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Full Idea
With Russell's antinomy, ...each tie the trouble comes of taking a membership condition that itself talks in turn of membership and non-membership.
Gist of Idea
Membership conditions which involve membership and non-membership are paradoxical
Source
Willard Quine (The Ways of Paradox [1961], p.13)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.13
A Reaction
Hence various stipulations to rule out vicious circles or referring to sets of the 'wrong type' are invoked to cure the problem. The big question is how strong to make the restrictions.
| 6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
| 13365 | Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell] |
| 10711 | Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell] |
| 21689 | A barber shaves only those who do not shave themselves. So does he shave himself? [Quine] |
| 21694 | Membership conditions which involve membership and non-membership are paradoxical [Quine] |
| 7701 | Can a Barber shave all and only those persons who do not shave themselves? [Jacquette] |
| 10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |