Space, Time, and Mathematics in the Critique of Pure Reason

Kant makes important claims about space, time, and mathematics in both the Transcendental Aesthetic and the Axioms of Intuition, claims that appear to overlap in some ways and contradict in others. Commentators have offered various interpretations to resolve these tensions, but most of them obscure the role of the Axioms of Intuition in Kant’s account of mathematical cognition and the nature of experience. Those who have considered the Axioms of Intuition agree that it is at least intended to justify the application of mathematics to the objects of experience. Some have held that the Axioms of Intuition also concerns a specific part of pure mathematics. Even these latter interpretations, however, underestimate the role of the Axioms in our cognition of both mathematics and experience. I argue in what follows that the outcome of the Axioms is twofold, concerning not only the applicability of mathematics but the possibility of any mathematical cognition whatsoever, whether pure or applied, general or specific. The interpretation for which I argue clears up some potential confusions concerning the treatment of space, time, and mathematics in the Transcendental Aesthetic and the Axioms. It also allows us to see that the Axioms of Intuition contains a substantial contribution to Kant’s theory of mathematical cognition that is at the heart of his account of our cognition of experience. There are, I think, various reasons why the Axioms of Intuition and the theory of magnitudes appearing in it have not earned more attention. First, many have held that Kant’s primary goal in the Critique of Pure Reason is to respond to Hume’s skepticism about causation, a response that culminates in the Second Analogy. Since the Axioms of Intuition makes little or no direct contribution to the argument leading up to the Second Analogy, many have