### Single Idea 15931

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

Full Idea

The iterative conception of sets does not tell us how far to iterate, and so we must start with an Axiom of Infinity. It also presupposes the notion of 'transfinite iteration'.

Gist of Idea

The iterative conception needs the Axiom of Infinity, to show how far we can iterate

Source

Shaughan Lavine (Understanding the Infinite [1994], V.5)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.148