Are all Cretan Liars as Epimenides says?

Death through pirates

Cretans are robbers, always, Never they think rightful.
Have you see any fair action done by Cretans?
In a similar way Cretans acted with me, Timolytos, when I with a small cargo
driving through the sea, was miserably thrown down.
Loudly now weep the gulls and seabirds for me
but in this grave Timolytos is not buried.
Epitaph of Timolytos

Are all Cretans robbers as the above epitaph suggests? And are all Cretans liars as Epimenides of Crete said?

Epimenides, Edward Bulwer-Lytton, Athens: Its Rise and Fall

At this time there lived in Crete one of those remarkable men common to the early ages of the world, who sought to unite with the honours of the sage the mysterious reputation of the magician. Epimenides, numbered by some among the seven wise men, was revered throughout Greece as one whom a heavenlier genius animated and inspired. Devoted to poetry, this crafty impostor carried its prerogatives of fiction into actual life; and when he declared--in one of his verses, quoted by St. Paul in his Epistle to Titus--that "the Cretans were great liars," we have no reason to exempt the venerable accuser from his own unpatriotic reproach. Among the various legends which attach to his memory is a tradition that has many a likeness both in northern and eastern fable:--he is said to have slept forty-seven years in a cave, and on his waking from that moderate repose, to have been not unreasonably surprised to discover the features of the country perfectly changed. Returning to Cnossus, of which he was a citizen, strange faces everywhere present themselves. At his father's door he is asked his business, and at length, with considerable difficulty. He succeeds in making himself known to his younger brother, whom he had left a boy, and now recognised in an old decrepit man. "This story," says a philosophical biographer, very gravely, "made a considerable sensation"--an assertion not to be doubted; but those who were of a more skeptical disposition, imagined that Epimenides had spent the years of his reputed sleep in travelling over foreign countries, and thus acquiring from men those intellectual acquisitions which he more piously referred to the special inspiration of the gods. Epimenides did not scruple to preserve the mysterious reputation he obtained from this tale by fables equally audacious. He endeavoured to persuade the people that he was Aeacus, and that he frequently visited the earth: he was supposed to be fed by the nymphs--was never seen to eat in public--he assumed the attributes of prophecy—and dying in extreme old age: was honoured by the Cretans as a god.

In addition to his other spiritual prerogatives, this reviler of "liars" boasted the power of exorcism; was the first to introduce into Greece the custom of purifying public places and private abodes, and was deemed peculiarly successful in banishing those ominous phantoms which were so injurious to the tranquillity of the inhabitants of Athens. Such a man was exactly the person born to relieve the fears of the Athenians, and accomplish the things dictated by the panting entrails of the sacred victims. Accordingly (just prior to the Cirrhaean war, B. C. 596), a ship was fitted out, in which an Athenian named Nicias was sent to Crete, enjoined to bring back the purifying philosopher, with all that respectful state which his celebrity demanded. Epimenides complied with the prayer of the Athenians he arrived at Athens, and completed the necessary expiation in a manner somewhat simple for so notable an exorcist. He ordered several sheep, some black and some white, to be turned loose in the Areopagus, directed them to be followed, and wherever they lay down, a sacrifice was ordained in honour of some one of the gods. "Hence," says the historian of the philosophers, "you may still see throughout Athens anonymous altars (i. e. altars uninscribed to a particular god), the memorials of that propitiation."

The order was obeyed--the sacrifice performed--and the phantoms were seen no more. Although an impostor, Epimenides was a man of sagacityand genius. He restrained the excess of funeral lamentation, which often led to unseasonable interruptions of business, and conduced to fallacious impressions of morality; and in return he accustomed the Athenians to those regular habits of prayer and divine worship, which ever tend to regulate and systematize the character of a people. He formed the closest intimacy with Solon, and many of the subsequent laws of the Athenian are said by Plutarch to have been suggested by the wisdom of the Cnossian sage. When the time arrived for the departure of Epimenides, the Athenians would have presented him with a talent in reward of his services, but the philosopher refused the offer; he besought the Athenians to a firm alliance with his countrymen; accepted of no other remuneration than a branch of the sacred olive which adorned the citadel, and was supposed the primeval gift of Minerva, and returned to his nativecity,--proving that a man in those days might be an impostor without seeking any other reward than the gratuitous honour of the profession.

Johann Wolfgang von Goeth, Des Epimenides Erwachen , 1815

All Cretans are liars (Wikipedia)
Epimenides the Cretan 6th century BC

This statement, because it was uttered by a Cretan, is true if and only if it is false. The Cretan Paradox, is the earliest known (attempt at formulating a) mathematical paradox.

One of themselves, even a prophet of their own, said, The Cretians are always liars, evil beasts, slow bellies. This witness is true. Wherefore rebuke them sharply, that they may be sound in the faith; Bible, Titus 1, verse 12-14

Interestingly, St. Paul makes reference to this paradox, in a way that shows he knew of it but did not understand it: He says of Cretans that "they are all liars, as one of their own has said." But the context (Titus 1:12-14) suggests that he took it seriously as a denunciation of Cretans.

The poet's (or prophet's) statement is sometimes wrongly considered to be paradoxical because he himself is a Cretan; it is not. It should not be confused with the Liar paradox, which is in fact paradoxical.

Common usage defines a "liar" as someone who occasionally produces answers that differ from the known truth. This presents no problem at all: the poet, while lying occasionally, this time spoke the truth.

However, most formulations of logic define a "liar" as an entity that always produces the negation of the true answer, that is, someone who lies always. Thus, the poet's statement cannot be true: if it were, then he himself would be a liar who just spoke the truth, but liars don't do that. However, no contradiction arises if the poet's statement is taken to be false: the negation of "All Cretans are liars" is "Some Cretans aren't liars" (see De Morgan's Laws), in other words: some Cretans sometimes speak the truth. This does not contradict the fact that our Cretan poet just lied.

Therefore, the statement "All Cretans are liars", if uttered by a Cretan, is necessarily false, but not paradoxical.

Even the statement "I am a liar" is not paradoxical; depending on the definition of "liar" it may be true or false.

There is a solution to the Epimenides Paradox (a.k.a. the Liar's Paradox) by David R. Tribble 1982.

The paradox goes like this:

1. Epimenides is a Cretan.
2. Epimenides states, "All Cretans are liars."

On the face of it, this appears to be a paradox. Epimenides, being a Cretan, must either be a liar or a truth-teller. Thus his statement must be either true or false. But if it's true, then he (being a Cretan) must be a liar, so the statement can't be true. On the other hand, his statement is false, then he can't be a liar, so the statement must be true. This is a paradox.

Or so it would seem. Actually, the trouble lies in the interpretation of the statement "The statement 'All Cretans are liars' is false".

The solution goes like this:

p1. Epimenides is a Cretan.
p2. Epimenides is either a liar or a truth-teller.
p3. His statement is either true or false.

Assume that there is more than one Cretan:

p4. There is more than one Cretan.

Also assume that Epimenides is indeed a liar:

p5. Epimenides is a liar.
p6. Thus Epimenides's statement is false.
p7. Thus "All Cretans are liars" is false.
p8. Thus not all Cretans are liars.
p9. Thus some (one or more but not all) Cretans are not liars.
p10. Thus at least one (but not all) of them is a liar.
p11. Thus Epimenides, a Cretan, could be a liar.

We assumed that Epimenides was a Cretan (p1) and a liar (p5). Therefore, there is no paradox.

Another way of looking at it is to realize that, unless there is only one member of a set, then the negation of "all members of the set", i.e., "not all members of the set", is not "no members" but "some members".

If Epimenides is the only Cretan (so the set of Cretans has only one member), then there would be a paradox, since "not all Cretans" would mean "no Cretans".

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