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   RustyBertrand (rustybertrand@social.vivaldi.net)'s status on Monday, 27-May-2024 06:25:06 JST RustyBertrand

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   Did fellow philosopher Ludwig Wittgenstein dispose of Bertrand Russell's paradox? ”... and that disposes of Russell's paradox.” In mathematical logic, Russell's paradox attempts to illustrate that every set theory that contains an unrestricted comprehension principle leads to contradictions. In 1923, Ludwig Wittgenstein proposed to ”dispose” of Russell's paradox as follows:

   ”The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself. For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition 'F(F(fx))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(f(x)) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of 'F(Fu)' we write '(do) : F(Ou) . Ou = Fu'.

   ... and that disposes of Russell's paradox.”

   — Ludwig Wittgenstein, Tractatus Logico-Philosophicus, 3.333