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Single Idea 13012

[from 'Investigations in the Foundations of Set Theory I' by Ernst Zermelo, in 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets ]

Full Idea

Zermelo proposed his listed of assumptions (including the controversial Axiom of Choice) in 1908, in order to secure his controversial proof of Cantor's claim that ' we can always bring any well-defined set into the form of a well-ordered set'.

Gist of Idea

Zermelo published his axioms in 1908, to secure a controversial proof

Source

report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1

Book Reference

-: 'Journal of Symbolic Logic' [-], p.483


A Reaction

This is interesting because it sometimes looks as if axiom systems are just a way of tidying things up. Presumably it is essential to get people to accept the axioms in their own right, the 'old-fashioned' approach that they be self-evident.