Epimenides paradox

Epimenides of Knossos (Crete) was a semi-mythical 7th or 6th century BC Greek seer and philosopher-poet.
While tending his father's sheep, Epimenides is said to have fallen asleep for fifty-seven years in a Cretan cave sacred to Zeus, after which he reportedly awoke with the gift of prophecy (Diogenes Laërtius i. 109–115). Plutarch writes that Epimenides purified Athens after the pollution brought by the Alcmeonidae, and that the seer's expertise in sacrifices and reform of funeral practices were of great help to Solon in his reform of the Athenian state. The only reward he would accept was a branch of the sacred olive, and a promise of perpetual friendship between Athens and Knossus (Plutarch, Life of Solon, 12; Aristotle, Ath. Pol. 1).

Paradox
Epimenides was a 6th-century BC philosopher and religious prophet who, against the general sentiment of Crete, proposed that Zeus was immortal, as in the following poem:

They fashioned a tomb for thee, O holy and high oneThe Cretans, always liars, evil beasts, idle bellies!But thou art not dead: thou livest and abidest forever,For in thee we live and move and have our being. (Epimenides, Cretica)

Epimenides paradox is 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 be 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.