2.
space and geometry: *
Kant rests his demonstration of the priority of space on the example of geometry. He provides a proof as well (this is what Spengler is referring to). He asks the reader to take the proposition, "two straight lines can neither contain any space nor, consequently, form a figure", and then to try to derive this proposition from the concepts of a straight line and the number two. He concludes that it is impossible via analytic reasoning, consequently it must be derived from an a priori intuition of space. It is not achieved via experience (a posteriori) otherwise the universal character of geometry would be lost. If geometry did not serve this pure a priori intuition, it would be empirical, experimental science; in fact geometry does not proceed by measurements but by demonstrations.
3.
time and arithmetic: *
He summarizes his theory of time with the idea that time possesses both “empirical reality” and “transcendental ideality”. Time is a pure a priori intuition that renders mathematics possible. Time is not a concept, since otherwise it would merely conform to formal logical analysis (and therefore, to the principle of non-contradiction). However, time makes it possible to deviate from the principle of non-contradiction: indeed, it is possible to say that A and non-A are in the same spatial location if one considers them in different times, and a sufficient alteration between states were to occur. Time and space cannot thus be regarded as existing in themselves. They are a priori forms of sensible intuition. What Kant does not do is provide any form of proof based in arithmetic (as he did with Space and geometry). What he does do is repeat his assertion. Spengler notes both the omission & the commission.