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Liar Paradox (Eubulid or Epimenides Paradox)


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#51 commisioner98

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Posted 18 October 2007 - 02:51 AM


BUT, even though he can't be telling the truth when he says, 'All cretans are liars...', he can't be telling the truth, because otherwise, if he were telling the truth, then he would say that he was a liar. Hmmmmm. AHA! If you want to know what is so 'Aha!', quote my quote.



Hmmm
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#52 LONGOVERDUE

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Posted 20 October 2007 - 03:48 AM

LIAR PARADOX:
THIS CRETAN THAT SAILED TO GREECE APPARENTLY BASED HIS OPION ON HIM SELF. HE HIM SELF IS GREEK. WHEN HE SAY ALL GREEKS ARE LIARERS THEN THEREFORE HE SPEAKS OF HIM SELF. ESPEACILY WHEN HE MENTION ALL. THEREFORE, HE IS A LIAR, DUE TO THE FACT HE DON'T KNOW ALL GREEKS.

THE SECOND WEEK THAT THIS CRETON TRAVELED TO GREECE HE WAS STILL TALKING ABOUT HIM SELF. THEREFORE, AT THAT MOMENT HE WAS TELLING THE TRUTH. THE SECOND TIME.
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#53 LONGOVERDUE

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Posted 20 October 2007 - 03:56 AM

LIAR PARADOX:
THIS CRETAN THAT SAILED TO GREECE APPARENTLY BASED HIS OPION ON HIM SELF. HE HIM SELF IS GREEK. WHEN HE SAY ALL GREEKS ARE LIARERS THEN THEREFORE HE SPEAKS OF HIM SELF. ESPEACILY WHEN HE MENTION ALL. THEREFORE, HE IS A LIAR, DO TO THE FACT HE DON'T KNOW ALL GREEKS. AHA!

THE SECOND WEEK THAT THIS CRETON TRAVELED TO GREECE HE WAS STILL TALKING ABOUT HIM SELF. THEREFORE, AT THAT MOMENT HE WAS TELLING THE TRUTH. THE SECOND TIME.

AND I "Aha!"
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#54 t1771

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Posted 20 October 2007 - 06:24 PM

This is not a true paradox because the gentleman stated clearly that his whole race speaks nothing but lies and that he was telling the truth in stating so, there for he is a liar to state that he was telling the truth about his race. He is a liar at heart but the qualifier statement to make his true would be that in the same breath he said that his race is a bunch of liars and of that he is telling the truth. Without the qualifier he would have been lying about this statement.
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#55 Pattofanatic

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Posted 21 October 2007 - 01:39 AM

he wasn't originally from crete, he is an immigrant, as revealed in his travels to the mainland. he may have been kicked out of crete, and maybe that's why he puts down cretans. it really brings up a very important debate: are expatriates to be considered the members of their original country? in our case, yes.
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#56 cassandrabadie

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Posted 21 October 2007 - 08:23 AM

i agree he starts by letting you know he is a liar, so there fore if he says he's telling the truth he is lying.
so perhaps some are liars and he is one
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#57 Maledicus

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Posted 21 October 2007 - 05:39 PM

this is not a paradox, its just a lie...

statement:"everything i say is a lie"

situation 1: the speaker has never told a lie in his life in which case he just lied so the statement is a lie

situation 2: everything the speaker has ever said has been a lie in which case he just told the truth so the statement is now a lie
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#58 Bach.nics

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Posted 23 October 2007 - 04:08 AM

davidsparkman was the first to make the point that "all Cretans are liars" is not equivalent to "all Cretans lie all the time." So many of you keyed on this same point. You are right of course, and this observation resolves the issue very easily. So easily, in fact, that you have to ask why this would be handed down over the generations as a paradox.

I believe the answer is that the original paradox meant the latter (agreeing strongly with oranfry and haxxor), and translations/semantics have added this extra discrepancy. Let's give Chrysippos the benefit and allow that "liar" means "lies all the time." We accept that in this situation each Cretan is either a full liar all the time or a full truth-teller all the time. Now we have something to really chew on.

While I would love to address sexsidexy's questions, in particular the issue about whether thick-crusted pizza is in fact Odysseus' favorite (I think he might say, "too much bread, needs more meat, give me the thin crust, good Esophitimenes, and pass the mead"), I'll stick to the paradox at hand.

Consider two possibilities: (1) "All Cretans are liars (lie all the time) or (2) "All Cretans are not liars (tell the truth all the time)."

If (1) is true, then the familiar Cretan would have been required to say that Cretans are truth-tellers. Since he didn't say this, then by contrapositive reasoning we can deduce that statement (1) is not true.

If (2) is true, then the familiar Cretan AGAIN would have been required to say that Cretans are truth-tellers. Since he didn't say this, then similarly we can deduce that statement (2) is not true.

The essence of this type of paradox is to get you to make the assumption that (1) and (2) are the only two possibilities. Then, seeing that both statements are false, you would be stuck with a paradox that has an irreconciliable contradiction (definition 2 in dictionary.com for paradox).

Of course, a paradox may have a resolution (definition 1 in dictionary.com; American Heritage also has both definitions). In this case, eliminating (1) and (2), you must accept the third possibility, that some Cretans are liars and some are truth-tellers. cpotting and Adeori first got at this and several others followed suit.

So, since we know that some Cretans are liars and some are not, the first statement made by the Cretan is a lie (or perhaps he was just innocently mistaken ... I'm kind of forgiving in this way...). Note that the narrator did not say that the Greeks were confused by this statement, probably because they were good at resolving paradoxes.

The second statement made by the familiar Cretan is an inherent contradiction. Given that he is truly a Cretan (a fact we did not question because it was provided by the narrator, whose integrity is not in question), his first clause applies to himself, so he must be a liar, but then in his second clause he states that he is a truth-teller. Such an inherent contradiction cannot be true regardless of whether Cretans are liars or not, so this is a paradox with no resolution.

Notice that it seems the familiar Cretan did not sail there a third time. I guess the Greeks made sure to get rid of that wacko.

Cheers!
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#59 eugene francis

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Posted 24 October 2007 - 10:54 AM

The cretan says the first time around "all cretans are liars". If that be true, he too was lying. The second time he qualifies it with "all I say is the truth" meaning he was a cretan so he was lying when he said all cretans are liars - not all are liars. and all he says is the truth - he was lying again - again all cretans are not liars!

Eugene
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#60 peseta

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Posted 24 October 2007 - 07:58 PM

Paradox: What I'm saying right now is a lie.
No, the 'papadox' here isn't a paradox, because it mis-states the original, which is in one of St Paul's letters in the New Testament.
Paul, clearly a jojker, tells the tale of the Cretan who says all Cretans are ALWAYS liars, and adds "This statement is true." NOW any Christian has a paradox-- how can good St Paul possibly be lying? But if he's NOT lying, then the ever-lying Cretan is telling the truth. Anf the lying Cretan IS lying, then so is good St Paul. Horrors! And in the Bible, at that!
But fear not-- Remember, I'm lying, comfortably.
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