Single Idea 9194

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

Full Idea

The main alternative to ZF is two-sorted theories, with some variables ranging over classes. Classes have more generous existence assumptions: there is a universal class, containing all sets, and a class containing all ordinals. Classes are not members.

Gist of Idea

The main alternative to ZF is one which includes looser classes as well as sets

Source

Michael Dummett (The Philosophy of Mathematics [1998], 7.1.1)

Book Reference

'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.168


A Reaction

My intuition is to prefer strict systems when it comes to logical theories. The whole point is precision. Otherwise we could just think about things, and skip all this difficult symbolic stuff.