“All Cretans are liars,” said Epimenides—at first sight a common-place scrap of mild xenophobia; about equal to “Taffy was a Welshman, Taffy was a thief” in charity and acumen. Not, one would suppose, a statement calculated to attract close attention from philosophers or logicians, or (despite the introduction of the offence of incitement to racial hatred) from lawyers.
But Epimenides' statement was widely discussed by the best thinkers of classical times and has kept its importance for the foundations of logic until the present century. To understand why, it is necessary to add two facts. First, Epimenides was himself a Cretan. Secondly, his statement was taken to mean not just that all Cretans lied from time to time but that everything ever said by any Cretan was false. It thus implies, in particular, that it is itself false. Not only can this be shown to lead to absurd consequences; it also suggests a simpler form of sentence which heightens the absurdity and best introduces the following discussion. It is: “This statement is false.” If that is true it is false, and if it is false it is true. So we have the paradox of a sentence which breaks no rule of formal grammar, is composed entirely of words whose sense is well understood, combines those words in such a way as to produce an apparently normal and meaningful statement, but turns out on investigation to have something radically wrong with it. We feel inclined to say that it has proved to be “meaningless” or “self-contradictory,” or to involve a “vicious circle.”