Dimitry Gawronsky: reality and actual infinitesimals

Dimitry Gawronsky: reality and actual infinitesimals

Hernán Pringe

The aim of this paper is to analyze Dimitry Gawronsky’s doctrine of actual infinitesimals. We study the peculiar connection that his critical idealism establishes between transcendental philosophy and mathematics. In particular, we reconstruct the relationship between Gawronsky’s differentials, Cantor’s transfinite numbers, Veronese’s transarchimedean numbers and Robinson’s hyperreal numbers. We argue that by means of his doctrine of actual infinitesimals, Gawronsky aims at providing an interpretation of calculus that eliminates any alleged given element in knowledge.