The problem of the present section is therefore solved. Pure mathematics is only possible as synthetic knowledge apri- ori, in so far as it refers simply to objects of sense, whose empirical intuition has for its foundation a pure intuition a priori (that of time and space), which intuition is able to serve as a foundation, because it is nothing more than the pure form of sensibility itself, that precedes the real appearance of objects, in that it makes them in the first place possible. Yet this faculty of intuiting apriori does not concern the matter of the phenomenon, i.e., that which is feeling (Empfind- ung) in the latter, for this constitutes the empirical element therein; but only its form, space and time. Should anybody cast the least doubt on the fact that neither of them are conditions of things in themselves, but only dependent on their relation to sensibility. I should be glad to be informed how he deems it possible to know apriori, and therefore before all acquaintance with the things, that is, before they are given us, how their intuition must be constructed, as is here the case with space and time. Yet this is quite conceivable, as soon as they both count for nothing more than formal determinations of our sensibility, and the objects merely as phenomena, for in that case the form of the phenomenon, that is, the pure intuition, can be conceived as coming from ourselves, in other words, as a priori.
- What makes mathematics possible? How can we anticipate geometrical features of all objects of possible experience before we experience them?
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