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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
Source
David Bostock (Philosophy of Mathematics [2009], 5.4)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.144
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] |