Liar paradox

In philosophy and logic, the classical liar paradox or liar's paradox is the statement of a liar who states that they are lying: for instance, declaring that "I am lying" or "everything I say is false". If they are indeed lying, they are telling the truth, which means they are lying. In "this sentence is a lie" the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar himself. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction.

If "this sentence is false" is true, then the sentence is false, but if the sentence states that it is false, and it is false, then it must be true, and so on.

History

The Epimenides paradox (circa 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The semi-mythical seer Epimenides, a Cretan, reportedly stated that "All Cretans are 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 precisely in order to avoid uncertainties deriving from the human factor and from fuzzy concepts that modern logicians proposed a "strengthened" liar such as the sentence "this sentence is false".