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Full Idea
Predicativists doubt the existence of sets with no predicative definition.
Gist of Idea
Predicativism says only predicated sets exist
Source
Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3)
Book Ref
Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.26
A Reaction
This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate?
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| 21695 | The set scheme discredited by paradoxes is actually the most natural one [Quine] |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 23623 | Predicativism says only predicated sets exist [Hossack] |