a different kind of authority for the law of causation or the axiom of permanency of substance from that belonging to the theory of gravitation or the hypothesis of natural selection. All alike are postulates – guesses made to explain facts and happily verified by them. This is all that can be said for their validity. And as to their origin, all alike have had an historical growth.
There is, I have said, no a priori knowledge. Kant's science of pure physics is made up of postulates, which it is true growing experience tends to establish. But mathematics, it will be objected, cannot thus be disposed of. The subject may be considered more fully at another time. Here it is necessary to distinguish between mathematics as a system of universal and necessary truths, and mathematics as a system of truths originating in independence of experience. As to the first point, I shall only observe that for my own part I am not more certain of a demonstration of Euclid than of a chemist's analysis of water into hydrogen and oxygen. And I believe a "plain" man of the necessary intelligence, unsophisticated by philosophy, would tell the same story. But if others on reflection find they make a different estimate of the two kinds of knowledge, their attention may for the present be called to the fact that the subject-matter of geometry is the simplest conceivable, – mere extension everywhere alike, – and that whatever certainty the human mind is capable of reaching it must attain in this science, though it does not therefore follow that the self-evidence of geometrical truth differs in kind from the probability which, in varying degrees, you find in the other sciences, and of which, in fact, it is only the vanishing point. And with regard to the second issue, the conception of mathematical propositions originating without experience, it may here suffice to ask whether any one devoid of sight and touch could even, for example, cross the pons asinorum. If geometry, for that matter like all other knowledge, is the product of the mind, it is not made without sense-experience. But these statements are premature till Kant's theory of mathematics has been examined. It is only intended here to
