The Early Cassirer and Hegel’s «Concrete Universal» in the Philosophy of Mathemati

Abstract

In this paper, I aim to reconstruct the train of thoughts that pushed Cassirer to incorporate «concrete universality» in his philosophy of mathematics. To accomplish this task, I will first concentrate on Hegel’s claims regarding the mathematical infinite in his Science of Logic, as well as the relationship of true infinity to the concept of function and the «concrete universal». I will then deal with the most relevant intermediate stages from Hegel to Cassirer. In particular, I will dwell upon Drobisch’s account of concrete universality in logic and mathematics and Cohen’s book on calculus. Finally, I will evaluate Cassirer’s early production to explain why his philosophy of mathematics is sympathetic with that of Hegel and how Cassirer radicalises Hegel’s position.