Epimenides Paradox

Image of Epimenides (Nuremberg Chronicles)

The Epimenides paradox is a form of the liar paradox related to philosophy and logic. It belongs to the group of falsidic paradoxes, since it appears to contradict itself if reasoning is followed, but it can be shown that said reasoning is not correct.

Formulation

Epimenides was a legendary poet and philosopher of the sixth century B.C. C. who is credited with having been asleep for fifty-seven years, although Plutarch affirms that it was only fifty.

Epimenides is credited with stating:

All the Cretans are liars..

Knowing he himself was a Cretan, was Epimenides telling the truth?

The Epimenides paradox can also be synthesized in <I lie. I speak.> This is how Michel Foucault proposes it in The Thought from the Outside. In this sense, fiction as it is known is also put to the test.

Sentence origin

Epimenides was a philosopher and religious prophet of the VI century B.C. C. that, against the general feeling of Crete, proposed that Zeus was immortal, as in the following poetry:

They made a grave for you, oh sacred and high! Cretans, always liars, evil beasts, idle belly!
But you are not dead: you live and remain forever,
Because in you we live and move and have our being.

Epimenides, Cretic

To deny 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 intention as Epimenides:

Oh, Zeus, some say you were born on the hills of Ida;
Others, O Zeus, say in Arcadia;
Did these or those lie, O Father? - “The Cretans are always liars.”
Yes, a grave, O Lord, the Cretans built;
But you did not die, because you are eternal forever.

Calymacus, Hymn to Zeus

The logical inconsistency of a Cretan in stating that all Cretans are always liars, may not have been noticed by either Epimenides or Callimachus, who used the phrase to emphasize their claim of Zeus' immortality, without irony.

In the I century d. C., the quote was mentioned by Paul of Tarsus as the word of & # 34; one of his prophets & # 34; To illustrate the behavior of the Cretans and the false teachers that existed before the establishment of the early church. Thus, Paul stresses the importance of the commission that is made to Titus (see chapter 1 of the Epistle to Titus).

One of the prophets of Crete said: "The Cretans are always liars, evil beasts, idle belly." He probably said the truth. For this reason, they must be corrected with severity, so that they may be firm in faith instead of paying attention to the Jewish fables and commandments of the people who turn their backs to the truth.

Epistle to Titus, 1:12–14

Clement of Alexandria, late II century d. C., when referring to this passage, does not indicate that there is an interpretive problem due to a logical paradox in the words of Epimenides:

In his Epistle to Titus, Paul of Tarsus wants to warn Titus that the Cretans do not believe in the only truth of Christianity, because "the Cretans are always liars." Apostle Paul quotes Epimenides.

Stromata 1.14

In the early IV century, Augustine of Hippo restates the closely related liar paradox in "Against the academics" (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, in the second volume of Dictionnaire Historique et Critique, Pierre Bayle explicitly connects Epimenides with the paradox, although Bayle calls the paradox a "sophism".

The Epimenides paradox has recently been discussed from multiple points of view. The most relevant has been the semantic analysis of the paradox.

References from other authors

All of Epimenides' works have been lost, known only through citations from other authors. The Cretica quote from Epimenides is given by R.N. Longenecker, "Acts of the Apostles,", in vol. 9 of The Expositor's Bible Commentary, Frank E. Gaebelein, editor (Grand Rapids, Michigan: Zondervan Corporation, 1976–1984), page 476. Longenecker, in turn, quotes MD Gibson: 'Horae Semiticae X' '(Cambridge: Cambridge University Press, 1913), page 40, "in Syriac.

An indirect 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), pp. 235–250. Johnson writes in a footnote,

Compare, for example, the occasions when fallacy is provided by "Epiménides is a liar" or "That surface is red", which can be resolved in "All or some statements by Epiménides are false", "All or some of the surfaces are red."

The epimenid paradox appears explicitly in Bertrand Russell's "Mathematical Logic According to the Theory of Types", in the "American Journal of Mathematics", volume 30, number 3 (July 1908), pages 222–262, which opens with the following text:

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

In that article, Russell uses the Epimenides paradox as a starting point for discussions of other problems, including the Burali-Forti paradox and the paradox now called Russell's paradox. Since Russell, the Epimenides paradox has been referenced repeatedly in logic texts. Typical of these references is Douglas Hofstadter's Gödel, Escher, Bach: An Eternal and Graceful Loop, which gives the paradox a prominent place in a discussion of self-reference.

Comment

Before we begin, we must clarify that it is established that a liar only makes statements that are false. This definition is common in the study of logic, and it is possible to obtain this paradox with less ambiguity (although also too much complexity) if it is formulated as All Cretans are people whose statements are always false.

Following this definition, at first sight it seems that the affirmation is self-contradictory, since Epimenides is affirming that he is lying (see the paradox of the liar). This is not actually true, as even though the statement may not be true, it could be false. If we assume that it is true, Epimenides is affirming that, like any Cretan, he is lying, and therefore the affirmation would be false, and would reach a self-contradiction. But if we assume that it is false, we do not reach a contradiction, since if the statement All Cretans lie is false, it means that there is at least one Cretan, not necessarily Epimenides, who tells the truth. Therefore, it is perfectly possible that the statement is false, and this statement is not a true paradox.

It is a false paradox, since in reality it commits a fallacy in its first proposition: all Cretans are liars. The propositions must be based on proven facts, and this is not really a proven fact, but an indeterminacy that must be justified as true. You cannot start an argument about an indeterminate proposition. You must start with a proven fact. And we do know that Epimenides is Cretan (proven fact) and claims to be (proven fact), so we must start the reasoning on this side:

1. Epimenides is cretense
2. Epimenides says it is.

→ Epimenides says the truth.

And from there you get:

1. All cretenses always lie
2. Epiménides is cretense and sometimes tells the truth

→ Then it is false to say that all the Cretans always lie

To finish posing correctly:

1. Not all cretenses always lie (made tested)
2. Epimenides says yes (proposition)

→ Epimenides lies (conclusion, proven)

Hence the paradox can be stated again: "if Epimenides lies, he is a liar". But if we first accept the definition of a liar as someone who ALWAYS tells lies, the logical approach once again derails the paradox:

1. Epimenides, as you believe, claims to be a liar: someone who always lies.
2. We know that Epimenides has said the truth sometime

→ Then it is false that Epimenides always lies

And since he is Cretan, it is false that all Cretans always lie.

In conclusion, this false paradox is based on two fallacies: taking a proposition for granted without being so, and a lexical fallacy that confuses the concepts "liar" and "someone who always tells lies". Strictly speaking, it cannot be affirmed that someone "is" liar; it is not an essence, but a state. One can lie, like Epimenides, but one can also tell the truth. Telling a lie does not make you a liar who always tells lies. That is why it is important before reasoning to clarify the definitions: if being a liar is someone who lies occasionally, or if it is someone who always lies. In the first case, if we define "liar" as someone who lies occasionally, the paradox is not such, but is once again a fallacy with a false conclusion:

1. Epimenides is a liar (sometimes lying)
2. Epimenides is cretense

→ All Cretans are liars (from time to time they lie)

The conclusion cannot be inferred from the propositions. It is not known if all Cretans are occasional liars. Only Epimenides is known to be.

Solution

All Cretans are liars, I am Cretan, therefore I lie. So what is stated in this sentence is a lie, lying again for each added morpheme.

Concepts to assess:

• Everyone.
• Bullshit.
• Crete.

To clarify the paradox, fuzzy logic should be applied, establishing that it tells the Truth, tells a Lie, or Ni fu ni fa >.

You want to compare the information

Citizen=Cretans/All 'This division will result in 1'

You want to count All Citizens, and for that you have to Calculate the Count:

Home Account

Person(Truth)

{

You have to know the Individue.(note= account + citizen)

If Information is equal to Truth

it is established that the Individual is a Person = Truth

If Information is equal to Mentira

it is established that the Individual is a Person = Liar

In any of the other cases

Null value to the person

!

If Person(truth) is Liar then

Add one to the Lies Account

If Person(truth) is Truth then

Add one to the Truth Account

any other case

Add one to the Account neither fu nor fa

Fin account

Now the Lies Account is compared to the value of all.

If they're equal, then all the Cretans are liars.

• This example shows that all will be liars for a particular case, and not for all cases that may arise. If it is assumed that they are for all cases, it carries a paradox. Unless all cases are examined one by one, therefore the assertion will be true for the information processed and not for the one that has not yet been prosecuted. This paradox, when absolute values are assumed, is usually used in the fallacy of the real Scots.