Of The Ground Of Induction.
§ 1. Induction properly so called, as distinguished from those mental
operations, sometimes, though improperly, designated by the name, which I
have attempted in the preceding chapter to characterize, may, then, be
summarily defined as Generalization from Experience. It consists in
inferring from some individual instances in which a phenomenon is observed
to occur, that it occurs in all instances of a certain class; namely, in
all which _resemble_ the former, in what are regarded as the material
circumstances.
In what way the material circumstances are to be distinguished from those
which are immaterial, or why some of the circumstances are material and
others not so, we are not yet ready to point out. We must first observe,
that there is a principle implied in the very statement of what Induction
is; an assumption with regard to the course of nature and the order of the
universe; namely, that there are such things in nature as parallel cases;
that what happens once, will, under a sufficient degree of similarity of
circumstances, happen again, and not only again, but as often as the same
circumstances recur. This, I say, is an assumption, involved in every case
of induction. And, if we consult the actual course of nature, we find that
the assumption is warranted. The universe, so far as known to us, is so
constituted, that whatever is true in any one case, is true in all cases
of a certain description; the only difficulty is, to find what
description.
This universal fact, which is our warrant for all inferences from
experience, has been described by different philosophers in different
forms of language: that the course of nature is uniform; that the universe
is governed by general laws; and the like. One of the most usual of these
modes of expression, but also one of the most inadequate, is that which
has been brought into familiar use by the metaphysicians of the school of
Reid and Stewart. The disposition of the human mind to generalize from
experience—a propensity considered by these philosophers as an instinct of
our nature—they usually describe under some such name as “our intuitive
conviction that the future will resemble the past.” Now it has been well
pointed out by Mr. Bailey,(107) that (whether the tendency be or not an
original and ultimate element of our nature), Time, in its modifications
of past, present, and future, has no concern either with the belief
itself, or with the grounds of it. We believe that fire will burn
to-morrow, because it burned to-day and yesterday; but we believe, on
precisely the same grounds, that it burned before we were born, and that
it burns this very day in Cochin-China. It is not from the past to the
future, as past and future, that we infer, but from the known to the
unknown; from facts observed to facts unobserved; from what we have
perceived, or been directly conscious of, to what has not come within our
experience. In this last predicament is the whole region of the future;
but also the vastly greater portion of the present and of the past.
Whatever be the most proper mode of expressing it, the proposition that
the course of nature is uniform, is the fundamental principle, or general
axiom of Induction. It would yet be a great error to offer this large
generalization as any explanation of the inductive process. On the
contrary, I hold it to be itself an instance of induction, and induction
by no means of the most obvious kind. Far from being the first induction
we make, it is one of the last, or at all events one of those which are
latest in attaining strict philosophical accuracy. As a general maxim,
indeed, it has scarcely entered into the minds of any but philosophers;
nor even by them, as we shall have many opportunities of remarking, have
its extent and limits been always very justly conceived. The truth is,
that this great generalization is itself founded on prior generalizations.
The obscurer laws of nature were discovered by means of it, but the more
obvious ones must have been understood and assented to as general truths
before it was ever heard of. We should never have thought of affirming
that all phenomena take place according to general laws, if we had not
first arrived, in the case of a great multitude of phenomena, at some
knowledge of the laws themselves; which could be done no otherwise than by
induction. In what sense, then, can a principle, which is so far from
being our earliest induction, be regarded as our warrant for all the
others? In the only sense, in which (as we have already seen) the general
propositions which we place at the head of our reasonings when we throw
them into syllogisms, ever really contribute to their validity. As
Archbishop Whately remarks, every induction is a syllogism with the major
premise suppressed; or (as I prefer expressing it) every induction may be
thrown into the form of a syllogism, by supplying a major premise. If this
be actually done, the principle which we are now considering, that of the
uniformity of the course of nature, will appear as the ultimate major
premise of all inductions, and will, therefore, stand to all inductions in
the relation in which, as has been shown at so much length, the major
proposition of a syllogism always stands to the conclusion; not
contributing at all to prove it, but being a necessary condition of its
being proved; since no conclusion is proved, for which there can not be
found a true major premise.(108)
The statement, that the uniformity of the course of nature is the ultimate
major premise in all cases of induction, may be thought to require some
explanation. The immediate major premise in every inductive argument, it
certainly is not. Of that, Archbishop Whately’s must be held to be the
correct account. The induction, “John, Peter, etc., are mortal, therefore
all mankind are mortal,” may, as he justly says, be thrown into a
syllogism by prefixing as a major premise (what is at any rate a necessary
condition of the validity of the argument), namely, that what is true of
John, Peter, etc., is true of all mankind. But how came we by this major
premise? It is not self-evident; nay, in all cases of unwarranted
generalization, it is not true. How, then, is it arrived at? Necessarily
either by induction or ratiocination; and if by induction, the process,
like all other inductive arguments, may be thrown into the form of a
syllogism. This previous syllogism it is, therefore, necessary to
construct. There is, in the long run, only one possible construction. The
real proof that what is true of John, Peter, etc., is true of all mankind,
can only be, that a different supposition would be inconsistent with the
uniformity which we know to exist in the course of nature. Whether there
would be this inconsistency or not, may be a matter of long and delicate
inquiry; but unless there would, we have no sufficient ground for the
major of the inductive syllogism. It hence appears, that if we throw the
whole course of any inductive argument into a series of syllogisms, we
shall arrive by more or fewer steps at an ultimate syllogism, which will
have for its major premise the principle, or axiom, of the uniformity of
the course of nature.(109)
It was not to be expected that in the case of this axiom, any more than of
other axioms, there should be unanimity among thinkers with respect to the
grounds on which it is to be received as true. I have already stated that
I regard it as itself a generalization from experience. Others hold it to
be a principle which, antecedently to any verification by experience, we
are compelled by the constitution of our thinking faculty to assume as
true. Having so recently, and at so much length, combated a similar
doctrine as applied to the axioms of mathematics, by arguments which are
in a great measure applicable to the present case, I shall defer the more
particular discussion of this controverted point in regard to the
fundamental axiom of induction, until a more advanced period of our
inquiry.(110) At present it is of more importance to understand thoroughly
the import of the axiom itself. For the proposition, that the course of
nature is uniform, possesses rather the brevity suitable to popular, than
the precision requisite in philosophical language: its terms require to be
explained, and a stricter than their ordinary signification given to them,
before the truth of the assertion can be admitted.
§ 2. Every person’s consciousness assures him that he does not always
expect uniformity in the course of events; he does not always believe that
the unknown will be similar to the known, that the future will resemble
the past. Nobody believes that the succession of rain and fine weather
will be the same in every future year as in the present. Nobody expects to
have the same dreams repeated every night. On the contrary, every body
mentions it as something extraordinary, if the course of nature is
constant, and resembles itself, in these particulars. To look for
constancy where constancy is not to be expected, as for instance that a
day which has once brought good fortune will always be a fortunate day, is
justly accounted superstition.
The course of nature, in truth, is not only uniform, it is also infinitely
various. Some phenomena are always seen to recur in the very same
combinations in which we met with them at first; others seem altogether
capricious; while some, which we had been accustomed to regard as bound
down exclusively to a particular set of combinations, we unexpectedly find
detached from some of the elements with which we had hitherto found them
conjoined, and united to others of quite a contrary description. To an
inhabitant of Central Africa, fifty years ago, no fact probably appeared
to rest on more uniform experience than this, that all human beings are
black. To Europeans, not many years ago, the proposition, All swans are
white, appeared an equally unequivocal instance of uniformity in the
course of nature. Further experience has proved to both that they were
mistaken; but they had to wait fifty centuries for this experience. During
that long time, mankind believed in a uniformity of the course of nature
where no such uniformity really existed.
According to the notion which the ancients entertained of induction, the
foregoing were cases of as legitimate inference as any inductions
whatever. In these two instances, in which, the conclusion being false,
the ground of inference must have been insufficient, there was,
nevertheless, as much ground for it as this conception of induction
admitted of. The induction of the ancients has been well described by
Bacon, under the name of “Inductio per enumerationem simplicem, ubi non
reperitur instantia contradictoria.” It consists in ascribing the
character of general truths to all propositions which are true in every
instance that we happen to know of. This is the kind of induction which is
natural to the mind when unaccustomed to scientific methods. The tendency,
which some call an instinct, and which others account for by association,
to infer the future from the past, the known from the unknown, is simply a
habit of expecting that what has been found true once or several times,
and never yet found false, will be found true again. Whether the instances
are few or many, conclusive or inconclusive, does not much affect the
matter: these are considerations which occur only on reflection; the
unprompted tendency of the mind is to generalize its experience, provided
this points all in one direction; provided no other experience of a
conflicting character comes unsought. The notion of seeking it, of
experimenting for it, of _interrogating_ nature (to use Bacon’s
expression) is of much later growth. The observation of nature, by
uncultivated intellects, is purely passive: they accept the facts which
present themselves, without taking the trouble of searching for more: it
is a superior mind only which asks itself what facts are needed to enable
it to come to a safe conclusion, and then looks out for these.
But though we have always a propensity to generalize from unvarying
experience, we are not always warranted in doing so. Before we can be at
liberty to conclude that something is universally true because we have
never known an instance to the contrary, we must have reason to believe
that if there were in nature any instances to the contrary, we should have
known of them. This assurance, in the great majority of cases, we can not
have, or can have only in a very moderate degree. The possibility of
having it, is the foundation on which we shall see hereafter that
induction by simple enumeration may in some remarkable cases amount
practically to proof.(111) No such assurance, however, can be had, on any
of the ordinary subjects of scientific inquiry. Popular notions are
usually founded on induction by simple enumeration; in science it carries
us but a little way. We are forced to begin with it; we must often rely on
it provisionally, in the absence of means of more searching investigation.
But, for the accurate study of nature, we require a surer and a more
potent instrument.
It was, above all, by pointing out the insufficiency of this rude and
loose conception of Induction, that Bacon merited the title so generally
awarded to him, of Founder of the Inductive Philosophy. The value of his
own contributions to a more philosophical theory of the subject has
certainly been exaggerated. Although (along with some fundamental errors)
his writings contain, more or less fully developed, several of the most
important principles of the Inductive Method, physical investigation has
now far outgrown the Baconian conception of Induction. Moral and political
inquiry, indeed, are as yet far behind that conception. The current and
approved modes of reasoning on these subjects are still of the same
vicious description against which Bacon protested; the method almost
exclusively employed by those professing to treat such matters
inductively, is the very _inductio per enumerationem simplicem_ which he
condemns; and the experience which we hear so confidently appealed to by
all sects, parties, and interests, is still, in his own emphatic words,
_mera palpatio_.
§ 3. In order to a better understanding of the problem which the logician
must solve if he would establish a scientific theory of Induction, let us
compare a few cases of incorrect inductions with others which are
acknowledged to be legitimate. Some, we know, which were believed for
centuries to be correct, were nevertheless incorrect. That all swans are
white, can not have been a good induction, since the conclusion has turned
out erroneous. The experience, however, on which the conclusion rested,
was genuine. From the earliest records, the testimony of the inhabitants
of the known world was unanimous on the point. The uniform experience,
therefore, of the inhabitants of the known world, agreeing in a common
result, without one known instance of deviation from that result, is not
always sufficient to establish a general conclusion.
But let us now turn to an instance apparently not very dissimilar to this.
Mankind were wrong, it seems, in concluding that all swans were white: are
we also wrong, when we conclude that all men’s heads grow above their
shoulders, and never below, in spite of the conflicting testimony of the
naturalist Pliny? As there were black swans, though civilized people had
existed for three thousand years on the earth without meeting with them,
may there not also be “men whose heads do grow beneath their shoulders,”
notwithstanding a rather less perfect unanimity of negative testimony from
observers? Most persons would answer No; it was more credible that a bird
should vary in its color, than that men should vary in the relative
position of their principal organs. And there is no doubt that in so
saying they would be right: but to say why they are right, would be
impossible, without entering more deeply than is usually done, into the
true theory of Induction.
Again, there are cases in which we reckon with the most unfailing
confidence upon uniformity, and other cases in which we do not count upon
it at all. In some we feel complete assurance that the future will
resemble the past, the unknown be precisely similar to the known. In
others, however invariable may be the result obtained from the instances
which have been observed, we draw from them no more than a very feeble
presumption that the like result will hold in all other cases. That a
straight line is the shortest distance between two points, we do not doubt
to be true even in the region of the fixed stars.(112) When a chemist
announces the existence and properties of a newly-discovered substance, if
we confide in his accuracy, we feel assured that the conclusions he has
arrived at will hold universally, though the induction be founded but on a
single instance. We do not withhold our assent, waiting for a repetition
of the experiment; or if we do, it is from a doubt whether the one
experiment was properly made, not whether if properly made it would be
conclusive. Here, then, is a general law of nature, inferred without
hesitation from a single instance; a universal proposition from a singular
one. Now mark another case, and contrast it with this. Not all the
instances which have been observed since the beginning of the world, in
support of the general proposition that all crows are black, would be
deemed a sufficient presumption of the truth of the proposition, to
outweigh the testimony of one unexceptionable witness who should affirm
that in some region of the earth not fully explored, he had caught and
examined a crow, and had found it to be gray.
Why is a single instance, in some cases, sufficient for a complete
induction, while in others, myriads of concurring instances, without a
single exception known or presumed, go such a very little way toward
establishing a universal proposition? Whoever can answer this question
knows more of the philosophy of logic than the wisest of the ancients, and
has solved the problem of induction.