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Bertrand Russell found Frege's famous error: Frege had overlooked what is now known as the Russell paradox. Namely, Frege's rules allowed one to define the class of x such that P is true for any "concept" P. Frege's idea was that such a class was an object itself, the class of objects "falling under the concept P." Russel used this principle to define the class R of concepts that do not fall under themselves. This concept leads to a contradiction... argument: if R falls under itself then it does not fall under itself; this contradiction shows that it does not fall under itself; therefore by definition it does fall under itself after all. (en) |
