Physics, philosophy, and the foundations of geometry

Abstract

Twentieth century philosophy of geometry is a development and continuation, of sorts, of late nineteenth century work on the mathematical foundations of geometry. Reichenbach, Schlick, and Carnap appealed to the earlier work of Riemann, Helmholtz, Poincare, and Hilbert, in particular, in articulating their new view of the nature and character of geometrical knowledge. This view took its starting point from a rejection of Kant's conception of the synthetic a priori status of specifically Euclidean geometry-and, indeed, from a rejection of any role at all for spatial intuition within pure mathematics.