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Full Idea
Our very notion of a set is that of an extensional plurality limited in size.
Gist of Idea
Limitation of size is part of the very conception of a set
Source
John Mayberry (What Required for Foundation for Maths? [1994], p.415-2)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.415
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] |