Arbitrary combination and the use of signs in mathematics: Kant’s 1763 Prize Essay and its Wolffian background

Abstract

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant’s 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional applicability of mathematical concepts.