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Liar Paradox (Eubulid or Epimenides Paradox)


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#41 BoilingOil

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Posted 26 September 2007 - 08:34 PM

Liar Paradox (Eubulid or Epimenides Paradox) - Back to the Paradoxes

About this best-known paradox wrote a great stoical logician Chrysippos from Solov 29 books and philosopher Filetos even died because of it (seeking for its solution was killing).

...

If somebody says about himself, that he lies, is it truth or lie?




The way I see it, if this Cretan was NOT a liar, he would not be making this statement, knowing that at least ONE Cretan (he himself) is NOT a liar. After all, this statement would then MAKE him a liar. So he is a liar.
Therefor the statement "All Cretans are liars." can not be true, which isn't to say that all Cretan are NOT liars, but just that not all Cretans are liars, but at least some - including HIM - actually ARE liars.

This works with both statements, by the way. With the second statement there is just the added confusion of him contradicting himself in one and the same sentence...


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#42 oranfry

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Posted 30 September 2007 - 10:35 PM

bonanova said:

[2] It is a contradiction. Here's why:

[a.] every declarative sentence, say "I am 66 years old." carries the implicit assertion
"It is true that ... I am 66 years old." equivalently,
"I speak the truth when I say that ... I am 66 years old.".

[b.] To pair that assertion with the assertion "I am lying as I speak"
transforms the statement into the contradiction
"I speak the truth when I tell you that ... I lie as I speak."


Thank you for making sense, it was about time someone did!

Would you agree, then, that if someone said "I lie as I speak", they would be making a false statement, since contradictions are false?
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#43 haxxor

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Posted 09 October 2007 - 01:36 AM

Technically it would seem there is no paradox, because the word liar means 'someone who lies repeatedly" but not all the time. In our contemporary definition of 'liar' it is assume that liars tell a little bit of truth and a lot of lies, thereby destroying the paradox as mentioned above. however, i think that some meaning is lost from the greek language, as surely Chrysippos meant that a liar always tells lie every time, and a truth-speaker always tells the truth every time. this was obviously the intent, since it is the only way for the statement to be a paradox. so far the only arguments against the paradox are based on what is in my view a misinterpretation, or bad translation of the word liar. Can anybody disprove the paradox assuming that:
liar = always tells lies
truth-speaker = always tells truth
?
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#44 1337Atreyu

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Posted 09 October 2007 - 04:18 AM

Well consider that perhaps the man is not dealing in absolutes. There is no true way to tell if he is a liar or not, but perhaps he lies half the time and tells the truth just as most humans do. Maybe not all of them lie, but he lied about his statement. Does that make sense?
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#45 cpotting

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Posted 09 October 2007 - 04:45 PM

You do not need to resort to vargaries like "do liars lie all the time" to see there isn't paradox here - even if you use the "honestants" and "swindlecats" scenarios, the statements do NOT present any kind of paradox.

A Cretan sails to Greece and says to Greek men who stands upon the shore: "All Cretans are liars." Did he speak the truth or did he lie?
A week later, the Cretan sailed to Greece again and said: "All Cretans are liars and all I say is the truth." Although the Greeks ashore weren't aware of what he said the first time, they were truly puzzled.
If someone says about himself that he always lies, is this the truth or a lie?


As I said in an earlier post:
If the population of Crete is composed of some people who tell the truth (either Honestants or just very honest people) and some who are liars (either Swindlecats or, like most people, those who lie sometimes) and the Cretan is a liar (Swindlecat), then we see that his first statement is a lie - not all Cretans are liars.

Again, he is a liar and his second statement is also a lie - not all Cretans are liars and he is not telling the truth.

There is NO paradox here - no big mystery. It is just two lies by a guy who likes to roam the Aegean spreading lies.
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#46 bobhog

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Posted 12 October 2007 - 06:37 AM

You may disect this paradox in many ways but always concluding that the statement negates itself (a liar saying he always lies is himself lying OR telling the truth). This paradox actually serves strategic and/or political points of view for the person or persons who choose to propagate it. For the Cretan to say to his enemies, the Greeks, that all Cretans, like himself are "always liars", he is planting the IDEA of duplicity in the minds of his enemies. In so doing, his enemy becomes confused, follows errant strategies, or pursues self-defeating political policies. The paradox serves its intended function.

George W. Bush tells us that "...this government does not torture people..." which may be seem paradoxical in the light of evidence to the contrary. But if you examine the words carefully, he says "the government", what he does not say is "...people hired by the government..." and he says "...people..." as opposed to "suspect" or "terrorist" which by his administration's own admission do not have rights guaranteed to them by Geneva convention or American civil rights because of the classification "enemy combatant". Paradoxical? Not really. The paradox serves its intended function.
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#47 dont_sing777

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Posted 14 October 2007 - 12:43 AM

The Truth: Not all Cretans are liars. Some tell the truth. Some still ARE liars.
What He Said: "All Cretans are liars. All I say is the truth."
Conclusion: Cretans sometimes lie, and sometimes don't.
-He lied about "All Cretans Are Liars".
-He was not one of the Cretans that tell the truth.
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#48 czor

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Posted 14 October 2007 - 06:38 AM

everyone lies time to time. there for everyone is a liar. so the cretan man tells the truth, the first time and lies the next time making his first statement true.
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#49 Q_Jordon

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Posted 16 October 2007 - 09:08 AM

It is simple - he is a liar.

The first statement is a lie, and the second statement is a lie.

He is a liar.
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#50 zaperrer

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Posted 17 October 2007 - 02:20 AM

Well now this is too obvious.
He has to be a liar.
Therefore not ALL Creatians are liars.
Therefore some Creatians are liars(which makes what he said a lie) and what he said is simply a lie(again making him a liar).
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