Central and East European
Society for Phenomenology

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Category theory and the foundations of mathematics

philosophical excavations

Jean-Pierre Marquis

pp. 421-447

Abstract

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression ‘foundations of’. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory.

Publication details

Published in:

(1995) Synthese 103 (3).

Pages: 421-447

DOI: 10.1007/BF01089735

Full citation:

Marquis Jean-Pierre (1995) „Category theory and the foundations of mathematics: philosophical excavations“. Synthese 103 (3), 421–447.