 The
Problems of Philosophy
Bertrand Russell
CHAPTER VI
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 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 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 it 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 thee 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 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 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 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 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 the sort A has been found associated with a thing
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 by 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.
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