Category theory as an autonomous foundation

Philosophia Mathematica 19 (3):227-254 (2011)
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Abstract

Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in other branches of contemporary mathematics. If such a specification suffices, then a category-theoretical approach will be highly appropriate. But if sets have a richer `nature' than is preserved under isomorphism, then such an approach will be inadequate.

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Author Profiles

Øystein Linnebo
University of Oslo
Richard Pettigrew
Bristol University

Citations of this work

Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - 2016 - British Journal for the Philosophy of Science:axw006.
What Types Should Not Be.Bruno Bentzen - 2020 - Philosophia Mathematica 28 (1):60-76.
On the Problem of Relation Without Relata.Aboutorab Yaghmaie - 2021 - Journal of Philosophical Investigations at University of Tabriz 14 (33):404-425.

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