more from Keith Hossack

### Single Idea 23625

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

Full Idea

The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC.

Gist of Idea

Limitation of Size justifies Replacement, but then has to appropriate Power Set

Source

Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9)

Book Reference

Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.147

A Reaction

Which suggests that the Power Set axiom is not as indispensable as it at first appears to be.

Related Idea

Idea 23624
The iterative conception has to appropriate Replacement, to justify the ordinals **[Hossack]**