more from this thinker | more from this text
Full Idea
The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes.
Gist of Idea
Limitation of Size is a vague intuition that over-large sets may generate paradoxes
Source
Penelope Maddy (Believing the Axioms I [1988], §1.3)
Book Ref
-: 'Journal of Symbolic Logic' [-], p.485
A Reaction
This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system.
| 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] |