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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 4 ideas from 'Letters to Frege'

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]
9127 Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
7531 We don't assert private thoughts; the objects are part of what we assert [Russell]