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As Wittgenstein correctly pointed out, Gödel's proposition "I'm unprovable" is not a proposition in Russell's system because it leads to inconsistency. Consequ
by carlehewitt 8y ago
As Wittgenstein correctly pointed out, Gödel's proposition "I'm unprovable" is not a proposition in Russell's system because it leads to inconsistency. Consequently, Gödel's incompleteness results are not valid for Russell's system.
The proposition "I'm unprovable" cannot be constructed as a fixed point of P |-> ~|-P because ~|-P has order one greater than the order of P.
- mietek 8y agoCould you give a reference for this claim of Wittgenstein’s, please?
- carlehewitt 8y agoA reference is: Ludwig Wittgenstein. 1956. Remarks on the Foundations of Mathematics, Revised Edition Basil Blackwell. 1978. There is a discussion here: https://hal.archives-ouvertes.fr/hal-01566393 https://hal.archives-ouvertes.fr/hal-01566393
- vyodaiken 8y agoThat seems entirely circular.
- carlehewitt 8y agoGödel's proposition "I'mUnprovable" cannot be constructed as a fixed point of P |-> ~|-P because ~|-P has order one greater than the order of P.