Kant and the Synthetic Nature of Geometry

Abstract

The purpose of this paper is to explore the significance of Kant's claim that geometry is synthetic. I begin by outlining certain criticisms of the Kantian position, criticisms selected with an eye to their popularity, rather than their importance in the abstract. I am no expert on the textual exegesis of Kant, and serious Kantian scholars would not, perhaps, be much troubled by the criticisms I propose to discuss: indeed, they might properly maintain that some of these problems (for example, the significance of non-Euclidean systems) were, for them, resolved long ago. But within the prevailing tradition of English-speaking philosophy certain sorts of criticism of Kant do seem to have sunk deep into our attitudes. It is with these criticisms that I hope to settle accounts. This small aim leads to the more difficult one of trying to understand what Kant means when he says that geometry is synthetic: about this larger task I will make only some preliminary remarks.