more from Penelope Maddy

### Single Idea 18195

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

Full Idea

A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction.

Gist of Idea

A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy

Source

Penelope Maddy (Naturalism in Mathematics [1997], I.5)

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.73