Single Idea 9193

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

Full Idea

ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical.

Gist of Idea

ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality

Source

Michael Dummett (The Philosophy of Mathematics [1998], 7)

Book Reference

'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.166


A Reaction

If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them.