Talk:Epimenides paradox

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[edit] Henry Poincare relates Russell's paradox to Epimenides

I wish to address a question for which I have some evidence but not the answer:

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)


[edit] This makes sense

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)

I feel by nature of making any verbal statement, he is in his mind a liar. I am sure words to him are inert as soon as uttered, rendering them dead, the antithesis of the immortality of the Creator, Zeus therefore in and of themselves it makes the statement a lie. In uttering this TRUTH through words, whether he explicitly states it or not, he is a liar and is clearly aware of it.

The following was removed:

[edit] Everything is relative...

"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)

[edit] A slight aside...

God Himself (via Saint Paul) re-iterates the Cretan liar steryotype, apparently without any sense of irony, in the Epistle to Titus, chapter 1, vv12 and 13:

"One of themselves, even a prophet of their own, said, The Cretians are alway liars, evil beasts, slow bellies. This witness is true. Wherefore rebuke them sharply, that they may be sound in the faith;"

There is nothing inherently wrong with including Bible verse, however, there needs to be more comentatry included with it. Otherwise the article has an uneeded religious feel to it. --maveric149

I'm not sure it should be included at all. The full quote is like this:

1:10 For there are many rebellious people, idle-talkers, and deceivers, especially those with Jewish connections,
1:11 who must be silenced because they mislead whole families by teaching for dishonest gain what ought not to be taught.
1:12 A certain one of them, in fact, one of their own prophets, said, "Cretans are always liars, evil beasts, lazy gluttons."
1:13 Such testimony is true. For this reason rebuke them sharply that they may be healthy in the faith
1:14 and not pay attention to Jewish myths and commands of people who reject the truth.
1:15 [...]

The writer is explaining to Titus why he has left him on Crete to "set in order the remaining matters and to appoint elders in every town". Seeing the remark in 1:13 the writer probably didn't get the paradoxical nature of the remark and was simply using a then famous Hellenistic "soundbite" to make his point. So to call it a different version of the paradox would be a bit misleading. -- JanHidders

"Different version" is not correct, I agree. How about: "it is also mentioned in the Bible..."? It's also interesting to note that St. Paul was apparently aware of the fact that the statement is not paradoxical, since he explicitly clarifies "Such testimony is true." --AxelBoldt

First, let me recant. I think the quote *should* be mentioned in the article because it is clearly a related piece of information. I'm not sure if St. Paul (or whoever wrote Titus) was aware that the Epimenides quote is not really paradoxical. He quotes him as saying that "Cretans are always liars". That makes it IMHO a bit less obvious that the remark does not really contradict itself when said by a Cretan, although I certainly wouldn't claim that it unambibuously does contradict itself. However, it doesn't make much sense to me that St. Paul would argue in his letter something like "More than 500 years ago there was a really important Cretan priest who said that all Cretans are always liars. But this is not really a paradox, so it is true." So I would say that the simplest explanation is that he just knew the quote but not the full story behind it. But I hasten to add that I certainly do not consider this "quite certain" or even "very likely". So, summarizing I would say that it is quite certain that the quote is related to Epimenides remark, but it is not clear whether St. Paul understood the reason that made it survive more than 5 centuries.

Unfortunately I don't have much time, or I would try to find out who was the first to refer to Epimenides' remark as a paradox. IIRC that would be Aristotle or Plato, but I'm not sure. --JanHidders

Heh. Did the quote survive for five centuries because the question of whether it was paradoxical was so interesting, or because it was a popular catch-phrase to diss those folks across the water from you, the way Americans in one state often try to diss neighboring states? The reasons for the quotes survival are just speculation, unless you find it in a centralized list of required reading for philosophy. Which would be unlikely, given that they didn't have huge universities then, AFAIK. At any rate, it's clear from context that Paul didn't bring up the quote to discuss that aspect of philosophy with Titus, but to discuss their character. I don't think one can conclude from the text that he did or did not know of its paradoxical properties. Don't know that it matters much one way or the other. --Wesley

[edit] Paradoxical?

"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

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

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

Not a paradox at all, except to professional philosophers with nothing better to do. Who has come across a liar? Who has come across a liar who always lies? Everyone has lied to different degrees of seriousness, at some time in their life. It seems random to define a liar to be "someone who always lies". For argument's sake, OK, but when you start imagining this to be the way "the man on the street" would understand Epimenides, then... you end up telling Paul off for not spotting said (imaginary) paradox.

[edit] Removed content

Moved here from the main page:

Addendum 1 : There is an old saying that the slickest way to lie is to tell half the truth and shut up.

Addendum 2 : What if the Cretans are scrupulously honest with themselves, where no one can tell?

Frankly, I don't see the relevance of add.1; as to add.2, that's certainly possible. If they are honest among themselves and occasionally lie to outsiders, then the poet's statement is true or false depending on the definition of "liar" employed. But it wouldn't be paradoxical. AxelBoldt 00:47 Oct 27, 2002 (UTC)

[edit] Am I missing something?

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.

[edit] An incorrect argument?

Moved here from the article:

This entry needs to be revised since the argument given above is simply incorrect. Even if the term "liar" is defined weakly (as suggested above), the paradox remains in all cases. The Cretan statement is only true if it is false and if it is false it denies itself. - --Steven Zenith 19:04, 16 May 2004 (UTC)
Simple example: "I always lie" is a paradox. "I am a liar" is not a paradox. Why? Because being a liar doesn't require that you *always* lie. Richard Brightwell 25 May 2004 18:34 UTC



[edit] Epimenides paradox vs. Liar paradox

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)

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)

[edit] How do we know Paul was quoting Epimenides?

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)

OK, I found the answer to my own question: [1] This site explain exactly the relationship of Paul's quote as well as some interesting Christian dilemmas arising from various ways to interpret it. Could the authors of this article incorporate some of this info so it makes more sense? Also, why not restrict the number of translations to the original koine and modern english to reduce distraction and the temptation to correct the Jacobean spelling. Having Latin, German, and Jacobean English versions does not help make the authors' points. Why not Farsi, Tagalog, and Klingon versions too? Maybe the other versions could be moved to the talk page if the author wants the evidence of his erudition preserved? Alteripse 13:48, 31 Aug 2004 (UTC)

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)

[edit] What's Paul got to do with it?

Hello. The article at present is slanted pretty heavily toward discussing a passage in the Bible. That seems quite strange to me. Can we get back on track here? The article states It was only much later that the aforementioned Bible quote was taken up again, considered paradoxical and referred to as the Epimenides paradox -- this seems unlikely, as Epimenides is not called by name in Titus, so the association of lying Cretans and Epimenides must be made some other way. Does someone have a reference for the history of the puzzle now customarily called "the Epimenides paradox"? Is there any other ancient source for the "Cretans are liars" statement aside from this passage in the Bible? Do we know who was the first author to write "paradox" after "Epimenides"? -- As it stands, the article appears to be original research on Titus 1:12. Regards & happy editing, Wile E. Heresiarch 01:35, 26 Sep 2004 (UTC)

The earliest citation I've found which suggests the Epimenides puzzle is "The Logical Calculus" by W. E. Johnson, Mind (New Series), Vol. 1, No. 2. (Apr., 1892), pp. 235-250 (available through Jstor). Johnson writes in a footnote,
Compare, for example, such occasions for fallacy as are supplied by "Epimenides is a liar" or "That surface is red," which may be resolved into "All or some statements of Epimenides are false," "All or some of the surface is red."
From this it appears that Epimenides was already commonly associated with a logic puzzle, hence his usefulness as an example to Johnson. -- See also "Mathematical Logic as Based on the Theory of Types", by Bertrand Russell, in American Journal of Mathematics, Vol. 30, No. 3. (Jul., 1908), pp. 222-262, which at the opening has:
The oldest contradiction of the kind in question is the Epimenides. Epimenides the Cretan said that all Cretans were liars, and all other other statements made by Cretans were certainly lies.
I'll see what else I can find on the history of the puzzle. Wile E. Heresiarch 02:07, 26 Sep 2004 (UTC)

[edit] Article rewritten

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)

[edit] Titus

I made some edits to the section mentioning Titus, without having looked carefully at the History or the Talk page. I hadn't intended to make controversial edits, but now that I have looked at the discussions, I imagine someone will find my edits controversial. I would appreciate a bit of further discussion, if there is interest. Thanks. 68.239.119.234 15:31, 6 Dec 2004 (UTC)

I've reverted the "History" section to the status quo ante. The text that was added had no substantiation. Feel free to bring it back when you find some references. Wile E. Heresiarch 05:01, 9 Dec 2004 (UTC)
What substantiation supports either of the following assertions (per the Dec. 9 reversion)? "In the Epistle to Titus, the phrase . . . is intended simply to defame the Cretans [and has no other intended meaning]"; OR "The inconsistency of a Cretan asserting [that] all Cretans are liars did not occur to Epimenides, nor to Callimachus, [nor to] the author of Titus. . . ." I see no substantiation for any part of either of these controversial statements. Especially because the paradox is so facially apparent in the text, one might expect the burden of substantiation to fall on anyone wishing to assert that the textual paradox was merely an accident. I would like to find time to look for theological and historical commentaries (especially scholarly speculation concerning the study of logic in the early Church), but I would think the burden of proof properly belongs to the reverter in this instance. Is there any substantiation for (are there any references to support) the reversion? Thanks.151.200.40.137 00:34, 13 Dec 2004 (UTC)
Here are a few more quick points about Epimenides/Titus and substantiation----The Dec. 9 reversion correctly points out that the "liar paradox was known in antiquity." Ancient awareness of the so-called pseudomenon undermines the assertion that the inconsistency simply "did not occur" to the author of Titus. There are other examples of this class of paradox having been studied within the early Christian Church. For example, Saint Augustine, Against the Academicians III.13.29. I think it is fair to say that variations on the pseudomenon (liar paradox) were actually rather thematically common in Greek and Roman thought. [See, for example, Aristotle, Sophistic Refutations 25, 180a27-b7; Cicero, Academica priora iixxix.95-xxx.97; A. Gellius, Attic Nights xviii,ii.10]. Finally, a quick google search on the internet returned a few references to a couple of theological or philosophical articles that are said to take the view that the author of Titus clearly intended to highlight the paradox: Anthony C. Thiselton, "The Logical Role of the Liar Paradox in Titus 1:12,13," 2.2 Biblical Interpretation 207-223 (1994); G.M. Lee, "Epimenides in the Epistle to Titus (1:12), 22 NovT 96 (1980). I want to emphasize here that I have not yet read the full text of either of those two articles cited, but what I did read written about those two articles suggests that these articles (when we do have the full text) will confirm that some commentators are convinced that the occurrence of the Cretan-liar paradox in Titus was intentional. The absence of medieval references to Titus (if true, and I have no particular reason to doubt it) does not necessarily determine how the passage was intended by its ancient author, or how it was read by contemporaries. I suppose more scholarly and historical sources need to be consulted before we could try to determine whether there is a "prevailing" view as to how this passage has been read over time. Anyway, until there is further research, here's what I propose: if it is true that none of the extant medieval texts discussing puzzles or paradoxes (concerning insolubles or inexplicables) specifically referenced the ancient passage in Titus, this seems worth mentioning (when mentioning the history of the Epimenides/Titus passage), but I think it goes beyond the evidence (and possibly even goes against the evidence), to deny flatly that the author of Titus was aware that this passage was logically rich. The notions of truth and falsehood seem thematically essential to the Epistle to Titus, which uses (1:2) the phrase "theos apseudes." So, I would propose using the text you did not like as a basis for editing, and working to improve that text (which built upon the reversion text). Do you have additoinal thoughts about this? Thanks. 151.200.40.137 03:20, 13 Dec 2004 (UTC)
The notion that the paradox is "facially apparent" in Titus 1:12 is tenable only if one ignores all context, as you have, starting with the ellipsis "One of them, a prophet of their own, said 'The Cretans are always liars . . .' This testimony is true." As you know, the missing text is "evil beasts, idle bellies", which is decidedly less fertile ground for paradox-hunters. The text leading up to verse 12 concerns what kind of people should be selected to become elders of the church. Verses 10 and 11 describe unworthy people, and verse 12 follows in precisely the same vein. As for verse 13, the implication of "This testimony is true" is not "Therefore this is a very interesting conundrum" but rather "Therefore, rebuke them sharply" which is much more consonant with the judgemental tone of the preceding verses. Chapter 1 closes with further description of unrighteous people. A consideration of the context of the phrase in Epimenides, Callimachus, and Clement immediately shows that nothing of a logical sort is intended. Epimenides and Callimachus are both concerned with theology. Clement enumerates the seven wise men of Greece, and names Epimenides as one. After a brief aside, he goes back to the seven wise men. The presence of the liar paradox in various ancient texts only makes it more surprising that the "All Cretans are liars" is not explicitly identified as a paradox in any of these texts. Augustine, in particular, apparently knew the liar paradox and presumably Titus 1:12 as well (if not the original work by Epimenides), yet he does not connect the liar with Epimenides.
The connection between Titus 1:12 and the liar paradox is at best speculative, so I'm afraid it's up to you come up with some evidence for it. At present the most that can be said is that the same speculations have been voiced by some commentators. These speculations don't deserve to be presented front and center, though. Frankly, I think you're grasping at straws. Wile E. Heresiarch 06:53, 23 Dec 2004 (UTC)

[edit] "Contingently false"

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)

[edit] Another real world example

The other day I went to a Chinese Restaurant for lunch, and as usual, got a fortune cookie along with the check. On the paper slip inside, the following advice was written:

If you wish good advice, consult your mother.

The question is, is this a good advice, or not? I feel that the lack of an article in front of "good" makes the case a lot stronger. The presence of an article, i.e., if you wish a good advice, would allow for the existence of oracles other than "your mother" capable of giving good advice. Without the article, however, the sentence conveys the meaning that only your mother is able to do that. Now unless the waitress who gave me the cookie was my mother, this particular advice was not given to me by my mother, therefore it should not be considered good. But then the whole reasoning is flawed, since the assumption that only my mother can give me good advice was based on the very advice I now declared as bad. Hence, it is a paradox.

If other editors consider this story good enough to be presented in the main article, I'd be happy to see it there. I can also attach a picture of the fortune slip which I saved, if it makes the example fly better.

--DHanak :-V 20:41, 24 Jan 2005 (UTC)

Hehe, that's very interesting. As a paradox, it's fairly easy to de-fuse, however - it doesn't say that good advice can't come from other sources, only that good advice does come from your mother. If we were to apply this idea to something else, like say apples ... you could say
"If you wish apples, go to the supermarket."
and that statement doesn't rule out the existence of apples in other place, ie. apple trees. Likewise, your fortune cookie statement doesn't nessecarily mean ONLY your mother has good advice.

--Oracleoftruth 07:14, May 26, 2005 (UTC)

And there are Cretans other than Epimenedes -- so it's quite similar! -Dan 13:22, 6 June 2006 (UTC)

From my talk page: !!Do you still have the picture? -Dan 2006. június 6., 15:25 (CEST)!!

Better yet: I still have the fortune slip. I'll take a picture and upload it soon. --DHanak :-V 14:47, 6 June 2006 (UTC)

[edit] Epimenides' paradox or Epimenides paradox

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)

[edit] Not A Paradox

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)


Better yet if he is lying then all that means is that he, and other Cretans, don't always lie. It doesn't seem to imply to me, without forcing the word lie to mean such, that you can't lie occasionally. Were I to say that I always lie that would be a lie however that doesn't imply that I'm telling the truth right then. From what I understand the only time it's really a paradox is if you force the word liar to mean someone who always lies or accept a logical fallacy of there only being two choices, someone who always tells the truth and someone who always lies, and disregard the possibility of an occasional liar. Anyone smarter than me want to explain this? - Unsigned as I don't (yet) have an account

[edit] undecidable

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)

[edit] Callimachus the author of the Epistle to Titus??

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.