Hegel and Modern Topology

TL;DR

This paper explores the philosophical connections between Hegel's logic and modern topology, illustrating how topological concepts can illuminate Hegelian ideas and vice versa, fostering a dialogue between philosophy and mathematics.

Contribution

It proposes a philosophical interpretation of modern topological concepts through Hegel's logic and demonstrates how topology can serve as a hermeneutic tool for understanding Hegel.

Findings

Modern topology concepts can be understood philosophically via Hegel's logic.

Topological ideas can illustrate and clarify Hegelian concepts.

A mutual support between philosophy and modern mathematics is possible.

Abstract

In this paper we sketch how some fundamental concepts of modern topology (as well as logic and category theory) can be understood philosophically in the light of Hegel's Science Logic as well how modern topological concepts can provide concrete illustrations of many of the concepts and deductions that Hegel used. Also these modern concepts can in turn be very powerful hermeneutic tools permitting a more rigorous and thorough grasp of Hegelian concepts. This paper can be seen as a continuation of our paper \cite{pro} where we argued that the prototypes of many fundamental notions of modern topology were already found in Aristotle's Physics. More generally it is hoped that this note makes a case for the possibility of a rigorous enriching interaction and mutual support between philosophy on one hand and modern logic and mathematics on the other. This paper is obviously meant only as a preliminary sketch and to offer some motivation for exploring in a more detailed and thorough way the subjects discussed.