Perhaps the most famous paradox discovered by the Greek philosophers is that of ‘the liar’. A Cretan says that all Cretans are liars: if what he says is true, then it is false. More simply, consider: ‘This sentence is false.’ If it is true it is false, if false, true. The ancients took this paradox seriously, since if the concept of truth is inherently contradictory, as the paradox implies, then all discourse, all argument, all rational decision-making, takes place in a void. One ancient philosopher, Philetas of Cos, in his despair at finding a solution, committed suicide. More recently, the great logician Alfred Tarski used the paradox to argue that truth can be defined in a language only through a ‘meta-language’ with an outside vantage-point. In Tarski’s view ‘This sentence is false’ is not a possible sentence. But I have just written it!
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