Absolute Selbstähnlichkeit in der euklidischen Geometrie. Zu Kants Erklärung der Möglichkeit der reinen Geometrie als einer synthetischen Erkenntnis a priori

Abstract

Kant's theory of space includes the idea that straight lines and planes can be defined in Euclidean geometry by a concept which nowadays has been revived in the field of fractal geometry: the concept of self-similarity. Absolute self-similarity of straight lines and planes distinguishes Euclidean space from any other geometrical space. Einstein missed this fact in his attempt to refute Kant's theory of space in his article Geometrie und Erfahrung. Following Hilbert and Schlick he took it for granted, mistakenly, that purely geometrical definitions of the concepts of straight line and plane are not feasible, except as implicit definitions. Therefore Einstein's criticism is not persuasive.