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Full Idea
In the case of Russell's antinomy, the tacit and trusted pattern of reasoning that is found wanting is this: for any condition you can formulate, there is a class whose members are the things meeting the condition.
Gist of Idea
Russell's antinomy challenged the idea that any condition can produce a set
Source
Willard Quine (The Ways of Paradox [1961], p.11)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.11
A Reaction
This is why Russell's Paradox is so important for set theory, which in turn makes it important for the foundations of mathematics.
| 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] |