tion, on the other hand, is one which, though it may be elicited by experience, is seen, when
known, to have a basis other than experience. A child learning arithmetic may be helped by
experiencing two marbles and two other marbles, and observing that altogether he is experiencing
four marbles. But when he has grasped the general proposition "two and two are four" he no
longer requires confirmation by instances; the proposition has a certainty which induction can
never give to a general law. All the propositions of pure mathematics are in this sense a priori.
Hume had proved that the law of causality is not analytic, and had inferred that we could not be
certain of its truth. Kant accepted the view that it is synthetic, but nevertheless maintained that it is
known a priori. He maintained that arithmetic and geometry are synthetic, but are likewise a
priori. He was thus led to formulate his problem in these terms:
How are synthetic judgements a priori possible?
The answer to this question, with its consequences, constitutes the main theme of The Critique of
Pure Reason.
Kant's solution of the problem was one in which he felt great confidence. He had spent twelve
years in looking for it, but took only a few months to write his whole long book after his theory
had taken shape. In the preface to the first edition he says: "I venture to assert that there is not a
single metaphysical problem which has not been solved, or for the solution of which the key at
least has not been supplied." In the preface to the second edition he compares himself to
Copernicus, and says that he has effected a Copernican revolution in philosophy.
According to Kant, the outer world causes only the matter of sensation, but our own mental
apparatus orders this matter in space and time, and supplies the concepts by means of which we
understand experience. Things in themselves, which are the causes of our sensations, are
unknowable; they are not in space or time, they are not substances, nor can they be described by
any of those other general concepts which Kant calls "categories." Space and time are subjective,
they are part of our apparatus of perception. But just because of this, we can be sure that whatever
we experience will exhibit the characteristics dealt with by geometry and the science of time. If
you always wore blue spectacles, you could be sure of seeing everything blue