The one question: synthetic a priori

Last lesson gave us one distinction: analytic vs. synthetic (is the predicate contained in the subject, or added to it?). Now Kant lays a second distinction across it, and the crossing point is the whole game. See Prolegomena to Any Future Metaphysics §5.

A priori vs. a posteriori is a distinction about justification, not content. A priori = knowable independently of experience; its two unmistakable marks are necessity (it couldn’t be otherwise) and strict universality (no exceptions, ever). A posteriori = knowable only through experience, and therefore merely contingent — it happens to be so, and experience could have shown otherwise.

Cross the two distinctions and you get four boxes. Three are unremarkable. Analytic a priori — “all bachelors are unmarried” (contained and known without looking). Synthetic a posteriori — “the table is brown” (new content, learned by looking). Analytic a posteriori is empty: if the predicate is already in the concept, you never needed experience. That leaves the one box that matters.

Synthetic a priori. A judgment that is ampliative — it adds real content, extends knowledge — and yet necessary and universal, knowable before any experience. New information you can be certain of without checking. The empiricists declared this box empty: certainty and novelty, they thought, cannot coexist. Kant answers that it is where our most important knowledge actually lives — and he names the tenants.

Here is Kant’s decisive move against the sceptic. He does not ask whether synthetic a priori knowledge exists. He treats that as settled: pure mathematics and pure natural science are actual, universally acknowledged bodies of exactly such knowledge — no serious person doubts that 7 + 5 = 12 or that every event has a cause. The only real question is how such knowledge is possible. See Prolegomena to Any Future Metaphysics §5.

Finally, the abstract problem “how are synthetic a priori judgments possible?” is too big to attack whole, so Kant splits it along the lines of the sciences that contain such judgments. Three questions, three parts of the book: How is pure mathematics possible? How is pure natural science possible? How is metaphysics possible? See Prolegomena to Any Future Metaphysics §5.