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,[8]
that (whether the tendency be or not an original and ultimate element of
our nature), Time, in its modifications of past, present, and future,
has no concern either with the belief itself, or with the grounds of it.
We believe that fire will burn to-morrow, because it burned to-day and
yesterday; but we believe, on precisely the same grounds, that it burned
before we were born, and that it burns this very day in Cochin-China. It
is not from the past to the future, as past and future, that we infer,
but from the known to the unknown; from facts observed to facts
unobserved; from what we have perceived, or been directly conscious of,
to what has not come within our experience. In this last predicament is
the whole region of the future; but also the vastly greater portion of
the present and of the past.
Whatever be the most proper mode of expressing it, the proposition that
the course of nature is uniform, is the fundamental principle, or
general axiom, of Induction. It would yet be a great error to offer this
large generalization as any explanation of the inductive process. On the
contrary, I hold it to be itself an instance of induction, and induction
by no means of the most obvious kind. Far from being the first induction
we make, it is one of the last, or at all events one of those which are
latest in attaining strict philosophical accuracy. As a general maxim,
indeed, it has scarcely entered into the minds of any but philosophers;
nor even by them, as we shall have many opportunities of remarking, have
its extent and limits been always very justly conceived. The truth is,
that this great generalization is itself founded on prior
generalizations. The obscurer laws of nature were discovered by means
of it, but the more obvious ones must have been understood and assented
to as general truths before it was ever heard of. We should never have
thought of affirming that all phenomena take place according to general
laws, if we had not first arrived, in the case of a great multitude of
phenomena, at some knowledge of the laws themselves; which could be done
no otherwise than by induction. In what sense, then, can a principle,
which is so far from being our earliest induction, be regarded as our
warrant for all the others? In the only sense, in which (as we have
already seen) the general propositions which we place at the head of our
reasonings when we throw them into syllogisms, ever really contribute to
their validity. As Archbishop Whately remarks, every induction is a
syllogism with the major premise suppressed; or (as I prefer expressing
it) every induction may be thrown into the form of a syllogism, by
supplying a major premise. If this be actually done, the principle which
we are now considering, that of the uniformity of the course of nature,
will appear as the ultimate major premise of all inductions, and will,
therefore, stand to all inductions in the relation in which, as has been
shown at so much length, the major proposition of a syllogism always
stands to the conclusion; not contributing at all to prove it, but being
a necessary condition of its being proved; since no conclusion is
proved, for which there cannot be found a true major premise.[9]
The statement, that the uniformity of the course of nature is the
ultimate major premise in all cases of induction, may be thought to
require some explanation. The immediate major premise in every inductive
argument, it certainly is not. Of that, Archbishop Whately's must be
held to be the correct account. The induction, "John, Peter, &c. are
mortal, therefore all mankind are mortal," may, as he justly says, be
thrown into a syllogism by prefixing as a major premise (what is at any
rate a necessary condition of the validity of the argument) namely, that
what is true of John, Peter, &c. is true of all mankind. But how came we
by this major premise? It is not self-evident; nay, in all cases of
unwarranted generalization, it is not true. How, then, is it arrived at?
Necessarily either by induction or ratiocination; and if by induction,
the process, like all other inductive arguments, may be thrown into the
form of a syllogism. This previous syllogism it is, therefore, necessary
to construct. There is, in the long run, only one possible construction.
The real proof that what is true of John, Peter, &c. is true of all
mankind, can only be, that a different supposition would be inconsistent
with the uniformity which we know to exist in the course of nature.
Whether there would be this inconsistency or not, may be a matter of
long and delicate inquiry; but unless there would, we have no sufficient
ground for the major of the inductive syllogism. It hence appears, that
if we throw the whole course of any inductive argument into a series of
syllogisms, we shall arrive by more or fewer steps at an ultimate
syllogism, which will have for its major premise the principle, or
axiom, of the uniformity of the course of nature.[10]
It was not to be expected that in the case of this axiom, any more than
of other axioms, there should be unanimity among thinkers with respect
to the grounds on which it is to be received as true. I have already
stated that I regard it as itself a generalization from experience.
Others hold it to be a principle which, antecedently to any verification
by experience, we are compelled by the constitution of our thinking
faculty to assume as true. Having so recently, and at so much length,
combated a similar doctrine as applied to the axioms of mathematics, by
arguments which are in a great measure applicable to the present case, I
shall defer the more particular discussion of this controverted point in
regard to the fundamental axiom of induction, until a more advanced
period of our inquiry.[11] At present it is of more importance to
understand thoroughly the import of the axiom itself. For the
proposition, that the course of nature is uniform, possesses rather the
brevity suitable to popular, than the precision requisite in
philosophical language: its terms require to be explained, and a
stricter than their ordinary signification given to them, before the
truth of the assertion can be admitted.
§ 2. Every person's consciousness assures him that he does not always
expect uniformity in the course of events; he does not always believe
that the unknown will be similar to the known, that the future will
resemble the past. Nobody believes that the succession of rain and fine
weather will be the same in every future year as in the present. Nobody
expects to have the same dreams repeated every night. On the contrary,
everybody mentions it as something extraordinary, if the course of
nature is constant, and resembles itself, in these particulars. To look
for constancy where constancy is not to be expected, as for instance
that a day which has once brought good fortune will always be a
fortunate day, is justly accounted superstition.
The course of nature, in truth, is not only uniform, it is also
infinitely various. Some phenomena are always seen to recur in the very
same combinations in which we met with them at first; others seem
altogether capricious; while some, which we had been accustomed to
regard as bound down exclusively to a particular set of combinations, we
unexpectedly find detached from some of the elements with which we had
hitherto found them conjoined, and united to others of quite a contrary
description. To an inhabitant of Central Africa, fifty years ago, no
fact probably appeared to rest on more uniform experience than this,
that all human beings are black. To Europeans, not many years ago, the
proposition, All swans are white, appeared an equally unequivocal
instance of uniformity in the course of nature. Further experience has
proved to both that they were mistaken; but they had to wait fifty
centuries for this experience. During that long time, mankind believed
in an uniformity of the course of nature where no such uniformity really
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
cannot have, or can have only in a very moderate degree. The possibility
of having it, is the foundation on which we shall see hereafter that
induction by simple enumeration may in some remarkable cases amount
practically to proof.[12] No such assurance, however, can be had, on any
of the ordinary subjects of scientific inquiry. Popular notions are
usually founded on induction by simple enumeration; in science it
carries us but a little way. We are forced to begin with it; we must
often rely on it provisionally, in the absence of means of more
searching investigation. But, for the accurate study of nature, we
require a surer and a more potent instrument.
It was, above all, by pointing out the insufficiency of this rude and
loose conception of Induction, that Bacon merited the title so generally
awarded to him, of Founder of the Inductive Philosophy. The value of his
own contributions to a more philosophical theory of the subject has
certainly been exaggerated. Although (along with some fundamental
errors) his writings contain, more or less fully developed, several of
the most important principles of the Inductive Method, physical
investigation has now far outgrown the Baconian conception of Induction.
Moral and political inquiry, indeed, are as yet far behind that
conception. The current and approved modes of reasoning on these
subjects are still of the same vicious description against which Bacon
protested; the method almost exclusively employed by those professing to
treat such matters inductively, is the very _inductio per enumerationem
simplicem_ which he condemns; and the experience which we hear so
confidently appealed to by all sects, parties, and interests, is still,
in his own emphatic words, _mera palpatio_.
§ 3. In order to a better understanding of the problem which the
logician must solve if he would establish a scientific theory of
Induction, let us compare a few cases of incorrect inductions with
others which are acknowledged to be legitimate. Some, we know, which
were believed for centuries to be correct, were nevertheless incorrect.
That all swans are white, cannot have been a good induction, since the
conclusion has turned out erroneous. The experience, however, on which
the conclusion rested, was genuine. From the earliest records, the
testimony of the inhabitants of the known world was unanimous on the
point. The uniform experience, therefore, of the inhabitants of the
known world, agreeing in a common result, without one known instance of
deviation from that result, is not always sufficient to establish a
general conclusion.
But let us now turn to an instance apparently not very dissimilar to
this. Mankind were wrong, it seems, in concluding that all swans were
white: are we also wrong, when we conclude that all men's heads grow
above their shoulders, and never below, in spite of the conflicting
testimony of the naturalist Pliny? As there were black swans, though
civilized people had existed for three thousand years on the earth
without meeting with them, may there not also be "men whose heads do
grow beneath their shoulders," notwithstanding a rather less perfect
unanimity of negative testimony from observers? Most persons would
answer No; it was more credible that a bird should vary in its colour,
than that men should vary in the relative position of their principal
organs. And there is no doubt that in so saying they would be right: but
to say why they are right, would be impossible, without entering more
deeply than is usually done, into the true theory of Induction.
Again, there are cases in which we reckon with the most unfailing
confidence upon uniformity, and other cases in which we do not count
upon it at all. In some we feel complete assurance that the future will
resemble the past, the unknown be precisely similar to the known. In
others, however invariable may be the result obtained from the instances
which have been observed, we draw from them no more than a very feeble
presumption that the like result will hold in all other cases. That a
straight line is the shortest distance between two points, we do not
doubt to be true even in the region of the fixed stars. When a chemist
announces the existence and properties of a newly-discovered substance,
if we confide in his accuracy, we feel assured that the conclusions he
has arrived at will hold universally, though the induction be founded
but on a single instance. We do not withhold our assent, waiting for a
repetition of the experiment; or if we do, it is from a doubt whether
the one experiment was properly made, not whether if properly made it
would be conclusive. Here, then, is a general law of nature, inferred
without hesitation from a single instance; an universal proposition from
a singular one. Now mark another case, and contrast it with this. Not
all the instances which have been observed since the beginning of the
world, in support of the general proposition that all crows are black,
would be deemed a sufficient presumption of the truth of the
proposition, to outweigh the testimony of one unexceptionable witness
who should affirm that in some region of the earth not fully explored,
he had caught and examined a crow, and had found it to be grey.
Why is a single instance, in some cases, sufficient for a complete
induction, while in others, myriads of concurring instances, without a
single exception known or presumed, go such a very little way towards
establishing an universal proposition? Whoever can answer this question
knows more of the philosophy of logic than the wisest of the ancients,
and has solved the problem of induction.