Talk:Epimenides paradox

message: I wish to address a question for which I have some evidence but not the answer: <BR> 
::Who was it that first related Russell's paradox to a.) the ancient "case of the liar" and b.) to Epimenides? 
In Part II of Science et Methode, published in Paris in 1908, Henry Poincare is found rubbishing and then ridiculing the British attempts to reduce mathematics to logic without any appeal to intuition. After broadening the scope of Russells paradox (relating it to contradictions discovered by Burali-Forti and to Cantor himself) in Chapter 5 (II,5,6) he opens:  
::What is Mr Russell's attitude in the face of these contradictions? After analysing those I have just spoken of, and quoting others, after putting them in a form that recalls Epimenides, he does not hesitate to conclude as follow.... 
and then  
::What Mr. Russell calls zigzagginess is no doubt this special character which distinguishes the argument of Epimenides. 
This Chapter is (as I understand from Monk's biography of Russell p187) a republications of a series of articles published earlier (1906?) in Revue de Metaphysique et de Morale. 
So, in regards to a.): my impression of the history is that it was in order to show how a reduction of mathmatics to the form of predicatic logic will necessarily fail that Henry Poincare offered Russell the mathematical and historical context of his logical antimomy.  In regards to b.): Poincare gives the historical context by a reference to the contradiction implicit in Epimenides as though this is already the paradigm of what the ancients called the case of the liar. Yet, as far as Wikipedia knows, reference to the contradiction implicit in Epimenides is new with this controversy. So when exaclty does the contradiction of Epimenides' claim become the paradigm for 'the case of the liar.'? This is not such an important problem, but, it is indeed curious because, if it is a modern innovation, then it suggests a modern discussion of the logical paradox prior to Russell. 
(Note that I am using here my copy of the (post-humous) English translation of Science et Methode to which Russell was asked to write the introduction. As with Wittgenstein, and to his credit, he obliged.) The Bernmeister (talk) 02:06, 30 May 2008 (UTC)
thread_title: Henry Poincare relates Russell's paradox to Epimenides

message: If he states all cretans are liars, he may be telling the truth about cretans, yet lying about himself being a liar. the tue statement would be "all cretans except me are liars." By leaving out the latter, he lies while subsequently justifying it.  —Preceding unsigned comment added by 67.101.67.234 (talk) 01:17, 21 January 2008 (UTC)
thread_title:  This makes sense 

message: "Everything is relative" seems good example of an Epimenides-type self-referential paradox.  Worth including in this article?
Oh I get it because by saying that your making an absolute statement. Though I think that almost the same thing as the original example.  —Preceding unsigned comment added by 65.30.72.135 (talk) 07:34, 4 June 2008 (UTC)
thread_title: Everything is relative...

message: "I am a liar" is paradoxical  if by "liar" we mean someone who always lies, as in this case from the statement we would deduce "I am lying now", the liar's paradox. If "liar" is taken in a wider sense, the statement would be true if uttered by somebody who lies occasionally. And false if the speaker weren't a liar, but in this case he would have uttered at least one false sentence.
I would suggest removing the last sentence. - Calypso
Agreed. --James
No: let's define a liar to be someone who always lies.  Suppose person A says "I am a liar". If that is the truth, then that means that A is a liar, and liars never speak the truth, a contradiction. So we conclude A did not speak the truth. That means A's statement "I am a liar" is false, meaning that A is in fact not a liar. A person who is not a liar occasionly speaks the truth, by our definition of liar that we agreed upon above. So A occasionly speaks the truth, but this time lied. That's just fine and dandy; there's no contradiction. So we conclude that A lied this time but does not always lie and is therefore not a liar.
--AxelBoldt
Who in the world defines "liar" as someone who exclusively lies? Then no one in the world would be a liar, despite the fact that everyone has told a lie. What a worthless word it would be then. --James
I'm afraid I don't follow you. If you assume that A's statement is true
"Suppose person A says "I am a liar". If that is the truth, "
and from there conclude that the statemente is false
"...means A's statement "I am a liar" is false"
then you have a paradox there (p is true implies p is not true), the same as in the case of the liar paradox. -Calypso
The fact (p is true implies p is not true) shows that p cannot be true. But no contradiction arises from assuming that p is false. That's why p is false, but not contradictory. If on the other hand q is the statement "I am lying now", then (q is true implies q not true) and also (q is not true implies q is true), and these two taken together make q paradoxical. --AxelBoldt
I see what you mean, thanks for the explanation!
-- Calypso
To AxelBoldt: Is the contradiction not; p is true implies p is not true, which must mean that p cannot be true which implies p must be true. mathematically you can not go from p=t --> p=/t --> p=/t that does not follow any logic at all. --LPU0302 (talk) 09:49, 5 May 2011 (UTC)
thread_title: Paradoxical?

message: I feel like I must be missing something, but I don't know what that is.  It seems like when Alice, a Cretan, says "All Cretans are liars" she is saying "I, Alice, am a liar, and that cretan over there is a liar, and ... ".  (I'm assuming we mean by "a liar" someone who never made a true statement in their entire life.)  OK, so this is "necessarily false".  Fine.  So there exists a Cretan who, at some time in his life told the truth.  But that's not a logical truth, that's synthetic.  So, quote it for me; give me the true statement spoken by a Cretan.  Can't?  Well, neither can I.  Maybe there isn't one.  Isn't that a problem?  Sure seems like one to me.  It seems like calling "All Cretans are liars" a false statement is just wishful thinking, as a way to run away from the paradox.
-- Richard.
:No, it is not. The problem is in the misunderstanding of the negation of "all" which is somehow, and I am unable to understand why, immediately understood as to be only "none". This is simply not true. The negation of "all" is "some". Therefore, by saying that "All Cretans are liars" is a false statement we are correct as SOME Cretans may well be liars, and one of them is thus Alice or Epimenedes, which ever Cretan is actually saying it while there are some who are not liars. The fact that not all, but some Cretans are liars make the statement "ALL Cretans are liars" false.--212.66.146.4 (talk) 15:41, 16 December 2014 (UTC)
thread_title: Am I missing something?

message: Hello. I see that a distinction is made at present between the liar paradox and the Epimenides paradox. From what I can tell the two are often not distinguished. For example Paradoxes from A to Z, a recent popular book on the topic, has an entry for "The Liar (Epimenides' Paradox)". I would suggest the articles be merged and one redirected to the other. Comments? Wile E. Heresiarch 19:13, 15 Aug 2004 (UTC)
replies: text: I gather there was some discussion about the question whether or not Epimenides paradox and Liar paradox are the same thing and should be merged or not. The consensus appeared to be what the articles reflect now (and indeed this appears to be the only logical option if you're asking me). RSpeer should be able to tell you more. (All this was before I ever joined the fray.) It is true however that there is literature out there that does not make that distinction. Maybe someone more familiar with such literature could include such references in both articles,  e.g. under "Alternative views"? Ropers 17:55, 28 Sep 2004 (UTC)
thread_title: Epimenides paradox vs. Liar paradox

message: What is conspicuously missing from this article is any evidence that Paul was consciously quoting Epimenides. If this cannot be demonstrated the entire article is a pointless display of misdirected erudition which could be summed up as "Paul's assertion in Titus reminds some people of the Liar paradox in philosophy but there is no internal, external, or logical evidence that this passage has anything to do with it other than the coincidental accusation that Cretans are liars; however if we pretend it might be an allusion to this paradox we can parse it logically to an indefensible statement and reject it." Could someone who expended all that energy on giving us the Bible passage in multiple translations please supply the connection? Thanks. Alteripse 12:50, 30 Aug 2004 (UTC)
replies: text: Well, it appears that web site has an agenda to push; the conclusion of the article is Therefore, Paul was not inspired. See also the statement at the bottom of the page. I'm not sure we want to copy stuff from that web site into the article. Wile E. Heresiarch 00:42, 28 Sep 2004 (UTC)
thread_title: How do we know Paul was quoting Epimenides?

message: Hello. I've rewritten the article to separate the logical analysis from the textual analysis and to give much more about the history of the Epimenides paradox, including references. I've left out the translations of Titus 1:12 into different languages, as that was beside the point. I believe the article as it stands is quite a bit stronger than before. Hope you like it. Regards, Wile E. Heresiarch 03:11, 4 Oct 2004 (UTC)
thread_title:  Article rewritten 

message: After I wrote this phrase ("contingently false"), I started to think more about what it might mean. The sentence I wrote isn't complete nonsense, but I would like to encourage some discussion of alternatives.151.200.182.26 06:21, 8 Dec 2004 (UTC)
thread_title:  "Contingently false" 

message: We use the latter, but Britanica uses the former. Other sources seem about evenly split. I think the possesive makes sense, but I'm no expert in this field (I was just casualy reading this article). What should be done?  Broken S 07:44, 27 December 2005 (UTC)
thread_title:  Epimenides' paradox  or Epimenides paradox

message: This might be somewhere else on this talk page, but I personally don't see how it is a paradox.
*Epimenides says that all Cretans are liars,
*If he is telling the truth, then it is a paradox,
*If he is lying, however, he is a liar but not necessarily all Cretans.
Do you see my point? ~  Ghelæ talkcontribs 11:03, 25 March 2006 (UTC)
replies: text: Right. Technically, the article needs to put a [sic] somewhere in the quotes that purport to call this a paradox and to point out that it's not a paradox at all. To assert Epimenides' statement is to deny it. To deny Epimenides' statement, however, is not to assert the statement back, but merely to assert that (a) some Cretans are not liars and (b) that Epimenides is a liar for having made the statement. In both cases it amounts to a confession of being a liar coupled with a compliment on the virtues possessed by some Cretans, present company excluded. If Epimenides were the only Cretan, then it would be a paradox.  — Preceding unsigned comment added by 64.136.26.17 (talk) 12:14, 30 May 2012 (UTC)
replies: text:  Shouldn't this be seen more as a logical puzzle? Since if we take the statement to be true, it leads to a paradox, so we have to conclude that the statement must be false making Epimenides a liar. I mean, thats the main difference from the actual paradox of the "I am a liar" phrase, that in this case we can learn something from what he said. --Kiesch (talk) 11:47, 23 January 2013 (UTC)
thread_title:  Not A Paradox 

message: to classify true or false you would have to be familiar with all statements made by all cretans. phyti-jun 05 2006
Well then maybe it should be changed more exact like: a Cretan says: "Everything a Cretan says is a lie"  —Preceding unsigned comment added by 65.30.72.135 (talk) 07:37, 4 June 2008 (UTC)
thread_title: undecidable

message: I have never heard this or read it anywhere but here. I'm not in a position to argue the theory but I think it's certainly an assertion that ought not be made without a citation... Certainly the mainstream view is that the Epistle to Titus was written by the Apostle Paul, one of the most literate and erudite men of his time.
The current version of the article does not say that Callimachus authored the epistle. Paradoctor (talk) 21:37, 3 January 2010 (UTC)
thread_title:  Callimachus the author of the Epistle to Titus?? 

message: > Just assume whoever stated that "Epimenides was a Cretan who made one immortal statement: 'All Cretans are liars.'" was a liar.
I call BS 69.107.141.19 (talk) 05:32, 2 March 2009 (UTC)
thread_title:  Solution is BS 

message: The portion of the text that states,
:The logical contradiction exists on Saint Paul's epistle rather than the poem of Epimenides:
: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. This forms a contradiction because he uses the words of a Cretan (always a liar) in order to prove that Cretans are always liars, also concluding that Epimenides (a Cretan) had surely told the truth (that Cretans are always liars).
Is an unfounded biased assertion. It is clearly biased because it makes the unfounded assertion that the contradiction is in Paul rather than in Epimenides.  Then it states the reason as 
:This forms a contradiction because he uses the words of a Cretan (always a liar) in order to prove that Cretans are always liars
This is no different from the problem adhering to the Epimenides statement itself.  Thus it is trying to transfer the apparent contradiction from the Epimenides statement to Paul's statement, without valid reason.
This statement therefore should be removed as not supplying anything helpful or valid to the article.  —Preceding unsigned comment added by Sdoherty777 (talk • contribs) 12:13, 4 January 2010 (UTC)
replies: text: If you read Epimenides' poem, you'll see that he wasn't talking about all Cretans, but only those Cretans who "fashioned a tomb" for Zeus, which excludes Epimenides. Regards, Paradoctor (talk) 13:51, 4 January 2010 (UTC)
thread_title:  Unfounded Biased Statement 

message: The article currently says, "The earliest unmistakable reference to the Epimenides paradox as it is known today is an article by Bertrand Russell on the theory of types dating to 1908."
That can't be correct.  A little work with Google books shows clear references to the Epimenides paradox as it would be stated today (as a rough version of the Liar paradox) in logical works by Lotze (1880), Fowler (1869), De Morgan (1847), and Bayle (1740).  I provide links to Google books references on the blog "Honest Toil" (http://hnsttl.blogspot.com/2010/09/who-first-linked-epimenides-to-semantic.html).
71.199.123.156 (talk) 02:24, 7 September 2010 (UTC)
thread_title:  References to the paradox 

message: From what I read here, "all" is made equivalent with "always."
My problem with this is that I do not know how the ancient Greek was translated, and why.  If these authors meant "all", which seems to be the case, why was "always" translated into modern English?  Do you see what I am getting at?
In the two Bible versions (New King James and New International) I have consulted, Paul is apparently quoting Epimendes, and I think "all" would be the more literal interpretation of what these authors meant in each context.
What I would like to know is, who decided to use "always" in these translations, and why?  In modern English there is an ambiguity here -- always sometimes means "for all time."
Taken in this sense, the authors could have meant "once a liar, always a liar."
Now, I do not believe an ambiguity was intended by either author, so why this particular translation?
Surely this equivalence is not so apparent in ancient Greek?  This would seem to be a huge coincidence.
Is there a flaw in my reasoning?  —Preceding unsigned comment added by 76.107.111.94 (talk) 08:01, 5 January 2011 (UTC)
thread_title:  All and Always 

message: I don't understand how this is supposed to be a paradox.
If he tells the truth then all Cretans are liars, which means he is a liar, which means his statement "all Cretans are liars" is untrue, but that doesn't mean all Cretans tell the turth. One single truthtelling Cretan would be enough for the statement "all Cretans are liars" to be untrue. Only because not all Cretans tell the truth doesn't mean that all Cretans lie.  — Preceding unsigned comment added by Leksu789 (talk • contribs) 18:35, 25 April 2012 (UTC)
thread_title:  This is not a paradox 

message: li·ar - noun - a person who tells lies.
The paradox does not exist. Someone who only tells one lie is a liar. Someone who is a liar may also tell the truth at times.  It is not a requirement to never tell the truth to be a liar.
To have a paradox we have to infer they never tell the truth, when that is not what is stated.  — Preceding unsigned comment added by 71.164.232.78 (talk) 22:12, 19 September 2012 (UTC)
thread_title:  definition of liar 

message: I did not see the following line of reasoning discussed yet so I thought it might be worth exploring. Can't one focus on the subject of the sentence as containing the falsehood (all Cretans) and resolve the paradox instead of whether or not Cretans lie?
As an example, Epimenides' statement "All Cretans are liars," asserts he too is a liar because he is of Crete. That's fine, but knowing this, it could be believed then, that only "Some Cretans are liars." Epimenides' lie (if we should be so dramatic) proves this. Therefore, the paradox is resolved.  — Preceding unsigned comment added by 170.2.52.28 (talk) 22:08, 29 November 2012 (UTC)
thread_title:  Some vs. all 

message: First of all, a liar is defined as someone who lies, not as someone who only lies, but even if the statement would have been "Everything I say is false.", there is no paradox: Assume that that sentence is false, the negation of that sentence is not "I only say the truth.", but rather "Not everything I say is false.", which is equivalent to "I say some true things." (or logically, ¬∀x: ¬true(x) ⇔ ∃x: true(x)), therefore that sentence can be false with no contradictions. 2607:FA48:6D0C:EA80:DD06:BFCA:CF24:3298 (talk) 02:44, 5 December 2014 (UTC)
thread_title:  This is not a paradox (The negation of "Everything I say is false" is "Not everything I say is false".) 

message: I changed the misinformation regarding Paul of Tarsus's opinion of Epimenides with a minor edit. It may break up the flow of the argument that past writers didn't realize the paradox, but considering I don't see any paradox either, since the clear meaning of the original quote is "routine liars" and not "exclusively liars" I thought it better to not mislead.
Paul is talking here about those he calls false teachers who do so for personal gain. He calls Epimenides one of these. He then quotes him and says "this testimony is true, so reprove them."  — Preceding unsigned comment added by 108.216.129.92 (talk) 04:59, 8 September 2015 (UTC)
thread_title:  Concerning slight edits to quote from the Epistle to Titus