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Full Idea
The class of teaspoons isn't a teaspoon, so isn't a member of itself; but the class of non-teaspoons is a member of itself. The class of all classes which are not members of themselves is a member of itself if it isn't a member of itself! Paradox.
Gist of Idea
The class of classes which lack self-membership leads to a contradiction
Source
report of Bertrand Russell (Mathematical logic and theory of types [1908]) by A.C. Grayling - Russell Ch.2
Book Ref
Grayling,A.C.: 'Russell' [OUP 1996], p.30
A Reaction
A very compressed version of Russell's famous paradox, often known as the 'barber' paradox. Russell developed his Theory of Types in an attempt to counter the paradox. Frege's response was to despair of his own theory.
| 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] |