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Single Idea 10711

[filed under theme 5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox ]

Full Idea

Russell's paradox showed that we cannot consistently assume what is sometimes called the 'naïve comprehension principle', namely that every property is collectivizing.

Gist of Idea

Russell's paradox means we cannot assume that every property is collectivizing

Source

comment on Bertrand Russell (Letters to Frege [1902]) by Michael Potter - Set Theory and Its Philosophy 03.6

Book Ref

Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.43

The 7 ideas with the same theme [problem with self-membership of a set]:

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]