Epimenides of Knossos
(semi-mythical 6. cent. BC)

'All Cretans are liars'

All the works of Epimenides (semi-mythical, 6th cent. BC) are now lost and only known through other authors. And he is only really famous for one particular sentence. Namely, the 'Epimenides Paradox' quoted above. Furthermore, it is unlikely, that Epimenides ever intended his words to be understood as a kind of 'liar's paradox'. It was probably only understood as such in the 20th century. Nevertheless, the recognition of ambiguities, equivocations, and unstated assumptions underlying sentences such as the 'Epimenides Paradox' has led to significant advances in science, philosophy and mathematics.

The puzzle lies in the following interpretation of the sentence:
First, If we take a 'liar' to mean someone whose every statement is false, the paradox translates to 'everything a Cretan says is false'. This being said by the Cretan Epimenides makes the statement not true. Second, if we take the two statements 'Epimenides said all Cretans are liars' and 'Epimenides is a Cretan' as true, this implies that a Cretan has truthfully said no Cretan speaks the truth. Then Epimenides’ statement is a counterexample of this, since he is Cretan who has just spoken the truth actually contradicting himself rendering his own statement 'All Cretans are liars' false.

The sentence is related to the 'liar's paradox' or 'pseudomenon' in Ancient Greek coming from the sentence: 'This sentence is false'. When trying to assign a classical binary truth value to the sentence (i.e. either something is true or it's false - it can't be both) it leads to a contradiction: 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 and so on...

The Epimenides paradox has been suggested as an example of the liar paradox, but actually they are not logically equivalent. The 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. This then is not a true paradox since Epimenides may know that at least one Cretan is, in fact, honest, and so is lying when he says that all Cretans are liars. There therefore need be no self-contradiction in what could simply be a false statement by a person who is himself a liar.

But - as mentioned above - Epimenides probably never intended his sentence to be understood as a paradox. The sentence comes from a poem in which Minos addresses Zeus. Epimenides considered Zeus to be immortal. However, apparently his fellow Cretans did not. And therefore, he called them liars. The poem says:

They fashioned a tomb for thee, O holy and high one
The 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.

It all began when Epimenides was a boy or a young man tending his fathers sheep. He happened to fall asleep in a Cretan Cave sacred to Zeus and when he woke up 57 years later !! he awoke with the gift of prophecy. This he used to help both in Athens and in Sparta and elsewhere until he finally died a very old man. According to the Cretans, who afterwards honoured him as a god, he lived to be about three hundred years old. But who knows. After all, 'all Cretans are liars'...

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