INTRODUCTION

In this appendix, I will try to say something about the implications of non-Euclidean geometry and especially its role in the theory of General Relativity for a rationalist view of a priori knowledge. There can be little doubt that from a historical standpoint, the development of non-Euclidean geometries was a major factor in producing the widespread conviction that a rationalist position is untenable. Euclidean geometry was after all the most striking example of seemingly substantive a priori knowledge of independent reality, invoked by Kant as one of the crucial examples of the synthetic a priori. But, according to the simplest version of the standard story, within a few years after Kant, the development of non-Euclidean geometry by Lobashevsky and others showed that Euclidean geometry was not necessarily true of physical space, making it an empirical issue which geometry correctly describes the physical world. And eventually, or so the story goes, this empirical question was resolved by General Relativity in favor of a version of Riemannian or elliptical geometry and against Euclid. The suggested further argument, often left fairly implicit, is that if the rationalist view fails in this paradigmatic case, there can be no good reason for thinking that it will in the end be any more acceptable elsewhere.