ON INDUCTION
BERTRAND RUSSELL
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Bertrand Russell led the British "revolt
against idealism" in the early 1900s.
He is considered one of the founders of analytic
philosophy along with his predecessor Gottlob
Frege and his protégé Ludwig Wittgenstein,
and is widely held to be one of the 20th
century's premier logicians. He co-authored,
with A. N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic.
His philosophical essay "On Denoting"
has been considered a "paradigm of philosophy."
His work has had a considerable influence
on logic, mathematics, set theory, linguistics,
and philosophy, especially philosophy of
language, epistemology, and metaphysics.
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Problems of Philosophy
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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