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Single Idea 17879

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets ]

Full Idea

Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation.

Gist of Idea

Axiomatising set theory makes it all relative

Source

Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296)

Book Ref

'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.296

The 5 ideas from Thoralf Skolem

17878 If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
17879 Axiomatising set theory makes it all relative [Skolem]
17880 Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
17881 Mathematician want performable operations, not propositions about objects [Skolem]
13536 Skolem did not believe in the existence of uncountable sets [Skolem]