liar paradox

Paradox derived from the statement attributed to the Cretan prophet Epimenides (6th century BC) 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's simplest form arises from considering the sentence “This sentence is false.” If it is true, then it is false, and if it is false, then it is true. Consideration of such semantic paradoxes led logicians to distinguish between object language and metalanguage and to conclude that no language can consistently contain a complete semantic theory for its own sentences.

(philosophy)

liar paradox - A sentence which asserts its own falsity, e.g. "This sentence is false" or "I am lying". These paradoxical assertions are meaningless in the sense that there is nothing in the world which could serve to either support or refute them. Philosophers, of course, have a great deal more to say on the subject.

["The Liar: an Essay on Truth and Circularity", Jon Barwise and John Etchemendy, Oxford University Press (1987). ISBN 0-19-505944-1 (PBK), Library of Congress BC199.P2B37].