In philosophy and logic, the liar paradox or liar's paradox (pseudomenon in Ancient Greek), is the statement "This sentence is false". Trying to assign to this statement a classical binary truth value leads to a contradiction (see Paradox).
If "This sentence is false" is true, then it is false, which would in turn mean that it is actually true, but this would mean that it is false, and so on ad infinitum.
Similarly, if "This sentence is false" is false, then it is true, which would in turn mean that it is actually false, but this would mean that it is true, and so on ad infinitum.
The Epimenides paradox (circa 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The fictional speaker Epimenides, a Cretan, reportedly stated that "The Cretans are always liars." However Epimenides' statement that all Cretans are liars can be resolved as false, given that he knows of at least one other Cretan who does not lie.
It is unlikely that Epimenides intended his words to be understood as a kind of liar paradox, and they were probably only understood as such much later in history.
The oldest known version of the actual liar paradox is attributed to the Greek philosopher Eubulides of Miletus who lived in the fourth century BC. It is very unlikely that he knew of Epimenides's words, even if they were intended as a paradox. Eubulides reportedly asked:
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