David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Solomon Feferman (2013). Foundations of Unlimited Category Theory: What Remains to Be Done. Review of Symbolic Logic 6 (1):6-15.
Similar books and articles
M. Kary (2009). (Math, Science, ?). Axiomathes 19 (3):61-86.
Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
Elaine Landry (2011). How to Be a Structuralist All the Way Down. Synthese 179 (3):435 - 454.
F. A. Muller (2001). Sets, Classes, and Categories. British Journal for the Philosophy of Science 52 (3):539-573.
Makmiller Pedroso (2009). On Three Arguments Against Categorical Structuralism. Synthese 170 (1):21 - 31.
Stewart Shapiro (2000). Set-Theoretic Foundations. The Proceedings of the Twentieth World Congress of Philosophy 2000:183-196.
Added to index2010-06-08
Total downloads121 ( #8,055 of 1,102,738 )
Recent downloads (6 months)8 ( #29,556 of 1,102,738 )
How can I increase my downloads?