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 P: 27 To see what is involved, lets replace "Sentence 1 " with a variable: 1 x is not true. 2 x = " x is not true." Sentence 1 is then no longer a sentence; its a sentence-function it has no truth value unless x is replaced with a name of a sentence, or a sentence inside quote signs. But sentence 2 is an identity, and we can get an equivalence: 3 x is true if and only if "x is not true" is true. Simplifying the right side we get a contradiction: 4 x is true if and only if x is not true. And we must deny sentence 2: 5 It is not true that x = "x is not true" Sentence 5 is a logical truth... its the law of identity: 6 x=x (law of identity) 7 -(x = -x) (from 6 by double negation) Sentences 5 and 7 has the same logical form since (-x) = "x is not true" Now let us again look at the foundation of the Liar Paradox: 1 Sentence 1 is not true. 2 Sentence 1 = "Sentence 1 is not true" Sentence 2 is a denial of the law of identity so it is logically false...and empirically true! This is because we were violating the law of identity when we created sentence 1! Sentence 1 is identical with its negation thereby making the logically false sentence 2 empirically true! So we can neither deny nor assert sentence 1 since its very existence is forbidden by Logic! The Laws of logic are prescriptions that CAN be broken... They are NOT Natural Laws! SO: Unless you violate the Laws of Logic you cant derive the Liar Paradox!