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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.
| 21689 | A barber shaves only those who do not shave themselves. So does he shave himself? [Quine] |
| 21690 | Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine] |
| 21691 | Antinomies contradict accepted ways of reasoning, and demand revisions [Quine] |
| 21692 | If we write it as '"this sentence is false" is false', there is no paradox [Quine] |
| 21693 | Russell's antinomy challenged the idea that any condition can produce a set [Quine] |
| 21694 | Membership conditions which involve membership and non-membership are paradoxical [Quine] |
| 21695 | The set scheme discredited by paradoxes is actually the most natural one [Quine] |