SYNTHETIC APRIORI

[A9/B13] How are synthetic a priori judgments possible? In short, synthetic a priori judgments give universal and necessary truths about the relation between appearances, namely, judgments based on investigations into the a priori conditions of experience, and in particular into the a priori conditions of human sensibility and understanding. In the course of these investigations, Kant "deduces" many propositions, principles, and laws, many of which are also synthetic a priori judgments. [A216/B262] For instance, Kant claims that the method of proof employed in the Analogies of Experience (which how appearances must be related in any possible experience) is important because it "supplies a rule to be followed in every other attempt to prove a priori propositions that are intellectual and also synthetic....namely, to investigate the possibility of experience as a knowledge wherein all objects--if their representation is to have objective reality for us--must finally be capable of being given to us". [A32/B48] Kant also claims that a certain kind of "transcendental exposition" of a concept can ground a body of synthetic a priori knowledge; he argues, for example, the our "concept" of space--of course, which is not a concept of all but a pure intuition--grounds our knowledge of geometry (which he claims is synthetic a priori; he also claims that all mathematical judgments are synthetic a priori, and their possibility is also grounded by space), and that the concept of time grounds "that body of a priori synthetic knowledge which is exhibited in the general doctrine of motion".