Russell's Paradox

Gottlob Frege 1848 - 1925	Bertrand Russell 1872 - 1970
Frege was one of the founders of modern symbolic logic putting forward the view that mathematics is reducible to logic.	In a long and varied career Russell published a vast number of books on logic, theory of knowledge, and many other topics. His best known work was Principia Mathematica

Let R be the set of all sets which are not members of themselves. Then R is neither a member of itself nor not a member of itself.
(June 16, 1902)

 

 

"A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press."

Frege, Grundgesetze der Arithmetik (1903)