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Single Idea 23625

[filed under theme 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 Ref

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]

The 8 ideas with the same theme [sets as only limited by vastness that gives problems]:

15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
13547 Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter]
18105 Replacement enforces a 'limitation of size' test for the existence of sets [Bostock]
17803 Limitation of size is part of the very conception of a set [Mayberry]
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
15933 Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine]
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]