Editing Epimenides paradox (section)

== Logical paradox ==

[[Thomas Fowler (university administrator)|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."<ref>{{cite book |title=The Elements of Deductive Logic |last= Fowler |first=Thomas |author-link=Thomas Fowler (university administrator) |year=1869 |publisher=Clarendon Press |location=Oxford |edition=3rd |page=[https://archive.org/details/elementsdeducti08fowlgoog/page/n187 163] |url=https://archive.org/details/elementsdeducti08fowlgoog |quote=epimenides. |access-date=1 April 2011}}</ref>

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 a contradiction since it is not required that this Cretan be Epimenides. This means 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.<ref>{{cite web |title=wolfram.com |url=http://mathworld.wolfram.com/EpimenidesParadox.html}}</ref> 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 [[Eubulides#Paradoxes of Eubulides|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 (disambiguation)|Socratic paradox]] and the [[Burali-Forti paradox]], all of which have self-reference in common with Epimenides. 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.

In other words, it is not a paradox once one realizes "All Cretans are liars" being untrue only means "Not all Cretans are liars" instead of the assumption that "All Cretans are honest".

Perhaps better put, for "All Cretans are liars" to be a true statement, it does not mean that all Cretans must lie all the time. In fact, Cretans could tell the truth quite often, but still all be liars in the sense that liars are people prone to deception for dishonest gain. Considering that "All Cretans are liars" has been seen as a paradox only since the 19th century, this seems to resolve the alleged paradox.  If 'all Cretans are continuous liars' is actually true, then asking a Cretan if they are honest would always elicit the dishonest answer 'yes'. So arguably the original proposition is not so much paradoxical as invalid.

A contextual reading of the contradiction may also provide an answer to the paradox. The original phrase, "The Cretans, always liars, evil beasts, idle bellies!" asserts not an intrinsic paradox, but rather an opinion of the Cretans from Epimenides. A stereotyping of his people not intended to be an absolute statement about the people as a whole. Rather it is a claim made about their position regarding their religious beliefs and socio-cultural attitudes. Within the context of his poem the phrase is specific to a certain belief, a context that Callimachus repeats in his poem regarding Zeus. Further, a more poignant answer to the paradox is simply that to be a ''liar'' is to state falsehoods, nothing in the statement asserts everything said is false, but rather they're "always" lying. This is not an absolute statement of fact and thus we cannot conclude there's a true contradiction made by Epimenides with this statement.