The Liar's Paradox

On the assumption that Cretans tell nothing but lies, it is impossible that any Cretan should say, ‘I am a liar.’ The so-called paradox arises because the paradoxer asserts two contradictory propositions. It impossible for both to be true. Therefore the person who wishes to puzzle us, if he is to say anything meaningful, must choose between asserting that all Cretans tell nothing but lies and the supposition that one Cretan says ‘I am a liar.’ The laws of logic, particularly the law of contradiction, forbid the insolubist from making both statements. And if he does not make both statements, there is no difficulty. To put it simply, no such Cretan would admit that he was a liar. – Gordon H. Clark, Language and Theology, Pg 13