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Single Idea 10222

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory ]

Full Idea

Foundationalists (e.g. Quine and Lewis) have shown that mathematics can be rendered in theories other than the iterative hierarchy of sets. A dedicated contingent hold that the category of categories is the proper foundation (e.g. Lawvere).

Gist of Idea

Mathematical foundations may not be sets; categories are a popular rival

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 3.3)

Book Ref

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.87

A Reaction

I like the sound of that. The categories are presumably concepts that generate sets. Tricky territory, with Frege's disaster as a horrible warning to be careful.