Liar Paradox (Eubulid or Epimenides Paradox)

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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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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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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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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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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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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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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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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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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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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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Could it be that all the Cretan was saying was that it is human nature to speak truth, and to lie? Is it possible that all he said is that we Cretans are human and nothing but, just like you?

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It depends,

If the Cretan has dual citizenship with Greece or

he was offered citizenship by Greek consulate,he might be teelling truth.

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He should have said

"All Cretan's except me are liars"

but by not saying that he lied

and hence what he said is true.

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well we don't have to think in his phrase: "I always say lies", we have to think that maybe he is lying(in that case he lies, but not everytime) or that he is saying the truth, although if he says the truth he lies; because he always lies except this time

it's a bit confusing but in conclusion he lies

I hope everyone to understand me because I don't know english very well...

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This is an example of a self referential paradox. There is no solution. A similar example is to fix the sentence, "This sentence no verb" to be correct.

Here is a nice discussion of the problem: http://linas.org/mirrors/www.ltn.lv/200 ... s/gt5.html

Go to the Gödel’s Proof part to see how powerful the self referential idea is when used by a great mathematician.

Gess

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If you take the paradox in its entirety, and rule out assumptions (i.e. not all Cretans are liars but some may be) the statement the man made is non-existent. To simply end the pondering of this thought all you would have to realize is that, had the man been telling the truth, he'd be lying. If he had been lying, he'd be telling the truth, being that you cannot tell a 100% lie and truth in the same statement, the man fails to exist. What he should have said was, all Cretans are non-existent. Now that's a brain teaser, what would you do if a man told you that his creed didn't exist?

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Its quite amazing how individual responses to said paradox tells more about the individual than the paradox, itself.

I refuse to fail victim, if anything, this challenges your ethics, social interaction, e.t.c

First setback: For critical thinkers to remotely believe an individual who GENERALIZES when he speaks or runs with stereotypes exclusive to one particular race, that nullifies the validity of his claim, or argument.

To add, remove, assume or completely uproot these statement from its original context used does no justice to it's author. To assume the author meant one thing isn't the same as perusing through in search of keywords to justify your conclusion.

In other words, this isn't a paradox. It's human psychology.

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A liar's goal is to win by means of trickery and to not get caught. In order to know non-truth, a liar must understand truth. Therefore, it is in the liar's best interest to tell the truth when they are winning, and to do contain insidious manipulation to when they are not winning. It is only when someone is not winning that the truth of their statements are evaluated. A liar's safety lies in confining their false statements to when they are not winning.

A common argument is that the definition of a liar is that they always lie. Well, be careful. In order to lie, a human or automaton must be able to determine the truth or falseness of a statement. In determining that a statement is false there must be an evaluation and verification of its non-truth. Therefore, liars must have an equal-to or greater-than ability to evaluate truth than people who tell the truth. After all, people who tell the truth have no motivation to not get caught telling the truth.

In the Epimenides Paradox, a Cretin sails to Greece and presents a message to the Greeks. The Cretin does this with no apparent vested interest, as they are not responding to a communication but rather initiating one. Therefore, the statement they are making is false, as the Cretin is not winning. The statement "all Cretans are liars" is false. Therefore, the statement "Some Cretans tell the truth" is true.

A week later, the Cretan returns and repeats the same statement, which we already know to be false, and an additional statement, which is the truth: "All I say is the truth." This is in integrity with the statement that must have been true the first trip, which was, "Some Cretans tell the truth" and "All I say is the truth". He is one of the Cretans that tell the truth.

There exists neither puzzle nor paradox. The Cretins statements, with the given that he is a liar, are consistent.

Eric Mumford

Waterford, NY

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Sorry, I was not able to edit my post. My revised solution is below.

---

A liar's goal is to win by means of trickery and to not get caught. In order to know non-truth, a liar must understand truth. Therefore, it is in the liar's best interest to tell the truth when they are winning, and to limit insidious manipulation to when they are not winning. It is only when someone is gaining something that the truth of their statements are evaluated. A liar's safety lies in confining their lies to when they are not winning in order to build a mirage to allow them the slight-of-hand to tell the truth and win through an environmental nimbus rather than direct risk.

A common argument is that the definition of a liar is that they always lie. Well, be careful. In order to lie, a human or automaton must be able to determine the truth or falseness of a statement. It is the nature of the self-sensing universe to absorb identity before evaluating difference. From computer chips to consciousness, identity must always baseline logical (and in most cases, biological) process. So, determining that a statement is false presupposes an evaluation and verification of its non-truth. Therefore, liars must have an equal-to or greater-than ability to evaluate truth than people who tell the truth. After all, people who tell the truth have no motivation to not get caught telling the truth.

The Liar's Paradox evaluates two things: identity (I Am) and the logical truth or falseness of the identity's statement.

In the Epimenides Paradox, a Cretin sails to Greece and presents a message to the Greeks. The Cretin does this with no apparent vested interest, as they are not responding to a communication but rather initiating one. "All Cretins are liars". A strange greeting, to be sure. Here are the possibilities.

Outcome 1: I am a Cretin, I identify with being a liar, and in telling you this therefore I am lying, which in truth must mean "Some Cretins are liars". The rest of Cretinism could be truth-tellers and this the only liar.

Outcome 2: I am a Cretin, I do not identify with being a liar, and in telling you this therefore I am telling the truth, which must mean "Some Cretins are liars". The rest of Cretinism could be liars and this is the only truth-teller.

The two outcomes are identical. Taking the necessity of identity into account, "All" becomes "Some". Some Cretins are liars.

A week later, the Cretan returns (apparently his village excels at making bag lunches) and repeats the same statement, which we've looked at, and an additional statement, which is the truth: "All I say is the truth." This could be in integrity with "Some Cretins are Liars", a complex equivalent being "Some Cretins tell the truth."

So the answer to the logic puzzle is that it cannot be determined. Hence, there exists neither puzzle nor paradox. The Cretins statements, with the given that he is a liar, may be consistent, but their truth cannot be determined given the recognition of identity.

Eric Mumford

Waterford, NY

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The term "liar" must be defined before attempting to resolve this.

If a "liar" may be understood as a person whose every statement is false, then...

"All Cretans are liars," spoken by a Cretan, is a lie.

"All Cretans are liars, and all I say is the truth," spoken by a Cretan, is also a lie.

If a "liar" may be understood as a person who sometimes makes false statements, then...

"All Cretans are liars," spoken by a Cretan, may be true or false.

"All Cretans are liars, and all I say is the truth," spoken by a Cretan, is a lie.

In either case, it seems fairly simple to me.

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Solution: Not all Cretans are liar but the Cretan in the story is a liar.

This solution match with his both statements.

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The Cretan says that all Cretans are liars. This does not mean however, that the statement is a lie. Given the pretense that they all are liars does not make everything that they say a lie. A more confusing version of this paradox and yet much simpler can be said, " Everything that Cretans say is a lie". This automatically proves that the statement in itself is a lie, meaning that not all Cretans are liars. HOWEVER, the fact that the statement was a lie DOES support the statement that " Everything that Cretans say is a lie", since all evidence so far points to that conclusion. BUT, if the second Cretan sailer were to tell the truth as he says he does (taking into stride that not EVERYTHING he says has to be a lie, giving him the ability to tell some truths) would provide evidence to the contrary and in fact prove that not every single thing that Cretans say is a lie, having the second sailer just tell a truth.Counter examples can continue to be given, so in the end the deciding factor is really how much the talker understands what they are saying themselves, how in depth they go, and their understanding of the listeners. (for example, if the Cretan thought that he was talking to stupid people, he might decide to use concepts understandable to them, which would be below his personal threshold of understanding, and thus might distort the final meaning and or message.)

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If you ever say these words,

"I always lie"

you are lying.

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According to the second case - there are two possibilities. One of them is that only some Cretans are liars and speaker is one of them. The second is far more interesting, because it assumes both that all the Cretans are liars and he is a liar.

Explenation:

We have two statements:

1) All Cretans are liars.

2) Speakers says the truth.

If speaker lies, then either 1) or 2) or both statements must be false. Let's assume 1) is true. Then 2) must be false. If it is false, then it means that one of statements is false. It's true, because, 2) is false. The odd fact is that 2) is false, because of no certain reason. It's just false, because it has to be, if the whole statement is false.

In fact, when one says, that what he says is true or false, it's neither true or false. The statement 2) in fact says:

"I speak the truth (at this moment)" It can be true and then he says the truth. It can be also false. He is a liar and what he says is a lie, because it's not true, that he speaks truth, because he's a liar. What he says is either true because it's true or false because it's false (like in the example with Cretans).

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He lied. Since he states all Cretans are liars, he admits his own lie.

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