埃庇米尼得斯悖论

有人就表示，既然埃庇米尼得斯是克里特人，那他自己就是骗子。但如果他是个骗子，那他所说的就是假话，因此克里特人不是骗子。另一方面，埃庇米尼得斯是克里特人，因此他对克里特人的形容应该是正确的，不过既然他说克里特人是骗子，那么埃庇米尼得斯本人也是骗子，那么他对克里特人的形容并不正确。如此循环往复，这样则可以不断交替证明埃庇米尼得斯与克里特人既诚实又虚伪。

The Epimenides paradox has to do with self-reference in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC) who said: "Cretans, liars always, evil beasts, idle bellies". A typical description of the problem (but with an inaccurate quote) is given in the book Gödel, Escher, Bach, by Douglas Hofstadter:

Epimenides was a Cretan who made the immortal statement: "All Cretans are liars."

It is often claimed that a paradox of self-reference arises when one considers whether it is possible for Epimenides to have spoken the truth, but in fact there is no paradox because it may simply be a false statement.

Mythology of lying Cretans

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.

Logical paradox

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." However, this exposition suffers from a logic error – if what Epimenides said is untrue, it does not follow that all Cretans are veracious. Some Cretans, such as Epimenides himself, could be liars.

Origin of the phrase

The phrase is found in the Epistle to Titus:

One of themselves, even a prophet of their own, said, The Cretians are alway liars, evil beasts, slow bellies.

Ancient authors such as Clement of Alexandria have informed us that this refers to Epimenides. A commentary on the Bible in Syriac contains a passage on Acts 17:18, apparently translated from Greek and quite possibly originally by Theodore of Mopsuestia, saying:

"In Him we live and move and have our being." The Cretans used to say of Zeus, that he was a prince and was ripped up by a wild boar, and he was buried: and lo! his grave is with us. Accordingly Minos, the son of Zeus, made over him a panegyric and in it he said:

Emergence as a logical contradiction

The logical inconsistency of a Cretan asserting all Cretans are always liars may not have occurred to Epimenides, nor to Callimachus, who both used the phrase to emphasize their point, without irony, perhaps meaning that all Cretans lie routinely, but not exclusively.

In the 1st century AD, the quote is mentioned in the Epistle to Titus as having been spoken truly by "one of their own prophets."

It was one of them, their very own prophet, who said, "Cretans are always liars, vicious brutes, lazy gluttons." That testimony is true. For this reason rebuke them sharply, so that they may become sound in the faith, not paying attention to Jewish myths or to commandments of those who reject the truth.

Clement of Alexandria, in the late 2nd century AD, fails to indicate that the concept of logical paradox is an issue:

References by other authors

An oblique reference to Epimenides in the context of logic appears in "The Logical Calculus" by W. E. Johnson, Mind (New Series), volume 1, number 2 (April, 1892), pages 235–250. Johnson writes in a footnote,

Compare, for example, such occasions for fallacy as are supplied by "Epimenides is a liar" or "That surface is red," which may be resolved into "All or some statements of Epimenides are false," "All or some of the surface is red."

The Epimenides paradox appears explicitly in "Mathematical Logic as Based on the Theory of Types", by Bertrand Russell, in the American Journal of Mathematics, volume 30, number 3 (July, 1908), pages 222–262, which opens with the following:

The oldest contradiction of the kind in question is the Epimenides. Epimenides the Cretan said that all Cretans were liars, and all other statements made by Cretans were certainly lies. Was this a lie?