Creating new concepts in mathematics: freedom and limitations. The case of Category Theory
Creating new concepts in mathematics: freedom and limitations. The case of Category Theory
Author(s): Zbigniew SemadeniSubject(s): Philosophy, Metaphysics, Epistemology, Logic, Special Branches of Philosophy, Philosophy of Science
Published by: Copernicus Center Press
Keywords: categories;functors;Eilenberg-Mac Lane Program;mathematical cognitive transgressions;phylogeny;platonism;
Summary/Abstract: In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning.We also investigate the emergence of category theory (CT) and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbiński and Tarski.
Journal: Zagadnienia Filozoficzne w Nauce
- Issue Year: 2020
- Issue No: 69
- Page Range: 33-65
- Page Count: 33
- Language: English