more from George Cantor

Single Idea 13483

[catalogued under 5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox]

Full Idea

The problem of Cantor's Paradox is that the power set of the universe has to be both bigger than the universe (by Cantor's theorem) and not bigger (since it is a subset of the universe).

Gist of Idea

Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it


report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 3

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.60

A Reaction

Russell eliminates the 'universe' in his theory of types. I don't see why you can't just say that the members of the set are hypothetical rather than real, and that hypothetically the universe might contain more things than it does.