Phenomena and Noumena
Having seen Kant's transcendental deduction of the categories as pure concepts of the understanding applicable a priori to every possible experience, we might naturally wish to ask the further question whether these regulative principles are really true. Are there substances? Does every event have a cause? Do all things interact? Given that we must suppose them in order to have any experience, do they obtain in the world itself? To these further questions, Kant firmly refused to offer any answer.
According to Kant, it is vital always to distinguish between the distinct realms of phenomena and noumena. Phenomena are the appearances, which constitute the our experience; noumena are the (presumed) things themselves, which constitute reality. All of our synthetic a priori judgments apply only to the phenomenal realm, not the noumenal. (It is only at this level, with respect to what we can experience, that we are justified in imposing the structure of our concepts onto the objects of our knowledge.) Since the thing in itself (Ding an sich) would by definition be entirely independent of our experience of it, we are utterly ignorant of the noumenal realm.
Thus, on Kant's view, the most fundamental laws of nature, like the truths of mathematics, are knowable precisely because they make no effort to describe the world as it really is but rather prescribe the structure of the world as we experience it. By applying the pure forms of sensible intuition and the pure concepts of the understanding, we achieve a systematic view of the phenomenal realm but learn nothing of the noumenal realm. Math and science are certainly true of the phenomena; only metaphysics claims to instruct us about the noumena.