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topynate comments on Unsolved Problems in Philosophy Part 1: The Liar's Paradox - Less Wrong
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When you state ~~A(S) iff ~S, you are formally substituting S for ~A(S), but the meaning of "~~A(S) iff ~S" is "the set of truth-conditions for ~~A(S) is the same as the set of truth-conditions for ~S". But this assumes that there exists a set of truth-conditions for ~S, which assumes that there exists a set of truth-conditions for S, i.e. that S is meaningful, by your definition.