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

Altenkirch, Thorsten

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