more from this thinker | more from this text
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 Ref
-: 'Mind' [-], p.27
15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |