Reading Kant’s doctrine of schematism algebraically

Kant’s investigations into so-called a priori judgments of pure mathematics in the Critique of Pure Reason (KrV) are mainly confined to geometry and arithmetic both of which are grounded on our pure forms of intuition, space, and time. Nevertheless, as regards notions such as irrational numbers and continuous magnitudes, such a restricted account is crucially problematic. I argue that algebra can play a transcendental role with respect to the two pure intuitive sciences, arithmetic and geometry, as the condition of their possibility. It follows that Kant’s schematism of the concept of magnitude ought to be quantitatively represented in algebraic formulas in general, and also undergo several modifications in order to suit continuities.