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Category Theory: The Language of Mathematics

Published online by Cambridge University Press:  01 April 2022

Elaine Landry
Elaine Landry*
Affiliation:
McGill University
*
‡Department of Philosophy, McGill University, Leacock Building, 855 Sherbrooke St. W., Montreal, Quebec, Canada, H3A 2T7
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Abstract

In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, then, as the structuralist sees mathematics as talking about structures and their morphology, I contend that category theory furnishes a framework for mathematical structuralism.

Type
Mathematics and Science
Information
Philosophy of Science , Volume 66 , Issue S3: Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers Sep., 1999 , 1999 , pp. S14 - S27
Copyright
Copyright © 1999 by the Philosophy of Science Association

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Footnotes

†

I would like to thank John Bell, Michael Hallett, Saunders Mac Lane, and Colin McLarty for their helpful comments and criticisms. The generous support of FCAR of Québec is also acknowledged.

References

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