Page:Russell - The Problems of Philosophy, 1912.djvu/134

130 the connection 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 connection 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