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Single Idea 15933

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

Full Idea

Limitation of Size has it that if a collection is the same size as a set, then it is a set. The Axiom of Replacement is characteristic of limitation of size.

Gist of Idea

Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement

Source

Shaughan Lavine (Understanding the Infinite [1994], V.5)

Book Ref

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.150

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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]