Epimenides paradox

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 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."

The Epimenides paradox in this form can however be solved. A paradox only results when the statement is assumed to be true. Namely, if the statement "all Cretans are liars" (stated by Epimenides, himself a Cretan) is true, then Epimenides, being a Cretan, would be a liar; making the assumption that liars only make false statements, the statement should be false. So assuming the statement is true leads us to conclude that the statement is false and cannot be accepted, therefore it must be true, continuing in a self-referential paradox.

However, 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 contradiction, since it is not required that this Cretan be Epimenides, meaning 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. The mistake made by Thomas Fowler (and many other people) above is to think that the negation of "all Cretans are liars" is "all Cretans are honest" (a paradox) when in fact the negation is "there exists a Cretan who is honest", or "not all Cretans are liars". The Epimenides paradox can be slightly modified as to not allow the kind of solution described above, as it was in the first paradox of Eubulides but instead leading to a non-avoidable self-contradiction. Paradoxical versions of the Epimenides problem are closely related to a class of more difficult logical problems, including the liar paradox, Socratic paradox, and the Burali-Forti paradox, all of which have self-reference in common with Epimenides. Indeed, the Epimenides paradox is usually classified as a variation on the liar paradox, and sometimes the two are not distinguished. The study of self-reference led to important developments in logic and mathematics in the twentieth century.

To psychology, scepticism and law

The Epimenides paradox is the same principle as psychologists and sceptics using arguments from psychology claiming humans to be unreliable. The paradox comes from the fact that the psychologists and sceptics are human themselves, meaning that they state themselves to be unreliable. This means that psychology is not a science.

The same goes for any statements that laws are necessary due to human nature, since the laws are written and enforced by human beings and so if that was the case the alleged human flaws would have been built into the laws and exaggerated by the enforcement into something worse than nothing.

Origin of the phrase

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 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.

Denying the immortality of Zeus, then, was the lie of the Cretans.

The phrase "Cretans, always liars" was quoted by the poet Callimachus in his Hymn to Zeus, with the same theological intent as Epimenides:

O Zeus, some say that thou wert born on the hills of Ida;
Others, O Zeus, say in Arcadia;
Did these or those, O Father lie? -- “Cretans are ever liars.”
Yea, a tomb, O Lord, for thee the Cretans builded;
But thou didst not die, for thou art for ever.

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 by Paul of Tarsus as the words of a man who was insubordinate, an empty talker and a deceiver, yet spoke truly in this statement.

One of Crete's own prophets has said it: 'Cretans are always liars, evil brutes, idle bellies'.
He has surely told the truth. For this reason correct them sternly, that they may be sound in faith instead of paying attention to Jewish fables and to commandments of people who turn their backs on the truth.

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

In his epistle to Titus, Apostle Paul wants to warn Titus that Cretans don't believe in the one truth of Christianity, because "Cretans are always liars". To justify his claim, Apostle Paul cites Epimenides.

During the early 4th century, Saint Augustine restates the closely related liar paradox in Against the Academicians (III.13.29), but without mentioning Epimenides.

In the Middle Ages, many forms of the liar paradox were studied under the heading of insolubilia, but these were not explicitly associated with Epimenides.

Finally, in 1740, the second volume of Pierre Bayle's Dictionnaire Historique et Critique explicitly connects Epimenides with the paradox, though Bayle labels the paradox a "sophisme".