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 Reference
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?