Riemann’s Philosophy of Geometry and Kant’s Pure Intuition

Abstract

The aim of this paper is twofold: first to explicate how Riemann’s philosophy of geometry is organized around the concept of manifold. Second, to argue that Riemann’s philosophy of geometry does not dismiss Kant’s spatial intuition. To this end, first I analyse Riemann’s Habilitationsvortrag with respect to interaction between philosophical, mathematical and physical perspectives. Then I will argue that although Riemann had no particular commitment to the truth of Euclidean geometry his alternative geometry does not necessarily dismiss Kant’s spatial intuition.

Keywords

• g.f.b. riemann
• kant
• pure intuition
• non-euclidean geometries