Critique of Kant on Arithmetic

Abstract

Arithmetical truths are a priori, but our understanding of them starts with the practical experience of counting. Whether arithmetic is analytic – or synthetic as Kant maintained – turns out to depend on what view we take about the precise scope of logic. A survey of mathematical theorizing about various kinds of numbers shows that there is more than one kind of “construction” or “intuition” involved. Kant’s conception of a priori intuition, as applied to arithmetic, seems to be just mathematical perception.