more from John Mayberry

Single Idea 17795

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

Full Idea

Set theory cannot be an axiomatic theory, because the very notion of an axiomatic theory makes no sense without it.

Gist of Idea

Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation


John Mayberry (What Required for Foundation for Maths? [1994], p.413-2)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.413

A Reaction

This will come as a surprise to Penelope Maddy, who battles with ways to accept the set theory axioms as the foundation of mathematics. Mayberry says that the basic set theory required is much more simple and intuitive.

Related Idea

Idea 17796 There is a semi-categorical axiomatisation of set-theory [Mayberry]