Kant on mathematical axioms

Abstract

This article is intended to explain the notion of “mathematical axioms” presented in Kant’s Critique of Pure Reason.
This notion is developed mainly within the framework of a justification of the thesis of the methodological dualism of the rational sciences (mathematics and metaphysics). We argue that there are significant differences between the critical notion of mathematical axioms, the pre-critical developments and the Wolffian definitions. The notion of “axiom” that Kant intends to take from mathematical procedures is inscribed in his peculiar way of thinking this science. This paper studies the considerations of (i) Wolff’s mathematical texts, (ii) the pre-critical texts and (iii) the Critique of Pure Reason, and mentions the differences between them in the conclusion.