 The
Problems of Philosophy
Bertrand Russell
CHAPTER VIII
HOW A PRIORI KNOWLEDGE IS POSSIBLE
IMMANUEL KANT is generally regarded as the greatest of
the modern philosophers. Though he lived through the Seven
Years War and the French Revolution, he never interrupted
his teaching of philosophy at Konigsberg in East Prussia.
His most distinctive contribution was the invention of what
he called the 'critical' philosophy, which, assuming as
a datum that there is knowledge of various kinds, inquired
how such knowledge comes to be possible, and deduced, from
the answer to this inquiry, many metaphysical results as
to the nature of the world. Whether these results were valid
may well be doubted. But Kant undoubtedly deserves credit
for two things: first, for having perceived that we have
a priori knowledge which is not purely 'analytic',
i.e. such that the opposite would be self-contradictory;
and secondly, for having made evident the philosophical
importance of the theory of knowledge.
Before the time of Kant, it was generally held that whatever
knowledge was a priori must be 'analytic'. What
this word means will be best illustrated by examples. If
I say, 'A bald man is a man', 'A plane figure is a figure',
'A bad poet is a poet', I make a purely analytic judgement:
the subject spoken about is given as having at least two
properties, of which one is singled out to be asserted of
it. Such propositions as the above are trivial, and would
never be enunciated in real life except by an orator preparing
the way for a piece of sophistry. They are called 'analytic'
because the predicate is obtained by merely analysing the
subject. Before the time of Kant it was thought that all
judgements of which we could be certain a priori
were of this kind: that in all of them there was a predicate
which was only part of the subject of which it was asserted.
If this were so, we should be involved in a definite contradiction
if we attempted to deny thinging that could be known a
priori. 'A bald man is not bald' would assert and deny
baldness of the same man, and would therefore contradict
itself. Thus according to the philosophers before Kant,
the law of contradiction, which asserts that nothing can
at the same time have and not have a certain property, sufficed
to establish the truth of all a priori knowledge.
Hume (1711-76), who preceded Kant, accepting the usual
view as to what makes knowledge a priori, discovered
that, in many cases which had previously been supposed analytic,
and notably in the case of cause and effect, the connexion
was really synthetic. Before Hume, rationalists at least
had supposed that the effect could be logically deduced
from the cause, if only we had sufficient knowledge. Hume
argued -- correctly, as would now be generally admitted
-- that this could not be done. Hence he inferred the far
more doubtful proposition that nothing could be known a
priori about the connexion of cause and effect. Kant,
who had been educated in the rationalist tradition, was
much perturbed by Hume's scepticism, and endeavoured to
find an answer to it. He perceived that not only the connexion
of cause and effect, but all the propositions of arithmetic
and geometry, are 'synthetic' i.e. not analytic: in all
these propositions, no analysis of the subject will reveal
the predicate. His stock instance was the proposition 7
+ 5 = 12. He pointed out, quite truly, that 7 and 5 have
to be put together to give 12: the idea of 12 is not contained
in them, nor even in the idea of adding them together. Thus
he was led to the conclusion that all pure mathematics,
though a priori, is synthetic; and this conclusion
raised a new problem of which he endeavoured to find the
solution.
The question which Kant put at the beginning of his philosophy,
namely 'How is pure mathematics possible?' is an interesting
and difficult one, to which every philosophy which is not
purely sceptical must find some answer. The answer of the
pure empiricists, that our mathematical knowledge is derived
by induction from particular instances, we have already
seen to be inadequate, for two reasons: first, that the
validity of the inductive principle itself cannot be proved
by induction; secondly, that the general propositions of
mathematics, such as 'two and two always make four', can
obviously be known with certainty by consideration of a
single instance, and gain nothing by enumeration of other
cases in which they have been found to be true. Thus our
knowledge of the general propositions of mathematics (and
the same applies to logic) must be accounted for otherwise
than our (merely probable) knowledge of empirical generalizations
such as 'all men are mortal'.
The problem arises through the fact that such knowledge
is general, whereas all experience is particular. It seems
strange that we should apparently be able to know some truths
in advance about particular things of which we have as yet
no experience; but it cannot easily be doubted that logic
and arithmetic will apply to such things. We do not know
who will be the inhabitants of London a hundred years hence;
but we know that any two of them and any other two of them
will make four of them. This apparent power of anticipating
facts about things of which we have no experience is certainly
surprising. Kant's solution of the problem, though not valid
in my opinion, is interesting. It is, however, very difficult,
and is differently understood by different philosophers.
We can, therefore, only give the merest outline of it, and
even that will be thought misleading by many exponents of
Kant's system.
What Kant maintained was that in all our experience there
are two elements to be distinguished, the one due to the
object (i.e. to what we have called the 'physical object'),
the other due to our own nature. We saw, in discussing matter
and sense-data, that the physical object is different from
the associated sense-data, and that the sense-data are to
be regarded as resulting from an interaction between the
physical object and ourselves. So far, we are in agreement
with Kant. But what is distinctive of Kant is the way in
which he apportions the shares of ourselves and the physical
object respectively. He considers that the crude material
given in sensation -- the colour, hardness etc. -- is due
to the object, and that what we supply is the arrangement
in space and time, and all the relations between sense-data
which result from comparison or from considering one as
the cause of the other or in any other way. His chief reason
in favour of this view is that we seem to have a priori
knowledge as to space and time and causality and comparison,
but not as to the actual crude material of sensation. We
can be sure, he says, that anything we shall ever experience
must show the characteristics affirmed of it in our a
priori knowledge, because these characteristics are
due to our own nature, and therefore nothing can ever come
into our experience without acquiring these characteristics.
The physical object, which he calls the 'thing in itself',*
he regards as essentially unknowable; what can be known
is the object as we have it in experience, which he calls
the 'phenomenon'. The phenomenon, being a joint product
of us and the thing in itself, is sure to have those characteristics
which are due to us, and is therefore sure to conform to
our a priori knowledge. Hence this knowledge, though
true of all actual and possible experience, must not be
supposed to apply outside experience. Thus in spite of the
existence of a priori knowledge, we cannot know
anything about the thing in itself or about what is not
an actual or possible object of experience. In this way
he tries to reconcile and harmonize the contentions of the
rationalists with the arguments of the empiricists.
-------------------
* Kant's 'thing in itself' is identical in definition
with the physical object, namely, it is the cause of sensations.
In the properties deduced from the definition it is not
identical, since Kant held (in spite of some inconsistency
as regards cause) that we can know that none of the categories
are applicable to the 'thing in itself'.
-------------------
Apart from minor grounds on which Kant's philosophy may
be criticized, there is one main objection which seems fatal
to any attempt to deal with the problem of a priori
knowledge by his method. The thing to be accounted for is
our certainty that the facts must always conform to logic
and arithmetic. To say that logic and arithmetic are contributed
by us does not account for this. Our nature is as much a
fact of the existing world as anything, and there can be
no certainty that it will remain constant. It might happen,
if Kant is right, that to-morrow our nature would so change
as to make two and two become five. This possibility seems
never to have occurred to him, yet it is one which utterly
destroys the certainty and universality which he is anxious
to vindicate for arithmetical propositions. It is true that
this possibility, formally, is inconsistent with the Kantian
view that time itself is a form imposed by the subject upon
phenomena, so that our real Self is not in time and has
no to-morrow. But he will still have to suppose that the
time-order of phenomena is determined by characteristics
of what is behind phenomena, and this suffices for the substance
of our argument.
Reflection, moreover, seems to make it clear that, if there
is any truth in our arithmetical beliefs, they must apply
to things equally whether we think of them or not. Two physical
objects and two other physical objects must make four physical
objects, even if physical objects cannot be experienced.
To assert this is certainly within the scope of what we
mean when we state that two and two are four. Its truth
is just as indubitable as the truth of the assertion that
two phenomena and two other phenomena make four phenomena.
Thus Kant's solution unduly limits the scope of a priori
propositions, in addition to failing in the attempt at explaining
their certainty.
Apart from the special doctrines advocated by Kant, it
is very common among philosophers to regard what is a
priori as in some sense mental, as concerned rather
with the way we must think than with any fact of the outer
world. We noted in the preceding chapter the three principles
commonly called 'laws of thought'. The view which led to
their being so named is a natural one, but there are strong
reasons for thinking that it is erroneous. Let us take as
an illustration the law of contradiction. This is commonly
stated in the form 'Nothing can both be and not be', which
is intended to express the fact that nothing can at once
have and not have a given quality. Thus, for example, if
a tree is a beech it cannot also be not a beech; if my table
is rectangular it cannot also be not rectangular, and so
on.
Now what makes it natural to call this principle a law
of thought is that it is by thought rather than
by outward observation that we persuade ourselves of its
necessary truth. When we have seen that a tree is a beech,
we do not need to look again in order to ascertain whether
it is also not a beech; thought alone makes us know that
this is impossible. But the conclusion that the law of contradiction
is a law of thought is nevertheless erroneous.
What we believe, when we believe the law of contradiction,
is not that the mind is so made that it must believe the
law of contradiction. This belief is a subsequent
result of psychological reflection, which presupposes the
belief in the law of contradiction. The belief in the law
of contradiction is a belief about things, not only about
thoughts. It is not, e.g., the belief that if we think
a certain tree is a beech, we cannot at the same time think
that it is not a beech; it is the belief that if a tree
is a beech, it cannot at the same time be
not a beech. Thus the law of contradiction is about things,
and not merely about thoughts; and although belief in the
law of contradiction is a thought, the law of contradiction
itself is not a thought, but a fact concerning the things
in the world. If this, which we believe when we believe
the law of contradiction, were not true of the things in
the world, the fact that we were compelled to think
it true would not save the law of contradiction from being
false; and this shows that the law is not a law of thought.
A similar argument applies to any other a priori
judgement. When we judge that two and two are four, we are
not making a judgement about our thoughts, but about all
actual or possible couples. The fact that our minds are
so constituted as to believe that two and two are four,
though it is true, is emphatically not what we assert when
we assert that two and two are four. And no fact about the
constitution of our minds could make it true that
two and two are four. Thus our a priori knowledge,
if it is not erroneous, is not merely knowledge about the
constitution of our minds, but is applicable to whatever
the world may contain, both what is mental and what is non-mental.
The fact seems to be that all our a priori knowledge
is concerned with entities which do not, properly speaking
exist, either in the mental or in the physical
world. These entities are such as can be named by parts
of speech which are not substantives; they are such entities
as qualities and relations. Suppose, for instance, that
I am in my room. I exist, and my room exists; but does 'in'
exist? Yet obviously the word 'in' has a meaning; it denotes
a relation which holds between me and my room. This relation
is something, although we cannot say that it exists in
the same sense in which I and my room exist. The relation
'in' is something which we can think about and understand,
for, if we could not understand it, we could not understand
the sentence 'I am in my room'. Many philosophers, following
Kant, have maintained that relations are the work of the
mind, that things in themselves have no relations, but that
the mind brings them together in one act of thought and
thus produces the relations which it judges them to have.
This view, however, seems open to objections similar to
those which we urged before against Kant. It seems plain
that it is not thought which produces the truth of the proposition
'I am in my room'. It may be true that an earwig is in my
room, even if neither I nor the earwig nor any one else
is aware of this truth; for this truth concerns only the
earwig and the room, and does not depend upon anything else.
Thus relations, as we shall see more fully in the next chapter,
must be placed in a world which is neither mental nor physical.
This world is of great importance to philosophy, and in
particular to the problems of a priori knowledge.
In the next chapter we shall proceed to develop its nature
and its bearing upon the questions with which we have been
dealing.
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