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Single Idea 21553

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

Full Idea

The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1.

Gist of Idea

It seems that the ordinal number of all the ordinals must be bigger than itself

Source

Douglas Lackey (Intros to Russell's 'Essays in Analysis. [1973], p.127)

A Reaction

Formulated by Burali-Forti in 1897.

Book Reference

Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.127