Concept
The Epimenides paradox reveals a problem with self-reference in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC) who is credited with the original statement. A typical description of the problem is given in the book Gödel, Escher, Bach, by Douglas Hofstadter: Epimenides was a Cretan who made the immortal statement: "All Cretans are liars." A paradox of self-reference arises when one considers whether it is possible for Epimenides to have spoken the truth. According to Ptolemaeus Chennus, Thetis and Medea had once argued in Thessaly over which was the most beautiful; they appointed the Cretan Idomeneus as the judge, who gave the victory to Thetis. In her anger, Medea called all Cretans liars, and cursed them to never say the truth. Thomas Fowler (1869) states the paradox as follows: "Epimenides the Cretan says, 'that all the Cretans are liars,' but Epimenides is himself a Cretan; therefore he is himself a liar. But if he is a liar, what he says is untrue, and consequently, the Cretans are veracious; but Epimenides is a Cretan, and therefore what he says is true; saying the Cretans are liars, Epimenides is himself a liar, and what he says is untrue. Thus we may go on alternately proving that Epimenides and the Cretans are truthful and untruthful." If we assume the statement is false and that Epimenides is lying about all Cretans being liars, then there must exist at least one Cretan who is honest. This does not lead to a contradiction since it is not required that this Cretan be Epimenides. This means that Epimenides can say the false statement that all Cretans are liars while knowing at least one honest Cretan and lying about this particular Cretan. Hence, from the assumption that the statement is false, it does not follow that the statement is true. So we can avoid a paradox as seeing the statement "all Cretans are liars" as a false statement, which is made by a lying Cretan, Epimenides.
