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Should Type Theory Replace Set Theory as the Foundation of Mathematics?

Altenkirch, Thorsten

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Abstract

Mathematicians often consider Zermelo-Fraenkel Set Theory with Choice (ZFC) as the only foundation of Mathematics, and frequently don’t actually want to think much about foundations. We argue here that modern Type Theory, i.e. Homotopy Type Theory (HoTT), is a preferable and should be considered as an alternative.

Citation

Altenkirch, T. (2023). Should Type Theory Replace Set Theory as the Foundation of Mathematics?. Global Philosophy, 33(1), Article 21. https://doi.org/10.1007/s10516-023-09676-0

Journal Article Type Article
Acceptance Date Jan 15, 2023
Online Publication Date Feb 13, 2023
Publication Date 2023-02
Deposit Date Feb 1, 2023
Publicly Available Date Feb 13, 2023
Journal Global Philosophy
Print ISSN 2948-152X
Electronic ISSN 2948-1538
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 33
Issue 1
Article Number 21
DOI https://doi.org/10.1007/s10516-023-09676-0
Public URL https://nottingham-repository.worktribe.com/output/16794923
Publisher URL https://link.springer.com/article/10.1007/s10516-023-09676-0

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