But I think this is wrong. S is logically & semantically equivalent to (S') "All statements, but this statement, are false and this statement is false". But S' is illogical since its part "this statement is false" can't be given a truth value. — Pippen
Then the falsity of "All statements are false" would just mean that some statements are true, and some statements are false. — Michael Ossipoff
But I say that "All statements are false" has no truth value and therefore can't be false. — Pippen
So you're saying S can't be false because S', the equivalent statement, can't be false because of the "S is false" part. — TheMadFool
which poisons the whole conjunction eventually — Pippen
Is nobody here with real university logic knowledge? — Pippen
University logic says you did not prove anything. Your statements are meaningless. — Meta
Because Your arguments can not be formalized. You can't speak about "all statements" formally. — Meta
2. Since we can always go from "All x are y" (x may stand for 1,2,3 here) to for instance "All x are y and 2 are y" without changing the truth value, it must hold that A is logically equivalent to (A') "All statements are false and this statement is false", so A <-> A'. — Pippen
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