more from John von Neumann

Single Idea 13672

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory]

Full Idea

There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory.

Gist of Idea

All the axioms for mathematics presuppose set theory


John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2

Book Reference

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.209

A Reaction

Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this.