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- Title
Stefania Centrone, Deborah Kant, and Deniz Sarikaya, eds, Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory, and General Thoughts.
- Authors
Kotzsch, Hans-Christoph
- Abstract
The advent of Homotopy Type Theory/Univalent Foundations (HoTT/UF) in recent years has given a new impetus to the ever ongoing philosophical discussion about foundations of mathematics. [Ternullo] addresses a specific currently much debated issue in between philosophy of set theory and set theory itself, the concept of multiverses, while [Welch] is a rather advanced account of using reflection principles for elucidating questions of independence in set theory. The papers devoted to set theory [Dzamonja/Kant], [Fontanella], [Ternullo], [Welch] should be accessible for any philosopher of mathematics, although they require a good understanding of classical set theory including models, independence results, and descriptive set theory for a deeper appreciation. However, structural set theory is arguably closer to mathematical practice outside of set theory, where the intricate |$\in$| -structure of material set theory is irrelevant and objects need only be defined up to isomorphism.".
- Subjects
SET theory; MATHEMATICS; MATHEMATICAL proofs; CATEGORIES (Mathematics); PHILOSOPHY of mathematics; UNIVALENT functions
- Publication
Philosophia Mathematica, 2022, Vol 30, Issue 1, p88
- ISSN
0031-8019
- Publication type
Article
- DOI
10.1093/philmat/nkab026