Single Idea 18105

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size]

Full Idea

The Axiom of Replacement (or the Axiom of Subsets, 'Aussonderung', Fraenkel 1922) in effect enforces the idea that 'limitation of size' is a crucial factor when deciding whether a proposed set or does not not exist.

Gist of Idea

Replacement enforces a 'limitation of size' test for the existence of sets


David Bostock (Philosophy of Mathematics [2009], 5.4)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.144