Liar paradox

Liar paradox, paradox derived from the statement attributed to the Cretan prophet Epimenides (6th century bce) that all Cretans are liars. If Epimenides’ statement is taken to imply that all statements made by Cretans are false, then, since Epimenides was a Cretan, his statement is false (i.e., not all Cretans are liars). The paradox in its simplest form arises from considering the sentence “This sentence is false.” If the sentence is true, then it is false, and if it is false, then it is true. The study of such semantic paradoxes led some logicians, notably Alfred Tarski, to distinguish between object language and metalanguage and to conclude that no language can consistently contain a complete semantic theory of its own sentences (see truth: Tarski and truth conditions; Kripke, Saul: Truth).