more from Shaughan Lavine

### Single Idea 15917

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity]

Full Idea

The paradox of the largest ordinal (the 'Burali-Forti') is that the class of all ordinal numbers is apparently well-ordered, and so it has an ordinal number as order type, which must be the largest ordinal - but all ordinals can be increased by one.

Gist of Idea

Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal

Source

Shaughan Lavine (Understanding the Infinite [1994], III.5)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.61

Related Idea

Idea 15918
Paradox: there is no largest cardinal, but the class of everything seems to be the largest **[Lavine]**