Page:Kant's Prolegomena etc (1883).djvu/149

Here is a great and established branch of knowledge, already of remarkable compass, and promising unbounded extension in the future, carrying with it a thorough apodictic certainty, i.e., absolute necessity, and thus resting on no empirical grounds, but being a pure product of the Reason, besides thoroughly synthetic. How is it possible for the human Reason to bring about such a branch of knowledge entirely à priori?" Does not this capacity, as it does not and cannot stand on experience, presuppose some ground of knowledge à priori, lying deep-hidden, but which might reveal itself through these its effects, if their first beginnings were only diligently searched for?

But we find that all mathematical knowledge has this speciality, that it must present its conception previously in intuition, and indeed à priori, that is, in an intuition that is not empirical but pure, without which means it cannot make a single step; its judgments therefore are always intuitive, whereas philosophy must be satisfied with discursive judgments out of mere conceptions; for though it can explain its apodictic doctrines by intuition, these can never be derived from such a source. This observation respecting the nature of mathematics, itself furnishes us with a guide as to the first and foremost condition of its possibility, namely, that some pure intuition must be at its foundation, wherein it can present all its conceptions in concreto and à priori at the same time, or as it is termed, construct them. If we can find out this pure intuition together with its possibility, it will be readily explicable how synthetic propositions à priori are possible in pure mathematics, and therefore, also, how