Single Idea 10485

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets]

Full Idea

The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set.

Gist of Idea

Naïve sets are inconsistent: there is no set for things that do not belong to themselves

Source

George Boolos (Must We Believe in Set Theory? [1997], p.127)

Book Reference

Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.127


A Reaction

As clear a summary of Russell's Paradox as you could ever hope for.