Single Idea 10492

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

Full Idea

Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement.

Gist of Idea

A few axioms of set theory 'force themselves on us', but most of them don't

Source

George Boolos (Must We Believe in Set Theory? [1997], p.130)

Book Reference

Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.130


A Reaction

Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture.