Liar paradox

Paradox allegedly owing to Epimenides . There are a number of paradoxes of the Liar family. The simplest example is the sentence ‘This sentence is false’, which must be false if it is true, and true if it is false. One suggestion is that the sentence fails to say anything. But sentences that fail to say anything are at least not true. In that case, we consider the sentence ‘This sentence is not true’, which, if it fails to say anything, is not true, and hence true (this kind of reasoning is sometimes called the strengthened Liar). Other versions of the Liar introduce pairs of sentences, as in a slogan on the front of a T-shirt saying ‘The sentence on the back of this T-shirt is false’, and one on the back saying ‘The sentence on the front of this T-shirt is true’. It is clear that each sentence individually is well formed, and, were it not for the other, might have said something true. So any attempt to dismiss the paradox by saying that the sentences involved are meaningless will face problems. See also semantic paradoxes.