Kant, Helmholtz, Riemann und der Ursprung der geometrischen Axiome

Abstract

The essay attempts to discuss one more time the relationship between the positions of Immanuel Kant and Hermann von Helmholtz concerning the problem of space. First, it is pointed out that the fundamental problem of Kant's philosophy of geometry is to show that the congruence of geometric figures cannot be reduced to the logical identity of concepts. The notion of congruence, as the basic notion of Kant's theory of space, offers therefore a tertium comparationis, that allows to compare Kant's doctrine of space, with the development of geometry in the 19 th century, especially with Bernhard Riemann's approach. Helmholtz's philosophy of geometry, that starts precisely with a definition of congruence, in this way represents a historic and systematic mediation.