Farhad Alavi

Kant defines the schema of reality as the continuous and uniform generation of a quantity ascribed to sensation through which it can more or less fill time. In this paper, I ask why Kant has to attribute uniformity to the schema of reality. Through an interpretation that takes the uniformity thesis as a crucial element in Kant’s formulation, I contend that, in contrast to prevailing scholarly literature, Kant’s schema of reality must be comprehended mathematically without relying on regulative principles of understanding like that of causality.

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.