more from Graham Priest

### Single Idea 13366

#### [catalogued under 5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox]

Full Idea

Burali-Forti: φ(x) is 'x is an ordinal', and so w is the set of all ordinals, On; δ(x) is the least ordinal greater than every member of x (abbreviation: log(x)). The contradiction is that log(On)∈On and log(On)∉On.

Gist of Idea

The least ordinal greater than the set of all ordinals is both one of them and not one of them

Source

Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2)

Book Reference

-: 'Mind' [-], p.27