be long ere they find, a
suitable definition of one of the earliest words in the vocabulary of the
human race, and one of those of which the popular sense is plainest and
best understood. The word I mean is Heat; and the source of the difficulty
is the imperfect state of our scientific knowledge, which has shown to us
multitudes of phenomena certainly connected with the same power which
causes what our senses recognise as heat, but has not yet taught us the
laws of those phenomena with sufficient accuracy to admit of our
determining under what characteristics the whole of those phenomena shall
ultimately be embodied as a class: which characteristics would of course
be so many differentiæ for the definition of the power itself. We have
advanced far enough to know that one of the attributes connoted must be
that of operating as a repulsive force; but this is certainly not all
which must ultimately be included in the scientific definition of heat.
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 any one differentia was deemed
sufficient. But to expound, or express in words, a distinction of Kind,
has already been shown to be an impossibility: the very meaning of a Kind
is, that the properties which distinguish it do not grow out of one
another, and cannot therefore be set forth in words, even by implication,
otherwise than by enumerating them all: and all are not known, nor ever
will be so. It is idle, therefore, to look to this as one of the purposes
of a definition: while, if it be only required that the definition of a
Kind should indicate what Kinds include it or are included by it, any
definitions which expound the connotation of the names will do this: for
the name of each class must necessarily connote enough of its properties
to fix the boundaries of the class. If the definition, therefore, be a
full statement of the connotation, it is all that a definition can be
required to be.
§ 5. Of the two incomplete or unscientific modes of definition, and in
what they differ from the complete or scientific 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 deservedly popular work,
Archbishop Whately’s _Logic_.(25) 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, cannot, as it appears to
us, be maintained. We apprehend that no definition is ever intended to
‘explain and unfold the nature of the thing.’ It is some confirmation of
our opinion, that none of those writers who have thought that there were
definitions of things, have ever succeeded in discovering any criterion by
which the definition of a thing can be distinguished from any other
proposition relating to the thing. The definition, they say, unfolds the
nature of the thing: but no definition can unfold its whole nature; and
every proposition in which any quality whatever is predicated of the
thing, unfolds some part of its nature. The true state of the case we take
to be this. All definitions are of names, and of names only; but, in some
definitions, it is clearly apparent, that nothing is intended except to
explain the meaning of the word; while in others, besides explaining the
meaning of the word, it is intended to be implied that there exists a
thing, corresponding to the word. Whether this be or be not implied in any
given case, cannot be collected from the mere form of the expression. ‘A
centaur is an animal with the upper parts of a man and the lower parts of
a horse,’ and ‘A triangle is a rectilineal figure with three sides,’ are,
in form, expressions precisely similar; although in the former it is not
implied that any _thing_, conformable to the term, really exists, while in
the latter it is; as may be seen by substituting, in both definitions, the
word _means_ for _is_. In the first expression, ‘A centaur means an
animal,’ &c., the sense would remain unchanged: in the second ‘A triangle
means,’ &c., the meaning would be altered, since it would be obviously
impossible to deduce any of the truths of geometry from a proposition
expressive only of the manner in which we intend to employ a particular
sign.
“There are, therefore, expressions, commonly passing for definitions,
which include in themselves more than the mere explanation of the meaning
of a term. But it is not correct to call an expression of this sort a
peculiar kind of definition. Its difference from the other kind consists
in this, that it is not a definition, but a definition and something more.
The definition above given of a triangle, obviously comprises not one, but
two propositions, perfectly distinguishable. The one is, ‘There may exist
a figure, bounded by three straight lines:’ the other, ‘And this figure
may be termed a triangle.’ The former of these propositions is not a
definition at all: the latter is a mere nominal definition, or explanation
of the use and application of a term. The first is susceptible of truth or
falsehood, and may therefore be made the foundation of a train of
reasoning. The latter can neither be true nor false; the only character it
is susceptible of is that of conformity or disconformity to the ordinary
usage of language.”
There is a real distinction, then, between definitions of names, and what
are erroneously called definitions of things; but it is, that the latter,
along with the meaning of a name, covertly asserts a matter of fact. This
covert assertion is not a definition, but a postulate. The definition is a
mere identical proposition, which gives information only about the use of
language, and from which no conclusions affecting matters of fact can
possibly be drawn. The accompanying postulate, on the other hand, affirms
a fact, which may lead to consequences of every degree of importance. It
affirms the real existence of Things possessing the combination of
attributes set forth in the definition; and this, if true, may be
foundation sufficient on which to build a whole fabric of scientific
truth.
We have already made, and shall often have to repeat, the remark, that the
philosophers who overthrew Realism by no means got rid of the consequences
of Realism, but retained long afterwards, in their own philosophy,
numerous propositions which could only have a rational meaning as part of
a Realistic system. It had been handed down from Aristotle, and probably
from earlier times, as an obvious truth, that the science of Geometry is
deduced from definitions. This, so long as a definition was considered to
be a proposition “unfolding the nature of the thing,” did well enough. But
Hobbes followed, and rejected utterly the notion that a definition
declares the nature of the thing, or does anything but state the meaning
of a name; yet he continued to affirm as broadly as any of his
predecessors, that the ἀρχαὶ, _principia_, or original premisses 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 premisses 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 premisses in
Euclid’s Elements; the definition, let us say, of a circle. This, being
analysed, consists of two propositions; the one an assumption with respect
to a matter of fact, the other a genuine definition. “A figure may exist,
having all the points in the line which bounds it equally distant from a
single point within it:” “Any figure possessing this property is called a
circle.” Let us look at one of the demonstrations which are said to depend
on this definition, and observe to which of the two propositions contained
in it the demonstration really appeals. “About the centre A, describe the
circle BCD.” 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 premisses 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 premisses in any of our reasonings, except such as relate to
words only. If this supposition were true, we might argue correctly from
true premisses, and arrive at a false conclusion. We should only have to
assume as a premiss 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 premisses 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 premisses are true and yet the conclusion false; which every
logician knows to be an absurdity. The conclusion being false and the
syllogism correct, the premisses cannot be true. But the premisses,
considered as parts of a definition, are true. Therefore, the premisses
considered as parts of a definition cannot be the real ones. The real
premisses must be—
A dragon is a _really existing_ thing which breathes flame:
A dragon is a _really existing_ serpent:
which implied premisses being false, the falsity of the conclusion
presents no absurdity.
If we would determine what conclusion follows from the same ostensible
premisses when the tacit assumption of real existence is left out, let us,
according to the recommendation in the Westminster Review, 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 premisses) 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 premisses; but the premisses 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.(26)
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 premiss, 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 realised by art. People had a difficulty, therefore, in
conceiving that the most certain of all conclusions could rest on
premisses 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 made up by the
mind, out of the materials in nature. The definition (it is said) is a
definition of this mental line, not of any actual line: and it is only of
the mental line, not of any line existing in nature, that the theorems of
geometry are accurately true.
Allowing this doctrine respecting the nature of demonstrative truth to be
correct, (which, in a subsequent place, I shall endeavour to prove that it
is not;) even on that supposition, the conclusions which seem to follow
from a definition, do not follow from the definition as such, but from an
implied postulate. Even if it be true that there is no object in nature
answering to the definition of a line, and that the geometrical properties
of lines are not true of any lines in nature, but only of the idea of a
line; the definition, at all events, postulates the real existence of such
an idea: it assumes that the mind can frame, or rather has framed, the
notion of length without breadth, and without any other sensible property
whatever. To me, indeed, it appears that the mind cannot form any such
notion; it cannot conceive length without breadth; it can only, in
contemplating objects, _attend_ to their length, exclusively of their
other sensible qualities, and so determine what properties may be
predicated of them in virtue of their length alone. If this be true, the
postulate involved in the geometrical definition of a line, is the real
existence, not of length without breadth, but merely of length, that is,
of long objects. This is quite enough to support all the truths of
geometry, since every property of a geometrical line is really a property
of all physical objects 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_: although, on the nature of
demonstrative truth, Dr. Whewell’s opinions are greatly at variance with
mine. And here, as in many other instances, I gladly acknowledge that his
writings are eminently serviceable in clearing from confusion the initial
steps in the analysis of the mental processes, even where his views
respecting the ultimate analysis are such as (though with unfeigned
respect) I cannot but regard as fundamentally erroneous.
§ 7. Although, according to the opinion here presented, Definitions are
properly of names only, and not of things, it does not follow from this
that definitions are arbitrary. How to define a name, may not only be an
inquiry of considerable difficulty and intricacy, but may involve
considerations going deep into the nature of the things which are denoted
by the name. Such, for instance, are the inquiries which form the subjects
of the most important of Plato’s Dialogues; as, “What is rhetoric?” the
topic of the Gorgias, or “What is justice?” that of the Republic. Such,
also, is the question scornfully asked by Pilate, “What is truth?” and the
fundamental question with speculative moralists in all ages, “What is
virtue?”
It would be a mistake to represent these difficult and noble inquiries as
having nothing in view beyond ascertaining the conventional meaning of a
name. They are inquiries not so much to determine what is, as what should
be, the meaning of a name; which, like other practical questions of
terminology, requires for its solution that we should enter, and sometimes
enter very deeply, into the properties not merely of names but of the
things named.
Although the meaning of every concrete general name resides in the
attributes which it connotes, the objects were named before the
attributes; as appears from the fact that in all languages, abstract names
are mostly compounds or other derivatives of the concrete names which
correspond to them. Connotative names, therefore, were, after proper
names, the first which were used: and in the simpler cases, no doubt, a
distinct connotation was present to the minds of those who first used the
name, and was distinctly intended by them to be conveyed by it. The first
person who used the word _white_, as applied to snow or to any other
object, knew, no doubt, very well what quality he intended to predicate,
and had a perfectly distinct conception in his mind of the attribute
signified by the name.
But where the resemblances and differences on which our classifications
are founded are not of this palpable and easily determinable kind;
especially where they consist not in any one quality but in a number of
qualities, the effects of which being blended together are not very easily
discriminated, and referred each to its true source; it often happens that
names are applied to nameable objects, with no distinct connotation
present to the minds of those who apply them. They are only influenced by
a general resemblance between the new object and all or some of the old
familiar objects which they have been accustomed to call by that name.
This, as we have seen, is the law which even the mind of the philosopher
must follow, in giving names to the simple elementary feelings of our
nature: but, where the things to be named are complex wholes, a
philosopher is not content with noticing a general resemblance; he
examines what the resemblance consists in: and he only gives the same name
to things which resemble one another in the same definite particulars. The
philosopher, therefore, habitually employs his general names with a
definite connotation. But language was not made, and can only in some
small degree be mended, by philosophers. In the minds of the real arbiters
of language, general names, especially where the classes they denote
cannot be brought before the tribunal of the outward senses to be
identified and discriminated, connote little more than a vague gross
resemblance to the things which they were earliest, or have been most,
accustomed to call by those names. When, for instance, ordinary persons
predicate the words _just_ or _unjust_ of any action, _noble_ or _mean_ of
any sentiment, expression, or demeanour, _statesman_ or _charlatan_ of any
personage figuring in politics, do they mean to affirm of those various
subjects any determinate attributes, of whatever kind? No: they merely
recognise, as they think, some likeness, more or less vague and loose,
between these and some other things which they have been accustomed to
denominate or to hear denominated by those appellations.
Language, as Sir James Mackintosh used to say of governments, “is not
made, but grows.” A name is not imposed at once and by previous purpose
upon a _class_ of objects, but is first applied to one thing, and then
extended by a series of transitions to another and another. By this
process (as has been remarked by several writers, and illustrated with
great force and clearness by Dugald Stewart, in his Philosophical Essays,)
a name not unfrequently passes by successive links of resemblance from one
object to another, until it becomes applied to things having nothing in
common with the first things to which the name was given; which, however,
do not, for that reason, drop the name; so that it at last denotes a
confused huddle of objects, having nothing whatever in common; and
connotes nothing, not even a vague and general resemblance. When a name
has fallen into this state, in which by predicating it of any object we
assert literally nothing about the object, it has become unfit for the
purposes either of thought or of the communication of thought; and can
only be made serviceable by stripping it of some part of its multifarious
denotation, and confining it to objects possessed of some attributes in
common, which it may be made to connote. Such are the inconveniences of a
language which “is not made, but grows.” Like the governments which are in
a similar case, it may be compared to a road which is not made but has
made itself: it requires continual mending in order to be passable.
From this it is already evident, why the question respecting the
definition of an abstract name is often one of so much difficulty. The
question, What is justice? is, in other words, What is the attribute which
mankind mean to predicate when they call an action just? To which the
first answer is, that having come to no precise agreement on the point,
they do not mean to predicate distinctly any attribute at all.
Nevertheless, all believe that there is some common attribute belonging to
all the actions which they are in the habit of calling just. The question
then must be, whether there is any such common attribute? and, in the
first place, whether mankind agree sufficiently with one another as to the
particular actions which they do or do not call just, to render the
inquiry, what quality those actions have in common, a possible one: if so,
whether the actions really have any quality in common; and if they have,
what it is. Of these three, the first alone is an inquiry into usage and
convention; the other two are inquiries into matters of fact. And if the
second question (whether the actions form a class at all) has been
answered negatively, there remains a fourth, often more arduous than all
the rest, namely, how best to form a class artificially, which the name
may denote.
And here it is fitting to remark, that the study of the spontaneous growth
of languages is of the utmost importance to those who would logically
remodel them. The classifications rudely made by established language,
when retouched, as they almost always require to be, by the hands of the
logician, are often in themselves excellently suited to his purposes. When
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, though it may be founded only on
a gross and general resemblance, is evidence, in the first place, that the
resemblance is obvious, and therefore considerable; and, in the next
place, that it is a resemblance which has struck great numbers of persons
during a series of years and ages. Even when a name, by successive
extensions, has come to be applied to things among which there does not
exist this gross resemblance common to them all, still at every step in
its progress we shall find such a resemblance. And these transitions of
the meaning of words are often an index to real connexions between the
things denoted by them, which might otherwise escape the notice of
thinkers; of those at least who, from using a different language, or from
any difference in their habitual associations, have fixed their attention
in preference on some other aspect of the things. The history of
philosophy abounds in examples of such oversights, committed for want of
perceiving the hidden link that connected together the seemingly disparate
meanings of some ambiguous word.(27)
Whenever the inquiry into the definition of the name of any real object
consists of anything else than a mere comparison of authorities, we
tacitly assume that a meaning must be found for the name, compatible with
its continuing to denote, if possible all, but at any rate the greater or
the more important part, of the things of which it is commonly predicated.
The inquiry, therefore, into the definition, is an inquiry into the
resemblances and differences among those things: whether there be any
resemblance running through them all; if not, through what portion of them
such a general resemblance can be traced: and finally, what are the common
attributes, the possession of which gives to them all, or to that portion
of them, the character of resemblance which has led to their being classed
together. When these common attributes have been ascertained and
specified, the name which belongs in common to the resembling objects
acquires a distinct instead of a vague connotation; and by possessing this
distinct connotation, becomes susceptible of definition.
In giving a distinct connotation to the general name, the philosopher will
endeavour to fix upon such attributes as, while they are common to all the
things usually denoted by the name, are also of greatest importance in
themselves; either directly, or from the number, the conspicuousness, or
the interesting character, of the consequences to which they lead. He will
select, as far as possible, such _differentiæ_ as lead to the greatest
number of interesting _propria_. For these, rather than the more obscure
and recondite qualities on which they often depend, give that general
character and aspect to a set of objects, which determine the groups into
which they naturally fall. But to penetrate to the more hidden agreement
on which these obvious and superficial agreements depend, is often one of
the most difficult of scientific problems. As it is among the most
difficult, so it seldom fails to be among the most important. And since
upon the result of this inquiry respecting the causes of the properties of
a class of things, there incidentally depends the question what shall be
the meaning of a word; some of the most profound and most valuable
investigations which philosophy presents to us, have been introduced by,
and have offered themselves under the guise of, inquiries into the
definition of a name.
BOOK II. OF REASONING.
Διωρισμένων δε τούτων, λέγωμεν ἤδη, διὰ τίνων, καὶ πότε, καὶ πῶς γίνεται
πᾶς συλλογισμός; ὕστερον δὲ λεκτέον περὶ ἀποδείξεως. Πρότερον γὰρ περὶ
συλλογισμοῦ λεκτέον, ἣ περὶ ἀποδείξεως, διὰ τὸ καθόλου μᾶλλον εἰναὶ τὸν
συλλογισμόν. Ἡ μὲν γὰρ ἀπόδειξις, συλλογισμός τις; ὁ συλλογισμός δὲ οὐ
πᾶς, ἀπόδειξις.
ARIST. _Analyt. Prior._ 1. 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 analysed
the import of each sort, and have ascertained the nature of the things
they relate to, and the nature of what they severally assert respecting
those things. We found that whatever be the form of the proposition, and
whatever its nominal subject or predicate, the real subject of every
proposition is some one or more facts or phenomena of consciousness, or
some one or more of the hidden causes or powers to which we ascribe those
facts; and that what is predicated or asserted, either in the affirmative
or negative, of those phenomena or those powers, is always either
Existence, Order in Place, Order in Time, Causation, or Resemblance. This,
then, is the theory of the Import of Propositions, reduced to its ultimate
elements: but there is another and a less abstruse expression for it,
which, though stopping short in an earlier stage of the analysis, is
sufficiently scientific for many of the purposes for which such a general
expression is required. This expression recognises the commonly received
distinction between Subject and Attribute, and gives the following as the
analysis of the meaning of propositions:—Every Proposition asserts, that
some given subject does or does not possess some attribute; or that some
attribute is or is not (either in all or in some portion of the subjects
in which it is met with) conjoined with some other attribute.
We shall now for the present take our leave of this portion of our
inquiry, and proceed to the peculiar problem of the Science of Logic,
namely, how the assertions, of which we have analysed the import, are
proved, or disproved: such of them, at least, as, not being amenable to
direct consciousness or intuition, are appropriate subjects of proof.
We say of a fact or statement, that it is proved, when we believe its
truth by reason of some other fact or statement from which it is said to
_follow_. Most of the propositions, whether affirmative or negative,
universal, particular, or singular, which we believe, are not believed on
their own evidence, but on the ground of something previously assented to,
and 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
early stage of our inquiry, and additional motives will be suggested by
the considerations on which we are now about to enter.
§ 2. In proceeding to take into consideration the cases in which
inferences can legitimately be drawn, we shall first mention some cases in
which the inference is apparent, not real; and which require notice
chiefly that they may not be confounded with cases of inference properly
so called. This occurs when the proposition ostensibly inferred from
another, appears on analysis to be merely a repetition of the same, or
part of the same, assertion, which was contained in the first. All the
cases mentioned in books of Logic as examples of æquipollency or
equivalence of propositions, are of this nature. Thus, if we were to
argue, No man is incapable of reason, for every man is rational; or, All
men are mortal, for no man is exempt from death; it would be plain that we
were not proving the proposition, but only appealing to another mode of
wording it, which may or may not be more readily comprehensible by the
hearer, or better adapted to suggest the real proof, but which contains in
itself no shadow of proof.
Another case is where, from an universal proposition, we affect to infer
another which differs from it only in being particular: as, All A is B,
therefore Some A is B: No A is B, therefore Some A is not B. This, too, is
not to conclude one proposition from another, but to repeat a second time
something which had been asserted at first; with the difference, that we
do not here repeat the whole of the previous assertion, but only an
indefinite part of it.
A third case is where, the antecedent having affirmed a predicate of a
given subject, the consequent affirms of the same subject something
already connoted by the former predicate: as, Socrates is a man, therefore
Socrates is a living creature; where all that is connoted by living
creature was affirmed of Socrates when he was asserted to be a man. If the
propositions are negative, we must invert their order, thus: Socrates is
not a living creature, therefore he is not a man; for if we deny the less,
the greater, which includes it, is already denied by implication. These,
therefore, are not really cases of inference; and yet the trivial examples
by which, in manuals of Logic, the rules of the syllogism are illustrated,
are often of this ill-chosen kind; demonstrations in form, of conclusions
to which whoever understands the terms used in the statement of the data,
has already, and consciously, assented.
The most complex case of this sort of apparent inference is what is called
the Conversion of Propositions; which consists in turning the predicate
into a subject, and the subject into a predicate, and framing out of the
same terms thus reversed, another proposition, which must be true if the
former is true. Thus, from the particular affirmative proposition, Some A
is B, we may infer that Some B is A. From the universal negative, No A is
B, we may conclude that No B is A. From the universal affirmative
proposition, All A is B, it cannot be inferred that All B is A; though all
water is liquid, it is not implied that all liquid is water; but it is
implied that some liquid is so; and hence the proposition, All A is B, is
legitimately convertible into Some B is A. This process, which converts an
universal proposition into a particular, is termed conversion _per
accidens_. From the proposition, Some A is not B, we cannot even infer
that some B is not A; though some men are not Englishmen, it does not
follow that some Englishmen are not men. The only legitimate conversion,
if such it can be called, of 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 altered.
Instead of [A] and [B], the terms of the new proposition are [a thing
which is not B], and [A]. The original proposition, Some A _is not_ B, is
first changed into a proposition æquipollent with it, Some A _is_ “a thing
which is not B”; and the proposition, being now no longer a particular
negative, but a particular affirmative, admits of conversion in the first
mode, or, as it is called, _simple_ conversion.
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
premisses, and obvious to whoever apprehends them. The fact asserted in
the conclusion is either the very same fact, or part of the fact, asserted
in the original proposition. This follows from our previous analysis of
the Import of Propositions. When we say, for example, that some lawful
sovereigns are tyrants, what is the meaning of the assertion? That the
attributes connoted by the term “lawful sovereign,” and the attributes
connoted by the term “tyrant,” sometimes coexist in the same individual.
Now this is also precisely what we mean, when we say that some tyrants are
lawful sovereigns; which, therefore, is not a second proposition inferred
from the first, any more than the English translation of Euclid’s Elements
is a collection of theorems different from, and consequences of, those
contained in the Greek original. Again, if we assert that no great general
is a rash man, we mean that the attributes connoted by “great general,”
and those connoted by “rash,” never coexist in the same subject; which is
also the exact meaning which would be expressed by saying, that no rash
man is a great general. When we say, that all quadrupeds are warm-blooded,
we assert, not only that the attributes connoted by “quadruped” and those
connoted by “warm-blooded” sometimes coexist, but that the former never
exist without the latter: now the proposition, Some warm-blooded creatures
are quadrupeds, expresses the first half of this meaning, dropping the
latter half; and, therefore, has been already affirmed in the antecedent
proposition, All quadrupeds are warm-blooded. But that _all_ warm-blooded
creatures are quadrupeds, or, in other words, that the attributes connoted
by “warm-blooded” never exist without those connoted by “quadruped,” has
not been asserted, and cannot be inferred. In order to reassert, in an
inverted form, the whole of what was affirmed in the proposition, All
quadrupeds are warm-blooded, we must convert it by contraposition, thus,
Nothing which is not warm-blooded is a quadruped. This proposition, and
the one from which it is derived, are exactly equivalent, and either of
them may be substituted for the other; for, to say that when the
attributes of a quadruped are present, those of a warm-blooded creature
are present, is to say that when the latter are absent the former are
absent.
In a manual for young students, it would be proper to dwell at greater
length on the conversion and æquipollency of propositions. For, although
that cannot be called reasoning or inference which is a mere reassertion
in different words of what had been asserted before, there is no more
important intellectual habit, nor any the cultivation of which falls more
strictly within the province of the art of logic, than that of discerning
rapidly and surely the identity of an assertion when disguised under
diversity of language. That important chapter in logical treatises which
relates to the Opposition of Propositions, and the excellent technical
language which logic provides for distinguishing the different kinds or
modes of opposition, are of use chiefly for this purpose. Such
considerations as these, that contrary propositions may both be false, but
cannot both be true; that sub-contrary propositions may both be true, but
cannot both be false; that of two contradictory propositions one must be
true and the other false; that of two subalternate propositions the truth
of the universal proves the truth of the particular, and the falsity of
the particular proves the falsity of the universal, but not _vice
versâ_(28); 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 premisses,
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 premisses. 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 are said to 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, so 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 afterwards made on the functions of the syllogism, and the
place which it holds in science.
To a legitimate syllogism it is essential that there should be three, and
no more than three, propositions, namely, the conclusion, or proposition
to be proved, and two other propositions which together prove it, and
which are called the premisses. It is essential that there should be
three, and no more than three, terms, namely, the subject and predicate of
the conclusion, and another called the middleterm, which must be found in
both premisses, 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 premisses, together with the
middleterm which is in them both. The premiss which contains the
middleterm and the major term is called the major premiss; that which
contains the middle term and the minor term is called the minor premiss.
Syllogisms are divided by some logicians into three _figures_, by others
into four, according to the position of the middleterm, which may either
be the subject in both premisses, the predicate in both, or the subject in
one and the predicate in the other. The most common case is that in which
the middleterm is the subject of the major premiss and the predicate of
the minor. This is reckoned as the first figure. When the middleterm is
the predicate in both premisses, the syllogism belongs to the second
figure; when it is the subject in both, to the third. In the fourth figure
the middleterm is the subject of the minor premiss 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 _modes_, 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 modes, that is, all those in which the
conclusion correctly follows from the premisses. A is the minor term, C
the major, B the middleterm.
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 C No B is C Some B is C All B is C Some B is No B is C
not C
All B is A All B is A All B is A Some B is A All B is A Some B is A
therefore therefore therefore therefore therefore therefore
Some A is C Some A is Some A is C Some A is C Some A is Some A is
not 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 of 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 mode of
the first figure.
The reasons why syllogisms in any of the above forms are legitimate, that
is, why, if the premisses be true, the conclusion must necessarily be so,
and why this is not the case in any other possible _mode_, (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 learnt from the common school books of the
syllogistic logic, or to be capable of divining 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 mode and figure.
Although 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 premisses. Thus an argument in the first mode 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 an universal
negative, admits of simple conversion, and may be changed into No B is C,
which, as we showed, is the very same assertion in other words—the same
fact differently expressed. This transformation having been effected, the
argument assumes the following form:—
No B is C
All A is B
therefore
No A is C,
which is a good syllogism in the second mode of the first figure. Again,
an argument in the first mode of the third figure must resemble the
following:—
All B is C
All B is A
therefore
Some A is C,
where the minor premiss, 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 mode 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 mode of the second, third, and fourth figures
may be reduced to some one of the four modes 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 premisses, 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;
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.
Although 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 ever yet made of the syllogistic doctrine, has
expressly examined what sorts of arguments fall most naturally and
suitably into each of the four figures; and his solution is characterized
by great ingenuity and clearness of thought.(29) The argument, however, is
one and the same, in whichever figure it is expressed; since, as we have
already seen, the premisses 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 premisses in everything except language, or, at
least, as much of them as contributes to the proof of the conclusion is
the same. We are therefore at liberty, in conformity with the general
opinion of logicians, to consider the two elementary forms of the first
figure as the universal types of all correct ratiocination; the one, when
the conclusion to be proved is affirmative, the other, when it is
negative; even though certain arguments may have a tendency to clothe
themselves in the forms of the second, third, and fourth figures; which,
however, cannot possibly happen with the only class of arguments which are
of first-rate scientific importance, those in which the conclusion is an
universal affirmative, such conclusions being susceptible of proof in the
first figure alone.
§ 2. On examining, then, these two general formulæ, we find that in both
of them, one premiss, the major, is an universal proposition; and
according as this is affirmative or negative, the conclusion is so too.
All ratiocination, therefore, starts from a _general_ proposition,
principle, or assumption: a proposition in which a predicate is affirmed
or denied of an entire class; that is, in which some attribute, or the
negation of some attribute, is asserted of an indefinite number of objects
distinguished by a common characteristic, and designated, in consequence,
by a common name.
The other premiss 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 premiss. It follows that the attribute affirmed or
denied of the entire class may (if there was truth in that affirmation or
denial) be affirmed or denied of the object or objects alleged to be
included in the class: and this is precisely the assertion made in the
conclusion.
Whether or not the foregoing is an adequate account of the constituent
parts of the syllogism, will be presently considered; but as far as it
goes it is a true account. It has accordingly been generalized, and
erected into a logical maxim, on which all ratiocination is said to be
founded, insomuch that to reason, and to apply the maxim, are supposed to
be one and the same thing. The maxim is, That whatever can be affirmed (or
denied) of a class, may be affirmed (or denied) of everything included in
the class. This axiom, supposed to be the basis of the syllogistic theory,
is termed by logicians the _dictum de omni et 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 were termed Universals were regarded as a
peculiar kind of substances, having an objective existence distinct from
the individual objects classed under them, the _dictum de omni_ conveyed
an important meaning; because it expressed the intercommunity of nature,
which it was necessary on that theory that we should suppose to exist
between those general substances and the particular substances which were
subordinated to them. That everything predicable of the universal was
predicable of the various individuals contained under it, was then no
identical proposition, but a statement of what was conceived as a
fundamental law of the universe. The assertion that the entire nature and
properties of the _substantia secunda_ formed part of the properties of
each of the individual substances called by the same name; that the
properties of Man, for example, were properties of all men; was a
proposition of real significance when man did not _mean_ all men, but
something inherent in men, and vastly superior to them in dignity. Now,
however, when it is known that a class, an universal, a genus or species,
is not an entity _per se_, but neither more nor less than the individual
substances themselves which are placed in the class, and that there is
nothing real in the matter except those objects, a common name given to
them, and common attributes indicated by the name; what, I should be glad
to know, do we learn by being told, that whatever can be affirmed of a
class, may be affirmed of every object contained in the class? The class
_is_ nothing but the objects contained in it: and the _dictum de omni_
merely amounts to the identical proposition, that whatever is true of
certain objects, is true of each of those objects. If all ratiocination
were no more than the application of this maxim to particular cases, the
syllogism would indeed be, what it has so often been declared to be,
solemn trifling. The _dictum de omni_ is on a par with another truth,
which in its time was also reckoned of great importance, “Whatever is,
is;” and not to be compared in point of significance to the cognate
aphorism, “It is impossible for the same thing to be and not to be;” since
this is, at the lowest, equivalent to the logical axiom that contradictory
propositions cannot both be true. 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 Kantians, has never
ceased to poison philosophy. Once accustomed to consider scientific
investigation as essentially consisting in the study of universals, men
did not drop this habit of thought when they ceased to regard universals
as possessing an independent existence: and even those who went the length
of considering them as mere names, could not free themselves from the
notion that the investigation of truth consisted entirely or partly in
some kind of conjuration or juggle with those names. When a philosopher
adopted fully the Nominalist view of the signification of general
language, retaining along with it the _dictum de omni_ as the foundation
of all reasoning, two such premisses 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 supposed to derive irresistible confirmation from the example
of algebra. If there were any process in sorcery or necromancy more
preternatural than this, I should be much surprised. The culminating point
of this philosophy is the noted aphorism of Condillac, that a science is
nothing, or scarcely anything, but _une langue bien faite_: in other
words, that the one sufficient rule for discovering the nature and
properties of objects is to name them properly: as if the reverse were not
the truth, that it is impossible to name them properly except in
proportion as we are already acquainted with their nature and properties.
Can it be necessary to say, that none, not even the most trivial knowledge
with respect to Things, ever was or could be originally got at by any
conceivable manipulation of mere names, as such; and that what can be
learnt from names, is only what somebody who used the names, knew before?
Philosophical analysis confirms the indication of common sense, that the
function of names is but that of enabling us to _remember_ and to
_communicate_ our thoughts. That they also strengthen, even to an
incalculable extent, the power of thought itself, is most true: but they
do this by no intrinsic and peculiar virtue; they do it by the power
inherent in an artificial memory, an instrument of which few have
adequately considered the immense potency. As an artificial memory,
language truly is, what it has so often been called, an instrument of
thought: but it is one thing to be the instrument, and another to be the
exclusive subject upon which the instrument is exercised. We think,
indeed, to a considerable extent, by means of names, but what we think of,
are the things called by those names; and there cannot be a greater error
than to imagine that thought can be carried on with nothing in our mind
but names, or that we can make the names think for us.
§ 3. Those who considered the _dictum de omni_ as the foundation of the
syllogism, looked upon arguments in a manner corresponding to the
erroneous view which Hobbes took of propositions. Because there are some
propositions which are merely verbal, Hobbes, in order apparently that his
definition might be rigorously universal, defined a proposition as if no
propositions declared anything except the meaning of words. If Hobbes was
right; if no further account than this could be given of the import of
propositions; no theory could be given but the commonly received one, of
the combination of propositions in a syllogism. If the minor premiss
asserted nothing more than that something belongs to a class, and if the
major premiss 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 artificial classification. It
asserts that a given object does or does not possess a given attribute; or
it asserts that two attributes, or sets of attributes, do or do not
(constantly or occasionally) coexist. Since such is the purport of all
propositions which convey any real knowledge, and since ratiocination is a
mode of acquiring real knowledge, any theory of ratiocination which does
not recognise this import of propositions, cannot, we may be sure, be the
true one.
Applying this view of propositions to the two premisses of a syllogism, we
obtain the following results. The major premiss, 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 premiss asserts that
the thing or set of things which are the subject of that premiss, 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 premiss are connotative terms,
denoting objects and connoting attributes. The assertion in the major
premiss 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
premiss 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 premisses are general propositions, as
All men are mortal,
All kings are men,
therefore
All kings are mortal,
the minor premiss 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 premiss 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 premiss, it is concluded, that the same
incompatibility exists between the attribute omnipotence and those
constituting a king. In a similar manner we might analyse any other
example of the syllogism.
If we generalize this process, and look out for the principle or law
involved in every such inference, and presupposed in every syllogism the
propositions of which are anything more than merely verbal; we find, not
the unmeaning _dictum de omni et nullo_, but a fundamental principle, or
rather two principles, strikingly resembling the axioms of mathematics.
The first, which is the principle of affirmative syllogisms, is, that
things which coexist with the same thing, coexist with one another. The
second is the principle of negative syllogisms, and is to this effect:
that a thing which coexists with another thing, with which other a third
thing does not coexist, is not coexistent with that third thing. These
axioms manifestly relate to facts, and not to conventions; and one or
other of them is the ground of the legitimacy of every argument in which
facts and not conventions are the matter treated of.
§ 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(30) 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,
A 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
possesses any mark, possesses that which it is a mark of. Or, when the
minor premiss 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.
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 anything more in the conclusion than was assumed in the premisses. 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
premisses. 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 cannot be assured of the
mortality of all men, unless we are already certain of the mortality of
every individual man: that if it be still doubtful whether Socrates, or
any other individual you choose to name, be mortal or not, the same degree
of uncertainty must hang over the assertion, All men are mortal: that the
general principle, instead of being given as evidence of the particular
case, cannot itself be taken for true without exception, until every
shadow of doubt which could affect any case comprised with it, is
dispelled by evidence _aliundè_; and then what remains for the syllogism
to prove? That, in short, no reasoning from generals to particulars can,
as such, prove anything: since from a general principle you cannot infer
any particulars, but those which the principle itself assumes as known.
This doctrine appears to me irrefragable; and if logicians, though unable
to dispute it, have usually exhibited a strong disposition to explain it
away, this was not because they could discover any flaw in the argument
itself, but because the contrary opinion seemed to rest on arguments
equally indisputable. In the syllogism last referred to, for example, or
in any of those which we previously constructed, is it not evident that
the conclusion may, to the person to whom the syllogism is presented, be
actually and _bonâ fide_ a new truth? Is it not matter of daily experience
that truths previously undreamt of, facts which have not been, and cannot
be, directly observed, are arrived at by way of general reasoning? We
believe that the Duke of Wellington is mortal. We do not know this by
direct observation, since he is not 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; although none of them has cleared up the difficulty which arises
from the inconsistency between that assertion, and the principle, that if
there be anything in the conclusion which was not already asserted in the
premisses, 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 premisses, and being
directly asserted in them. When Archbishop Whately, for example, says,(31)
that the object of reasoning is “merely to expand and unfold the
assertions wrapt up, as it were, and implied in those with which we set
out, and to bring a person to perceive and acknowledge the full force of
that which he has admitted,” he does not, I think, meet the real
difficulty requiring to be explained, namely, how it happens that a
science, like geometry, _can_ be all “wrapt up” in a few definitions and
axioms. Nor does this defence of the syllogism differ much from what its
assailants urge against it as an accusation, when they charge it with
being of no use except to those who seek to press the consequences of an
admission into which a person has been entrapped without having considered
and understood its full force. When you admitted the major premiss, you
asserted the conclusion; but, says Archbishop Whately, you asserted it by
implication merely: this, however, can here only mean that you asserted it
unconsciously; that you did not know you were asserting it; but, if so,
the difficulty revives in this shape—Ought you not to have known? Were you
warranted in asserting the general proposition without having satisfied
yourself of the truth of everything which it fairly includes? And if not,
what then is the syllogistic art but a contrivance for catching you in a
trap, and holding you fast in it?(32)
§ 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 the two parts of the process of philosophizing, the inferring
part, and the registering part; and ascribing to the latter the functions
of the former. The mistake is that of referring a person to his own notes
for the origin of his knowledge. If a person is asked a question, and is
at the moment unable to answer it, he may refresh his memory by turning to
a memorandum which he carries about with him. But if he were asked, how
the fact came to his knowledge, he would scarcely answer, because it was
set down in his note-book: unless the book was written, like the Koran,
with a quill from the wing of the angel Gabriel.
Assuming that the proposition, The Duke of Wellington is mortal, is
immediately an inference from the proposition, All men are mortal; whence
do we derive our knowledge of that general truth? Of course from
observation. Now, all which man can observe are individual cases. From
these all general truths must be drawn, and into these they may be again
resolved: for a general truth is but an aggregate of particular truths; a
comprehensive expression, by which an indefinite number of individual
facts are affirmed or denied at once. But a general proposition is not
merely a compendious form for recording and preserving in the memory a
number of particular facts, all of which have been observed.
Generalization is not a process of mere naming, it is also a process of
inference. From instances which we have observed, we feel warranted in
concluding, that what we found true in those instances, holds in all
similar ones, past, present, and future, however numerous they may be. We
then, by that valuable contrivance of language which enables us to speak
of many as if they were one, record all that we have observed, together
with all that we infer from our observations, in one concise expression;
and have thus only one proposition, instead of an endless number, to
remember or to communicate. The results of many observations and
inferences, and instructions for making innumerable inferences in
unforeseen cases, are compressed into one short sentence.
When, therefore, we conclude from the death of John and Thomas, and every
other person we ever heard of in whose case the experiment had been fairly
tried, that the Duke of Wellington is mortal like the rest; we may,
indeed, pass through the generalization, All men are mortal, as an
intermediate stage; but it is not in the latter half of the process, the
descent from all men to the Duke of Wellington, that the _inference_
resides. The inference is finished when we have asserted that all men are
mortal. What remains to be performed afterwards is merely decyphering our
own notes.
Archbishop Whately has contended that syllogising, or reasoning from
generals to particulars, is not, agreeably to the vulgar idea, a peculiar
_mode_ of reasoning, but the philosophical analysis of _the_ mode in which
all men reason, and must do so if they reason at all. With the deference
due to so high an authority, I cannot help thinking that the vulgar notion
is, in this case, the more correct. If, from our experience of John,
Thomas, &c., who once were living, but are now dead, we are entitled to
conclude that all human beings are mortal, we might surely without any
logical inconsequence have concluded at once from those instances, that
the Duke of Wellington is mortal. The mortality of John, Thomas, and
company is, after all, the whole evidence we have for the mortality of the
Duke of Wellington. Not one iota is added to the proof by interpolating a
general proposition. Since the individual cases are all the evidence we
can possess, evidence which no logical form into which we choose to throw
it can make greater than it is; and since that evidence is either
sufficient in itself, or, if insufficient for the one purpose, cannot be
sufficient for the other; I am unable to see why we should be forbidden to
take the shortest cut from these sufficient premisses to the conclusion,
and constrained to travel the “high priori road,” by the arbitrary fiat of
logicians. I cannot perceive why it should be impossible to journey from
one place to another unless we “march up a hill, and then march down
again.” It may be the safest road, and there may be a resting place at the
top of the hill, affording a commanding view of the surrounding country;
but for the mere purpose of arriving at our journey’s end, our taking that
road is perfectly optional; it is a question of time, trouble, and danger.
Not only _may_ we reason from particulars to particulars without passing
through generals, but we perpetually do so reason. All our earliest
inferences are of this nature. From the first dawn of intelligence we draw
inferences, but years elapse before we learn the use of general language.
The child, who, having burnt his fingers, avoids to thrust them again into
the fire, has reasoned or inferred, though he has never thought of the
general maxim, Fire burns. He knows from memory that he has been burnt,
and on this evidence believes, when he sees a candle, that if he puts his
finger into the flame of it, he will be burnt again. He believes this in
every case which happens to arise; but without looking, in each instance,
beyond the present case. He is not generalizing; he is inferring a
particular from particulars. In the same way, also, brutes reason. There
is no ground for attributing to any of the lower animals the use of signs,
of such a nature as to render general propositions possible. But those
animals profit by experience, and avoid what they have found to cause them
pain, in the same manner, though not always with the same skill, as a
human creature. Not only the burnt child, but the burnt dog, dreads the
fire.
I believe that, in point of fact, when drawing inferences from our
personal experience, and not from maxims handed down to us by books or
tradition, we much oftener conclude from particulars to particulars
directly, than through the intermediate agency of any general proposition.
We are constantly reasoning from ourselves to other people, or from one
person to another, without giving ourselves the trouble to erect our
observations into general maxims of human or external nature. When we
conclude that some person will, on some given occasion, feel or act so and
so, we sometimes judge from an enlarged consideration of the manner in
which human beings in general, or persons of some particular character,
are accustomed to feel and act; but much oftener from having known the
feelings and conduct of the same person in some previous instance, or from
considering how we should feel or act ourselves. It is not only the
village matron who, when called to a consultation upon the case of a
neighbour’s child, pronounces on the evil and its remedy simply on the
recollection and authority of what she accounts the similar case of her
Lucy. We all, where we have no definite maxims to steer by, guide
ourselves in the same way; and if we have an extensive experience, and
retain its impressions strongly, we may acquire in this manner a very
considerable power of accurate judgment, which we may be utterly incapable
of justifying or of communicating to others. Among the higher order of
practical intellects, there have been many of whom it was remarked how
admirably they suited their means to their ends, without being able to
give any sufficient reasons for what they did; and applied, or seemed to
apply, recondite principles which they were wholly unable to state. This
is a natural consequence of having a mind stored with appropriate
particulars, and having been long accustomed to reason at once from these
to fresh particulars, without practising the habit of stating to oneself
or to others the corresponding general propositions. An old warrior, on a
rapid glance at the outlines of the ground, is able at once to give the
necessary orders for a skilful arrangement of his troops; though if he has
received little theoretical instruction, and has seldom been called upon
to answer to other people for his conduct, he may never have had in his
mind a single general theorem respecting the relation between ground and
array. But his experience of encampments, in circumstances more or less
similar, has left a number of vivid, unexpressed, ungeneralized analogies
in his mind, the most appropriate of which, instantly suggesting itself,
determines him to a judicious arrangement.
The skill of an uneducated person in the use of weapons, or of tools, is
of a precisely similar nature. The savage who executes unerringly the
exact throw which brings down his game, or his enemy, in the manner most
suited to his purpose, under the operation of all the conditions
necessarily involved, the weight and form of the weapon, the direction and
distance of the object, the action of the wind, &c., owes this power to a
long series of previous experiments, the results of which he certainly
never framed into any verbal theorems or rules. The same thing may
generally be said of any other extraordinary manual dexterity. Not long
ago a Scotch manufacturer procured from England, at a high rate of wages,
a working dyer, famous for producing very fine colours, with the view of
teaching to his other workmen the same skill. The workman came; but his
mode of proportioning the ingredients, in which lay the secret of the
effects he produced, was by taking them up in handfuls, while the common
method was to weigh them. The manufacturer sought to make him turn his
handling system into an equivalent weighing system, that the general
principle of his peculiar mode of proceeding might be ascertained. This,
however, the man found himself quite unable to do, and therefore could
impart his skill to nobody. He had, from the individual cases of his own
experience, established a connexion in his mind between fine effects of
colour, and tactual perceptions in handling his dyeing materials; and from
these perceptions he could, in any particular case, infer the means to be
employed, and the effects which would be produced, but could not put
others in possession of the grounds on which he proceeded, from having
never generalized them in his own mind, or expressed them in language.
Almost every one knows Lord Mansfield’s advice to a man of practical good
sense, who, being appointed governor of a colony, had to preside in its
court of justice, without previous judicial practice or legal education.
The advice was to give his decision boldly, for it would probably be
right; but never to venture on assigning reasons, for they would almost
infallibly be wrong. In cases like this, which are of no uncommon
occurrence, it would be absurd to suppose that the bad reason was the
source of the good decision. Lord Mansfield knew that if any reason were
assigned it would be necessarily an afterthought, the judge being _in
fact_ guided by impressions from past experience, without the circuitous
process of framing general principles from them, and that if he attempted
to frame any such he would assuredly fail. Lord Mansfield, however, would
not have doubted that a man of equal experience, who had also a mind
stored with general propositions derived by legitimate induction from that
experience, would have been greatly preferable as a judge, to one, however
sagacious, who could not be trusted with the explanation and justification
of his own judgments. The cases of men of talent performing wonderful
things they know not how, are examples of the rudest and most spontaneous
form of the operations of superior minds; it is a defect in them, and
often a source of errors, not to have generalized as they went on; but
generalization, though a help, the most important indeed of all helps, is
not an essential.
Even the scientifically instructed, who possess, in the form of general
propositions, a systematic record of the results of the experience of
mankind, need not always revert to those general propositions in order to
apply that experience to a new case. It is justly remarked by Dugald
Stewart, that though our 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 A B is equal to C D because each of them is equal to E F,
the most uncultivated understanding, as soon as the propositions were
understood, would assent to the inference, without having ever heard of
the general truth that “things which are equal to the same thing are equal
to one another.” This remark of Stewart, consistently followed out, goes
to the root, as I conceive, of the philosophy of ratiocination; and it is
to be regretted that he himself stopt short at a much more limited
application of it. He saw that the general propositions on which a
reasoning is said to depend, may, in certain cases, be altogether omitted,
without impairing its probative force. But he imagined this to be a
peculiarity belonging to axioms; and argued from it, that axioms are not
the foundations or first principles of geometry, from which all the other
truths of the science are synthetically deduced (as the laws of motion and
of the composition of forces in dynamics, the equal mobility of fluids in
hydrostatics, the laws of reflection and refraction in optics, are the
first principles of those sciences); but are merely necessary assumptions,
self-evident indeed, and the denial of which would annihilate all
demonstration, but from which, as premisses, 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 pit of darkness, and not seeing
that this is equally true in every other case of generalization, he
contended that axioms are in their nature barren of consequences, and that
the really fruitful truths, the real first principles of geometry, are the
definitions; that the definition, for example, of the circle is to the
properties of the circle, what the laws of equilibrium and of the pressure
of the atmosphere are to the rise of the mercury in the Torricellian tube.
Yet all that he had asserted respecting the function to which the axioms
are confined in the demonstrations of geometry, holds equally true of the
definitions. Every demonstration in Euclid might be carried on without
them. This is apparent from the ordinary process of proving a proposition
of geometry by means of a diagram. What assumption, in fact, do we set out
from, to demonstrate by a diagram any of the properties of the circle? Not
that in all circles the radii are equal, but only that they are so in the
circle ABC. As our warrant for assuming this, we appeal, it is true, to
the definition of a circle in general; but it is only necessary that the
assumption be granted in the case of the particular circle supposed. From
this, which is not a general but a singular proposition, combined with
other propositions of a similar kind, some of which _when generalized_ are
called definitions, and others axioms, we prove that a certain conclusion
is true, not of all circles, but of the particular circle ABC; or at least
would be so, if the facts precisely accorded with our assumptions. The
enunciation, as it is called, that is, the general theorem which stands at
the head of the demonstration, is not the proposition actually
demonstrated. One instance only is demonstrated: but the process by which
this is done, is a process which, when we consider its nature, we perceive
might be exactly copied in an indefinite number of other instances; in
every instance which conforms to certain conditions. The contrivance of
general language furnishing us with terms which connote these conditions,
we are able to assert this indefinite multitude of truths in a single
expression, and this expression is the general theorem. By dropping the
use of diagrams, and substituting, in the demonstrations, general phrases
for the letters of the alphabet, we might prove the general theorem
directly, that is, we might demonstrate all the cases at once; and to do
this we must, of course, employ as our premisses, 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 if you deny the assumption as a general
truth, you deny the right to make it in the particular instance.
There are, undoubtedly, the most ample reasons for stating both the
principles and the theorems in their general form, and these will be
explained presently, so far as explanation is requisite. But, that
unpractised learners, even in making use of one theorem to demonstrate
another, reason rather from particular to particular than from the general
proposition, is manifest from the difficulty they find in applying a
theorem to a case in which the configuration of the diagram is extremely
unlike that of the diagram by which the original theorem was demonstrated.
A difficulty which, except in cases of unusual mental power, long practice
can alone remove, and removes chiefly by rendering us familiar with all
the configurations consistent with the general conditions of the theorem.
§ 4. From the considerations now adduced, the following conclusions seem
to be established. All inference is from particulars to particulars:
General propositions are merely registers of such inferences already made,
and short formulæ for making more: The major premiss 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 premisses, being the
particular facts from which the general proposition was collected by
induction. Those facts, and the individual instances which supplied them,
may have been forgotten; but a record remains, not indeed descriptive of
the facts themselves, but showing how those cases may be distinguished
respecting which the facts, when known, were considered to warrant a given
inference. According to the indications of this record we draw our
conclusion; which is, to all intents and purposes, a conclusion from the
forgotten facts. For this it is essential that we should read the record
correctly: and the rules of the syllogism are a set of precautions to
ensure our doing so.
This view of the functions of the syllogism is confirmed by the
consideration of precisely those cases which might be expected to be least
favourable to it, namely, those in which ratiocination is independent of
any previous induction. We have already observed that the syllogism, in
the ordinary course of our reasoning, is only the latter half of the
process of travelling from premisses 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 a certain description, 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 the generalization may not be,
in the ordinary sense, an assertion at all, but a command; a law, not in
the philosophical, but in the moral and political sense of the term: an
expression of the desire of a superior, that we, or any number of other
persons, shall conform our conduct to certain general instructions. So far
as this asserts a fact, namely, a volition of the legislator, that fact is
an individual fact, and the proposition, therefore, is not a general
proposition. But the description therein contained of the conduct which it
is the will of the legislator that his subjects should observe, is
general. The proposition asserts, not that all men _are_ anything, but
that all men _shall_ do something.
In both these cases the generalities are the original data, and the
particulars are elicited from them by a process which correctly resolves
itself into a series of syllogisms. The real nature, however, of the
supposed deductive process, is evident enough. The only point to be
determined is, whether the authority which declared the general
proposition, intended to include this case in it; and whether the
legislator intended his command to apply to the present case among others,
or not. This is ascertained by examining whether the case possesses the
marks by which, as those authorities have signified, the cases which they
meant to certify or to influence may be known. The object of the inquiry
is to make out the witness’s or the legislator’s intention, through the
indication given by their words. This is a question, as the Germans
express it, of hermeneutics. The operation is not a process of inference,
but a process of interpretation.
In this last phrase we have obtained an expression which appears to me to
characterize, more aptly than any other, the functions of the syllogism in
all cases. When the premisses 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 premisses
are derived from observation, the function of Reasoning is to ascertain
what we (or our predecessors) formerly thought might be inferred from the
observed facts, and to do this by interpreting a memorandum of ours, or of
theirs. The memorandum reminds us, that from evidence, more or less
carefully weighed, it formerly appeared that a certain attribute might be
inferred wherever we perceive a certain mark. The proposition, All men are
mortal, (for instance) shows that we have had experience from which we
thought it followed that the attributes connoted by the term man, are a
mark of mortality. But when we conclude that the Duke of Wellington is
mortal, we do not infer this from the memorandum, but from the former
experience. All that we infer from the memorandum, is our own previous
belief, (or that of those who transmitted to us the proposition,)
concerning the inferences which that former experience would warrant.
This view of the nature of the syllogism renders consistent and
intelligible what otherwise remains obscure and confused in the theory of
Archbishop Whately and other enlightened defenders of the syllogistic
doctrine, respecting the limits to which its functions are confined. They
affirm in as explicit terms as can be used, that the sole office of
general reasoning is to prevent inconsistency in our opinions; to prevent
us from assenting to anything, the truth of which would contradict
something to which we had previously on good grounds given our assent. And
they tell us, that the sole ground which a syllogism affords for assenting
to the conclusion, is that the supposition of its being false, combined
with the supposition that the premisses are true, would lead to a
contradiction in terms. Now this would be but a lame account of the real
grounds which we have for believing the facts which we learn from
reasoning, in contradistinction to observation. The true reason why we
believe that the Duke of Wellington will die, is that his fathers, and our
fathers, and all other persons who were cotemporary with them, have died.
Those facts are the real premisses of the reasoning. But we are not led to
infer the conclusion from those premisses, by the necessity of avoiding
any verbal inconsistency. There is no contradiction in supposing that all
those persons have died, and that the Duke of Wellington may,
notwithstanding, live for ever. But there would be a contradiction if we
first, on the ground of those same premisses, 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 clearly shown, that,
although 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 a 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 anything.
This throwing of the whole body of possible inferences from a given set of
particulars, into one general expression, operates as a security for their
being just inferences, in more ways than one. First, the general principle
presents a larger object to the imagination than any of the singular
propositions which it contains. A process of thought which leads to a
comprehensive generality, is felt as of greater importance than one which
terminates in an insulated fact; and the mind is, even unconsciously, led
to bestow greater attention upon the process, and to weigh more carefully
the sufficiency of the experience appealed to, for supporting the
inference grounded upon it. There is another, and a more important,
advantage. In reasoning from a course of individual observations to some
new and unobserved case, which we are but imperfectly acquainted with (or
we should not be inquiring into it), and in which, since we are inquiring
into it, we probably feel a peculiar interest; there is very little to
prevent us from giving way to negligence, or to any bias which may affect
our wishes or our imagination, and, under that influence, accepting
insufficient evidence as sufficient. But if, instead of concluding
straight to the particular case, we place before ourselves an entire class
of facts—the whole contents of a general proposition, every tittle of
which is legitimately inferrible from our premisses, if that one
particular conclusion is so; there is then a considerable likelihood that
if the premisses 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 what the schoolmen termed 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
conclude 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 conclusion could not be justifiable unless from the same
evidence he was also 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 premisses, would have warned him that those premisses
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.
These are the uses of syllogism, as a mode of verifying any given
argument. Its ulterior uses, as respects the general course of our
intellectual operations, hardly require illustration, being in fact the
acknowledged uses of general language. They amount substantially to this,
that the inductions may be made once for all: a single careful
interrogation of experience may suffice, and the result may be registered
in the form of a general proposition, which is committed to memory or to
writing, and from which afterwards we have only to syllogize. The
particulars of our experiments may then be dismissed from the memory, in
which it would be impossible to retain so great a multitude of details;
while the knowledge which those details afforded for future use, and which
would otherwise be lost as soon as the observations were forgotten, or as
their record became too bulky for reference, is retained in a commodious
and immediately available shape by means of general language.
Against this advantage is to be set the countervailing inconvenience, that
inferences originally made on insufficient evidence, become consecrated,
and, as it were, hardened into general maxims; and the mind cleaves to
them from habit, after it has outgrown any liability to be misled by
similar fallacious appearances if they were now for the first time
presented; but having forgotten the particulars, it does not think of
revising its own former decision. An inevitable drawback, which, however
considerable in itself, forms evidently but a small deduction from the
immense advantages 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, or the same minds without 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 premiss, 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 premisses 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 one of the
philosophers to whom mental science is most indebted, but who, though a
very penetrating, was a very hasty thinker, and whose want of due
circumspection rendered him fully as remarkable for what he did not see,
as for what he saw. I allude to Dr. Thomas Brown, whose theory of
ratiocination is peculiar. He saw the _petitio principii_ which is
inherent in every syllogism, if we consider the major to be itself the
evidence by which the conclusion is proved, instead of being, what in fact
it is, an assertion of the existence of evidence sufficient to prove any
conclusion of a given description. Seeing this, Dr. Brown not only failed
to see the immense advantage, in point of security for correctness, which
is gained by interposing this step between the real evidence and the
conclusion; but he thought it incumbent on him to strike out the major
altogether from the reasoning process, without substituting anything else,
and maintained that our reasonings consist only of the minor premiss and
the conclusion, Socrates is a man, therefore Socrates is mortal: thus
actually suppressing, as an unnecessary step in the argument, the appeal
to former experience. The absurdity of this was disguised from him by the
opinion he adopted, that reasoning is merely analysing our own general
notions, or abstract ideas; and that the proposition, Socrates is mortal,
is evolved from the proposition, Socrates is a man, simply by recognising
the notion of mortality as already contained in the notion we form of a
man.
After the explanations so fully entered into on the subject of
propositions, much further discussion cannot be necessary to make the
radical error of this view of ratiocination apparent. If the word man
connoted mortality; if the meaning of “mortal” were involved in the
meaning of “man;” we might, undoubtedly, evolve the conclusion from the
minor alone, because the minor would have distinctly asserted it. But if,
as is in fact the case, the word man does not connote mortality, how does
it appear that in the mind of every person who admits Socrates to be a
man, the idea of man must include the idea of mortality? Dr. Brown could
not help seeing this difficulty, and in order to avoid it, was led,
contrary to his intention, to re-establish, under another name, that step
in the argument which corresponds to the major, by affirming the necessity
of _previously perceiving_ the relation between the idea of man and the
idea of mortal. If the reasoner has not previously perceived this
relation, he will not, says Dr. Brown, infer because Socrates is a man,
that Socrates is mortal. But even this admission, though amounting to a
surrender of the doctrine that an argument consists of the minor and the
conclusion alone, will not save the remainder of Dr. Brown’s theory. The
failure of assent to the argument does not take place merely because the
reasoner, for want of due analysis, does not perceive that his idea of man
includes the idea of mortality; it takes place, much more commonly,
because in his mind that relation between the two ideas has never existed.
And in truth it never does exist, except as the result of experience.
Consenting, for the sake of the argument, to discuss the question on a
supposition of which we have recognised the radical incorrectness, namely,
that the meaning of a proposition relates to the ideas of the things
spoken of, and not to the things themselves; I must yet observe, that the
idea of man, as an universal idea, the common property of all rational
creatures, cannot involve anything but what is strictly implied in the
name. If any one includes in his own private idea of man, as no doubt is
almost 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 premiss 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
premiss is the result.
In the argument, then, which proves that Socrates is mortal, one
indispensable part of the premisses 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 premiss, 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
from this we conclude that he further resembles them in the attribute
mortality.
§ 7. We have thus obtained what we were seeking, an universal type of the
reasoning process. We find it resolvable in all cases into the following
elements: Certain individuals have a given attribute; an individual or
individuals resemble the former in certain other attributes; therefore
they resemble them also in the given attribute. This type of ratiocination
does not claim, like the syllogism, to be conclusive from the mere form of
the expression; nor can it possibly be so. That one proposition does or
does not assert the very fact which was already asserted in another, may
appear from the form of the expression, that is, from a comparison of the
language; but when the two propositions assert facts which are _bonâ fide_
different, whether the one fact proves the other or not can never appear
from the language, but must depend on other considerations. Whether, from
the attributes in which Socrates resembles those men who have heretofore
died, it is allowable to infer that he resembles them also in being
mortal, is a question of Induction; and is to be decided by the principles
or canons which we shall hereafter recognise as tests of the correct
performance of that great mental operation.
Meanwhile, however, it is certain, as before remarked, that if this
inference can be drawn as to Socrates, it can be drawn as to all others
who resemble the observed individuals in the same attributes in which he
resembles them; that is (to express the thing concisely), of all mankind.
If, therefore, the argument be conclusive 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
premisses are particulars, whether we conclude from particulars to a
general formula, or from particulars to other particulars according to
that formula, are equally Induction; we shall yet, conformably to usage,
consider the name Induction as more peculiarly belonging to the process of
establishing the general proposition, and the remaining operation, which
is substantially that of interpreting the general proposition, we shall
call by its usual name, Deduction. And we shall consider every process by
which anything is inferred respecting an unobserved case, as consisting of
an Induction followed by a Deduction; because, although the process needs
not necessarily be carried on in this form, it is always susceptible of
the form, and must be thrown into it when assurance of scientific accuracy
is needed and desired.
NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.
This theory of the syllogism, (which has received the important
adhesion of Dr. Whewell,(33)) has been controverted by a writer in
the “British Quarterly Review.”(34) The doctrine being new,
discussion respecting it is extremely desirable, to ensure that
nothing essential to the question escapes observation; and I
shall, therefore, reply to this writer’s objections with somewhat
more minuteness than their strength may seem to require.
The reviewer denies that there is a _petitio principii_ in the
syllogism, or that the proposition, All men are mortal, asserts or
assumes that Socrates is mortal. In support of this denial, he
argues that we may, and in fact do, admit the general proposition
that all men are mortal, without having particularly examined the
case of Socrates, and even without knowing whether the individual
so named is a man or not. But this of course was never denied.
That we can and do draw conclusions concerning cases specifically
unknown to us, is the datum from which all who discuss this
subject must set out. The question is, in what terms the evidence,
or ground, on which we draw these conclusions, may best be
designated—whether it is most correct to say, that the unknown
case is proved by known cases, or that it is proved by a general
proposition, including both sets of cases, the unknown and the
known? I contend for the former mode of expression. I hold it an
abuse of language to say, that the proof that Socrates is mortal,
is that all men are mortal. Turn it in what way we will, this
seems to me to be asserting that a thing is the proof of itself.
Whoever pronounces the words, All men are mortal, has affirmed
that Socrates is mortal, though he may never have heard of
Socrates; for since Socrates, whether known to be so or not,
really is a man, he is included in the words, All men, and in
every assertion of which they are the subject. If the reviewer
does not see that there is a difficulty here, I can only advise
him to reconsider the subject until he does: after which he will
be a more competent judge of the success or failure of an attempt
to remove the difficulty.(35) That he had reflected very little on
the point when he wrote his remarks, is shown by his oversight
respecting the _dictum de omni et nullo_. He acknowledges that
this maxim as commonly expressed,—“Whatever is true of a class, is
true of everything included in the class,” is a mere identical
proposition, since the class _is_ nothing but the things included
in it. But he thinks this defect would be cured by wording the
maxim thus,—“Whatever is true of a class, is true of everything
which _can be shown_ to be a member of the class:” as if a thing
could “be shown” to be a member of the class without being one. If
a class means the sum of all the things included in the class, the
things which “can be shown” to be included in it are a part of
these; it is the sum of them too, and the _dictum_ is as much an
identical proposition with respect to them as to the rest. One
would almost imagine that, in the reviewer’s opinion, things are
not members of a class until they are called up publicly to take
their place in it—that so long, in fact, as Socrates is not known
to be a man, he _is not_ a man, and any assertion which can be
made concerning men does not at all regard him, nor is affected as
to its truth or falsity by anything in which he is concerned.
The reviewer says that if the major premiss included the
conclusion, “we should be able to affirm the conclusion without
the intervention of the minor premiss; but every one sees that
that is impossible.” It does not follow, because the major premiss
contains the conclusion, that the words themselves must show all
the conclusions which it contains, and which, or evidence of
which, it presupposes. The minor is equally required on both
theories. It is respecting the functions of the major premiss that
the theories differ; whether that premiss merely affirms the
existence of proof, or is itself part of the proof—whether the
conclusion follows from the minor and major, or from the minor and
the particular instances which are the foundation of the major. On
either supposition, it is necessary that the new case should be
perceived to be one coming within the description of those to
which the previous experience is applicable; which is the purport
of the minor premiss. When we say that all men are mortal, we make
an assertion reaching beyond the sphere of our knowledge of
individual cases; and when a new individual, Socrates, is brought
within the field of our knowledge by means of the minor premiss,
we learn that we have already made an assertion respecting
Socrates without knowing it: our own general formula is, to that
extent, for the first time _interpreted_ to us. But according to
the reviewer’s theory, it is our having _made_ the assertion which
proves the assertion: while I contend that the proof is not the
assertion, but the grounds (of experience) on which the assertion
was made, and by which it must be justified.
The reviewer comes much nearer to the gist of the question, when
he objects that the formula in which the major is left out—“A, B,
C, &c., were mortal, therefore the Duke of Wellington is mortal,”
does not express all the steps of the mental process, but omits
one of the most essential, that which consists in recognising the
cases A, B, C, as _sufficient evidence_ of what is true of the
Duke of Wellington. This recognition of the sufficiency of the
induction he calls an “inference,” and says, that its result must
be interpolated between the cases A, B, C, and the case of the
Duke of Wellington; and that “our final conclusion is from what is
thus interpolated, and not directly from the individual facts that
A, B, C, &c. were mortal.” On this it may first be observed, that
the formula does express all that takes place in ordinary
unscientific reasoning. Mankind in general conclude at once from
experience of death in past cases, to the expectation of it in
future, without testing the experience by any principles of
induction, or passing through any general proposition. This is not
safe reasoning, but it is reasoning; and the syllogism, therefore,
is not the universal type of reasoning, but only a form in which
it is _desirable_ that we should reason. But, in the second place,
suppose that the enquirer does logically satisfy himself that the
conditions of legitimate induction are realized in the cases A, B,
C. It is still obvious, that if he knows the Duke of Wellington to
be a man, he is as much justified in concluding at once that the
Duke of Wellington is mortal, as in concluding that all men are
mortal. The general conclusion is not 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.(36) That the process of testing the sufficiency of an
inductive inference is an operation of a general character, I
readily concede to the reviewer; I had myself said as much, by
laying down as a fundamental law, that whenever there is ground
for drawing any conclusion at all from particular instances, there
is ground for a _general_ conclusion. But that this general
conclusion should be actually drawn, however useful, cannot be an
indispensable condition of the validity of the inference in the
particular case. A man gives away sixpence by the same power by
which he disposes of his whole fortune; but it is not necessary to
the lawfulness of his doing the one, that he should formally
assert, even to himself, his right to do the other.
The reviewer has recourse for an example, to syllogisms in the
second figure (though all are, by a mere verbal transformation,
reducible to the first), and asks, where is the _petitio
principii_ in this syllogism, “Every poet is a man of genius, A B
is not a man of genius, therefore A B is not a poet.” It is true
that in a syllogism of this particular type, the _petitio
principii_ is disguised. A B is not included in the terms, every
poet. But the proposition, “every poet is a man of genius” (a very
questionable proposition, by the way), cannot have been
inductively proved, unless the negative branch of the enquiry has
been attended to as well as the positive; unless it has been fully
considered whether among persons who are not “men of genius,”
there are not some who ought to be termed poets, and unless this
has been determined in the negative. Therefore, the case of A B
has been decided by implication, as much as the case of Socrates
in the first example. The proposition, Every poet is a man of
genius, is confessedly æquipollent with “No one who is not a man
of genius is a poet,” and in this the _petitio principii_, as
regards A B, is no longer implied, but express, as in an ordinary
syllogism of the first figure.
Another critic has endeavoured to get rid of the _petitio
principii_ in the syllogism by substituting for the common form of
expression, the following form—All _known_ men were mortal,
Socrates is a man, therefore Socrates is mortal. To this, however,
there is the fatal objection, that the syllogism, thus
transformed, does not prove the conclusion; it wants not the form
only, but the substance of proof. It is not merely because a thing
is true in all _known_ instances that it can be inferred to be
true in any new instance: many things may be true of all known men
which would not be true of all men; while, on the other hand, a
thing may be superabundantly proved true of all men, without
having been ascertained by actual experience to be true of all
known men, or even of the hundredth part of them.
CHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
§ 1. In our analysis of the syllogism it appeared that the minor premiss
always affirms a resemblance between a new case, and some cases previously
known; while the major premiss 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 premiss, the examples
which were exclusively employed in the preceding chapter; if the
resemblance, which that premiss asserts, were obvious to the senses, as in
the proposition “Socrates is a man,” or were at once ascertainable by
direct observation; there would be no necessity for trains of reasoning,
and Deductive or Ratiocinative Sciences would not exist. Trains of
reasoning exist only for the sake of extending an induction, founded, as
all inductions must be, on observed cases, to other cases in which we not
only cannot directly observe what is to be proved, but cannot directly
observe even the mark which is to prove it.
§ 2. Suppose the syllogism to be, All cows ruminate, the animal which is
before me is a cow, therefore it ruminates. The minor, if true at all, is
obviously so: the only premiss the establishment of which requires any
anterior process of inquiry, is the major; and provided the induction of
which that premiss 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 forms
a compound with hydrogen, which yields a black precipitate with nitrate of
silver, 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 the given
precipitate, and found that they possessed the properties connoted by the
word arsenic; they were metallic, volatile, their vapour had a smell of
garlic, and so forth. Next, we, or others for us, have examined various
specimens which possessed this metallic and volatile character, whose
vapour had this smell, &c., and have invariably found that they were
poisonous. The first observation we judge that we may extend to all
substances whatever which yield the precipitate: the second, to all
metallic and volatile substances resembling those we examined; and
consequently, not to those only which are seen to be such, but to those
which are concluded to be such by the prior induction. The substance
before us is only seen to come within one of these inductions; but by
means of this one, it is brought within the other. We are still, as
before, concluding from particulars to particulars; but we are now
concluding from particulars observed, to other particulars which are not,
as in the simple case, _seen_ to resemble them in the material points, but
_inferred_ to do so, because resembling them in something else, which we
have been led by quite a different set of instances to consider as a mark
of the former resemblance.
This first example of a train of reasoning is still extremely simple, the
series consisting of only two syllogisms. The following is somewhat more
complicated:—No government, which earnestly seeks the good of its
subjects, is likely to be overthrown; some particular government earnestly
seeks the good of its subjects, therefore it is not likely to be
overthrown. The major premiss in this argument we shall suppose not to be
derived from considerations _à priori_, but to be a generalization from
history, which, whether correct or erroneous, must have been founded on
observation of governments concerning whose desire of the good of their
subjects there was no doubt. It has been found, or thought to be found,
that these were not likely to be overthrown, and it has been deemed that
those instances warranted an extension of the same predicate to any and
every government which resembles them in the attribute of desiring
earnestly the good of its subjects. But _does_ the government in question
thus resemble them? This may be debated _pro_ and _con_ by many arguments,
and must, in any case, be proved by another induction; for we cannot
directly observe the sentiments and desires of the persons who carry on
the government. To prove the minor, therefore, we require an argument in
this form: Every government which acts in a certain manner, desires the
good of its subjects; the supposed government acts in that particular
manner, therefore it desires the good of its subjects. But is it true that
the government acts in the manner supposed? This minor also may require
proof; still another induction, as thus:—What is asserted by intelligent
and disinterested witnesses, may be believed to be true; that the
government acts in this manner, is asserted by such witnesses, therefore
it may be believed to be true. The argument hence consists of three steps.
Having the evidence of our senses that the case of the government under
consideration resembles a number of former cases, in the circumstance of
having something asserted respecting it by intelligent and disinterested
witnesses, we infer, first, that, as in those former instances, so in this
instance, the assertion is true. Secondly, what was asserted of the
government being that it acts in a particular manner, and other
governments or persons having been observed to act in the same manner, the
government in question is brought into known resemblance with those other
governments or persons; and since they were known to desire the good of
the people, it is thereupon, by a second induction, inferred that the
particular government spoken of, desires the good of the people. This
brings that government into known resemblance with the other governments
which were thought likely to escape revolution, and thence, by a third
induction, it is predicted 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 cannot, we determine once for all what are the
distinguishing marks by which such cases may be recognised. The subsequent
process is merely that of identifying an object, and ascertaining it to
have those marks; whether we identify it by the very marks themselves, or
by others which we have ascertained (through another and a similar
process) to be marks of those marks. The real inference is always from
particulars to particulars, from the observed instances to an unobserved
one: but in drawing this inference, we conform to a formula which we have
adopted for our guidance in such operations, and which is a record of the
criteria by which we thought we had ascertained that we might distinguish
when the inference could, and when it could not, be drawn. The real
premisses are the individual observations, even though they may have been
forgotten, or, being the observations of others and not of ourselves, may,
to us, never have been known: but we have before us proof that we or
others once thought them sufficient for an induction, and we have marks to
show whether any new case is one of those to which, if then known, the
induction would have been deemed to extend. These marks we either
recognise at once, or by the aid of other marks, which by another previous
induction we collected to be marks of _them_. Even these marks of marks
may only be recognised through a third set of marks; and we may have a
train of reasoning, of any length, to bring a new case within the scope of
an induction grounded on particulars its similarity to which is only
ascertained in this indirect manner.
Thus, in the preceding example, the ultimate inductive inference was, that
a certain government was not likely to be overthrown: this inference was
drawn according to a formula in which desire of the public good was set
down as a mark of not being likely to be overthrown; a mark of this mark
was, acting in a particular manner; and a mark of acting in that manner
was, being asserted to do so by intelligent and disinterested witnesses:
this mark, the government under discussion was recognised by the senses as
possessing. Hence that government fell within the last induction, and by
it was brought within all the others. The perceived resemblance of the
case to one set of observed particular cases, brought it into known
resemblance with another set, and that with a third.
In the more complex branches of knowledge, the deductions seldom consist,
as in the examples hitherto exhibited, of a single chain, _a_ a mark of
_b_, _b_ of _c_, _c_ of _d_, therefore _a_ a mark of _d_. They consist (to
carry on the same metaphor) of several chains united at the extremity, as
thus: _a_ a mark of _d_, _b_ of _e_, _c_ of _f_, _d e f_ of _n_, therefore
_a b c_ a mark of _n_. Suppose, for example, the following combination of
circumstances: 1st, rays of light impinging on a reflecting surface; 2nd,
that surface parabolic; 3rd, those rays parallel to each other and to the
axis of the surface. It is to be proved that the concourse of these three
circumstances is a mark that the reflected rays will pass through the
focus of the parabolic surface. Now, each of the three circumstances is
singly a mark of something material to the case. Rays of light impinging
on a reflecting surface, are a mark that those rays will be reflected at
an angle equal to the angle of incidence. The parabolic form of the
surface is a mark that, from any point of it, a line drawn to the focus
and a line parallel to the axis will make equal angles with the surface.
And finally, the parallelism of the rays to the axis is a mark that their
angle of incidence coincides with one of these equal angles. The three
marks taken together are therefore a mark of all these three things
united. But the three united are evidently a mark that the angle of
reflexion must coincide with the other of the two equal angles, that
formed by a line drawn to the focus; and this again, by the fundamental
axiom concerning straight lines, is a mark that the reflected rays pass
through the focus. Most chains of physical deduction are of this more
complicated type; and even in mathematics such are abundant, as in all
propositions where the hypothesis includes numerous conditions: “_If_ a
circle be taken, and _if_ within that circle a point be taken, not the
centre, and _if_ straight lines be drawn from that point to the
circumference, then,” &c.
§ 4. The considerations now stated remove a serious difficulty from the
view we have taken of reasoning; which view might otherwise have seemed
not easily 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 cannot be directly
seen to be included.
When the more obvious of the inductions which can be made in any science
from direct observations, have been made, and general formulas have been
framed, determining the limits within which these inductions are
applicable; as often as a new case can be at once seen to come within one
of the formulas, the induction is applied to the new case, and the
business is ended. But new cases are continually arising, which do not
obviously come within any formula whereby the question we want solved in
respect of them could be answered. Let us take an instance from geometry;
and as it is taken only for illustration, let the reader concede to us for
the present, what we shall endeavour to prove in the next chapter, that
the first principles of geometry are results of induction. Our example
shall be the fifth proposition of the first book of Euclid. The inquiry
is, Are the angles at the base of an isosceles triangle equal or unequal?
The first thing to be considered is, what inductions we have, from which
we can infer equality or inequality. For inferring equality we have the
following formulæ:—Things which being applied to each other coincide, are
equals. Things which are equal to the same thing are equals. A whole and
the sum of its parts are equals. The sums of equal things are equals. The
differences of equal things are equals. There are no other formulæ to
prove equality. For inferring inequality we have the following:—A whole
and its parts are unequals. The sums of equal things and unequal things
are unequals. The differences of equal things and unequal things are
unequals. In all, eight formulæ. The angles at the base of an isosceles
triangle do not obviously come within any of these. The formulæ specify
certain marks of equality and of inequality, but the angles cannot be
perceived intuitively to have any of those marks. We can, however, examine
whether they have properties which, in any other formulæ, are set down as
marks of those marks. On examination it appears that they have; and we
ultimately succeed in bringing them within this formula, “The differences
of equal things are equal.” Whence comes the difficulty in recognising
these angles as the differences of equal things? Because each of them is
the difference not of one pair only, but of innumerable pairs of angles;
and out of these we had to imagine and select two, which could either be
intuitively perceived to be equals, or possessed some of the marks of
equality set down in the various formulæ. By an exercise of ingenuity,
which, on the part of the first inventor, deserves to be regarded as
considerable, two pairs of angles were hit upon, which united these
requisites. First, it could be perceived intuitively that their
differences were the angles at the base; and, secondly; they possessed one
of the marks of equality, namely, coincidence when applied to one another.
This coincidence, however, was not perceived intuitively, but inferred, in
conformity to another 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 premisses 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._
A D and A E are sums of equals by the supposition. Having that mark of
equality, they are concluded by this formula to be equal.
SECOND FORMULA. _Equal straight lines being applied to one another
coincide_.
A C, A B, are within this formula by supposition; A D, A E, have been
brought within it by the preceding step. Both these pairs of straight
lines have the property of equality; which, according to the second
formula, is a mark that, if applied to each other, they will coincide.
Coinciding altogether means coinciding in every part, and of course at
their extremities, D, E, and B, C.
THIRD FORMULA. _Straight lines, having their extremities coincident,
coincide_.
B E and C D 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 B E and C D coincide, and the second
that A B, A C, coincide, the angles A B E and A C D are thereby brought
within the fourth formula, and accordingly coincide.
FIFTH FORMULA. _Things which coincide are equal_.
The angles A B E and A C D are brought within this formula by the
induction immediately preceding. This train of reasoning being also
applicable, _mutatis mutandis_, to the angles E B C, D C B, these also are
brought within the fifth formula. And, finally,
SIXTH FORMULA. _The differences of equals are equal_.
The angle A B C being the difference of A B E, C B E, and the angle A C B
being the difference of A C D, D C B; which have been proved to be equals;
A B C and A C B 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 A B C, 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 idea, 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 that there are weighty scientific reasons
for giving to every science as much of the character of a Deductive
Science as possible; for endeavouring to construct the science from the
fewest and the simplest possible inductions, and to make these, by any
combinations however complicated, suffice for proving even such truths,
relating to complex cases, as could be proved, if we chose, by inductions
from specific experience. Every branch of natural philosophy was
originally experimental; each generalization rested on a special
induction, and was derived from its own distinct set of observations and
experiments. From being sciences of pure experiment, as the phrase is, or,
to speak more correctly, sciences in which the reasonings mostly consist
of no more than one step, and are expressed by single syllogisms, all
these sciences have become to some extent, and some of them in nearly the
whole of their extent, sciences of pure reasoning; whereby multitudes of
truths, already known by induction from as many different sets of
experiments, have come to be exhibited as deductions or corollaries from
inductive propositions of a simpler and more universal character. Thus
mechanics, hydrostatics, optics, acoustics, and thermology, have
successively been rendered mathematical; and astronomy was brought by
Newton within the laws of general mechanics. Why it is that the
substitution of this circuitous mode of proceeding for a process
apparently much easier and more natural, is held, and justly, to be the
greatest triumph of the investigation of nature, we are not, in this stage
of our inquiry, prepared to examine. But it is necessary to remark, that
although, by this progressive transformation, all sciences tend to become
more and more Deductive, they are not therefore the less Inductive; every
step in the Deduction is still an Induction. The opposition is not between
the terms Deductive and Inductive, but between Deductive and Experimental.
A science is experimental, in proportion as every new case, which presents
any peculiar features, stands in need of a new set of observations and
experiments, a fresh induction. It is Deductive, in proportion as it can
draw conclusions, respecting cases of a new kind, by processes which bring
those cases under old inductions; by ascertaining that cases which cannot
be observed to have the requisite marks, have, however, marks of those
marks.
We can now, therefore, perceive what is the generic distinction between
sciences which can be made Deductive, and those which must as yet remain
Experimental. The difference consists in our having been able, or not yet
able, to discover marks of marks. If by our various inductions we have
been able to proceed no further than to such propositions as these, _a_ a
mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of _d_, or
_c_ and _d_ marks of one another, without anything to connect _a_ or _b_
with _c_ or _d_; we have a science of detached and mutually independent
generalizations, such as these, that acids redden vegetable blues, and
that alkalies colour them green; from neither of which propositions could
we, directly or indirectly, infer the other: and a science, so far as it
is composed of such propositions, is purely experimental. Chemistry, in
the present state of our knowledge, has not yet thrown off this character.
There are other sciences, however, of which the propositions are of this
kind: _a_ a mark of _b_, _b_ a mark of _c_, _c_ of _d_, _d_ of _e_, &c. In
these sciences we can mount the ladder from _a_ to _e_ by a process of
ratiocination; we can conclude that _a_ is a mark of _e_, and that every
object which has the mark _a_ has the property _e_, although, perhaps, we
never were able to observe _a_ and _e_ together, and although even _d_,
our only direct mark of _e_, may be not perceptible in those objects, but
only inferrible. Or varying the first metaphor, we may be said to get from
_a_ to _e_ underground: the marks _b_, _c_, _d_, which indicate the route,
must all be possessed somewhere by the objects concerning which we are
inquiring; but they are below the surface: _a_ is the only mark that is
visible, and by it we are able to trace in succession all the rest.
§ 6. We can now understand how an experimental may transform itself into a
deductive science by the mere progress of experiment. In an experimental
science, the inductions, as we have said, lie detached, as, _a_ a mark of
_b_, _c_ a mark of _d_, _e_ a mark of _f_, and so on: now, a new set of
instances, and a consequent new induction, may at any time bridge over the
interval between two of these unconnected arches; _b_, for example, may be
ascertained to be a mark of _c_, which enables us thenceforth to prove
deductively that _a_ is a mark of _c_. Or, as sometimes happens, some
comprehensive induction may raise an arch high in the air, which bridges
over hosts of them at once: _b_, _d_, _f_, and all the rest, turning out
to be marks of some one thing, or of things between which a connexion has
already been traced. As when Newton discovered that the motions, whether
regular or apparently anomalous, of all the bodies of the solar system,
(each of which motions had been inferred by a separate logical operation,
from separate marks,) were all marks of moving round a common centre, with
a centripetal force varying directly as the mass, and inversely as the
square of the distance from that centre. This is the greatest example
which has yet occurred of the transformation, at one stroke, of a science
which was still to a great degree merely experimental, into a deductive
science.
Transformations of the same nature, but on a smaller scale, continually
take place in the less advanced branches of physical knowledge, without
enabling them to throw off the character of experimental sciences. Thus
with regard to the two unconnected propositions before cited, namely,
Acids redden vegetable blues, Alkalies make them green; it is remarked by
Liebig, that all blue colouring matters which are reddened by acids (as
well as, reciprocally, all red colouring matters which are rendered blue
by alkalies) contain nitrogen: and it is quite possible that this
circumstance may one day furnish a bond of connexion between the two
propositions in question, by showing that the antagonist action of acids
and alkalies in producing or destroying the colour blue, is the result of
some one, more general, law. Although this connecting of detached
generalizations is so much gain, it tends but little to give a deductive
character to any science as a whole; because the new courses of
observation and experiment, which thus enable us to connect together a few
general truths, usually make known to us a still greater number of
unconnected new ones. Hence chemistry, though similar extensions and
simplifications of its generalizations are continually taking place, is
still in the main an experimental science; and is likely so to continue,
unless some comprehensive induction should be hereafter arrived at, which,
like Newton’s, shall connect a vast number of the smaller known inductions
together, and change the whole method of the science at once. Chemistry
has already one great generalization, which, though relating to one of the
subordinate aspects of chemical phenomena, possesses within its limited
sphere this comprehensive character; the principle of Dalton, called the
atomic theory, or the doctrine of chemical equivalents: which by enabling
us to a certain extent to foresee the proportions in which two substances
will combine, before the experiment has been tried, constitutes
undoubtedly a source of new chemical truths obtainable by deduction, as
well as a connecting principle for all truths of the same description
previously obtained by experiment.
§ 7. The discoveries which change the method of a science from
experimental to deductive, mostly consist in establishing, either by
deduction or by direct experiment, that the varieties of a particular
phenomenon uniformly accompany the varieties of some other phenomenon
better known. Thus the science of sound, which previously stood in the
lowest rank of merely experimental science, became deductive when it was
proved by experiment that every variety of sound was consequent on, and
therefore a mark of, a distinct and definable variety of oscillatory
motion among the particles of the transmitting medium. When this was
ascertained, it followed that every relation of succession or coexistence
which obtained between phenomena of the more known class, obtained also
between the phenomena which corresponded to them in the other class. Every
sound, being a mark of a particular oscillatory motion, became a mark of
everything which, by the laws of dynamics, was known to be inferrible from
that motion; and everything which by those same laws was a mark of any
oscillatory motion among the particles of an elastic medium, became a mark
of the corresponding sound. And thus many truths, not before suspected,
concerning sound, become deducible from the known laws of the propagation
of motion through an elastic medium; while facts already empirically known
respecting sound, become an indication of corresponding properties of
vibrating bodies, previously undiscovered.
But the grand agent for transforming experimental into deductive sciences,
is the science of number. The properties of numbers, alone among all known
phenomena, are, in the most rigorous sense, properties of all things
whatever. All things are not coloured, or ponderable, or even extended;
but all things are numerable. And if we consider this science in its whole
extent, from common arithmetic up to the calculus of variations, the
truths already ascertained seem all but infinite, and admit of indefinite
extension.
These truths, though affirmable of all things whatever, of course apply to
them only in respect of their quantity. But if it comes to be discovered
that variations of quality in any class of phenomena, correspond regularly
to variations of quantity either in those same or in some other phenomena;
every formula of mathematics applicable to quantities which vary in that
particular manner, becomes a mark of a corresponding general truth
respecting the variations in quality which accompany them: and the science
of quantity being (as far as any science can be) altogether deductive, the
theory of that particular kind of qualities becomes, to this extent,
deductive likewise.
The most striking instance in point which history affords (though not an
example of an experimental science rendered deductive, but of an
unparalleled extension given to the deductive process in a science which
was deductive already,) is the revolution in geometry which originated
with Descartes, and was completed by Clairaut. These great mathematicians
pointed out the importance of the fact, that to every variety of position
in points, direction in lines, or form in curves or surfaces, (all of
which are Qualities,) there corresponds a peculiar relation of quantity
between either two or three rectilineal co-ordinates; insomuch that if the
law were known according to which those co-ordinates vary relatively to
one another, every other geometrical property of the line or surface in
question, whether relating to quantity or quality, would be capable of
being inferred. Hence it followed that every geometrical question could be
solved, if the corresponding algebraical one could; and geometry received
an accession (actual or potential) of new truths, corresponding to every
property of numbers which the progress of the calculus had brought, or
might in future bring, to light. In the same general manner, mechanics,
astronomy, and in a less degree, every branch of natural philosophy
commonly so called, have been made algebraical. The varieties of physical
phenomena with which those sciences are conversant, have been found to
answer to determinable varieties in the quantity of some circumstance or
other; or at least to varieties of form or position, for which
corresponding equations of quantity had already been, or were susceptible
of being, discovered by geometers.
In these various transformations, the propositions of the science of
number do but fulfil the function proper to all propositions forming a
train of reasoning, viz. that of enabling us to arrive in an indirect
method, by marks of marks, at such of the properties of objects as we
cannot directly ascertain (or not so conveniently) by experiment. We
travel from a given visible or tangible fact, through the truths of
numbers, to the fact sought. The given fact is a mark that a certain
relation subsists between the quantities of some of the elements
concerned; while the fact sought presupposes a certain relation between
the quantities of some other elements: now, if these last quantities are
dependent in some known manner upon the former, or _vice 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 many) 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 descriptions, as far as they go, of the objects with
which geometry is conversant. Now we have pointed out that, from a
definition as such, no proposition, unless it be one concerning the
meaning of a word, can ever follow; and that what apparently follows from
a definition, follows in reality from an implied assumption that there
exists a real thing conformable thereto. This assumption, in the case of
the definitions of geometry, is false: there exist no real things exactly
conformable to the definitions. There exist no points without magnitude;
no lines without breadth, nor perfectly straight; no circles with all
their radii exactly equal, nor squares with all their angles perfectly
right. It will perhaps be said that the assumption does not extend to the
actual, but only to the possible, existence of such things. I answer that,
according to any test we have of possibility, they are not even possible.
Their existence, so far as we can form any judgment, would seem to be
inconsistent with the physical constitution of our planet at least, if not
of the universe. To get rid of this difficulty, and at the same time to
save the credit of the supposed system of necessary truth, it is customary
to say that the points, lines, circles, and squares which are the subject
of geometry, exist in our conceptions merely, and are part of our minds;
which minds, by working on their own materials, construct an _à priori_
science, the evidence of which is purely mental, and has nothing whatever
to do with outward experience. By howsoever high authorities this doctrine
may have been sanctioned, it appears to me psychologically incorrect. The
points, lines, circles, and squares, which any one has in his mind, are (I
apprehend) simply copies of the points, lines, circles, and squares which
he has known in his experience. Our idea of a point, I apprehend to be
simply our idea of the _minimum visibile_, the smallest portion of surface
which we can see. A line, as defined by geometers, is wholly
inconceivable. We can reason about a line as if it had no breadth; because
we have a power, which is the foundation of all the control we can
exercise over the operations of our minds; the power, when a perception is
present to our senses, or a conception to our intellects, of _attending_
to a part only of that perception or conception, instead of the whole. But
we cannot _conceive_ a line without breadth; we can form no mental picture
of such a line: all the lines which we have in our minds are lines
possessing breadth. If any one doubts this, we may refer him to his own
experience. I much question if any one who fancies that he can conceive
what is called a mathematical line, thinks so from the evidence of his
consciousness: I suspect it is rather because he supposes that unless such
a conception were possible, mathematics could not exist as a science: a
supposition which there will be no difficulty in showing to be entirely
groundless.
Since, then, neither in nature, nor in the human mind, do there exist any
objects exactly corresponding to the definitions of geometry, while yet
that science cannot be supposed to be conversant about non-entities;
nothing remains but to consider geometry as conversant with such lines,
angles, and figures, as really exist; and the definitions, as they are
called, must be regarded as some of our first and most obvious
generalizations concerning those natural objects. The correctness of those
generalizations, _as_ generalizations, is without a flaw: the equality of
all the radii of a circle is true of all circles, so far as it is true of
any one: but it is not exactly true of any circle: it is only nearly true;
so nearly that no error of any importance in practice will be incurred by
feigning it to be exactly true. When we have occasion to extend these
inductions, or their consequences, to cases in which the error would be
appreciable—to lines of perceptible breadth or thickness, parallels which
deviate sensibly from equidistance, and the like—we correct our
conclusions, by combining with them a fresh set of propositions relating
to the aberration; just as we also take in propositions relating to the
physical or chemical properties of the material, if those properties
happen to introduce any modification into the result; which they easily
may, even with respect to figure and magnitude, as in the case, for
instance, of expansion by heat. So long, however, as there exists no
practical necessity for attending to any of the properties of the object
except its geometrical properties, or to any of the natural irregularities
in those, it is convenient to neglect the consideration of the other
properties and of the irregularities, and to reason as if these did not
exist: accordingly, we formally announce, in the definitions, that we
intend to proceed on this plan. But it is an error to suppose, because we
resolve to confine our attention to a certain number of the properties of
an object, that we therefore conceive, or have an idea of the object,
denuded of its other properties. We are thinking, all the time, of
precisely such objects as we have seen and touched, and with all the
properties which naturally belong to them; but for scientific convenience,
we feign them to be divested of all properties, except those which are
material to our purpose, and in regard to which we design to consider
them.
The peculiar accuracy, supposed to be characteristic of the first
principles of geometry, thus appears to be fictitious. The assertions on
which the reasonings of the science are founded, do not, any more than in
other sciences, exactly correspond with the fact; but we _suppose_ that
they do so, for the sake of tracing the consequences which follow from the
supposition. The opinion of Dugald Stewart respecting the foundations of
geometry, is, I conceive, substantially correct; that it is built on
hypotheses; that it owes to this alone the peculiar certainty supposed to
distinguish it; and that in any science whatever, by reasoning from a set
of hypotheses, we may obtain a body of conclusions as certain as those of
geometry, that is, as strictly in accordance with the hypotheses, and as
irresistibly compelling assent, _on condition_ that those hypotheses are
true.
When, therefore, it is affirmed that the conclusions of geometry are
necessary truths, the necessity consists in reality only in this, that
they necessarily 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 necessarily following from some
assumption, which, by the conditions of the inquiry, is not to be
questioned. In this relation, of course, the derivative truths of every
deductive science must stand to the inductions, or assumptions, on which
the science is founded, and which, whether true or untrue, certain or
doubtful in themselves, are always supposed certain for the purposes of
the particular science. And therefore the conclusions of all deductive
sciences were said by the ancients to be necessary propositions. We have
observed already that to be predicated necessarily was characteristic of
the predicable Proprium, and that a proprium was any property of a thing
which could be deduced from its essence, that is, from the properties
included in its definition.
§ 2. The important doctrine of Dugald Stewart, which I have endeavoured to
enforce, has been contested by Dr. Whewell, both in the dissertation
appended to his excellent _Mechanical Euclid_, and in his more recent
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 premisses 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.”(37) And this is true; but this has never been
contradicted. Those who say that the premisses of geometry are hypotheses,
are not bound to maintain them to be hypotheses which have no relation
whatever to fact. Since an hypothesis framed for the purpose of scientific
inquiry must relate to something which has real existence, (for there can
be no science respecting non-entities,) it follows that any hypothesis we
make respecting an object, to facilitate our study of it, must not involve
anything which is distinctly false, and repugnant to its real nature: we
must not ascribe to the thing any property which it has not; our liberty
extends only to suppressing some of those which it has, 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. In their positive part they are
observed facts; it is only in their negative part that they are
hypothetical. 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 although 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 although these and several
others may be struck out of the list of first principles, because, though
not requiring demonstration, they are susceptible of it; there will be
found in the list of axioms two or three fundamental truths, not capable
of being demonstrated: among which must be reckoned the proposition that
two straight lines cannot inclose a space, (or its equivalent, Straight
lines which coincide in two points coincide altogether,) and some property
of parallel lines, other than that which constitutes their definition: the
most suitable, perhaps, being that selected by Professor Playfair: “Two
straight lines which intersect each other cannot both of them be parallel
to a third straight line.”(38)
The axioms, as well those which are indemonstrable as those which admit of
being demonstrated, differ from that other class of fundamental principles
which are involved in the definitions, in this, that they are true without
any mixture of hypothesis. That things which are equal to the same thing
are equal to one another, is as true of the lines and figures in nature,
as it would be of the imaginary ones assumed in the definitions. In this
respect, however, mathematics are only on a par with most other sciences.
In almost all sciences there are some general propositions which are
exactly true, while the greater part are only more or less distant
approximations to the truth. Thus in mechanics, the first law of motion
(the continuance of a movement once impressed, until stopped or slackened
by some resisting force) is true without qualification or error. The
rotation of the earth in twenty-four hours, of the same length as in our
time, has gone on since the first accurate observations, without the
increase or diminution of one second in all that period. These are
inductions which require no fiction to make them be received as accurately
true: but along with them there are others, as for instance the
propositions respecting the figure of the earth, which are but
approximations to the truth; and in order to use them for the further
advancement of our knowledge, we must feign that they are exactly true,
though they really want something of being so.
§ 4. It remains to inquire, what is the ground of our belief in
axioms—what is the evidence on which they rest? I answer, they are
experimental truths; generalizations from observation. The proposition,
Two straight lines cannot inclose a space—or in other words, Two straight
lines which have once met, do not meet again, but continue to diverge—is
an induction from the evidence of our senses.
This opinion runs counter to a scientific prejudice of long standing and
great strength, and there is probably no one proposition enunciated in
this work for which a more unfavourable reception is to be expected. It
is, however, no new opinion; and even if it were so, would be entitled to
be judged, not by its novelty, but by the strength of the arguments by
which it can be supported. I consider it very fortunate that so eminent a
champion of the contrary opinion as Dr. Whewell, has recently found
occasion for a most elaborate treatment of the whole theory of axioms, in
attempting to construct the philosophy of the mathematical and physical
sciences on the basis of the doctrine against which I now contend. Whoever
is anxious that a discussion should go to the bottom of the subject, must
rejoice to see the opposite side of the question worthily represented. If
what is said by Dr. Whewell, in support of an opinion which he has made
the foundation of a systematic work, can be shown not to be conclusive,
enough will have been done without going further to seek stronger
arguments and a more powerful adversary.
It is not necessary to show that the truths which we call axioms are
originally _suggested_ by observation, and that we should never have known
that two straight lines cannot inclose a space if we had never seen a
straight line: thus much being admitted by Dr. Whewell, and by all, in
recent times, who have taken his view of the subject. But they contend,
that it is not experience which _proves_ the axiom; but that its truth is
perceived _à priori_, by the constitution of the mind itself, from the
first moment when the meaning of the proposition is apprehended; and
without any necessity for verifying it by repeated trials, as is requisite
in the case of truths really ascertained by observation.
They cannot, however, but allow that the truth of the axiom, Two straight
lines cannot inclose a space, even if evident independently of experience,
is also evident from experience. Whether the axiom _needs_ confirmation or
not, it _receives_ confirmation in almost every instant of our lives;
since we cannot look at any two straight lines which intersect one
another, without seeing that from that point they continue to diverge more
and more. Experimental proof crowds in upon us in such endless profusion,
and without one instance in which there can be even a suspicion of an
exception to the rule, that we should soon have a stronger ground for
believing the axiom, even as an experimental truth, than we have for
almost any of the general truths which we confessedly learn from the
evidence of our senses. Independently of _à priori_ evidence, we should
certainly believe it with an intensity of conviction far greater than we
accord to any ordinary physical truth: and this too at a time of life much
earlier than that from which we date almost any part of our acquired
knowledge, and much too early to admit of our retaining any recollection
of the history of our intellectual operations at that period. Where then
is the necessity for assuming that our recognition of these truths has a
different origin from the rest of our knowledge, when its existence is
perfectly accounted for by supposing its origin to be the same? when the
causes which produce belief in all other instances, exist in this
instance, and in a degree of strength as much superior to what exists in
other cases, as the intensity of the belief itself is superior? The burden
of proof lies on the advocates of the contrary opinion: it is for them to
point out some fact, inconsistent with the supposition that this part of
our knowledge of nature is derived from the same sources as every other
part.
This, for instance, they would be able to do, if they could prove
chronologically that we had the conviction (at least practically) so early
in infancy as to be anterior to those impressions on the senses, upon
which, on the other theory, the conviction is founded. This, however,
cannot be proved: the point being too far back to be within the reach of
memory, and too obscure for external observation. The advocates of the _à
priori_ theory are obliged to have recourse to other arguments. These are
reducible to two, which I shall endeavour to state as clearly and as
forcibly as possible.
§ 5. In the first place it is said, that if our assent to the proposition
that two straight lines cannot inclose a space, were derived from the
senses, we could only be convinced of its truth by actual trial, that is,
by seeing or feeling the straight lines; whereas in fact it is seen to be
true by merely thinking of them. That a stone thrown into water goes to
the bottom, may be perceived by our senses, but mere thinking of a stone
thrown into the water would never have led us to that conclusion: not so,
however, with the axioms relating to straight lines: if I could be made to
conceive what a straight line is, without having seen one, I should at
once recognise that two such lines cannot inclose a space. Intuition is
“imaginary looking;”(39) but experience must be real looking: if we see a
property of straight lines to be true by merely fancying ourselves to be
looking at them, the ground of our belief cannot be the senses, or
experience; it must be something mental.
To this argument it might be added in the case of this particular axiom,
(for the assertion would not be true of all axioms,) that the evidence of
it from actual ocular inspection, is not only unnecessary, but
unattainable. What says the axiom? That two straight lines _cannot_
inclose a space; that after having once intersected, if they are prolonged
to infinity they do not meet, but continue to diverge from one another.
How can this, in any single case, be proved by actual observation? We may
follow the lines to any distance we please; but we cannot follow them to
infinity: for aught our senses can testify, they may, immediately beyond
the farthest point to which we have traced them, begin to approach, and at
last meet. Unless, therefore, we had some other proof of the impossibility
than observation affords us, we should have no ground for believing the
axiom at all.
To these arguments, which I trust I cannot be accused of understating, a
satisfactory answer will, I conceive, be found, if we advert to one of the
characteristic properties of geometrical forms—their capacity of being
painted in the imagination with a distinctness equal to reality: in other
words, the exact resemblance of our ideas of form to the sensations which
suggest them. This, in the first place, enables us to make (at least with
a little practice) mental pictures of all possible combinations of lines
and angles, which resemble the realities quite as well as any which we
could make on paper; and in the next place, makes those pictures just as
fit subjects of geometrical experimentation as the realities themselves;
inasmuch as pictures, if sufficiently accurate, exhibit of course all the
properties which would be manifested by the realities at one given
instant, and on simple inspection: and in geometry we are concerned only
with such properties, and not with that which pictures could not exhibit,
the mutual action of bodies one upon another. The foundations of geometry
would therefore be laid in direct experience, even if the experiments
(which in this case consist merely in attentive contemplation) were
practised solely upon what we call our ideas, that is, upon the diagrams
in our minds, and not upon outward objects. For in all systems of
experimentation we take some objects to serve as representatives of all
which resemble them; and in the present case the conditions which qualify
a real object to be the representative of its class, are completely
fulfilled by an object existing only in our fancy. Without denying,
therefore, the possibility of satisfying ourselves that two straight lines
cannot inclose a space, by merely thinking of straight lines without
actually looking at them; I contend, that we do not believe this truth on
the ground of the imaginary intuition simply, but because we know that the
imaginary lines exactly resemble real ones, and that we may conclude from
them to real ones with quite as much certainty as we could conclude from
one real line to another. The conclusion, therefore, is still an induction
from observation. And we should not be authorized to substitute
observation of the image in our mind, for observation of the reality, if
we had not learnt by long-continued experience that the properties of the
reality are faithfully represented in the image; just as we should be
scientifically warranted in describing an animal which we had never seen,
from a picture made of it with a daguerreotype; but not until we had
learnt by ample experience, that observation of such a picture is
precisely equivalent to observation of the original.
These considerations also remove the objection arising from the
impossibility of ocularly following the lines in their prolongation to
infinity, for though, in order actually to see that two given lines never
meet, it would be necessary to follow them to infinity; yet without doing
so we may know that if they ever do meet, or if, after diverging from one
another, they begin again to approach, this must take place not at an
infinite, but at a finite distance. Supposing, therefore, such to be the
case, we can transport ourselves thither in imagination, and can frame a
mental image of the appearance which one or both of the lines must present
at that point, which we may rely on as being precisely similar to the
reality. Now, whether we fix our contemplation upon this imaginary
picture, or call to mind the generalizations we have had occasion to make
from former ocular observation, we learn by the evidence of experience,
that a line which, after diverging from another straight line, begins to
approach to it, produces the impression on our senses which we describe by
the expression, “a bent line,” not by the expression, “a straight
line.”(40)
§ 6. The first of the two arguments in support of the theory that axioms
are _à priori_ truths, having, I think, been sufficiently answered; I
proceed to the second, which is usually the most relied on. Axioms (it is
asserted) are conceived by us not only as true, but as universally and
necessarily true. Now, experience cannot possibly give to any proposition
this character. I may have seen snow a hundred times, and may have seen
that it was white, but this cannot give me entire assurance even that all
snow is white; much less that snow _must_ be white. “However many
instances we may have observed of the truth of a proposition, there is
nothing to assure us that the next case shall not be an exception to the
rule. If it be strictly true that every ruminant animal yet known has
cloven hoofs, we still cannot be sure that some creature will not
hereafter be discovered which has the first of these attributes, without
having the other.... Experience must always consist of a limited number of
observations; and, however numerous these may be, they can show nothing
with regard to the infinite number of cases in which the experiment has
not been made.” Besides, axioms are not only universal, they are also
necessary. Now “experience cannot offer the smallest ground for the
necessity of a proposition. She can observe and record what has happened;
but she cannot find, in any case, or in any accumulation of cases, any
reason for what _must_ happen. She may see objects side by side; but she
cannot see a reason why they must ever be side by side. She finds certain
events to occur in succession; but the succession supplies, in its
occurrence, no reason for its recurrence. She contemplates external
objects; but she cannot detect any internal bond, which indissolubly
connects the future with the past, the possible with the real. To learn a
proposition by experience, and to see it to be necessarily true, are two
altogether different processes of thought.”(41) 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.”(42)
In the following passage, we are told what the distinction is, the
non-recognition of which incurs this denunciation. “Necessary truths are
those in which we not only learn that the proposition _is_ true, but see
that it _must be_ true; in which the negation of the truth is not only
false, but impossible; in which we cannot, even by an effort of
imagination, or in a supposition, conceive the reverse of that which is
asserted. That there are such truths cannot be doubted. We may take, for
example, all relations of number. Three and Two, added together, make
Five. We cannot conceive it to be otherwise. We cannot, by any freak of
thought, imagine Three and Two to make Seven.”(43)
Although Dr. Whewell has naturally and properly employed a variety of
phrases to bring his meaning more forcibly home, he will, I presume, allow
that they are all equivalent; and that what he means by a necessary truth,
would be sufficiently defined, a proposition the negation of which is not
only false but inconceivable. I am unable to find in any of his
expressions, turn them what way you will, a meaning beyond this, and I do
not believe he would contend that they mean anything more.
This, therefore, is the principle asserted: that propositions, the
negation of which is inconceivable, or in other words, which we cannot
figure to ourselves as being false, must rest on evidence of a higher and
more cogent description than any which experience can afford. And we have
next to consider whether there is any ground for this assertion.
Now I cannot but wonder that so much stress should be laid on the
circumstance of inconceivableness, when there is such ample experience to
show, that our capacity or incapacity of conceiving a thing has very
little to do with the possibility of the thing in itself; but is in truth
very much an affair of accident, and depends on the past history and
habits of our own minds. There is no more generally acknowledged fact in
human nature, than the extreme difficulty at first felt in conceiving
anything as possible, which is in contradiction to long established and
familiar experience; or even to old familiar habits of thought. And this
difficulty is a necessary result of the fundamental laws of the human
mind. When we have often seen and thought of two things together, and have
never in any one instance either seen or thought of them separately, there
is by the primary law of association an increasing difficulty, which may
in the end become insuperable, of conceiving the two things apart. This is
most of all conspicuous in uneducated persons, who are in general utterly
unable to separate any two ideas which have once become firmly associated
in their minds; and if persons of cultivated intellect have any advantage
on the point, it is only because, having seen and heard and read more, and
being more accustomed to exercise their imagination, they have experienced
their sensations and thoughts in more varied combinations, and have been
prevented from forming many of these inseparable associations. But this
advantage has necessarily its limits. The most practised intellect is not
exempt from the universal laws of our conceptive faculty. If daily habit
presents to any one for a long period two facts in combination, and if he
is not led during that period either by accident or by his voluntary
mental operations to think of them apart, he will probably in time become
incapable of doing so even by the strongest effort; and the supposition
that the two facts can be separated in nature, will at last present itself
to his mind with all the characters of an inconceivable phenomenon.(44)
There are remarkable instances of this in the history of science:
instances in which the most instructed men rejected as impossible, because
inconceivable, things which their posterity, by earlier practice and
longer perseverance in the attempt, found it quite easy to conceive, and
which everybody now knows to be true. There was a time when men of the
most cultivated intellects, and the most emancipated from the dominion of
early prejudice, could not credit the existence of antipodes; were unable
to conceive, in opposition to old association, the force of gravity acting
upwards instead of downwards. The Cartesians long rejected the Newtonian
doctrine of the gravitation of all bodies towards one another, on the
faith of a general proposition, the reverse of which seemed to them to be
inconceivable—the proposition that a body cannot act where it is not. All
the cumbrous machinery of imaginary vortices, assumed without the smallest
particle of evidence, appeared to these philosophers a more rational mode
of explaining the heavenly motions, than one which involved what seemed to
them so great an absurdity.(45) And they no doubt found it as impossible
to conceive that a body should act upon the earth, at the distance of the
sun or moon, as we find it to conceive an end to space or time, or two
straight lines inclosing a space. Newton himself had not been able to
realize the conception, or we should not have had his hypothesis of a
subtle ether, the occult cause of gravitation; and his writings prove,
that although he deemed the particular nature of the intermediate agency a
matter of conjecture, the necessity of _some_ such agency appeared to him
indubitable. It would seem that even now the majority of scientific men
have not completely got over this very difficulty; for though they have at
last learnt to conceive the sun _attracting_ the earth without any
intervening fluid, they cannot yet conceive the sun _illuminating_ the
earth without some such medium.
If, then, it be so natural to the human mind, even in a high state of
culture, to be incapable of conceiving, and on that ground to believe
impossible, what is afterwards not only found to be conceivable but proved
to be true; what wonder if in cases where the association is still older,
more confirmed, and more familiar, and in which nothing ever occurs to
shake our conviction, or even suggest to us any conception at variance
with the association, the acquired incapacity should continue, and be
mistaken for a natural incapacity? It is true, our experience of the
varieties in nature enables us, within certain limits, to conceive other
varieties analogous to them. We can conceive the sun or moon falling; for
although we never saw them fall, nor ever perhaps imagined them falling,
we have seen so many other things fall, that we have innumerable familiar
analogies to assist the conception; which, after all, we should probably
have some difficulty in framing, were we not well accustomed to see the
sun and moon move, (or appear to move,) so that we are only called upon to
conceive a slight change in the direction of motion, a circumstance
familiar to our experience. But when experience affords no model on which
to shape the new conception, how is it possible for us to form it? How,
for example, can we imagine an end to space or time? We never saw any
object without something beyond it, nor experienced any feeling without
something following it. When, therefore, we attempt to conceive the last
point of space, we have the idea irresistibly raised of other points
beyond it. When we try to imagine the last instant of time, we cannot help
conceiving another instant after it. Nor is there any necessity to assume,
as is done by a modern school of metaphysicians, a peculiar fundamental
law of the mind to account for the feeling of infinity inherent in our
conceptions of space and time; that apparent infinity is sufficiently
accounted for by simpler and universally acknowledged laws.
Now, in the case of a geometrical axiom, such, for example, as that two
straight lines cannot inclose a space,—a truth which is testified to us by
our very earliest impressions of the external world,—how is it possible
(whether those external impressions be or be not the ground of our belief)
that the reverse of the proposition _could_ be otherwise than
inconceivable to us? What analogy have we, what similar order of facts in
any other branch of our experience, to facilitate to us the conception of
two straight lines inclosing a space? Nor is even this all. I have already
called attention to the peculiar property of our impressions of form, that
the ideas or mental images exactly resemble their prototypes, and
adequately represent them for the purposes of scientific observation. From
this, and from the intuitive character of the observation, which in this
case reduces itself to simple inspection, we cannot so much as call up in
our imagination two straight lines, in order to attempt to conceive them
inclosing a space, without by that very act repeating the scientific
experiment which establishes the contrary. Will it really be contended
that the inconceivableness of the thing, in such circumstances, proves
anything against the experimental origin of the conviction? Is it not
clear that in whichever mode our belief in the proposition may have
originated, the impossibility of our conceiving the negative of it must,
on either hypothesis, be the same? As, then, Dr. Whewell exhorts those who
have any difficulty in recognising the distinction held by him between
necessary and contingent truths, to study geometry,—a condition which I
can assure him I have conscientiously fulfilled,—I, in return, with equal
confidence, exhort those who agree with him, to study the elementary laws
of association; being convinced that nothing more is requisite than a
moderate familiarity with those laws, to dispel the illusion which
ascribes a peculiar necessity to our earliest inductions from experience,
and measures the possibility of things in themselves, by the human
capacity of conceiving them.
I hope to be pardoned for adding, that Dr. Whewell himself has both
confirmed by his testimony the effect of habitual association in giving to
an experimental truth the appearance of a necessary one, and afforded a
striking instance of that remarkable law in his own person. In his
_Philosophy of the Inductive Sciences_ he continually asserts, that
propositions which not only are not self-evident, but which we know to
have been discovered gradually, and by great efforts of genius and
patience, have, when once established, appeared so self-evident that, but
for historical proof, it would have been impossible to conceive that they
had not been recognised from the first by all persons in a sound state of
their faculties. “We now despise those who, in the Copernican controversy,
could not conceive the apparent motion of the sun on the heliocentric
hypothesis; or those who, in opposition to Galileo, thought that a uniform
force might be that which generated a velocity proportional to the space;
or those who held there was something absurd in Newton’s doctrine of the
different refrangibility of differently coloured rays; or those who
imagined that when elements combine, their sensible qualities must be
manifest in the compound; or those who were reluctant to give up the
distinction of vegetables into herbs, shrubs, and trees. We cannot help
thinking that men must have been singularly dull of comprehension to find
a difficulty in admitting what is to us so plain and simple. We have a
latent persuasion that we in their place should have been wiser and more
clearsighted; 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._”(46)
This last proposition is precisely what I contend for; and I ask no more,
in order to overthrow the whole theory of its author on the nature of the
evidence of axioms. For what is that theory? That the truth of axioms
cannot have been learnt from experience, because their falsity is
inconceivable. But Dr. Whewell himself says, that we are continually led
by the natural progress of thought, to regard as inconceivable what our
forefathers not only conceived but believed, nay even (he might have
added) were unable to conceive the contrary of. He cannot intend to
justify this mode of thought: he cannot mean to say, that we can be
_right_ in regarding as inconceivable what others have conceived, and as
self-evident what to others did not appear evident at all. After so
complete an admission that inconceivableness is an accidental thing, not
inherent in the phenomenon itself, but dependent on the mental history of
the person who tries to conceive it, how can he ever call upon us to
reject a proposition as impossible on no other ground than its
inconceivableness? Yet he not only does so, but has unintentionally
afforded some of the most remarkable examples which can be cited of the
very illusion which he has himself so clearly pointed out. I select as
specimens, his remarks on the evidence of the three laws of motion, and of
the atomic theory.
With respect to the laws of motion, Dr. Whewell says: “No one can doubt
that, in historical fact, these laws were collected from experience. That
such is the case, is no matter of conjecture. We know the time, the
persons, the circumstances, belonging to each step of each discovery.”(47)
After this testimony, to adduce evidence of the fact would be superfluous.
And not only were these laws by no means intuitively evident, but some of
them were originally paradoxes. The first law was especially so. That a
body, once in motion, would continue for ever to move in the same
direction with undiminished velocity unless acted upon by some new force,
was a proposition which mankind found for a long time the greatest
difficulty in crediting. It stood opposed to apparent experience of the
most familiar kind, which taught that it was the nature of motion to abate
gradually, and at last terminate of itself. Yet when once the contrary
doctrine was firmly established, mathematicians, as Dr. Whewell observes,
speedily began to believe that laws, thus contradictory to first
appearances, and which, even after full proof had been obtained, it had
required generations to render familiar to the minds of the scientific
world, were under “a demonstrable necessity, compelling them to be such as
they are and no other;” and he himself, though not venturing “absolutely
to pronounce” that _all_ these laws “can be rigorously traced to an
absolute necessity in the nature of things,”(48) does actually think in
that manner of the law just mentioned; of which he says: “Though the
discovery of the first law of motion was made, historically speaking, by
means of experiment, we have now attained a point of view in which we see
that it might have been certainly known to be true, independently of
experience.”(49) Can there be a more striking exemplification than is here
afforded, of the effect of association which we have described?
Philosophers, for generations, have the most extraordinary difficulty in
putting certain ideas together; they at last succeed in doing so; and
after a sufficient repetition of the process, they first fancy a natural
bond between the ideas, then experience a growing difficulty, which at
last, by the continuation of the same progress, becomes an impossibility,
of severing them from one another. If such be the progress of an
experimental conviction of which the date is of yesterday, and which is in
opposition to first appearances, how must it fare with those which are
conformable to appearances familiar from the first dawn of intelligence,
and of the conclusiveness of which, from the earliest records of human
thought, no sceptic has suggested even a momentary doubt?
The other instance which I shall quote is a truly astonishing one, and may
be called the _reductio ad absurdum_ of the theory of inconceivableness.
Speaking of the laws of chemical composition, Dr. Whewell says:(50) “That
they could never have been clearly understood, and therefore never firmly
established, without laborious and exact experiments, is certain; but yet
we may venture to say, that being once known, they possess an evidence
beyond that of mere experiment. _For how, in fact, can we conceive
combinations, otherwise than as definite in kind and quality?_ If we were
to suppose each element ready to combine with any other indifferently, and
indifferently in any quantity, we should have a world in which all would
be confusion and indefiniteness. There would be no fixed kinds of bodies;
salts, and stones, and ores, would approach to and graduate into each
other by insensible degrees. Instead of this, we know that the world
consists of bodies distinguishable from each other by definite
differences, capable of being classified and named, and of having general
propositions asserted concerning them. And as _we cannot conceive a world
in which this should not be the case_, it would appear that we cannot
conceive a state of things in which the laws of the combination of
elements should not be of that definite and measured kind which we have
above asserted.”(51)
That a philosopher of Dr. Whewell’s eminence should gravely assert that we
cannot conceive a world in which the simple elements would combine in
other than definite proportions; that by dint of meditating on a
scientific truth, the original discoverer of which was still living, he
should have rendered the association in his own mind between the idea of
combination and that of constant proportions so familiar and intimate as
to be unable to conceive the one fact without the other; is so signal an
instance of the mental law for which I am contending, that one word more
in illustration must be superfluous.(52)
CHAPTER VI. THE SAME SUBJECT CONTINUED.
§ 1. In the examination which formed the subject of the last chapter, into
the nature of the evidence of those deductive sciences which are commonly
represented to be systems of necessary truth, we have been led to the
following conclusions. The results of those sciences are indeed necessary,
in the sense of necessarily following from certain first principles,
commonly called axioms and definitions; of being certainly true if those
axioms and definitions are so. But their claim to the character of
necessity in any sense beyond this, as implying an evidence independent of
and superior to observation and experience, must depend on the previous
establishment of such a claim in favour of the definitions and axioms
themselves. With regard to axioms, we found that, considered as
experimental truths, they rest on superabundant and obvious evidence. We
inquired, whether, since this is the case, it be necessary to suppose any
other evidence of those truths than experimental evidence, any other
origin for our belief of them than an experimental origin. We decided,
that the burden of proof lies with those who maintain the affirmative, and
we examined, at considerable length, such arguments as they have produced.
The examination having led to the rejection of those arguments, we have
thought ourselves warranted in concluding that axioms are but a class, the
highest class, of inductions from experience; the simplest and easiest
cases of generalization from the facts furnished to us by our senses or by
our internal consciousness.
While the axioms of demonstrative sciences thus appeared to be
experimental truths, the definitions, as they are incorrectly called, in
those sciences, were found by us to be generalizations from experience
which are not even, accurately speaking, truths; being propositions in
which, while we assert of some kind of object, some property or properties
which observation shows to belong to it, we at the same time deny that it
possesses any other properties, although in truth other properties do in
every individual instance accompany, and in almost all instances modify,
the property thus exclusively predicated. The denial, therefore, is a mere
fiction, or supposition, made for the purpose of excluding the
consideration of those modifying circumstances, when their influence is of
too trifling amount to be worth considering, or adjourning it, when
important, to a more convenient moment.
From these considerations it would appear that Deductive or Demonstrative
Sciences are all, without exception, Inductive Sciences; that their
evidence is that of experience; but that they are also, in virtue of the
peculiar character of one indispensable portion of the general formulas
according to which their inductions are made, Hypothetical Sciences. Their
conclusions are only true on certain suppositions, which are, or ought to
be, approximations to the truth, but are seldom, if ever, exactly true;
and to this hypothetical character is to be ascribed the peculiar
certainty, which is supposed to be inherent in demonstration.
What we have now asserted, however, cannot be received as universally true
of Deductive or Demonstrative Sciences, until verified by being applied to
the most remarkable of all those sciences, that of Numbers; the theory of
the Calculus; Arithmetic and Algebra. It is harder to believe of the
doctrines of this science than of any other, either that they are not
truths _à priori_, but experimental truths, or that their peculiar
certainty is owing to their being not absolute but only conditional
truths. This, therefore, is a case which merits examination apart; and the
more so, because on this subject we have a double set of doctrines to
contend with; that of the _à priori_ philosophers on one side; and on the
other, a theory the most opposite to theirs, which was at one time very
generally received, and is still far from being altogether exploded among
metaphysicians.
§ 2. This theory attempts to solve the difficulty apparently inherent in
the case, by representing the propositions of the science of numbers as
merely verbal, and its processes as simple transformations of language,
substitutions of one expression for another. The proposition, Two and one
are equal to three, according to these writers, is not a truth, is not the
assertion of a really existing fact, but a definition of the word three; a
statement that mankind have agreed to use the name three as a sign exactly
equivalent to two and one; to call by the former name whatever is called
by the other more clumsy phrase. According to this doctrine, the longest
process in algebra is but a succession of changes in terminology, by which
equivalent expressions are substituted one for another; a series of
translations of the same fact, from one into another language; though how,
after such a series of translations, the fact itself comes out changed,
(as when we demonstrate a new geometrical theorem by algebra,) they have
not explained; and it is a difficulty which is fatal to their theory.
It must be acknowledged that there are peculiarities in the processes of
arithmetic and algebra which render the theory in question very plausible,
and have not unnaturally made those sciences the stronghold of Nominalism.
The doctrine that we can discover facts, detect the hidden processes of
nature, by an artful manipulation of language, is so contrary to common
sense, that a person must have made some advances in philosophy to believe
it; men fly to so paradoxical a belief to avoid, as they think, some even
greater difficulty, which the vulgar do not see. What has led many to
believe that reasoning is a mere verbal process, is, that no other theory
seemed reconcileable with the nature of the Science of Numbers. For we do
not carry any ideas along with us when we use the symbols of arithmetic or
of algebra. In a geometrical demonstration we have a mental diagram, if
not one on paper; AB, AC, are present to our imagination as lines,
intersecting other lines, forming an angle with one another, and the like;
but not so _a_ and _b_. These may represent lines or any other magnitudes,
but those magnitudes are never thought of; nothing is realized in our
imagination but _a_ and _b_. The ideas which, on the particular occasion,
they happen to represent, are banished from the mind during every
intermediate part of the process, between the beginning, when the
premisses are translated from things into signs, and the end, when the
conclusion is translated back from signs into things. Nothing, then, being
in the reasoner’s mind but the symbols, what can seem more inadmissible
than to contend that the reasoning process has to do with anything more?
We seem to have come to one of Bacon’s Prerogative Instances; an
_experimentum crucis_ on the nature of reasoning itself.
Nevertheless, it will appear on consideration, that this apparently so
decisive instance is no instance at all; that there is in every step of an
arithmetical or algebraical calculation a real induction, a real inference
of facts from facts; and that what disguises the induction is simply its
comprehensive nature, and the consequent extreme generality of the
language. All numbers must be numbers of something: there are no such
things as numbers in the abstract. _Ten_ must mean ten bodies, or ten
sounds, or ten beatings of the pulse. But though numbers must be numbers
of something, they may be numbers of anything. Propositions, therefore,
concerning numbers, have the remarkable peculiarity that they are
propositions concerning all things whatever; all objects, all existences
of every kind, known to our experience. All things possess quantity;
consist of parts which can be numbered; and in that character possess all
the properties which are called properties of numbers. That half of four
is two, must be true whatever the word four represents, whether four men,
four miles, or four pounds weight. We need only conceive a thing divided
into four equal parts, (and all things may be conceived as so divided,) to
be able to predicate of it every property of the number four, that is,
every arithmetical proposition in which the number four stands on one side
of the equation. Algebra extends the generalization still farther: every
number represents that particular number of all things without
distinction, but every algebraical symbol does more, it represents all
numbers without distinction. As soon as we conceive a thing divided into
equal parts, without knowing into what number of parts, we may call it _a_
or _x_, and apply to it, without danger of error, every algebraical
formula in the books. The proposition, 2(_a_ + _b_) = 2_a_ + 2_b_, is a
truth coextensive with all nature. Since then algebraical truths are true
of all things whatever, and not, like those of geometry, true of lines
only or angles only, it is no wonder that the symbols should not excite in
our minds ideas of any things in particular. When we demonstrate the
forty-seventh proposition of Euclid, it is not necessary that the words
should raise in us an image of all right-angled triangles, but only of
some one right-angled triangle: so in algebra we need not, under the
symbol _a_, picture to ourselves all things whatever, but only some one
thing; why not, then, the letter itself? The mere written characters, _a_,
_b_, _x_, _y_, _z_, serve as well for representatives of Things in
general, as any more complex and apparently more concrete conception. That
we are conscious of them however in their character of things, and not of
mere signs, is evident from the fact that our whole process of reasoning
is carried on by predicating of them the properties of things. In
resolving an algebraic equation, by what rules do we proceed? By applying
at each step to _a_, _b_, and _x_ the proposition that equals added to
equals make equals; that equals taken from equals leave equals; and other
propositions founded on these two. These are not properties of language,
or of signs as such, but of magnitudes, which is as much as to say, of all
things. The inferences, therefore, which are successively drawn, are
inferences concerning things, not symbols; although as any Things whatever
will serve the turn, there is no necessity for keeping the idea of the
Thing at all distinct, and consequently the process of thought may, in
this case, be allowed without danger to do what all processes of thought,
when they have been performed often, will do if permitted, namely, to
become entirely mechanical. Hence the general language of algebra comes to
be used familiarly without exciting ideas, as all other general language
is prone to do from mere habit, though in no other case than this can it
be done with complete safety. But when we look back to see from whence the
probative force of the process is derived, we find that at every single
step, unless we suppose ourselves to be thinking and talking of the
things, and not the mere symbols, the evidence fails.
There is another circumstance, which, still more than that which we have
now mentioned, gives plausibility to the notion that the propositions of
arithmetic and algebra are merely verbal. This is, that when considered as
propositions respecting Things, they all have the appearance of being
identical propositions. The assertion, Two and one are equal to three,
considered as an assertion respecting objects, as for instance “Two
pebbles and one pebble are equal to three pebbles,” does not affirm
equality between two collections of pebbles, but absolute identity. It
affirms that if we put one pebble to two pebbles, those very pebbles are
three. The objects, therefore, being the very same, and the mere assertion
that “objects are themselves” being insignificant, it seems but natural to
consider the proposition, Two and one are equal to three, as asserting
mere identity of signification between the two names.
This, however, though it looks so plausible, will not bear examination.
The expression “two pebbles and one pebble,” and the expression, “three
pebbles,” stand indeed for the same aggregation of objects, but they by no
means stand for the same physical fact. They are names of the same
objects, but of those objects in two different states: though they
_de_note the same things, their _con_notation is different. Three pebbles
in two separate parcels, and three pebbles in one parcel, do not make the
same impression on our senses; and the assertion that the very same
pebbles may by an alteration of place and arrangement be made to produce
either the one set of sensations or the other, though a very familiar
proposition, is not an identical one. It is a truth known to us by early
and constant experience: an inductive truth; and such truths are the
foundation of the science of Number. The fundamental truths of that
science all rest on the evidence of sense; they are proved by showing to
our eyes and our fingers that any given number of objects, ten balls for
example, may by separation and re-arrangement exhibit to our senses all
the different sets of numbers the sum of which is equal to ten. All the
improved methods of teaching arithmetic to children proceed on a knowledge
of this fact. All who wish to carry the child’s _mind_ along with them in
learning arithmetic; all who wish to teach numbers, and not mere
ciphers—now teach it through the evidence of the senses, in the manner we
have described.
We may, if we please, call the proposition “Three is two and one,” a
definition of the number three, and assert that arithmetic, as it has been
asserted that geometry, is a science founded on definitions. But they are
definitions in the geometrical sense, not the logical; asserting not the
meaning of a term only, but along with it an observed matter of fact. The
proposition, “A circle is a figure bounded by a line which has all its
points equally distant from a point within it,” is called the definition
of a circle; but the proposition from which so many consequences follow,
and which is really a first principle in geometry, is, that figures
answering to this description exist. And thus we may call, “Three is two
and one,” a definition of three; but the calculations which depend on that
proposition do not follow from the definition itself, but from an
arithmetical theorem presupposed in it, namely, that collections of
objects exist, which while they impress the senses thus, [Symbol: three
circles, two above one], may be separated into two parts, thus, [Symbol:
two circles, a space, and a third circle]. This proposition being granted,
we term all such parcels Threes, after which the enunciation of the
above-mentioned physical fact will serve also for a definition of the word
Three.
The Science of Number is thus no exception to the conclusion we previously
arrived at, that the processes even of deductive sciences are altogether
inductive, and that their first principles are generalizations from
experience. It remains to be examined whether this science resembles
geometry in the further circumstance, that some of its inductions are not
exactly true; and that the peculiar certainty ascribed to it, on account
of which its propositions are called Necessary Truths, is fictitious and
hypothetical, being true in no other sense than that those propositions
necessarily follow from the hypothesis of the truth of premisses which are
avowedly mere approximations to truth.
§ 3. The inductions of arithmetic are of two sorts: first, those which we
have just expounded, such as One and one are two, Two and one are three,
&c., which may be called the definitions of the various numbers, in the
improper or geometrical sense of the word Definition; and secondly, the
two following axioms: The sums of equals are equal, The differences of
equals are equal. These two are sufficient; for the corresponding
propositions respecting unequals may be proved from these, by a _reductio
ad absurdum_.
These axioms, and likewise the so-called definitions, are, as already
shown, results of induction; true of all objects whatever, and, as it may
seem, exactly true, without the hypothetical assumption of unqualified
truth where an approximation to it is all that exists. The conclusions,
therefore, it will naturally be inferred, are exactly true, and the
science of number is an exception to other demonstrative sciences in this,
that the absolute certainty which is predicable of its demonstrations is
independent of all hypothesis.
On more accurate investigation, however, it will be found that, even in
this case, there is one hypothetical element in the ratiocination. In all
propositions concerning numbers, a condition is implied, without which
none of them would be true; and that condition is an assumption which may
be false. The condition is, that 1 = 1; that all the numbers are numbers
of the same or of equal units. Let this be doubtful, and not one of the
propositions of arithmetic will hold true. How can we know that one pound
and one pound make two pounds, if one of the pounds may be troy, and the
other avoirdupois? They may not make two pounds of either, or of any
weight. How can we know that a forty-horse power is always equal to
itself, unless we assume that all horses are of equal strength? It is
certain that 1 is always equal in _number_ to 1; and where the mere number
of objects, or of the parts of an object, without supposing them to be
equivalent in any other respect, is all that is material, the conclusions
of arithmetic, so far as they go to that alone, are true without mixture
of hypothesis. There are a few such cases; as, for instance, an inquiry
into the amount of the population of any country. It is indifferent to
that inquiry whether they are grown people or children, strong or weak,
tall or short; the only thing we want to ascertain is their number. But
whenever, from equality or inequality of number, equality or inequality in
any other respect is to be inferred, arithmetic carried into such
inquiries becomes as hypothetical a science as geometry. All units must be
assumed to be equal in that other respect; and this is never practically
true, for one actual pound weight is not exactly equal to another, nor one
mile’s length to another; a nicer balance, or more accurate measuring
instruments, would always detect some difference.
What is commonly called mathematical certainty, therefore, which comprises
the twofold conception of unconditional truth and perfect accuracy, is not
an attribute of all mathematical truths, but of those only which relate to
pure Number, as distinguished from Quantity in the more enlarged sense;
and only so long as we abstain from supposing that the numbers are a
precise index to actual quantities. The certainty usually ascribed to the
conclusions of geometry, and even to those of mechanics, is nothing
whatever but certainty of inference. We can have full assurance of
particular results under particular suppositions, but we cannot have the
same assurance that these suppositions are accurately true, nor that they
include all the data which may exercise an influence over the result in
any given instance.
§ 4. It appears, therefore, that the method of all Deductive Sciences is
hypothetical. They proceed by tracing the consequences of certain
assumptions; leaving for separate consideration whether the assumptions
are true or not, and if not exactly true, whether they are a sufficiently
near approximation to the truth. The reason is obvious. Since it is only
in questions of pure number that the assumptions are exactly true, and
even there, only so long as no conclusions except purely numerical ones
are to be founded on them; it must, in all other cases of deductive
investigation, form a part of the inquiry, to determine how much the
assumptions want of being exactly true in the case in hand. This is
generally a matter of observation, to be repeated in every fresh case; or
if it has to be settled by argument instead of observation, may require in
every different case different evidence, and present every degree of
difficulty from the lowest to the highest. But the other part of the
process—namely, to determine what else may be concluded if we find, and in
proportion as we find, the assumptions to be true—may be performed once
for all, and the results held ready to be employed as the occasions turn
up for use. We thus do all beforehand that can be so done, and leave the
least possible work to be performed when cases arise and press for a
decision. This inquiry into the inferences which can be drawn from
assumptions, is what properly constitutes Demonstrative Science.
It is of course quite as practicable to arrive at new conclusions from
facts assumed, as from facts observed; from fictitious, as from real,
inductions. Deduction, as we have seen, consists of a series of inferences
in this form—_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_
is a mark of _d_, which last may be a truth inaccessible to direct
observation. In like manner it is allowable to say, _Suppose_ that _a_
were a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a mark of
_d_, which last conclusion was not thought of by those who laid down the
premisses. A system of propositions as complicated as geometry might be
deduced from assumptions which are false; as was done by Ptolemy,
Descartes, and others, in their attempts to explain synthetically the
phenomena of the solar system on the supposition that the apparent motions
of the heavenly bodies were the real motions, or were produced in some way
more or less different from the true one. Sometimes the same thing is
knowingly done, for the purpose of showing the falsity of the assumption;
which is called a _reductio ad absurdum_. In such cases, the reasoning is
as follows: _a_ is a mark of _b_, and _b_ of _c_; now if _c_ were also a
mark of _d_, _a_ would be a mark of _d_; but _d_ is known to be a mark of
the absence of _a_; consequently _a_ would be a mark of its own absence,
which is a contradiction; therefore _c_ is not a mark of _d_.
§ 5. It has even been held by some writers, that all ratiocination rests
in the last resort on a _reductio ad absurdum_; since the way to enforce
assent to it, in case of obscurity, would be to show that if the
conclusion be denied we must deny some one at least of the premisses,
which, as they are all supposed true, would be a contradiction. And in
accordance with this, many have thought that the peculiar nature of the
evidence of ratiocination consisted in the impossibility of admitting the
premisses and rejecting the conclusion without a contradiction in terms.
This theory, however is inadmissible as an explanation of the grounds on
which ratiocination itself rests. If any one denies the conclusion
notwithstanding his admission of the premisses, he is not involved in any
direct and express contradiction until he is compelled to deny some
premiss; and he can only be forced to do this by a _reductio ad absurdum_,
that is, by another ratiocination: now, if he denies the validity of the
reasoning process itself, he can no more be forced to assent to the second
syllogism than to the first. In truth, therefore, no one is ever forced to
a contradiction in terms: he can only be forced to a contradiction (or
rather an infringement) of the fundamental maxim of ratiocination, namely,
that whatever has a mark, has what it is a mark of; or, (in the case of
universal propositions,) that whatever is a mark of anything, is a mark of
whatever else that thing is a mark of. For in the case of every correct
argument, as soon as thrown into the syllogistic form, it is evident
without the aid of any other syllogism, that he who, admitting the
premisses, fails to draw the conclusion, does not conform to the above
axiom.
Without attaching exaggerated importance to the distinction now drawn, I
think it enables us to characterize in a more accurate manner than is
usually done, the nature of demonstrative evidence and of logical
necessity. That is necessary, from which to withhold assent would be to
violate the above axiom. And since the axiom can only be violated by
assenting to premisses and rejecting a legitimate conclusion from them,
nothing is necessary, except the connexion between a conclusion and
premisses; of which doctrine, the whole of this and the preceding chapter
are submitted as the proof.
We have now proceeded as far in the theory of Deduction as we can advance
in the present stage of our inquiry. Any further insight into the subject
requires that the foundation shall have been laid of the philosophic
theory of Induction itself; in which theory that of deduction, as a mode
of induction, which we have now shown it to be, will assume spontaneously
the place which belongs to it, and will receive its share of whatever
light may be thrown upon the great intellectual operation of which it
forms so important a part.
We here, therefore, close the Second Book. The theory of Induction, in the
most comprehensive sense of the term, will form the subject of the Third.
BOOK III. OF INDUCTION.
“According to the doctrine now stated, the highest, or rather the
only proper object of physics, is to ascertain those established
conjunctions of successive events, which constitute the order of
the universe; to record the phenomena which it exhibits to our
observations, or which it discloses to our experiments; and to
refer these phenomena to their general laws.”—D. STEWART,
_Elements of the Philosophy of the Human Mind_, vol. ii. chap. iv.
sect. 1.
CHAPTER I. PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.
§ 1. The portion of the present inquiry upon which we are now about to
enter, may be considered as the principal, both from its surpassing in
intricacy all the other branches, and because it relates to a process
which has been shown in the preceding Book to be that in which the
investigation of nature essentially consists. We have found that all
Inference, consequently all Proof, and all discovery of truths not
self-evident, consists of inductions, and the interpretation of
inductions: that all our knowledge, not intuitive, comes to us exclusively
from that source. What Induction is, therefore, and what conditions render
it legitimate, cannot but be deemed the main question of the science of
logic—the question which includes all others. It is, however, one which
professed writers on logic have almost entirely passed over. The
generalities of the subject have not been altogether neglected by
metaphysicians; but, for want of sufficient acquaintance with the
processes by which science has actually succeeded in establishing general
truths, their analysis of the inductive operation, even when
unexceptionable as to correctness, has not been specific enough to be made
the foundation of practical rules, which might be for induction itself
what the rules of the syllogism are for the interpretation of induction:
while those by whom physical science has been carried to its present state
of improvement—and who, to arrive at a complete theory of the process,
needed only to generalize, and adapt to all varieties of problems, the
methods which they themselves employed in their habitual pursuits—never
until very lately made any serious attempt to philosophize on the subject,
nor regarded the mode in which they arrived at their conclusions as
deserving of study, independently of the conclusions themselves.
§ 2. For the purposes of the present inquiry, Induction may be defined,
the operation of discovering and proving general propositions. It is true
that (as already shown) the process of indirectly ascertaining individual
facts, is as truly inductive as that by which we establish general truths.
But it is not a different kind of induction; it is another form of the
very same process: since, on the one hand, generals are but collections of
particulars, definite in kind but indefinite in number; and on the other
hand, whenever the evidence which we derive from observation of known
cases justifies us in drawing an inference respecting even one unknown
case, we should on the same evidence be justified in drawing a similar
inference with respect to a whole class of cases. The inference either
does not hold at all, or it holds in all cases of a certain description;
in all cases which, in certain definable respects, resemble those we have
observed.
If these remarks are just; if the principles and rules of inference are
the same whether we infer general propositions or individual facts; it
follows that a complete logic of the sciences would be also a complete
logic of practical business and common life. Since there is no case of
legitimate inference from experience, in which the conclusion may not
legitimately be a general proposition; an analysis of the process by which
general truths are arrived at, is virtually an analysis of all induction
whatever. Whether we are inquiring into a scientific principle or into an
individual fact, and whether we proceed by experiment or by ratiocination,
every step in the train of inferences is essentially inductive, and the
legitimacy of the induction depends in both cases on the same conditions.
True it is that in the case of the practical inquirer, who is endeavouring
to ascertain facts not for the purposes of science but for those of
business, such for instance as the advocate or the judge, the chief
difficulty is one in which the principles of induction will afford him no
assistance. It lies not in _making_ his inductions but in the _selection_
of them; in choosing from among all general propositions ascertained to be
true, those which furnish marks by which he may trace whether the given
subject possesses or not the predicate in question. In arguing a doubtful
question of fact before a jury, the general propositions or principles to
which the advocate appeals are mostly, in themselves, sufficiently trite,
and assented to as soon as stated: his skill lies in bringing his case
under those propositions or principles; in calling to mind such of the
known or received maxims of probability as admit of application to the
case in hand, and selecting from among them those best adapted to his
object. Success is here dependent on natural or acquired sagacity, aided
by knowledge of the particular subject, and of subjects allied with it.
Invention, though it can be cultivated, cannot be reduced to rule; there
is no science which will enable a man to bethink himself of that which
will suit his purpose.
But when he _has_ thought of something, science can tell him whether that
which he has thought of will suit his purpose or not. The inquirer or
arguer must be guided by his own knowledge and sagacity in the choice of
the inductions out of which he will construct his argument. But the
validity of the argument when constructed, depends on principles and must
be tried by tests which are the same for all descriptions of inquiries,
whether the result be to give A an estate, or to enrich science with a new
general truth. In the one case and in the other, the senses, or testimony,
must decide on the individual facts; the rules of the syllogism will
determine whether, those facts being supposed correct, the case really
falls within the formulæ of the different inductions under which it has
been successively brought; and finally, the legitimacy of the inductions
themselves must be decided by other rules, and these it is now our purpose
to investigate. If this third part of the operation be, in many of the
questions of practical life, not the most, but the least arduous portion
of it, we have seen that this is also the case in some great departments
of the field of science; in all those which are principally deductive, and
most of all in mathematics; where the inductions themselves are few in
number, and so obvious and elementary that they seem to stand in no need
of the evidence of experience, while to combine them so as to prove a
given theorem or solve a problem, may call for the utmost powers of
invention and contrivance with which our species is gifted.
If the identity of the logical processes which prove particular facts and
those which establish general scientific truths, required any additional
confirmation, it would be sufficient to consider that in many branches of
science, single facts have to be proved, as well as principles; facts as
completely individual as any that are debated in a court of justice; but
which are proved in the same manner as the other truths of the science,
and without disturbing in any degree the homogeneity of its method. A
remarkable example of this is afforded by astronomy. The individual facts
on which that science grounds its most important deductions, such facts as
the magnitudes of the bodies of the solar system, their distances from one
another, the figure of the earth, and its rotation, are scarcely any of
them accessible to our means of direct observation: they are proved
indirectly, by the aid of inductions founded on other facts which we can
more easily reach. For example, the distance of the moon from the earth
was determined by a very circuitous process. The share which direct
observation had in the work consisted in ascertaining, at one and the same
instant, the zenith distances of the moon, as seen from two points very
remote from one another on the earth’s surface. The ascertainment of these
angular distances ascertained their supplements; and since the angle at
the earth’s centre subtended by the distance between the two places of
observation was deducible by spherical trigonometry from the latitude and
longitude of those places, the angle at the moon subtended by the same
line became the fourth angle of a quadrilateral of which the other three
angles were known. The four angles being thus ascertained, and two sides
of the quadrilateral being radii of the earth; the two remaining sides and
the diagonal, or in other words, the moon’s distance from the two places
of observation and from the centre of the earth, could be ascertained, at
least in terms of the earth’s radius, from elementary theorems of
geometry. At each step in this demonstration we take in a new induction,
represented, in the aggregate of its results, by a general proposition.
Not only is the process by which an individual astronomical fact was thus
ascertained, exactly similar to those by which the same science
establishes its general truths, but also (as we have shown to be the case
in all legitimate reasoning) a general proposition might have been
concluded instead of a single fact. In strictness, indeed, the result of
the reasoning _is_ a general proposition; a theorem respecting the
distance, not of the moon in particular, but of any inaccessible object;
showing in what relation that distance stands to certain other quantities.
And although the moon is almost the only heavenly body the distance of
which from the earth can really be thus ascertained, this is merely owing
to the accidental circumstances of the other heavenly bodies, which render
them incapable of affording such data as the application of the theorem
requires; for the theorem itself is as true of them as it is of the
moon.(53)
We shall fall into no error, then, if in treating of Induction, we limit
our attention to the establishment of general propositions. The principles
and rules of Induction, as directed to this end, are the principles and
rules of all Induction; and the logic of Science is the universal Logic,
applicable to all inquiries in which man can engage.