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)
Book Reference
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.127
A Reaction
Formulated by Burali-Forti in 1897.