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Ideas from 'An Axiomatization of Set Theory' by John von Neumann [1925], by Theme Structure

[found in 'From Frege to Gödel 1879-1931' (ed/tr Heijenoort,Jean van) [Harvard 1967,0-674-32449-8]].

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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong
                        Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong.
                        From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory
                        Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory.
                        From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2
                        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.