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 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.