Philosophia Mathematica 19 (3):227-254 (2011)
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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References found in this work BETA
Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2007 - Philosophia Mathematica 16 (3):388-396.
An Answer to Hellman's Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’.Steve Awodey - 2004 - Philosophia Mathematica 12 (1):54-64.
Does Category Theory Provide a Framework for Mathematical Structuralism?Geoffrey Hellman - 2003 - Philosophia Mathematica 11 (2):129-157.
Three Varieties of Mathematical Structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
Citations of this work BETA
Identity in Homotopy Type Theory, Part I: The Justification of Path Induction.James Ladyman & Stuart Presnell - 2015 - Philosophia Mathematica 23 (3):386-406.
Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - forthcoming - British Journal for the Philosophy of Science:axw006.
Foundations of Unlimited Category Theory: What Remains to Be Done.Solomon Feferman - 2013 - Review of Symbolic Logic 6 (1):6-15.
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