Chapter XXV.

Of The Grounds Of Disbelief.

§ 1. The method of arriving at general truths, or general propositions fit

to be believed, and the nature of the evidence on which they are grounded,

have been discussed, as far as space and the writer’s faculties permitted,

in the twenty-four preceding chapters. But the result of the examination

of evidence is not always belief, nor even suspension of judgment; it is

sometimes disbelief. The philosophy, therefore, of induction and

experimental inquiry is incomplete, unless the grounds not only of belief,

but of disbelief, are treated of; and to this topic we shall devote one,

and the final, chapter.

By disbelief is not here to be understood the mere absence of belief. The

ground for abstaining from belief is simply the absence or insufficiency

of proof; and in considering what is sufficient evidence to support any

given conclusion, we have already, by implication, considered what

evidence is not sufficient for the same purpose. By disbelief is here

meant, not the state of mind in which we form no opinion concerning a

subject, but that in which we are fully persuaded that some opinion is not

true; insomuch that if evidence, even of great apparent strength (whether

grounded on the testimony of others or on our own supposed perceptions),

were produced in favor of the opinion, we should believe that the

witnesses spoke falsely, or that they, or we ourselves if we were the

direct percipients, were mistaken.

That there are such cases, no one is likely to dispute. Assertions for

which there is abundant positive evidence are often disbelieved, on

account of what is called their improbability, or impossibility. And the

question for consideration is what, in the present case, these words mean,

and how far and in what circumstances the properties which they express

are sufficient grounds for disbelief.

§ 2. It is to be remarked, in the first place, that the positive evidence

produced in support of an assertion which is nevertheless rejected on the

score of impossibility or improbability, is never such as amounts to full

proof. It is always grounded on some approximate generalization. The fact

may have been asserted by a hundred witnesses; but there are many

exceptions to the universality of the generalization that what a hundred

witnesses affirm is true. We may seem to ourselves to have actually seen

the fact; but that we really see what we think we see, is by no means a

universal truth; our organs may have been in a morbid state; or we may

have inferred something, and imagined that we perceived it. The evidence,

then, in the affirmative being never more than an approximate

generalization, all will depend on what the evidence in the negative is.

If that also rests on an approximate generalization, it is a case for

comparison of probabilities. If the approximate generalizations leading to

the affirmative are, when added together, less strong, or, in other words,

farther from being universal, than the approximate generalizations which

support the negative side of the question, the proposition is said to be

improbable, and is to be disbelieved provisionally. If, however, an

alleged fact be in contradiction, not to any number of approximate

generalizations, but to a completed generalization grounded on a rigorous

induction, it is said to be impossible, and is to be disbelieved totally.

This last principle, simple and evident as it appears, is the doctrine

which, on the occasion of an attempt to apply it to the question of the

credibility of miracles, excited so violent a controversy. Hume’s

celebrated doctrine, that nothing is credible which is contradictory to

experience, or at variance with laws of nature, is merely this very plain

and harmless proposition, that whatever is contradictory to a complete

induction is incredible. That such a maxim as this should either be

accounted a dangerous heresy, or mistaken for a great and recondite truth,

speaks ill for the state of philosophical speculation on such subjects.

But does not (it may be asked) the very statement of the proposition imply

a contradiction? An alleged fact, according to this theory, is not to be

believed if it contradict a complete induction. But it is essential to the

completeness of an induction that it shall not contradict any known fact.

Is it not, then, a _petitio principii_ to say, that the fact ought to be

disbelieved because the induction opposed to it is complete? How can we

have a right to declare the induction complete, while facts, supported by

credible evidence, present themselves in opposition to it?

I answer, we have that right whenever the scientific canons of induction

give it to us; that is, whenever the induction _can_ be complete. We have

it, for example, in a case of causation in which there has been an

_experimentum crucis_. If an antecedent A, superadded to a set of

antecedents in all other respects unaltered, is followed by an effect B

which did not exist before, A is, in that instance at least, the cause of

B, or an indispensable part of its cause; and if A be tried again with

many totally different sets of antecedents and B still follows, then it is

the whole cause. If these observations or experiments have been repeated

so often, and by so many persons, as to exclude all supposition of error

in the observer, a law of nature is established; and so long as this law

is received as such, the assertion that on any particular occasion A took

place, and yet B did not follow, _without any counteracting cause_, must

be disbelieved. Such an assertion is not to be credited on any less

evidence than what would suffice to overturn the law. The general truths,

that whatever has a beginning has a cause, and that when none but the same

causes exist, the same effects follow, rest on the strongest inductive

evidence possible; the proposition that things affirmed by even a crowd of

respectable witnesses are true, is but an approximate generalization;

and—even if we fancy we actually saw or felt the fact which is in

contradiction to the law—what a human being can see is no more than a set

of appearances; from which the real nature of the phenomenon is merely an

inference, and in this inference approximate generalizations usually have

a large share. If, therefore, we make our election to hold by the law, no

quantity of evidence whatever ought to persuade us that there has occurred

any thing in contradiction to it. If, indeed, the evidence produced is

such that it is more likely that the set of observations and experiments

on which the law rests should have been inaccurately performed or

incorrectly interpreted, than that the evidence in question should be

false, we may believe the evidence; but then we must abandon the law. And

since the law was received on what seemed a complete induction, it can

only be rejected on evidence equivalent; namely, as being inconsistent not

with any number of approximate generalizations, but with some other and

better established law of nature. This extreme case, of a conflict between

two supposed laws of nature, has probably never actually occurred where,

in the process of investigating both the laws, the true canons of

scientific induction had been kept in view; but if it did occur, it must

terminate in the total rejection of one of the supposed laws. It would

prove that there must be a flaw in the logical process by which either one

or the other was established; and if there be so, that supposed general

truth is no truth at all. We can not admit a proposition as a law of

nature, and yet believe a fact in real contradiction to it. We must

disbelieve the alleged fact, or believe that we were mistaken in admitting

the supposed law.

But in order that any alleged fact should be contradictory to a law of

causation, the allegation must be, not simply that the cause existed

without being followed by the effect, for that would be no uncommon

occurrence; but that this happened in the absence of any adequate

counteracting cause. Now in the case of an alleged miracle, the assertion

is the exact opposite of this. It is, that the effect was defeated, not in

the absence, but in consequence of a counteracting cause, namely, a direct

interposition of an act of the will of some being who has power over

nature; and in particular of a Being, whose will being assumed to have

endowed all the causes with the powers by which they produce their

effects, may well be supposed able to counteract them. A miracle (as was

justly remarked by Brown)(202) is no contradiction to the law of cause and

effect; it is a new effect, supposed to be produced by the introduction of

a new cause. Of the adequacy of that cause, if present, there can be no

doubt; and the only antecedent improbability which can be ascribed to the

miracle, is the improbability that any such cause existed.

All, therefore, which Hume has made out, and this he must be considered to

have made out, is, that (at least in the imperfect state of our knowledge

of natural agencies, which leaves it always possible that some of the

physical antecedents may have been hidden from us) no evidence can prove a

miracle to any one who did not previously believe the existence of a being

or beings with supernatural power; or who believes himself to have full

proof that the character of the Being whom he recognizes is inconsistent

with his having seen fit to interfere on the occasion in question.

If we do not already believe in supernatural agencies, no miracle can

prove to us their existence. The miracle itself, considered merely as an

extraordinary fact, may be satisfactorily certified by our senses or by

testimony; but nothing can ever prove that it is a miracle; there is still

another possible hypothesis, that of its being the result of some unknown

natural cause; and this possibility can not be so completely shut out, as

to leave no alternative but that of admitting the existence and

intervention of a being superior to nature. Those, however, who already

believe in such a being have two hypotheses to choose from, a supernatural

and an unknown natural agency; and they have to judge which of the two is

the most probable in the particular case. In forming this judgment, an

important element of the question will be the conformity of the result to

the laws of the supposed agent, that is, to the character of the Deity as

they conceive it. But with the knowledge which we now possess of the

general uniformity of the course of nature, religion, following in the

wake of science, has been compelled to acknowledge the government of the

universe as being on the whole carried on by general laws, and not by

special interpositions. To whoever holds this belief, there is a general

presumption against any supposition of divine agency not operating through

general laws, or, in other words, there is an antecedent improbability in

every miracle, which, in order to outweigh it, requires an extraordinary

strength of antecedent probability derived from the special circumstances

of the case.

§ 3. It appears from what has been said, that the assertion that a cause

has been defeated of an effect which is connected with it by a completely

ascertained law of causation, is to be disbelieved or not, according to

the probability or improbability that there existed in the particular

instance an adequate counteracting cause. To form an estimate of this, is

not more difficult than of other probabilities. With regard to all _known_

causes capable of counteracting the given causes, we have generally some

previous knowledge of the frequency or rarity of their occurrence, from

which we may draw an inference as to the antecedent improbability of their

having been present in any particular case. And neither in respect to

known nor unknown causes are we required to pronounce on the probability

of their existing in nature, but only of their having existed at the time

and place at which the transaction is alleged to have happened. We are

seldom, therefore, without the means (when the circumstances of the case

are at all known to us) of judging how far it is likely that such a cause

should have existed at that time and place without manifesting its

presence by some other marks, and (in the case of an unknown cause)

without having hitherto manifested its existence in any other instance.

According as this circumstance, or the falsity of the testimony, appears

more improbable—that is, conflicts with an approximate generalization of a

higher order—we believe the testimony, or disbelieve it; with a stronger

or a weaker degree of conviction, according to the preponderance; at least

until we have sifted the matter further.

So much, then, for the case in which the alleged fact conflicts, or

appears to conflict, with a real law of causation. But a more common case,

perhaps, is that of its conflicting with uniformities of mere

co-existence, not proved to be dependent on causation; in other words,

with the properties of Kinds. It is with these uniformities principally

that the marvelous stories related by travelers are apt to be at variance;

as of men with tails, or with wings, and (until confirmed by experience)

of flying fish; or of ice, in the celebrated anecdote of the Dutch

travelers and the King of Siam. Facts of this description, facts

previously unheard of, but which could not from any known law of causation

be pronounced impossible, are what Hume characterizes as not contrary to

experience, but merely unconformable to it; and Bentham, in his treatise

on Evidence, denominates them facts disconformable _in specie_, as

distinguished from such as are disconformable _in toto_ or in _degree_

In a case of this description, the fact asserted is the existence of a new

Kind; which in itself is not in the slightest degree incredible, and only

to be rejected if the improbability that any variety of object existing at

the particular place and time should not have been discovered sooner, be

greater than that of error or mendacity in the witnesses. Accordingly,

such assertions, when made by credible persons, and of unexplored places,

are not disbelieved, but at most regarded as requiring confirmation from

subsequent observers; unless the alleged properties of the supposed new

Kind are at variance with known properties of some larger kind which

includes it; or, in other words, unless, in the new Kind which is asserted

to exist, some properties are said to have been found disjoined from

others which have always been known to accompany them; as in the case of

Pliny’s men, or any other kind of animal of a structure different from

that which has always been found to co-exist with animal life. On the mode

of dealing with any such case, little needs be added to what has been said

on the same topic in the twenty-second chapter.(203) When the uniformities

of co-existence which the alleged fact would violate, are such as to raise

a strong presumption of their being the result of causation, the fact

which conflicts with them is to be disbelieved; at least provisionally,

and subject to further investigation. When the presumption amounts to a

virtual certainty, as in the case of the general structure of organized

beings, the only question requiring consideration is whether, in phenomena

so little understood, there may not be liabilities to counteraction from

causes hitherto unknown; or whether the phenomena may not be capable of

originating in some other way, which would produce a different set of

derivative uniformities. Where (as in the case of the flying fish, or the

ornithorhynchus) the generalization to which the alleged fact would be an

exception is very special and of limited range, neither of the above

suppositions can be deemed very improbable; and it is generally, in the

case of such alleged anomalies, wise to suspend our judgment, pending the

subsequent inquiries which will not fail to confirm the assertion if it be

true. But when the generalization is very comprehensive, embracing a vast

number and variety of observations, and covering a considerable province

of the domain of nature; then, for reasons which have been fully

explained, such an empirical law comes near to the certainty of an

ascertained law of causation; and any alleged exception to it can not be

admitted, unless on the evidence of some law of causation proved by a

still more complete induction.

Such uniformities in the course of nature as do not bear marks of being

the results of causation are, as we have already seen, admissible as

universal truths with a degree of credence proportioned to their

generality. Those which are true of all things whatever, or at least which

are totally independent of the varieties of Kinds, namely, the laws of

number and extension, to which we may add the law of causation itself, are

probably the only ones, an exception to which is absolutely and

permanently incredible. Accordingly, it is to assertions supposed to be

contradictory to these laws, or to some others coming near to them in

generality, that the word impossibility (at least _total_ impossibility)

seems to be generally confined. Violations of other laws, of special laws

of causation, for instance, are said, by persons studious of accuracy in

expression, to be impossible _in the circumstances of the case_; or

impossible unless some cause had existed which did not exist in the

particular case.(204) Of no assertion, not in contradiction to some of

these very general laws, will more than improbability be asserted by any

cautious person; and improbability not of the highest degree, unless the

time and place in which the fact is said to have occurred, render it

almost certain that the anomaly, if real, could not have been overlooked

by other observers. Suspension of judgment is in all other cases the

resource of the judicious inquirer; provided the testimony in favor of the

anomaly presents, when well sifted, no suspicious circumstances.

But the testimony is scarcely ever found to stand that test, in cases in

which the anomaly is not real. In the instances on record in which a great

number of witnesses, of good reputation and scientific acquirements, have

testified to the truth of something which has turned out untrue, there

have almost always been circumstances which, to a keen observer who had

taken due pains to sift the matter, would have rendered the testimony

untrustworthy. There have generally been means of accounting for the

impression on the senses or minds of the alleged percipients, by

fallacious appearances; or some epidemic delusion, propagated by the

contagious influence of popular feeling, has been concerned in the case;

or some strong interest has been implicated—religious zeal, party feeling,

vanity, or at least the passion for the marvelous, in persons strongly

susceptible of it. When none of these or similar circumstances exist to

account for the apparent strength of the testimony; and where the

assertion is not in contradiction either to those universal laws which

know no counteraction or anomaly, or to the generalizations next in

comprehensiveness to them, but would only amount, if admitted, to the

existence of an unknown cause or an anomalous Kind, in circumstances not

so thoroughly explored but that it is credible that things hitherto

unknown may still come to light; a cautious person will neither admit nor

reject the testimony, but will wait for confirmation at other times and

from other unconnected sources. Such ought to have been the conduct of the

King of Siam when the Dutch travelers affirmed to him the existence of

ice. But an ignorant person is as obstinate in his contemptuous

incredulity as he is unreasonably credulous. Any thing unlike his own

narrow experience he disbelieves, if it flatters no propensity; any

nursery tale is swallowed implicitly by him if it does.

§ 4. I shall now advert to a very serious misapprehension of the

principles of the subject, which has been committed by some of the writers

against Hume’s Essay on Miracles, and by Bishop Butler before them, in

their anxiety to destroy what appeared to them a formidable weapon of

assault against the Christian religion; and the effect of which is

entirely to confound the doctrine of the Grounds of Disbelief. The mistake

consists in overlooking the distinction between (what may be called)

improbability before the fact and improbability after it; or (since, as

Mr. Venn remarks, the distinction of past and future is not the material

circumstance) between the improbability of a mere guess being right, and

the improbability of an alleged fact being true.

Many events are altogether improbable to us, before they have happened, or

before we are informed of their happening, which are not in the least

incredible when we are informed of them, because not contrary to any, even

approximate, induction. In the cast of a perfectly fair die, the chances

are five to one against throwing ace, that is, ace will be thrown on an

average only once in six throws. But this is no reason against believing

that ace was thrown on a given occasion, if any credible witness asserts

it; since though ace is only thrown once in six times, _some_ number which

is only thrown once in six times must have been thrown if the die was

thrown at all. The improbability, then, or, in other words, the

unusualness, of any fact, is no reason for disbelieving it, if the nature

of the case renders it certain that either that or something equally

improbable, that is, equally unusual, did happen. Nor is this all; for

even if the other five sides of the die were all twos, or all threes, yet

as ace would still, on the average, come up once in every six throws, its

coming up in a given throw would be not in any way contradictory to

experience. If we disbelieved all facts which had the chances against them

beforehand, we should believe hardly any thing. We are told that A. B.

died yesterday; the moment before we were so told, the chances against his

having died on that day may have been ten thousand to one; but since he

was certain to die at some time or other, and when he died must

necessarily die on some particular day, while the preponderance of chances

is very great against every day in particular, experience affords no

ground for discrediting any testimony which may be produced to the event’s

having taken place on a given day.

Yet it has been considered by Dr. Campbell and others, as a complete

answer to Hume’s doctrine (that things are incredible which are _contrary_

to the uniform course of experience), that we do not disbelieve, merely

because the chances were against them, things in strict _conformity_ to

the uniform course of experience; that we do not disbelieve an alleged

fact merely because the combination of causes on which it depends occurs

only once in a certain number of times. It is evident that whatever is

shown by observation, or can be proved from laws of nature, to occur in a

certain proportion (however small) of the whole number of possible cases,

is not contrary to experience; though we are right in disbelieving it, if

some other supposition respecting the matter in question involves, on the

whole, a less departure from the ordinary course of events. Yet on such

grounds as this have able writers been led to the extraordinary

conclusion, that nothing supported by credible testimony ought ever to be

disbelieved.

§ 5. We have considered two species of events, commonly said to be

improbable; one kind which are in no way extraordinary, but which, having

an immense preponderance of chances against them, are improbable until

they are affirmed, but no longer; another kind which, being contrary to

some recognized law of nature, are incredible on any amount of testimony

except such as would be sufficient to shake our belief in the law itself.

But between these two classes of events, there is an intermediate class,

consisting of what are commonly termed Coincidences: in other words, those

combinations of chances which present some peculiar and unexpected

regularity, assimilating them, in so far, to the results of law. As if,

for example, in a lottery of a thousand tickets, the numbers should be

drawn in the exact order of what are called the natural numbers, 1, 2, 3,

etc. We have still to consider the principles of evidence applicable to

this case: whether there is any difference between coincidences and

ordinary events, in the amount of testimony or other evidence necessary to

render them credible.

It is certain that on every rational principle of expectation, a

combination of this peculiar sort may be expected quite as often as any

other given series of a thousand numbers; that with perfectly fair dice,

sixes will be thrown twice, thrice, or any number of times in succession,

quite as often in a thousand or a million throws, as any other succession

of numbers fixed upon beforehand; and that no judicious player would give

greater odds against the one series than against the other.

Notwithstanding this, there is a general disposition to regard the one as

much more improbable than the other, and as requiring much stronger

evidence to make it credible. Such is the force of this impression, that

it has led some thinkers to the conclusion, that nature has greater

difficulty in producing regular combinations than irregular ones; or in

other words, that there is some general tendency of things, some law,

which prevents regular combinations from occurring, or at least from

occurring so often as others. Among these thinkers may be numbered

D’Alembert; who, in an Essay on Probabilities to be found in the fifth

volume of his _Mélanges_, contends that regular combinations, though

equally probable according to the mathematical theory with any others, are

physically less probable. He appeals to common sense, or, in other words,

to common impressions; saying, if dice thrown repeatedly in our presence

gave sixes every time, should we not, before the number of throws had

reached ten (not to speak of thousands of millions), be ready to affirm,

with the most positive conviction, that the dice were false?

The common and natural impression is in favor of D’Alembert: the regular

series would be thought much more unlikely than an irregular. But this

common impression is, I apprehend, merely grounded on the fact, that

scarcely any body remembers to have ever seen one of these peculiar

coincidences: the reason of which is simply that no one’s experience

extends to any thing like the number of trials, within which that or any

other given combination of events can be expected to happen. The chance of

sixes on a single throw of two dice being ¹⁄₃₆, the chance of sixes ten

times in succession is 1 divided by the tenth power of 36; in other words,

such a concurrence is only likely to happen once in 3,656,158,440,062,976

trials, a number which no dice-player’s experience comes up to a millionth

part of. But if, instead of sixes ten times, any other given succession of

ten throws had been fixed upon, it would have been exactly as unlikely

that in any individual’s experience that particular succession had ever

occurred; although this does not _seem_ equally improbable, because no one

would be likely to have remembered whether it had occurred or not, and

because the comparison is tacitly made, not between sixes ten times and

any one particular series of throws, but between all regular and all

irregular successions taken together.

That (as D’Alembert says) if the succession of sixes was actually thrown

before our eyes, we should ascribe it not to chance, but to unfairness in

the dice, is unquestionably true. But this arises from a totally different

principle. We should then be considering, not the probability of the fact

in itself, but the comparative probability with which, when it is known to

have happened, it may be referred to one or to another cause. The regular

series is not at all less likely than the irregular one to be brought

about by chance, but it is much more likely than the irregular one to be

produced by design; or by some general cause operating through the

structure of the dice. It is the nature of casual combinations to produce

a repetition of the same event, as often and no oftener than any other

series of events. But it is the nature of general causes to reproduce, in

the same circumstances, always the same event. Common sense and science

alike dictate that, all other things being the same, we should rather

attribute the effect to a cause which if real would be very likely to

produce it, than to a cause which would be very unlikely to produce it.

According to Laplace’s sixth theorem, which we demonstrated in a former

chapter, the difference of probability arising from the superior

_efficacy_ of the constant cause, unfairness in the dice, would after a

very few throws far outweigh any antecedent probability which there could

be against its existence.

D’Alembert should have put the question in another manner. He should have

supposed that we had ourselves previously tried the dice, and knew by

ample experience that they were fair. Another person then tries them in

our absence, and assures us that he threw sixes ten times in succession.

Is the assertion credible or not? Here the effect to be accounted for is

not the occurrence itself, but the fact of the witness’s asserting it.

This may arise either from its having really happened, or from some other

cause. What we have to estimate is the comparative probability of these

two suppositions.

If the witness affirmed that he had thrown any other series of numbers,

supposing him to be a person of veracity, and tolerable accuracy, and to

profess that he took particular notice, we should believe him. But the ten

sixes are exactly as likely to have been really thrown as the other

series. If, therefore, this assertion is less credible than the other, the

reason must be, not that it is less likely than the other to be made

truly, but that it is more likely than the other to be made falsely.

One reason obviously presents itself why what is called a coincidence,

should be oftener asserted falsely than an ordinary combination. It

excites wonder. It gratifies the love of the marvelous. The motives,

therefore, to falsehood, one of the most frequent of which is the desire

to astonish, operate more strongly in favor of this kind of assertion than

of the other kind. Thus far there is evidently more reason for

discrediting an alleged coincidence, than a statement in itself not more

probable, but which if made would not be thought remarkable. There are

cases, however, in which the presumption on this ground would be the other

way. There are some witnesses who, the more extraordinary an occurrence

might appear, would be the more anxious to verify it by the utmost

carefulness of observation before they would venture to believe it, and

still more before they would assert it to others.

§ 6. Independently, however, of any peculiar chances of mendacity arising

from the nature of the assertion, Laplace contends, that merely on the

general ground of the fallibility of testimony, a coincidence is not

credible on the same amount of testimony on which we should be warranted

in believing an ordinary combination of events. In order to do justice to

his argument, it is necessary to illustrate it by the example chosen by

himself.

If, says Laplace, there were one thousand tickets in a box, and one only

has been drawn out, then if an eye-witness affirms that the number drawn

was 79, this, though the chances were 999 in 1000 against it, is not on

that account the less credible; its credibility is equal to the antecedent

probability of the witness’s veracity. But if there were in the box 999

black balls and only one white, and the witness affirms that the white

ball was drawn, the case according to Laplace is very different: the

credibility of his assertion is but a small fraction of what it was in the

former case; the reason of the difference being as follows:

The witnesses of whom we are speaking must, from the nature of the case,

be of a kind whose credibility falls materially short of certainty; let us

suppose, then, the credibility of the witness in the case in question to

be ⁹⁄₁₀; that is, let us suppose that in every ten statements which the

witness makes, nine on an average are correct, and one incorrect. Let us

now suppose that there have taken place a sufficient number of drawings to

exhaust all the possible combinations, the witness deposing in every one.

In one case out of every ten in all these drawings he will actually have

made a false announcement. But in the case of the thousand tickets these

false announcements will have been distributed impartially over all the

numbers, and of the 999 cases in which No. 79 was not drawn, there will

have been only one case in which it was announced. On the contrary, in the

case of the thousand balls (the announcement being always either “black”

or “white”), if white was not drawn, and there was a false announcement,

that false announcement _must_ have been white; and since by the

supposition there was a false announcement once in every ten times, white

will have been announced falsely in one-tenth part of all the cases in

which it was not drawn, that is, in one-tenth part of 999 cases out of

every thousand. White, then, is drawn, on an average, exactly as often as

No. 79, but it is announced, without having been really drawn, 999 times

as often as No. 79; the announcement, therefore, requires a much greater

amount of testimony to render it credible.(205)

To make this argument valid it must of course be supposed, that the

announcements made by the witness are average specimens of his general

veracity and accuracy; or, at least, that they are neither more nor less

so in the case of the black and white balls, than in the case of the

thousand tickets. This assumption, however, is not warranted. A person is

far less likely to mistake, who has only one form of error to guard

against, than if he had 999 different errors to avoid. For instance, in

the example chosen, a messenger who might make a mistake once in ten times

in reporting the number drawn in a lottery, might not err once in a

thousand times if sent simply to observe whether a ball was black or

white. Laplace’s argument, therefore, is faulty even as applied to his own

case. Still less can that case be received as completely representing all

cases of coincidence. Laplace has so contrived his example, that though

black answers to 999 distinct possibilities, and white only to one, the

witness has nevertheless no bias which can make him prefer black to white.

The witness did not know that there were 999 black balls in the box and

only one white; or if he did, Laplace has taken care to make all the 999

cases so undistinguishably alike, that there is hardly a possibility of

any cause of falsehood or error operating in favor of any of them, which

would not operate in the same manner if there were only one. Alter this

supposition, and the whole argument falls to the ground. Let the balls,

for instance, be numbered, and let the white ball be No. 79. Considered in

respect of their color, there are but two things which the witness can be

interested in asserting, or can have dreamed or hallucinated, or has to

choose from if he answers at random, viz., black and white; but considered

in respect of the numbers attached to them, there are a thousand; and if

his interest or error happens to be connected with the numbers, though the

only assertion he makes is about the color, the case becomes precisely

assimilated to that of the thousand tickets. Or instead of the balls

suppose a lottery, with 1000 tickets and but one prize, and that I hold

No. 79, and being interested only in that, ask the witness not what was

the number drawn, but whether it was 79 or some other. There are now only

two cases, as in Laplace’s example; yet he surely would not say that if

the witness answered 79, the assertion would be in an enormous proportion

less credible, than if he made the same answer to the same question asked

in the other way. If, for instance (to put a case supposed by Laplace

himself), he has staked a large sum on one of the chances, and thinks that

by announcing its occurrence he shall increase his credit; he is equally

likely to have betted on any one of the 999 numbers which are attached to

black balls, and so far as the chances of mendacity from this cause are

concerned, there will be 999 times as many chances of his announcing black

falsely as white.

Or suppose a regiment of 1000 men, 999 Englishmen and one Frenchman, and

that of these one man has been killed, and it is not known which. I ask

the question, and the witness answers, the Frenchman. This was not only as

improbable _a priori_, but is in itself as singular a circumstance, as

remarkable a coincidence, as the drawing of the white ball; yet we should

believe the statement as readily, as if the answer had been John Thompson.

Because, though the 999 Englishmen were all alike in the point in which

they differed from the Frenchman, they were not, like the 999 black balls,

undistinguishable in every other respect; but being all different, they

admitted as many chances of interest or error, as if each man had been of

a different nation; and if a lie was told or a mistake made, the

misstatement was as likely to fall on any Jones or Thompson of the set, as

on the Frenchman.

The example of a coincidence selected by D’Alembert, that of sixes thrown

on a pair of dice ten times in succession, belongs to this sort of cases

rather than to such as Laplace’s. The coincidence is here far more

remarkable, because of far rarer occurrence, than the drawing of the white

ball. But though the improbability of its really occurring is greater, the

superior probability of its being announced falsely can not be established

with the same evidence. The announcement “black” represented 999 cases,

but the witness may not have known this, and if he did, the 999 cases are

so exactly alike, that there is really only one set of possible causes of

mendacity corresponding to the whole. The announcement “sixes _not_ drawn

ten times,” represents, and is known by the witness to represent, a great

multitude of contingencies, every one of which being unlike every other,

there may be a different and a fresh set of causes of mendacity

corresponding to each.

It appears to me, therefore, that Laplace’s doctrine is not strictly true

of any coincidences, and is wholly inapplicable to most; and that to know

whether a coincidence does or does not require more evidence to render it

credible than an ordinary event, we must refer, in every instance, to

first principles, and estimate afresh what is the probability that the

given testimony would have been delivered in that instance, supposing the

fact which it asserts not to be true.

With these remarks we close the discussion of the Grounds of Disbelief;

and along with it, such exposition as space admits, and as the writer has

it in his power to furnish, of the Logic of Induction.

Book IV.

OF OPERATIONS SUBSIDIARY TO INDUCTION.

“Clear and distinct ideas are terms which, though familiar and

frequent in men’s mouths, I have reason to think every one who

uses does not perfectly understand. And possibly it is but here

and there one who gives himself the trouble to consider them so

far as to know what he himself or others precisely mean by them; I

have, therefore, in most places, chose to put determinate or

determined, instead of clear and distinct, as more likely to

direct men’s thoughts to my meaning in this matter.”—LOCKE’S

_Essay on the Human Understanding_; Epistle to the Reader.

“Il ne peut y avoir qu’une méthode parfaite, qui est la _méthode

naturelle_; on nomme ainsi un arrangement dans lequel les êtres du

même genre seraient plus voisins entre eux que ceux de tous les

autres genres; les genres du même ordre, plus que ceux de tous les

autres ordres; et ainsi de suite. Cette méthode est l’idéal auquel

l’histoire naturelle doit tendre; car il est évident que si l’on y

parvenait, l’on aurait l’expression exacte et complète de la

nature entière.”—CUVIER, _Règne Animal_, Introduction.

“Deux grandes notions philosophiques dominent la théorie

fondamentale de la méthode naturelle proprement dite, savoir la

formation des groupes naturels, et ensuite leur succession

hiérarchique.”—COMTE, _Cours de Philosophie Positive_, 42me leçon.

Chapter I.

Of Observation And Description.

§ 1. The inquiry which occupied us in the two preceding Books, has

conducted us to what appears a satisfactory solution of the principal

problem of Logic, according to the conception I have formed of the

science. We have found, that the mental process with which Logic is

conversant, the operation of ascertaining truths by means of evidence, is

always, even when appearances point to a different theory of it, a process

of induction. And we have particularized the various modes of induction,

and obtained a clear view of the principles to which it must conform, in

order to lead to results which can be relied on.

The consideration of Induction, however, does not end with the direct

rules for its performance. Something must be said of those other

operations of the mind, which are either necessarily presupposed in all

induction, or are instrumental to the more difficult and complicated

inductive processes. The present Book will be devoted to the consideration

of these subsidiary operations; among which our attention must first be

given to those, which are indispensable preliminaries to all induction

whatsoever.

Induction being merely the extension to a class of cases, of something

which has been observed to be true in certain individual instances of the

class; the first place among the operations subsidiary to induction, is

claimed by Observation. This is not, however, the place to lay down rules

for making good observers; nor is it within the competence of Logic to do

so, but of the art of intellectual Education. Our business with

observation is only in its connection with the appropriate problem of

logic, the estimation of evidence. We have to consider, not how or what to

observe, but under what conditions observation is to be relied on; what is

needful, in order that the fact, supposed to be observed, may safely be

received as true.

§ 2. The answer to this question is very simple, at least in its first

aspect. The sole condition is, that what is supposed to have been observed

shall really have been observed; that it be an observation, not an

inference. For in almost every act of our perceiving faculties,

observation and inference are intimately blended. What we are said to

observe is usually a compound result, of which one-tenth may be

observation, and the remaining nine-tenths inference.

I affirm, for example, that I hear a man’s voice. This would pass, in

common language, for a direct perception. All, however, which is really

perception, is that I hear a sound. That the sound is a voice, and that

voice the voice of a man, are not perceptions but inferences. I affirm,

again, that I saw my brother at a certain hour this morning. If any

proposition concerning a matter of fact would commonly be said to be known

by the direct testimony of the senses, this surely would be so. The truth,

however, is far otherwise. I only saw a certain colored surface; or rather

I had the kind of visual sensations which are usually produced by a

colored surface; and from these as marks, known to be such by previous

experience, I concluded that I saw my brother. I might have had sensations

precisely similar, when my brother was not there. I might have seen some

other person so nearly resembling him in appearance, as, at the distance,

and, with the degree of attention which I bestowed, to be mistaken for

him. I might have been asleep, and have dreamed that I saw him; or in a

state of nervous disorder, which brought his image before me in a waking

hallucination. In all these modes, many have been led to believe that they

saw persons well known to them, who were dead or far distant. If any of

these suppositions had been true, the affirmation that I saw my brother

would have been erroneous; but whatever was matter of direct perception,

namely the visual sensations, would have been real. The inference only

would have been ill grounded; I should have ascribed those sensations to a

wrong cause.

Innumerable instances might be given, and analyzed in the same manner, of

what are vulgarly called errors of sense. There are none of them properly

errors of sense; they are erroneous inferences from sense. When I look at

a candle through a multiplying glass, I see what seems a dozen candles

instead of one; and if the real circumstances of the case were skillfully

disguised, I might suppose that there were really that number; there would

be what is called an optical deception. In the kaleidoscope there really

is that deception; when I look through the instrument, instead of what is

actually there, namely a casual arrangement of colored fragments, the

appearance presented is that of the same combination several times

repeated in symmetrical arrangement round a point. The delusion is of

course effected by giving me the same sensations which I should have had

if such a symmetrical combination had really been presented to me. If I

cross two of my fingers, and bring any small object, a marble for

instance, into contact with both, at points not usually touched

simultaneously by one object, I can hardly, if my eyes are shut, help

believing that there are two marbles instead of one. But it is not my

touch in this case, nor my sight in the other, which is deceived; the

deception, whether durable or only momentary, is in my judgment. From my

senses I have only the sensations, and those are genuine. Being accustomed

to have those or similar sensations when, and only when, a certain

arrangement of outward objects is present to my organs, I have the habit

of instantly, when I experience the sensations, inferring the existence of

that state of outward things. This habit has become so powerful, that the

inference, performed with the speed and certainty of an instinct, is

confounded with intuitive perceptions. When it is correct, I am

unconscious that it ever needed proof; even when I know it to be

incorrect, I can not without considerable effort abstain from making it.

In order to be aware that it is not made by instinct but by an acquired

habit, I am obliged to reflect on the slow process through which I learned

to judge by the eye of many things which I now appear to perceive directly

by sight; and on the reverse operation performed by persons learning to

draw, who with difficulty and labor divest themselves of their acquired

perceptions, and learn afresh to see things as they appear to the eye.

It would be easy to prolong these illustrations, were there any need to

expatiate on a topic so copiously exemplified in various popular works.

From the examples already given, it is seen sufficiently, that the

individual facts from which we collect our inductive generalizations are

scarcely ever obtained by observation alone. Observation extends only to

the sensations by which we recognize objects; but the propositions which

we make use of, either in science or in common life, relate mostly to the

objects themselves. In every act of what is called observation, there is

at least one inference—from the sensations to the presence of the object;

from the marks or diagnostics, to the entire phenomenon. And hence, among

other consequences, follows the seeming paradox, that a general

proposition collected from particulars is often more certainly true than

any one of the particular propositions from which, by an act of induction,

it was inferred. For, each of those particular (or rather singular)

propositions involved an inference, from the impression on the senses to

the fact which caused that impression; and this inference may have been

erroneous in any one of the instances, but can not well have been

erroneous in all of them, provided their number was sufficient to

eliminate chance. The conclusion, therefore, that is, the general

proposition, may deserve more complete reliance than it would be safe to

repose in any one of the inductive premises.

The logic of observation, then, consists solely in a correct

discrimination between that, in a result of observation, which has really

been perceived, and that which is an inference from the perception.

Whatever portion is inference, is amenable to the rules of induction

already treated of, and requires no further notice here; the question for

us in this place is, when all which is inference is taken away what

remains? There remains, in the first place, the mind’s own feelings or

states of consciousness, namely, its outward feelings or sensations, and

its inward feelings—its thoughts, emotions, and volitions. Whether any

thing else remains, or all else is inference from this; whether the mind

is capable of directly perceiving or apprehending any thing except states

of its own consciousness—is a problem of metaphysics not to be discussed

in this place. But after excluding all questions on which metaphysicians

differ, it remains true, that for most purposes the discrimination we are

called upon practically to exercise is that between sensations or other

feelings, of our own or of other people, and inferences drawn from them.

And on the theory of Observation this is all which seems necessary to be

said for the purposes of the present work.

§ 3. If, in the simplest observation, or in what passes for such, there is

a large part which is not observation but something else; so in the

simplest description of an observation, there is, and must always be, much

more asserted than is contained in the perception itself. We can not

describe a fact, without implying more than the fact. The perception is

only of one individual thing; but to describe it is to affirm a connection

between it and every other thing which is either denoted or connoted by

any of the terms used. To begin with an example, than which none can be

conceived more elementary: I have a sensation of sight, and I endeavor to

describe it by saying that I see something white. In saying this, I do not

solely affirm my sensation; I also class it. I assert a resemblance

between the thing I see, and all things which I and others are accustomed

to call white. I assert that it resembles them in the circumstance in

which they all resemble one another, in that which is the ground of their

being called by the name. This is not merely one way of describing an

observation, but the only way. If I would either register my observation

for my own future use, or make it known for the benefit of others, I must

assert a resemblance between the fact which I have observed and something

else. It is inherent in a description, to be the statement of a

resemblance, or resemblances.

We thus see that it is impossible to express in words any result of

observation, without performing an act possessing what Dr. Whewell

considers to be characteristic of Induction. There is always something

introduced which was not included in the observation itself; some

conception common to the phenomenon with other phenomena to which it is

compared. An observation can not be spoken of in language at all without

declaring more than that one observation; without assimilating it to other

phenomena already observed and classified. But this identification of an

object—this recognition of it as possessing certain known

characteristics—has never been confounded with Induction. It is an

operation which precedes all induction, and supplies it with its

materials. It is a perception of resemblances, obtained by comparison.

These resemblances are not always apprehended directly, by merely

comparing the object observed with some other present object, or with our

recollection of an object which is absent. They are often ascertained

through intermediate marks, that is, deductively. In describing some new

kind of animal, suppose me to say that it measures ten feet in length,

from the forehead to the extremity of the tail. I did not ascertain this

by the unassisted eye. I had a two-foot rule which I applied to the

object, and, as we commonly say, measured it; an operation which was not

wholly manual, but partly also mathematical, involving the two

propositions, Five times two is ten, and Things which are equal to the

same thing are equal to one another. Hence, the fact that the animal is

ten feet long is not an immediate perception, but a conclusion from

reasoning; the minor premises alone being furnished by observation of the

object. Nevertheless, this is called an observation, or a description of

the animal, not an induction respecting it.

To pass at once from a very simple to a very complex example: I affirm

that the earth is globular. The assertion is not grounded on direct

perception; for the figure of the earth can not, by us, be directly

perceived, though the assertion would not be true unless circumstances

could be supposed under which its truth could be so perceived. That the

form of the earth is globular is inferred from certain marks, as for

instance from this, that its shadow thrown upon the moon is circular; or

this, that on the sea, or any extensive plain, our horizon is always a

circle; either of which marks is incompatible with any other than a

globular form. I assert further, that the earth is that particular kind of

a globe which is termed an oblate spheroid; because it is found by

measurement in the direction of the meridian, that the length on the

surface of the earth which subtends a given angle at its centre,

diminishes as we recede from the equator and approach the poles. But these

propositions, that the earth is globular, and that it is an oblate

spheroid, assert, each of them, an individual fact; in its own nature

capable of being perceived by the senses when the requisite organs and the

necessary position are supposed, and only not actually perceived because

those organs and that position are wanting. This identification of the

earth, first as a globe, and next as an oblate spheroid, which, if the

fact could have been seen, would have been called a description of the

figure of the earth, may without impropriety be so called when, instead of

being seen, it is inferred. But we could not without impropriety call

either of these assertions an induction from facts respecting the earth.

They are not general propositions collected from particular facts, but

particular facts deduced from general propositions. They are conclusions

obtained deductively, from premises originating in induction: but of these

premises some were not obtained by observation of the earth, nor had any

peculiar reference to it.

If, then, the truth respecting the figure of the earth is not an

induction, why should the truth respecting the figure of the earth’s orbit

be so? The two cases only differ in this, that the form of the orbit was

not, like the form of the earth itself, deduced by ratiocination from

facts which were marks of ellipticity, but was got at by boldly guessing

that the path was an ellipse, and finding afterward, on examination, that

the observations were in harmony with the hypothesis. According to Dr.

Whewell, however, this process of guessing and verifying our guesses is

not only induction, but the whole of induction: no other exposition can be

given of that logical operation. That he is wrong in the latter assertion,

the whole of the preceding book has, I hope, sufficiently proved; and that

the process by which the ellipticity of the planetary orbits was

ascertained, is not induction at all, was attempted to be shown in the

second chapter of the same Book.(206) We are now, however, prepared to go

more into the heart of the matter than at that earlier period of our

inquiry, and to show, not merely what the operation in question is not,

but what it is.

§ 4. We observed, in the second chapter, that the proposition “the earth

moves in an ellipse,” so far as it only serves for the colligation or

connecting together of actual observations (that is, as it only affirms

that the observed positions of the earth may be correctly represented by

as many points in the circumference of an imaginary ellipse), is not an

induction, but a description: it is an induction, only when it affirms

that the intermediate positions, of which there has been no direct

observation, would be found to correspond to the remaining points of the

same elliptic circumference. Now, though this real induction is one thing,

and the description another, we are in a very different condition for

making the induction before we have obtained the description, and after

it. For inasmuch as the description, like all other descriptions, contains

the assertion of a resemblance between the phenomenon described and

something else; in pointing out something which the series of observed

places of a planet resembles, it points out something in which the several

places themselves agree. If the series of places correspond to as many

points of an ellipse, the places themselves agree in being situated in

that ellipse. We have, therefore, by the same process which gave us the

description, obtained the requisites for an induction by the Method of

Agreement. The successive observed places of the earth being considered as

effects, and its motion as the cause which produces them, we find that

those effects, that is, those places, agree in the circumstance of being

in an ellipse. We conclude that the remaining effects, the places which

have not been observed, agree in the same circumstance, and that the _law_

of the motion of the earth is motion in an ellipse.

The Colligation of Facts, therefore, by means of hypotheses, or, as Dr.

Whewell prefers to say, by means of Conceptions, instead of being, as he

supposes, Induction itself, takes its proper place among operations

subsidiary to Induction. All Induction supposes that we have previously

compared the requisite number of individual instances, and ascertained in

what circumstances they agree. The Colligation of Facts is no other than

this preliminary operation. When Kepler, after vainly endeavoring to

connect the observed places of a planet by various hypotheses of circular

motion, at last tried the hypotheses of an ellipse and found it answer to

the phenomena; what he really attempted, first unsuccessfully and at last

successfully, was to discover the circumstance in which all the observed

positions of the planet agreed. And when he in like manner connected

another set of observed facts, the periodic times of the different

planets, by the proposition that the squares of the times are proportional

to the cubes of the distances, what he did was simply to ascertain the

property in which the periodic times of all the different planets agreed.

Since, therefore, all that is true and to the purpose in Dr. Whewell’s

doctrine of Conceptions might be fully expressed by the more familiar term

Hypothesis; and since his Colligation of Facts by means of appropriate

Conceptions, is but the ordinary process of finding by a comparison of

phenomena, in what consists their agreement or resemblance; I would

willingly have confined myself to those better understood expressions, and

persevered to the end in the same abstinence which I have hitherto

observed from ideological discussions; considering the mechanism of our

thoughts to be a topic distinct from and irrelevant to the principles and

rules by which the trustworthiness of the results of thinking is to be

estimated. Since, however, a work of such high pretensions, and, it must

also be said, of so much real merit, has rested the whole theory of

Induction upon such ideological considerations, it seems necessary for

others who follow to claim for themselves and their doctrines whatever

position may properly belong to them on the same metaphysical ground. And

this is the object of the succeeding chapter.

Chapter II.

Of Abstraction, Or The Formation Of Conceptions.

§ 1. The metaphysical inquiry into the nature and composition of what have

been called Abstract Ideas, or, in other words, of the notions which

answer in the mind to classes and to general names, belongs not to Logic,

but to a different science, and our purpose does not require that we

should enter upon it here. We are only concerned with the universally

acknowledged fact, that such notions or conceptions do exist. The mind can

conceive a multitude of individual things as one assemblage or class; and

general names do really suggest to us certain ideas or mental

representations, otherwise we could not use the names with consciousness

of a meaning. Whether the idea called up by a general name is composed of

the various circumstances in which all the individuals denoted by the name

agree, and of no others (which is the doctrine of Locke, Brown, and the

Conceptualists); or whether it be the idea of some one of those

individuals, clothed in its individualizing peculiarities, but with the

accompanying knowledge that those peculiarities are not properties of the

class (which is the doctrine of Berkeley, Mr. Bailey,(207) and the modern

Nominalists); or whether (as held by Mr. James Mill) the idea of the class

is that of a miscellaneous assemblage of individuals belonging to the

class; or whether, finally, it be any one or any other of all these,

according to the accidental circumstances of the case; certain it is, that

_some_ idea or mental conception is suggested by a general name, whenever

we either hear it or employ it with consciousness of a meaning. And this,

which we may call, if we please, a general idea, _represents_ in our minds

the whole class of things to which the name is applied. Whenever we think

or reason concerning the class, we do so by means of this idea. And the

voluntary power which the mind has, of attending to one part of what is

present to it at any moment, and neglecting another part, enables us to

keep our reasonings and conclusions respecting the class unaffected by any

thing in the idea or mental image which is not really, or at least which

we do not really believe to be common, to the whole class.(208)

There are, then, such things as general conceptions, or conceptions by

means of which we can think generally; and when we form a set of phenomena

into a class, that is, when we compare them with one another to ascertain

in what they agree, some general conception is implied in this mental

operation. And inasmuch as such a comparison is a necessary preliminary to

Induction, it is most true that Induction could not go on without general

conceptions.

§ 2. But it does not therefore follow that these general conceptions must

have existed in the mind previously to the comparison. It is not a law of

our intellect, that in comparing things with each other and taking note of

their agreement we merely recognize as realized in the outward world

something that we already had in our minds. The conception originally

found its way to us as the _result_ of such a comparison. It was obtained

(in metaphysical phrase) by _abstraction_ from individual things. These

things may be things which we perceived or thought of on former occasions,

but they may also be the things which we are perceiving or thinking of on

the very occasion. When Kepler compared the observed places of the planet

Mars, and found that they agreed in being points of an elliptic

circumference, he applied a general conception which was already in his

mind, having been derived from his former experience. But this is by no

means universally the case. When we compare several objects and find them

to agree in being white, or when we compare the various species of

ruminating animals and find them to agree in being cloven-footed, we have

just as much a general conception in our minds as Kepler had in his: we

have the conception of “a white thing,” or the conception of “a

cloven-footed animal.” But no one supposes that we necessarily bring these

conceptions with us, and _superinduce_ them (to adopt Dr. Whewell’s

expression) upon the facts: because in these simple cases every body sees

that the very act of comparison which ends in our connecting the facts by

means of the conception, may be the source from which we derive the

conception itself. If we had never seen any white object or had never seen

any cloven-footed animal before, we should at the same time and by the

same mental act acquire the idea, and employ it for the colligation of the

observed phenomena. Kepler, on the contrary, really had to bring the idea

with him, and superinduce it upon the facts; he could not evolve it out of

them: if he had not already had the idea, he would not have been able to

acquire it by a comparison of the planet’s positions. But this inability

was a mere accident; the idea of an ellipse could have been acquired from

the paths of the planets as effectually as from any thing else, if the

paths had not happened to be invisible. If the planet had left a visible

track, and we had been so placed that we could see it at the proper angle,

we might have abstracted our original idea of an ellipse from the

planetary orbit. Indeed, every conception which can be made the instrument

for connecting a set of facts, might have been originally evolved from

those very facts. The conception is a conception _of_ something; and that

which it is a conception of, is really _in_ the facts, and might, under

some supposable circumstances, or by some supposable extension of the

faculties which we actually possess, have been detected in them. And not

only is this always in itself possible, but it actually happens in almost

all cases in which the obtaining of the right conception is a matter of

any considerable difficulty. For if there be no new conception required;

if one of those already familiar to mankind will serve the purpose, the

accident of being the first to whom the right one occurs, may happen to

almost any body; at least in the case of a set of phenomena which the

whole scientific world are engaged in attempting to connect. The honor, in

Kepler’s case, was that of the accurate, patient, and toilsome

calculations by which he compared the results that followed from his

different guesses, with the observations of Tycho Brahe; but the merit was

very small of guessing an ellipse; the only wonder is that men had not

guessed it before, nor could they have failed to do so if there had not

existed an obstinate _a priori_ prejudice that the heavenly bodies must

move, if not in a circle, in some combination of circles.

The really difficult cases are those in which the conception destined to

create light and order out of darkness and confusion has to be sought for

among the very phenomena which it afterward serves to arrange. Why,

according to Dr. Whewell himself, did the ancients fail in discovering the

laws of mechanics, that is, of equilibrium and of the communication of

motion? Because they had not, or at least had not clearly, the ideas or

conceptions of pressure and resistance, momentum, and uniform and

accelerating force. And whence could they have obtained these ideas except

from the very facts of equilibrium and motion? The tardy development of

several of the physical sciences, for example, of optics, electricity,

magnetism, and the higher generalizations of chemistry, he ascribes to the

fact that mankind had not yet possessed themselves of the Idea of

Polarity, that is, the idea of opposite properties in opposite directions.

But what was there to suggest such an idea, until, by a separate

examination of several of these different branches of knowledge, it was

shown that the facts of each of them did present, in some instances at

least, the curious phenomenon of opposite properties in opposite

directions? The thing was superficially manifest only in two cases, those

of the magnet and of electrified bodies; and there the conception was

encumbered with the circumstance of material poles, or fixed points in the

body itself, in which points this opposition of properties seemed to be

inherent. The first comparison and abstraction had led only to this

conception of poles; and if any thing corresponding to that conception had

existed in the phenomena of chemistry or optics, the difficulty now justly

considered so great, would have been extremely small. The obscurity arose

from the fact, that the polarities in chemistry and optics were distinct

species, though of the same genus, with the polarities in electricity and

magnetism; and that in order to assimilate the phenomena to one another,

it was necessary to compare a polarity without poles, such for instance as

is exemplified in the polarization of light, and the polarity with

(apparent) poles, which we see in the magnet; and to recognize that these

polarities, while different in many other respects, agree in the one

character which is expressed by the phrase, opposite properties in

opposite directions. From the result of such a comparison it was that the

minds of scientific men formed this new general conception; between which,

and the first confused feeling of an analogy between some of the phenomena

of light and those of electricity and magnetism, there is a long interval,

filled up by the labors and more or less sagacious suggestions of many

superior minds.

The conceptions, then, which we employ for the colligation and

methodization of facts, do not develop themselves from within, but are

impressed upon the mind from without; they are never obtained otherwise

than by way of comparison and abstraction, and, in the most important and

the most numerous cases, are evolved by abstraction from the very

phenomena which it is their office to colligate. I am far, however, from

wishing to imply that it is not often a very difficult thing to perform

this process of abstraction well, or that the success of an inductive

operation does not, in many cases, principally depend on the skill with

which we perform it. Bacon was quite justified in designating as one of

the principal obstacles to good induction, general conceptions wrongly

formed, “notiones temerè à rebus abstractæ;” to which Dr. Whewell adds,

that not only does bad abstraction make bad induction, but that, in order

to perform induction well, we must have abstracted well; our general

conceptions must be “clear” and “appropriate” to the matter in hand.

§ 3. In attempting to show what the difficulty in this matter really is,

and how it is surmounted, I must beg the reader, once for all, to bear

this in mind; that although, in discussing the opinions of a different

school of philosophy, I am willing to adopt their language, and to speak,

therefore, of connecting facts through the instrumentality of a

conception, this technical phraseology means neither more nor less than

what is commonly called comparing the facts with one another and

determining in what they agree. Nor has the technical expression even the

advantage of being metaphysically correct. The facts are not _connected_,

except in a merely metaphorical acceptation of the term. The _ideas_ of

the facts may become connected, that is, we may be led to think of them

together; but this consequence is no more than what may be produced by any

casual association. What really takes place, is, I conceive, more

philosophically expressed by the common word Comparison, than by the

phrases “to connect” or “to superinduce.” For, as the general conception

is itself obtained by a comparison of particular phenomena, so, when

obtained, the mode in which we apply it to other phenomena is again by

comparison. We compare phenomena with each other to get the conception,

and we then compare those and other phenomena _with_ the conception. We

get the conception of an animal (for instance) by comparing different

animals, and when we afterward see a creature resembling an animal, we

compare it with our general conception of an animal; and if it agrees with

that general conception, we include it in the class. The conception

becomes the type of comparison.

And we need only consider what comparison is, to see that where the

objects are more than two, and still more when they are an indefinite

number, a type of some sort is an indispensable condition of the

comparison. When we have to arrange and classify a great number of objects

according to their agreements and differences, we do not make a confused

attempt to compare all with all. We know that two things are as much as

the mind can easily attend to at a time, and we therefore fix upon one of

the objects, either at hazard or because it offers in a peculiarly

striking manner some important character, and, taking this as our

standard, compare it with one object after another. If we find a second

object which presents a remarkable agreement with the first, inducing us

to class them together, the question instantly arises, in what particular

circumstances do they agree? and to take notice of these circumstances is

already a first stage of abstraction, giving rise to a general conception.

Having advanced thus far, when we now take in hand a third object we

naturally ask ourselves the question, not merely whether this third object

agrees with the first, but whether it agrees with it in the same

circumstances in which the second did? in other words, whether it agrees

with the general conception which has been obtained by abstraction from

the first and second? Thus we see the tendency of general conceptions, as

soon as formed, to substitute themselves as types, for whatever individual

objects previously answered that purpose in our comparisons. We may,

perhaps, find that no considerable number of other objects agree with this

first general conception; and that we must drop the conception, and

beginning again with a different individual case, proceed by fresh

comparisons to a different general conception. Sometimes, again, we find

that the same conception will serve, by merely leaving out some of its

circumstances; and by this higher effort of abstraction, we obtain a still

more general conception; as in the case formerly referred to, the

scientific world rose from the conception of poles to the general

conception of opposite properties in opposite directions; or as those

South-Sea islanders, whose conception of a quadruped had been abstracted

from hogs (the only animals of that description which they had seen), when

they afterward compared that conception with other quadrupeds, dropped

some of the circumstances, and arrived at the more general conception

which Europeans associate with the term.

These brief remarks contain, I believe, all that is well grounded in the

doctrine, that the conception by which the mind arranges and gives unity

to phenomena must be furnished by the mind itself, and that we find the

right conception by a tentative process, trying first one and then another

until we hit the mark. The conception is not furnished _by_ the mind until

it has been furnished _to_ the mind; and the facts which supply it are

sometimes extraneous facts, but more often the very facts which we are

attempting to arrange by it. It is quite true, however, that in

endeavoring to arrange the facts, at whatever point we begin, we never

advance three steps without forming a general conception, more or less

distinct and precise; and that this general conception becomes the clue

which we instantly endeavor to trace through the rest of the facts, or

rather, becomes the standard with which we thenceforth compare them. If we

are not satisfied with the agreements which we discover among the

phenomena by comparing them with this type, or with some still more

general conception which by an additional stage of abstraction we can form

from the type; we change our path, and look out for other agreements; we

recommence the comparison from a different starting-point, and so generate

a different set of general conceptions. This is the tentative process

which Dr. Whewell speaks of; and which has not unnaturally suggested the

theory, that the conception is supplied by the mind itself; since the

different conceptions which the mind successively tries, it either already

possessed from its previous experience, or they were supplied to it in the

first stage of the corresponding act of comparison; so that, in the

subsequent part of the process, the conception manifested itself as

something compared with the phenomena, not evolved from them.

§ 4. If this be a correct account of the instrumentality of general

conceptions in the comparison which necessarily precedes Induction, we are

now able to translate into our own language what Dr. Whewell means by

saying that conceptions, to be subservient to Induction, must be “clear”

and “appropriate.”

If the conception corresponds to a real agreement among the phenomena; if

the comparison which we have made of a set of objects has led us to class

them according to real resemblances and differences; the conception which

does this can not fail to be appropriate, for some purpose or other. The

question of appropriateness is relative to the particular object we have

in view. As soon as, by our comparison, we have ascertained some

agreement, something which can be predicated in common of a number of

objects; we have obtained a basis on which an inductive process is capable

of being founded. But the agreements, or the ulterior consequences to

which those agreements lead, may be of very different degrees of

importance. If, for instance, we only compare animals according to their

color, and class those together which are colored alike, we form the

general conceptions of a white animal, a black animal, etc., which are

conceptions legitimately formed; and if an induction were to be attempted

concerning the causes of the colors of animals, this comparison would be

the proper and necessary preparation for such an induction, but would not

help us toward a knowledge of the laws of any other of the properties of

animals; while if, with Cuvier, we compare and class them according to the

structure of the skeleton, or, with Blainville, according to the nature of

their outward integuments, the agreements and differences which are

observable in these respects are not only of much greater importance in

themselves, but are marks of agreements and differences in many other

important particulars of the structure and mode of life of the animals.

If, therefore, the study of their structure and habits be our object, the

conceptions generated by these last comparisons are far more “appropriate”

than those generated by the former. Nothing, other than this, can be meant

by the appropriateness of a conception.

When Dr. Whewell says that the ancients, or the school-men, or any modern

inquirers, missed discovering the real law of a phenomenon because they

applied to it an inappropriate instead of an appropriate conception; he

can only mean that in comparing various instances of the phenomenon, to

ascertain in what those instances agreed, they missed the important points

of agreement; and fastened upon such as were either imaginary, and not

agreements at all, or, if real agreements, were comparatively trifling,

and had no connection with the phenomenon, the law of which was sought.

Aristotle, philosophizing on the subject of motion, remarked that certain

motions apparently take place spontaneously; bodies fall to the ground,

flame ascends, bubbles of air rise in water, etc.; and these he called

natural motions; while others not only never take place without external

incitement, but even when such incitement is applied, tend spontaneously

to cease; which, to distinguish them from the former, he called violent

motions. Now, in comparing the so-called natural motions with one another,

it appeared to Aristotle that they agreed in one circumstance, namely,

that the body which moved (or seemed to move) spontaneously, was moving

_toward its own place_; meaning thereby the place from whence it

originally came, or the place where a great quantity of matter similar to

itself was assembled. In the other class of motions, as when bodies are

thrown up in the air, they are, on the contrary, moving _from_ their own

place. Now, this conception of a body moving toward its own place may

justly be considered inappropriate; because, though it expresses a

circumstance really found in some of the most familiar instances of motion

apparently spontaneous, yet, first, there are many other cases of such

motion, in which that circumstance is absent; the motion, for instance, of

the earth and planets. Secondly, even when it is present, the motion, on

closer examination, would often be seen not to be spontaneous; as, when

air rises in water, it does not rise by its own nature, but is pushed up

by the superior weight of the water which presses upon it. Finally, there

are many cases in which the spontaneous motion takes place in the contrary

direction to what the theory considers as the body’s own place; for

instance, when a fog rises from a lake, or when water dries up. The

agreement, therefore, which Aristotle selected as his principle of

classification, did not extend to all cases of the phenomenon he wanted to

study, spontaneous motion; while it did include cases of the absence of

the phenomenon, cases of motion not spontaneous. The conception was hence

“inappropriate.” We may add that, in the case in question, no conception

would be appropriate; there is no agreement which runs through all the

cases of spontaneous or apparently spontaneous motion and no others; they

can not be brought under one law; it is a case of Plurality of

Causes.(209)

§ 5. So much for the first of Dr. Whewell’s conditions, that conceptions

must be appropriate. The second is, that they shall be “clear:” and let us

consider what this implies. Unless the conception corresponds to a real

agreement, it has a worse defect than that of not being clear: it is not

applicable to the case at all. Among the phenomena, therefore, which we

are attempting to connect by means of the conception, we must suppose that

there really is an agreement, and that the conception is a conception of

that agreement. In order, then, that it may be clear, the only requisite

is, that we shall know exactly in what the agreement consists; that it

shall have been carefully observed, and accurately remembered. We are said

not to have a clear conception of the resemblance among a set of objects,

when we have only a general feeling that they resemble, without having

analyzed their resemblance, or perceived in what points it consists, and

fixed in our memory an exact recollection of those points. This want of

clearness, or, as it may be otherwise called, this vagueness in the

general conception, may be owing either to our having no accurate

knowledge of the objects themselves, or merely to our not having carefully

compared them. Thus a person may have no clear idea of a ship because he

has never seen one, or because he remembers but little, and that faintly,

of what he has seen. Or he may have a perfect knowledge and remembrance of

many ships of various kinds, frigates among the rest, but he may have no

clear but only a confused idea of a frigate, because he has never been

told, and has not compared them sufficiently to have remarked and

remembered, in what particular points a frigate differs from some other

kind of ship.

It is not, however, necessary, in order to have clear ideas, that we

should know all the common properties of the things which we class

together. That would be to have our conception of the class complete as

well as clear. It is sufficient if we never class things together without

knowing exactly why we do so—without having ascertained exactly what

agreements we are about to include in our conception; and if, after having

thus fixed our conception, we never vary from it, never include in the

class any thing which has not those common properties, nor exclude from it

any thing which has. A clear conception means a determinate conception;

one which does not fluctuate, which is not one thing to-day and another

to-morrow, but remains fixed and invariable, except when, from the

progress of our knowledge, or the correction of some error, we consciously

add to it or alter it. A person of clear ideas is a person who always

knows in virtue of what properties his classes are constituted; what

attributes are connoted by his general names.

The principal requisites, therefore, of clear conceptions, are habits of

attentive observation, an extensive experience, and a memory which

receives and retains an exact image of what is observed. And in proportion

as any one has the habit of observing minutely and comparing carefully a

particular class of phenomena, and an accurate memory for the results of

the observation and comparison, so will his conceptions of that class of

phenomena be clear; provided he has the indispensable habit (naturally,

however, resulting from those other endowments), of never using general

names without a precise connotation.

As the clearness of our conceptions chiefly depends on the _carefulness_

and _accuracy_ of our observing and comparing faculties, so their

appropriateness, or rather the chance we have of hitting upon the

appropriate conception in any case, mainly depends on the _activity_ of

the same faculties. He who by habit, grounded on sufficient natural

aptitude, has acquired a readiness in accurately observing and comparing

phenomena, will perceive so many more agreements, and will perceive them

so much more rapidly than other people, that the chances are much greater

of his perceiving, in any instance, the agreement on which the important

consequences depend.

§ 6. It is of so much importance that the part of the process of

investigating truth, discussed in this chapter, should be rightly

understood, that I think it is desirable to restate the results we have

arrived at, in a somewhat different mode of expression.

We can not ascertain general truths, that is, truths applicable to

classes, unless we have formed the classes in such a manner that general

truths can be affirmed of them. In the formation of any class, there is

involved a conception of it as a class, that is, a conception of certain

circumstances as being those which characterize the class, and distinguish

the objects composing it from all other things. When we know exactly what

these circumstances are, we have a clear idea (or conception) of the

class, and of the meaning of the general name which designates it. The

primary condition implied in having this clear idea, is that the class be

really a class; that it correspond to a real distinction; that the things

it includes really do agree with one another in certain particulars, and

differ, in those same particulars, from all other things. A person without

clear ideas is one who habitually classes together, under the same general

names, things which have no common properties, or none which are not

possessed also by other things; or who, if the usage of other people

prevents him from actually misclassing things, is unable to state to

himself the common properties in virtue of which he classes them rightly.

But is it not the sole requisite of classification that the classes should

be real classes, framed by a legitimate mental process? Some modes of

classing things are more valuable than others for human uses, whether of

speculation or of practice; and our classifications are not well made,

unless the things which they bring together not only agree with each other

in something which distinguishes them from all other things, but agree

with each other and differ from other things in the very circumstances

which are of primary importance for the purpose (theoretical or practical)

which we have in view, and which constitutes the problem before us. In

other words, our conceptions, though they may be clear, are not

_appropriate_ for our purpose, unless the properties we comprise in them

are those which will help us toward what we wish to understand—_i.e._,

either those which go deepest into the nature of the things, if our object

be to understand that, or those which are most closely connected with the

particular property which we are endeavoring to investigate.

We can not, therefore, frame good general conceptions beforehand. That the

conception we have obtained is the one we want, can only be known when we

have done the work for the sake of which we wanted it; when we completely

understand the general character of the phenomena, or the conditions of

the particular property with which we concern ourselves. General

conceptions formed without this thorough knowledge, are Bacon’s “notiones

temerè à rebus abstractæ.” Yet such premature conceptions we must be

continually making up, in our progress to something better. They are an

impediment to the progress of knowledge, only when they are permanently

acquiesced in. When it has become our habit to group things in wrong

classes—in groups which either are not really classes, having no

distinctive points of agreement (absence of _clear_ ideas), or which are

not classes of which any thing important to our purpose can be predicated

(absence of _appropriate_ ideas); and when, in the belief that these badly

made classes are those sanctioned by nature, we refuse to exchange them

for others, and can not or will not make up our general conceptions from

any other elements; in that case all the evils which Bacon ascribes to his

“notiones temerè abstractæ” really occur. This was what the ancients did

in physics, and what the world in general does in morals and politics to

the present day.

It would thus, in my view of the matter, be an inaccurate mode of

expression to say, that obtaining appropriate conceptions is a condition

precedent to generalization. Throughout the whole process of comparing

phenomena with one another for the purpose of generalization, the mind is

trying to make up a conception; but the conception which it is trying to

make up is that of the really important point of agreement in the

phenomena. As we obtain more knowledge of the phenomena themselves, and of

the conditions on which their important properties depend, our views on

this subject naturally alter; and thus we advance from a less to a more

“appropriate” general conception, in the progress of our investigations.

We ought not, at the same time, to forget that the really important

agreement can not always be discovered by mere comparison of the very

phenomena in question, without the aid of a conception acquired elsewhere;

as in the case, so often referred to, of the planetary orbits.

The search for the agreement of a set of phenomena is in truth very

similar to the search for a lost or hidden object. At first we place

ourselves in a sufficiently commanding position, and cast our eyes round

us, and if we can see the object it is well; if not, we ask ourselves

mentally what are the places in which it may be hid, in order that we may

there search for it: and so on, until we imagine the place where it really

is. And here too we require to have had a previous conception, or

knowledge, of those different places. As in this familiar process, so in

the philosophical operation which it illustrates, we first endeavor to

find the lost object or recognize the common attribute, without

conjecturally invoking the aid of any previously acquired conception, or,

in other words, of any hypothesis. Having failed in this, we call upon our

imagination for some hypothesis of a possible place, or a possible point

of resemblance, and then look to see whether the facts agree with the

conjecture.

For such cases something more is required than a mind accustomed to

accurate observation and comparison. It must be a mind stored with general

conceptions, previously acquired, of the sorts which bear affinity to the

subject of the particular inquiry. And much will also depend on the

natural strength and acquired culture of what has been termed the

scientific imagination; on the faculty possessed of mentally arranging

known elements into new combinations, such as have not yet been observed

in nature, though not contradictory to any known laws.

But the variety of intellectual habits, the purposes which they serve, and

the modes in which they may be fostered and cultivated, are considerations

belonging to the Art of Education: a subject far wider than Logic, and

which this treatise does not profess to discuss. Here, therefore, the

present chapter may properly close.

Chapter III.

Of Naming, As Subsidiary To Induction.

§ 1. It does not belong to the present undertaking to dwell on the

importance of language as a medium of human intercourse, whether for

purposes of sympathy or of information. Nor does our design admit of more

than a passing allusion to that great property of names, on which their

functions as an intellectual instrument are, in reality, ultimately

dependent; their potency as a means of forming, and of riveting,

associations among our other ideas; a subject on which an able

thinker(210) has thus written:

“Names are impressions of sense, and as such take the strongest hold on

the mind, and of all other impressions can be most easily recalled and

retained in view. They therefore serve to give a point of attachment to

all the more volatile objects of thought and feeling. Impressions that

when passed might be dissipated forever, are, by their connection with

language, always within reach. Thoughts, of themselves, are perpetually

slipping out of the field of immediate mental vision; but the name abides

with us, and the utterance of it restores them in a moment. Words are the

custodiers of every product of mind less impressive than themselves. All

extensions of human knowledge, all new generalizations, are fixed and

spread, even unintentionally, by the use of words. The child growing up

learns, along with the vocables of his mother-tongue, that things which he

would have believed to be different are, in important points, the same.

Without any formal instruction, the language in which we grow up teaches

us all the common philosophy of the age. It directs us to observe and know

things which we should have overlooked; it supplies us with

classifications ready made, by which things are arranged (as far as the

light of by-gone generations admits) with the objects to which they bear

the greatest total resemblance. The number of general names in a language,

and the degree of generality of those names, afford a test of the

knowledge of the era, and of the intellectual insight which is the

birthright of any one born into it.”

It is not, however, of the functions of Names, considered generally, that

we have here to treat, but only of the manner and degree in which they are

directly instrumental to the investigation of truth; in other words, to

the process of induction.

§ 2. Observation and Abstraction, the operations which formed the subject

of the two foregoing chapters, are conditions indispensable to induction;

there can be no induction where they are not. It has been imagined that

Naming is also a condition equally indispensable. There are thinkers who

have held that language is not solely, according to a phrase generally

current, _an_ instrument of thought, but _the_ instrument; that names, or

something equivalent to them, some species of artificial signs, are

necessary to reasoning; that there could be no inference, and consequently

no induction, without them. But if the nature of reasoning was correctly

explained in the earlier part of the present work, this opinion must be

held to be an exaggeration, though of an important truth. If reasoning be

from particulars to particulars, and if it consist in recognizing one fact

as a mark of another, or a mark of a mark of another, nothing is required

to render reasoning possible, except senses and association; senses to

perceive that two facts are conjoined; association, as the law by which

one of those two facts raises up the idea of the other.(211) For these

mental phenomena, as well as for the belief or expectation which follows,

and by which we recognize as having taken place, or as about to take

place, that of which we have perceived a mark, there is evidently no need

of language. And this inference of one particular fact from another is a

case of induction. It is of this sort of induction that brutes are

capable; it is in this shape that uncultivated minds make almost all their

inductions, and that we all do so in the cases in which familiar

experience forces our conclusions upon us without any active process of

inquiry on our part, and in which the belief or expectation follows the

suggestion of the evidence with the promptitude and certainty of an

instinct.(212)

§ 3. But though inference of an inductive character is possible without

the use of signs, it could never, without them, be carried much beyond the

very simple cases which we have just described, and which form, in all

probability, the limit of the reasonings of those animals to whom

conventional language is unknown. Without language, or something

equivalent to it, there could only be as much reasoning from experience as

can take place without the aid of general propositions. Now, though in

strictness we may reason from past experience to a fresh individual case

without the intermediate stage of a general proposition, yet without

general propositions we should seldom remember what past experience we

have had, and scarcely ever what conclusions that experience will warrant.

The division of the inductive process into two parts, the first

ascertaining what is a mark of the given fact, the second whether in the

new case that mark exists, is natural, and scientifically indispensable.

It is, indeed, in a majority of cases, rendered necessary by mere distance

of time. The experience by which we are to guide our judgments may be

other people’s experience, little of which can be communicated to us

otherwise than by language; when it is our own, it is generally experience

long past; unless, therefore, it were recorded by means of artificial

signs, little of it (except in cases involving our intenser sensations or

emotions, or the subjects of our daily and hourly contemplation) would be

retained in the memory. It is hardly necessary to add, that when the

inductive inference is of any but the most direct and obvious nature—when

it requires several observations or experiments, in varying circumstances,

and the comparison of one of these with another—it is impossible to

proceed a step, without the artificial memory which words bestow. Without

words, we should, if we had often seen A and B in immediate and obvious

conjunction, expect B whenever we saw A; but to discover their conjunction

when not obvious, or to determine whether it is really constant or only

casual, and whether there is reason to expect it under any given change of

circumstances, is a process far too complex to be performed without some

contrivance to make our remembrance of our own mental operations accurate.

Now, language is such a contrivance. When that instrument is called to our

aid, the difficulty is reduced to that of making our remembrance of the

meaning of words accurate. This being secured, whatever passes through our

minds may be remembered accurately, by putting it carefully into words,

and committing the words either to writing or to memory.

The function of Naming, and particularly of General Names, in Induction,

may be recapitulated as follows. Every inductive inference which is good

at all, is good for a whole class of cases; and, that the inference may

have any better warrant of its correctness than the mere clinging together

of two ideas, a process of experimentation and comparison is necessary; in

which the whole class of cases must be brought to view, and some

uniformity in the course of nature evolved and ascertained, since the

existence of such a uniformity is required as a justification for drawing

the inference in even a single case. This uniformity, therefore, may be

ascertained once for all; and if, being ascertained, it can be remembered,

it will serve as a formula for making, in particular cases, all such

inferences as the previous experience will warrant. But we can only secure

its being remembered, or give ourselves even a chance of carrying in our

memory any considerable number of such uniformities, by registering them

through the medium of permanent signs; which (being, from the nature of

the case, signs not of an individual fact, but of a uniformity, that is,

of an indefinite number of facts similar to one another) are general

signs; universals; general names, and general propositions.

§ 4. And here I can not omit to notice an oversight committed by some

eminent thinkers; who have said that the cause of our using general names

is the infinite multitude of individual objects, which, making it

impossible to have a name for each, compels us to make one name serve for

many.

This is a very limited view of the function of general names. Even if

there were a name for every individual object, we should require general

names as much as we now do. Without them we could not express the result

of a single comparison, nor record any one of the uniformities existing in

nature; and should be hardly better off in respect to Induction than if we

had no names at all. With none but names of individuals (or, in other

words, proper names), we might, by pronouncing the name, suggest the idea

of the object, but we could not assert any proposition; except the

unmeaning ones formed by predicating two proper names one of another. It

is only by means of general names that we can convey any information,

predicate any attribute, even of an individual, much more of a class.

Rigorously speaking, we could get on without any other general names than

the abstract names of attributes; all our propositions might be of the

form “such an individual object possesses such an attribute,” or “such an

attribute is always (or never) conjoined with such another attribute.” In

fact, however, mankind have always given general names to objects as well

as attributes, and indeed before attributes: but the general names given

to objects imply attributes, derive their whole meaning from attributes;

and are chiefly useful as the language by means of which we predicate the

attributes which they connote.

It remains to be considered what principles are to be adhered to in giving

general names, so that these names, and the general propositions in which

they fill a place, may conduce most to the purposes of Induction.

Chapter IV.

Of The Requisites Of A Philosophical Language, And The Principles Of

Definition.

§ 1. In order that we may possess a language perfectly suitable for the

investigation and expression of general truths, there are two principal,

and several minor requisites. The first is, that every general name should

have a meaning, steadily fixed, and precisely determined. When, by the

fulfillment of this condition, such names as we possess are fitted for the

due performance of their functions, the next requisite, and the second in

order of importance, is that we should possess a name wherever one is

needed; wherever there is any thing to be designated by it, which it is of

importance to express.

The former of these requisites is that to which our attention will be

exclusively directed in the present chapter.

§ 2. Every general name, then, must have a certain and knowable meaning.

Now the meaning (as has so often been explained) of a general connotative

name, resides in the connotation; in the attribute on account of which,

and to express which, the name is given. Thus, the name animal being given

to all things which possess the attributes of sensation and voluntary

motion, the word connotes those attributes exclusively, and they

constitute the whole of its meaning. If the name be abstract, its

denotation is the same with the connotation of the corresponding concrete;

it designates directly the attribute, which the concrete term implies. To

give a precise meaning to general names is, then, to fix with steadiness

the attribute or attributes connoted by each concrete general name, and

denoted by the corresponding abstract. Since abstract names, in the order

of their creation, do not precede but follow concrete ones, as is proved

by the etymological fact that they are almost always derived from them; we

may consider their meaning as determined by, and dependent on, the meaning

of their concrete; and thus the problem of giving a distinct meaning to

general language, is all included in that of giving a precise connotation

to all concrete general names.

This is not difficult in the case of new names; of the technical terms

created by scientific inquirers for the purposes of science or art. But

when a name is in common use, the difficulty is greater; the problem in

this case not being that of choosing a convenient connotation for the

name, but of ascertaining and fixing the connotation with which it is

already used. That this can ever be a matter of doubt, is a sort of

paradox. But the vulgar (including in that term all who have not accurate

habits of thought) seldom know exactly what assertion they intend to make,

what common property they mean to express, when they apply the same name

to a number of different things. All which the name expresses with them,

when they predicate it of an object, is a confused feeling of resemblance

between that object and some of the other things which they have been

accustomed to denote by the name. They have applied the name Stone to

various objects previously seen; they see a new object, which appears to

them somewhat like the former, and they call it a stone, without asking

themselves in what respect it is like, or what mode or degree of

resemblance the best authorities, or even they themselves, require as a

warrant for using the name. This rough general impression of resemblance

is, however, made up of particular circumstances of resemblance; and into

these it is the business of the logician to analyze it; to ascertain what

points of resemblance among the different things commonly called by the

name, have produced in the common mind this vague feeling of likeness;

have given to the things the similarity of aspect, which has made them a

class, and has caused the same name to be bestowed upon them.

But though general names are imposed by the vulgar without any more

definite connotation than that of a vague resemblance; general

propositions come in time to be made, in which predicates are applied to

those names, that is, general assertions are made concerning the _whole_

of the things which are denoted by the name. And since by each of these

propositions some attribute, more or less precisely conceived, is of

course predicated, the ideas of these various attributes thus become

associated with the name, and in a sort of uncertain way it comes to

connote them; there is a hesitation to apply the name in any new case in

which any of the attributes familiarly predicated of the class do not

exist. And thus, to common minds, the propositions which they are in the

habit of hearing or uttering concerning a class make up in a loose way a

sort of connotation for the class name. Let us take, for instance, the

word Civilized. How few could be found, even among the most educated

persons, who would undertake to say exactly what the term Civilized

connotes. Yet there is a feeling in the minds of all who use it, that they

are using it with a meaning; and this meaning is made up, in a confused

manner, of every thing which they have heard or read that civilized men or

civilized communities are, or may be expected to be.

It is at this stage, probably, in the progress of a concrete name, that

the corresponding abstract name generally comes into use. Under the notion

that the concrete name must of course convey a meaning, or, in other

words, that there is some property common to all things which it denotes,

people give a name to this common property; from the concrete Civilized,

they form the abstract Civilization. But since most people have never

compared the different things which are called by the concrete name, in

such a manner as to ascertain what properties these things have in common,

or whether they have any; each is thrown back upon the marks by which he

himself has been accustomed to be guided in his application of the term;

and these, being merely vague hearsays and current phrases, are not the

same in any two persons, nor in the same person at different times. Hence

the word (as Civilization, for example) which professes to be the

designation of the unknown common property, conveys scarcely to any two

minds the same idea. No two persons agree in the things they predicate of

it; and when it is itself predicated of any thing, no other person knows,

nor does the speaker himself know with precision, what he means to assert.

Many other words which could be named, as the word _honor_, or the word

_gentleman_, exemplify this uncertainty still more strikingly.

It needs scarcely be observed, that general propositions of which no one

can tell exactly what they assert, can not possibly have been brought to

the test of a correct induction. Whether a name is to be used as an

instrument of thinking, or as a means of communicating the result of

thought, it is imperative to determine exactly the attribute or attributes

which it is to express; to give it, in short, a fixed and ascertained

connotation.

§ 3. It would, however, be a complete misunderstanding of the proper

office of a logician in dealing with terms already in use, if we were to

think that because a name has not at present an ascertained connotation,

it is competent to any one to give it such a connotation at his own

choice. The meaning of a term actually in use is not an arbitrary quantity

to be fixed, but an unknown quantity to be sought.

In the first place, it is obviously desirable to avail ourselves, as far

as possible, of the associations already connected with the name; not

enjoining the employment of it in a manner which conflicts with all

previous habits, and especially not so as to require the rupture of those

strongest of all associations between names, which are created by

familiarity with propositions in which they are predicated of one another.

A philosopher would have little chance of having his example followed, if

he were to give such a meaning to his terms as should require us to call

the North American Indians a civilized people, or the higher classes in

Europe savages; or to say that civilized people live by hunting, and

savages by agriculture. Were there no other reason, the extreme difficulty

of effecting so complete a revolution in speech would be more than a

sufficient one. The endeavor should be, that all generally received

propositions into which the term enters, should be at least as true after

its meaning is fixed, as they were before; and that the concrete name,

therefore, should not receive such a connotation as shall prevent it from

denoting things which, in common language, it is currently affirmed of.

The fixed and precise connotation which it receives should not be in

deviation from, but in agreement (as far as it goes) with, the vague and

fluctuating connotation which the term already had.

To fix the connotation of a concrete name, or the denotation of the

corresponding abstract, is to define the name. When this can be done

without rendering any received assertions inadmissible, the name can be

defined in accordance with its received use, which is vulgarly called

defining not the name but the thing. What is meant by the improper

expression of defining a thing (or rather a class of things—for nobody

talks of defining an individual), is to define the name, subject to the

condition that it shall denote those things. This, of course, supposes a

comparison of the things, feature by feature and property by property, to

ascertain what attributes they agree in; and not unfrequently an operation

strictly inductive, for the purpose of ascertaining some unobvious

agreement, which is the cause of the obvious agreements.