Single Idea 10484

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets]

Full Idea

According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage.

Gist of Idea

The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first

Source

George Boolos (Must We Believe in Set Theory? [1997], p.126)

Book Reference

Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.126


A Reaction

He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent.