more from this thinker | more from this text
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]
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] |