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
Königsberg 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 anything 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',[1] 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.
[1] 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 the 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 iaw 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.
