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Full Idea
In current set theory Russell's Paradox is avoided by saying that a condition can only be defined on already existing sets.
Clarification
See Idea 6407 for Russell's Paradox
Gist of Idea
Nowadays conditions are only defined on existing sets
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.19
A Reaction
A response to Idea 9613. This leaves us with no account of how sets are created, so we have the modern notion that absolutely any grouping of daft things is a perfectly good set. The logicians seem to have hijacked common sense.
Related Idea
Idea 9613 Naïve set theory assumed that there is a set for every condition [Brown,JR]
| 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] |