more from Michèle Friend

### Single Idea 8710

#### [catalogued under 5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox]

Full Idea

Cantor's Paradox says that the powerset of a set has a cardinal number strictly greater than the original set, but that means that the powerset of the set of all the cardinal numbers is greater than itself.

Clarification

For 'powerset' see Idea 8672

Gist of Idea

The powerset of all the cardinal numbers is required to be greater than itself

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007])

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.113

A Reaction

Friend cites this with the Burali-Forti paradox and the Russell paradox as the best examples of the problems of set theory in the early twentieth century. Did this mean that sets misdescribe reality, or that we had constructed them wrongly?