Burali-Forti paradox

Definitions

The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.

Examples

“1984, Michael Hallett, Cantorian Set⟳ Theory and Limitation of Size, Oxford University Press⟳ (Clarendon Press⟳), 1986, Paperback, page 186, Like⟳ them, Mirimanoff concentrates on the Burali-Forti paradox, and like⟳ Russell's analysis before, Mirimanoff shows how. in terms of size, the Burali-Forti paradox is basic and that if we solve⟳ this the other paradoxes will be solved too.”

“1994 [Routledge], Ivor Grattan-Guinness (editor), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Volume 1, 2003, Johns Hopkins University Press⟳, Paperback, page 632, In the first place⟳, Berry rejected Russell's solution to the Burali-Forti paradox, claiming that it was easy to prove⟳ that the set⟳ of all ordinal numbers was a well-ordered set⟳ (and that Cantor had actually done it).”

“The Burali-Forti paradox was discovered by Cantor in 1895 and Burali-Forti in 1897, but was not regarded by them as a paradox.”

CEFR level