FOUNDATIONS AS TRUTHS WHICH ORGANIZE MATHEMATICS

Author:

MCLARTY COLIN

Abstract

The article looks briefly at Feferman’s most sweeping claims about categorical foundations, focuses on narrower points raised in Berkeley, and asks some questions about Feferman’s own foundations. Among many different senses of foundations, the one that mathematics needs in practice is a recognized body of truths adequate to organize definitions and proofs. Finding concise principles of this kind has been a huge achievement by mathematicians and logicians. We put ZFC and categorical foundations both into this context.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy,Mathematics (miscellaneous)

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Critical Studies/Book Reviews;Philosophia Mathematica;2021-10-08

2. Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic;SSRN Electronic Journal;2021

3. What is a Higher-Level Set?;Philosophia Mathematica;2017-01-11

4. Set-theoretic foundations;Foundations of Mathematics;2017

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