Non-Euclidean Geometry and Einstein’s General Relativity: Cassirer’s View in 1921

Abstract

This chapter gives a brief account of the debate about the foundations of geometry after general relativity, with a special focus on Cassirer’s view in 1921. Cassirer emphasized that the geometrical hypotheses of general relativity differed completely from those of Newtonian mechanics and of special relativity. Therefore, in 1921, he revised his argument for the aprioricity of geometry as stated in 1910. Nevertheless, Cassirer argued for continuity across theory change with regard to the symbolic function of geometry in its correlation with the empirical manifold of physical events. In this regard, he reaffirmed his conviction that neo-Kantian views were compatible with empiricist arguments such as Helmholtz’s. Not only did Helmholtz offer an argument for the generalization of the Kantian theory of space, but he influenced the view that the principles of measurement play some a priori role relative to physical theories and can be subject to revision for considerations of uniformity in the formulation of physical laws and empirical evidence.