Note 481 — THE TRANSCENDENTAL AESTHETIC SECTION I SPACE METAPHYSICAL EXPOSITION OF THE CONCEPTION OF SPACE[422]

This important and far-reaching assertion we cannot at this point discuss. Kant’s reasoning is really circular in the bad sense. Kant may legitimately argue from the a priori character of space to the apodictic character of pure mathematical science; but when he proceeds similarly to infer the apodictic character of applied mathematics, he is constrained to make the further assumption that space is a fixed and absolutely uniform mode in which alone members of the human species can intuit objects. That, as we point out below (p. 120), is an assumption which Kant does not really succeed in proving. In any case the requirements of the strict synthetic method preclude him from arguing, as he does both in the Dissertation (§ 15) and in the third space argument of the first edition, that the a priori certitude of applied mathematics affords proof of the necessary uniformity of all space.