liar paradox

a logical paradox that results from consideration of statements of the form "This statement is false." If the statement is true, then it is false, whereas if it is false, then it is true.
[1935-40]

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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.

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also called  Epimenides' paradox 

      the paradox that if “This sentence is not true” is true, then it is not true, and if it is not true, then it is true. This example shows that certain formulations of words, though grammatically correct, are logically nonsensical. The English philosopher Bertrand Russell, in developing the theory of types, used the following illustration: the statement, “I am lying” is true only if it is false, and false if it is true. Epimenides, a 6th-century-BC Cretan prophet, first recorded such a paradox.

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Universalium. 2010.

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