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Single Idea 13547

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

Full Idea

Weak Limitation of Size: If there are no more Fs than Gs and the Gs form a collection, then Fs form a collection. Strong Limitation of Size: A property F fails to be collectivising iff there are as many Fs as there are objects.

Gist of Idea

Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects)

Source

report of George Boolos (Iteration Again [1989]) by Michael Potter - Set Theory and Its Philosophy 13.5

Book Ref

Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.227

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]