ON INDUCTION
In almost all our previous discussions we have been concerned in the
attempt to get clear as to our data in the way of knowledge of
existence. What things are there in the universe whose existence is
known to us owing to our being acquainted with them? So far, our
answer has been that we are acquainted with our sense-data, and,
probably, with ourselves. These we know to exist. And past
sense-data which are remembered are known to have existed in the past.
This knowledge supplies our data.
But if we are to be able to draw inferences from these data--if we are
to know of the existence of matter, of other people, of the past
before our individual memory begins, or of the future, we must know
general principles of some kind by means of which such inferences can
be drawn. It must be known to us that the existence of some one sort
of thing, A, is a sign of the existence of some other sort of thing,
B, either at the same time as A or at some earlier or later time, as,
for example, thunder is a sign of the earlier existence of lightning.
If this were not known to us, we could never extend our knowledge
beyond the sphere of our private experience; and this sphere, as we
have seen, is exceedingly limited. The question we have now to
consider is whether such an extension is possible, and if so, how it
is effected.
Let us take as an illustration a matter about which none of us, in
fact, feel the slightest doubt. We are all convinced that the sun
will rise to-morrow. Why? Is this belief a mere blind outcome of
past experience, or can it be justified as a reasonable belief? It is
not easy to find a test by which to judge whether a belief of this
kind is reasonable or not, but we can at least ascertain what sort of
general beliefs would suffice, if true, to justify the judgement that
the sun will rise to-morrow, and the many other similar judgements
upon which our actions are based.
It is obvious that if we are asked why we believe that the sun will
rise to-morrow, we shall naturally answer 'Because it always has risen
every day'. We have a firm belief that it will rise in the future,
because it has risen in the past. If we are challenged as to why we
believe that it will continue to rise as heretofore, we may appeal to
the laws of motion: the earth, we shall say, is a freely rotating
body, and such bodies do not cease to rotate unless something
interferes from outside, and there is nothing outside to interfere
with the earth between now and to-morrow. Of course it might be
doubted whether we are quite certain that there is nothing outside to
interfere, but this is not the interesting doubt. The interesting
doubt is as to whether the laws of motion will remain in operation
until to-morrow. If this doubt is raised, we find ourselves in the
same position as when the doubt about the sunrise was first raised.
The _only_ reason for believing that the laws of motion will remain in
operation is that they have operated hitherto, so far as our knowledge
of the past enables us to judge. It is true that we have a greater
body of evidence from the past in favour of the laws of motion than we
have in favour of the sunrise, because the sunrise is merely a
particular case of fulfilment of the laws of motion, and there are
countless other particular cases. But the real question is: Do _any_
number of cases of a law being fulfilled in the past afford evidence
that it will be fulfilled in the future? If not, it becomes plain
that we have no ground whatever for expecting the sun to rise
to-morrow, or for expecting the bread we shall eat at our next meal
not to poison us, or for any of the other scarcely conscious
expectations that control our daily lives. It is to be observed that
all such expectations are only _probable_; thus we have not to seek
for a proof that they _must_ be fulfilled, but only for some reason in
favour of the view that they are _likely_ to be fulfilled.
Now in dealing with this question we must, to begin with, make an
important distinction, without which we should soon become involved in
hopeless confusions. Experience has shown us that, hitherto, the
frequent repetition of some uniform succession or coexistence has been
a _cause_ of our expecting the same succession or coexistence on the
next occasion. Food that has a certain appearance generally has a
certain taste, and it is a severe shock to our expectations when the
familiar appearance is found to be associated with an unusual taste.
Things which we see become associated, by habit, with certain tactile
sensations which we expect if we touch them; one of the horrors of a
ghost (in many ghost-stories) is that it fails to give us any
sensations of touch. Uneducated people who go abroad for the first
time are so surprised as to be incredulous when they find their native
language not understood.
And this kind of association is not confined to men; in animals also
it is very strong. A horse which has been often driven along a
certain road resists the attempt to drive him in a different
direction. Domestic animals expect food when they see the person who
usually feeds them. We know that all these rather crude expectations
of uniformity are liable to be misleading. The man who has fed the
chicken every day throughout its life at last wrings its neck instead,
showing that more refined views as to the uniformity of nature would
have been useful to the chicken.
But in spite of the misleadingness of such expectations, they
nevertheless exist. The mere fact that something has happened a
certain number of times causes animals and men to expect that it will
happen again. Thus our instincts certainly cause us to believe that
the sun will rise to-morrow, but we may be in no better a position
than the chicken which unexpectedly has its neck wrung. We have
therefore to distinguish the fact that past uniformities _cause_
expectations as to the future, from the question whether there is any
reasonable ground for giving weight to such expectations after the
question of their validity has been raised.
The problem we have to discuss is whether there is any reason for
believing in what is called 'the uniformity of nature'. The belief in
the uniformity of nature is the belief that everything that has
happened or will happen is an instance of some general law to which
there are no exceptions. The crude expectations which we have been
considering are all subject to exceptions, and therefore liable to
disappoint those who entertain them. But science habitually assumes,
at least as a working hypothesis, that general rules which have
exceptions can be replaced by general rules which have no exceptions.
'Unsupported bodies in air fall' is a general rule to which balloons
and aeroplanes are exceptions. But the laws of motion and the law of
gravitation, which account for the fact that most bodies fall, also
account for the fact that balloons and aeroplanes can rise; thus the
laws of motion and the law of gravitation are not subject to these
exceptions.
The belief that the sun will rise to-morrow might be falsified if the
earth came suddenly into contact with a large body which destroyed its
rotation; but the laws of motion and the law of gravitation would not
be infringed by such an event. The business of science is to find
uniformities, such as the laws of motion and the law of gravitation,
to which, so far as our experience extends, there are no exceptions.
In this search science has been remarkably successful, and it may be
conceded that such uniformities have held hitherto. This brings us
back to the question: Have we any reason, assuming that they have
always held in the past, to suppose that they will hold in the future?
It has been argued that we have reason to know that the future will
resemble the past, because what was the future has constantly become
the past, and has always been found to resemble the past, so that we
really have experience of the future, namely of times which were
formerly future, which we may call past futures. But such an argument
really begs the very question at issue. We have experience of past
futures, but not of future futures, and the question is: Will future
futures resemble past futures? This question is not to be answered by
an argument which starts from past futures alone. We have therefore
still to seek for some principle which shall enable us to know that
the future will follow the same laws as the past.
The reference to the future in this question is not essential. The
same question arises when we apply the laws that work in our
experience to past things of which we have no experience--as, for
example, in geology, or in theories as to the origin of the Solar
System. The question we really have to ask is: 'When two things have
been found to be often associated, and no instance is known of the one
occurring without the other, does the occurrence of one of the two, in
a fresh instance, give any good ground for expecting the other?' On
our answer to this question must depend the validity of the whole of
our expectations as to the future, the whole of the results obtained
by induction, and in fact practically all the beliefs upon which our
daily life is based.
It must be conceded, to begin with, that the fact that two things have
been found often together and never apart does not, by itself, suffice
to _prove_ demonstratively that they will be found together in the
next case we examine. The most we can hope is that the oftener things
are found together, the more probable it becomes that they will be
found together another time, and that, if they have been found
together often enough, the probability will amount _almost_ to
certainty. It can never quite reach certainty, because we know that
in spite of frequent repetitions there sometimes is a failure at the
last, as in the case of the chicken whose neck is wrung. Thus
probability is all we ought to seek.
It might be urged, as against the view we are advocating, that we know
all natural phenomena to be subject to the reign of law, and that
sometimes, on the basis of observation, we can see that only one law
can possibly fit the facts of the case. Now to this view there are
two answers. The first is that, even if _some_ law which has no
exceptions applies to our case, we can never, in practice, be sure
that we have discovered that law and not one to which there are
exceptions. The second is that the reign of law would seem to be
itself only probable, and that our belief that it will hold in the
future, or in unexamined cases in the past, is itself based upon the
very principle we are examining.
The principle we are examining may be called the _principle of
induction_, and its two parts may be stated as follows:
(a) When a thing of a certain sort A has been found to be associated
with a thing of a certain other sort B, and has never been found
dissociated from a thing of the sort B, the greater the number of
cases in which A and B have been associated, the greater is the
probability that they will be associated in a fresh case in which one
of them is known to be present;
(b) Under the same circumstances, a sufficient number of cases of
association will make the probability of a fresh association nearly a
certainty, and will make it approach certainty without limit.
As just stated, the principle applies only to the verification of our
expectation in a single fresh instance. But we want also to know that
there is a probability in favour of the general law that things of the
sort A are _always_ associated with things of the sort B, provided a
sufficient number of cases of association are known, and no cases of
failure of association are known. The probability of the general law
is obviously less than the probability of the particular case, since
if the general law is true, the particular case must also be true,
whereas the particular case may be true without the general law being
true. Nevertheless the probability of the general law is increased by
repetitions, just as the probability of the particular case is. We
may therefore repeat the two parts of our principle as regards the
general law, thus:
(a) The greater the number of cases in which a thing of the sort A has
been found associated with a thing of the sort B, the more probable it
is (if no cases of failure of association are known) that A is always
associated with B;
(b) Under the same circumstances, a sufficient number of cases of the
association of A with B will make it nearly certain that A is always
associated with B, and will make this general law approach certainty
without limit.
It should be noted that probability is always relative to certain
data. In our case, the data are merely the known cases of coexistence
of A and B. There may be other data, which _might_ be taken into
account, which would gravely alter the probability. For example, a
man who had seen a great many white swans might argue, by our
principle, that on the data it was _probable_ that all swans were
white, and this might be a perfectly sound argument. The argument is
not disproved ny the fact that some swans are black, because a thing
may very well happen in spite of the fact that some data render it
improbable. In the case of the swans, a man might know that colour is
a very variable characteristic in many species of animals, and that,
therefore, an induction as to colour is peculiarly liable to error.
But this knowledge would be a fresh datum, by no means proving that
the probability relatively to our previous data had been wrongly
estimated. The fact, therefore, that things often fail to fulfil our
expectations is no evidence that our expectations will not _probably_
be fulfilled in a given case or a given class of cases. Thus our
inductive principle is at any rate not capable of being _disproved_ by
an appeal to experience.
The inductive principle, however, is equally incapable of being
_proved_ by an appeal to experience. Experience might conceivably
confirm the inductive principle as regards the cases that have been
already examined; but as regards unexamined cases, it is the inductive
principle alone that can justify any inference from what has been
examined to what has not been examined. All arguments which, on the
basis of experience, argue as to the future or the unexperienced parts
of the past or present, assume the inductive principle; hence we can
never use experience to prove the inductive principle without begging
the question. Thus we must either accept the inductive principle on
the ground of its intrinsic evidence, or forgo all justification of
our expectations about the future. If the principle is unsound, we
have no reason to expect the sun to rise to-morrow, to expect bread to
be more nourishing than a stone, or to expect that if we throw
ourselves off the roof we shall fall. When we see what looks like our
best friend approaching us, we shall have no reason to suppose that
his body is not inhabited by the mind of our worst enemy or of some
total stranger. All our conduct is based upon associations which have
worked in the past, and which we therefore regard as likely to work in
the future; and this likelihood is dependent for its validity upon the
inductive principle.
The general principles of science, such as the belief in the reign of
law, and the belief that every event must have a cause, are as
completely dependent upon the inductive principle as are the beliefs
of daily life All such general principles are believed because mankind
have found innumerable instances of their truth and no instances of
their falsehood. But this affords no evidence for their truth in the
future, unless the inductive principle is assumed.
Thus all knowledge which, on a basis of experience tells us something
about what is not experienced, is based upon a belief which experience
can neither confirm nor confute, yet which, at least in its more
concrete applications, appears to be as firmly rooted in us as many of
the facts of experience. The existence and justification of such
beliefs--for the inductive principle, as we shall see, is not the only
example--raises some of the most difficult and most debated problems
of philosophy. We will, in the next chapter, consider briefly what
may be said to account for such knowledge, and what is its scope and
its degree of certainty.
