Kant’s Prize Essay and Nineteenth Century Formalism

Kant’s Prize Essay of 1764 emphasizes the importance for mathematical cognition of manipulating signs according to rules, which has led some recent commentators to ask whether Kant’s position there is a species of mathematical formalism. While most have hesitated to find formalism in the Prize Essay, this hesitation derives from misconceptions about what formalists actually believe. I therefore examine some nineteenth century formalists who were in dialogue with Kant, using their views as a model against which to compare the Prize Essay. I argue that Kant’s view in the Prize Essay is continuous with their formalism, since the Prize Essay shares the essential aspects of their views about the sign-signified relation in mathematics and the role of signs in mathematical reasoning.