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Liar Paradox (Eubulid or Epimenides Paradox)


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The statements: "...always tell lies," or, "...I am lying," cannot be true, since that would be contradictory. They are not intended to be true, or to elucidate, but to confuse. The speaker is not intending to teach anything, or to inform, but to confuse; if you try to decide truth or fiction, you will be confused. That would be the lesson of this.

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False statements and lies are not the same thing. Whereas false statements are simply inaccuracies ("All Cretians are liars" is incorrect), lies must meet three conditions: existence, awareness, AND intent ("All Cretians are liars" is a lie if the Cretian speaker meets all three conditions for a lie). Wikipedia's definition of a lie confirms the three conditions: "...to state something..." defines existence of the statement; "...disregard to the truth..." defines active awareness of the reality of the statement; and "...with the intention that people will accept the statement as truth" defines the intent of the statement. Our Cretian says, "All Cretians are liars," but either speaks with blatant sarcasm (third condition not met--he wouldn't have ever intended for the listener to believe the statement) or speaks with no awareness (second condition not met--he either does not know he said it or does not believe Cretians are not liars). The Cretian will not either have lied (existence, awareness, and intent to lie) or have told the truth (existence, awareness, and intent to tell the truth). At closest, our Cretian will have been inaccurate and/or silly. I believe the paradox has been broken.

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This is not a paradox.

So, person A: Everything I say is a lie.

This is a lie, and some of what he says is a lie. In truth, he would be saying this:

Person A (Revised): Some of what I say is a lie.

Apply this concept to what the Cretan said, and you receive the same results. The flaw in this is that it is assumed that a "lie" is the opposite of the truth. However, it is a lie if it is not the truth and a lie is not required to be the opposite of truth.

I was kind of shocked to see this when I could figure it out but I seemed to think that there was only one Creatian talking all the time! :blush:

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  • 2 weeks later...
  • 3 weeks later...

I believe that this can be solved really easily.

If he says the truth, all Cretans are liars, and so he is a liar and he is not saying the truth. Okay, so this is not possible.

If he is telling a lie, all that we know is that not all Cretans are liars, we can't imply that all Cretans are truth-speakers.

A week later, he says that all Cretans are liars, which he have already discovered that isn't true, because he lied, and contradicts him. Because, in the previous week we proved that he was saying lies, so he is a liar, therefore in the second sentence he is lying too because he lies by saying that he is not a liar.

Edited by Lidia Freitas
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  • 2 weeks later...

in the first instance, he could easily be telling the truth.

saying "all cretans are liars" only clearly states that all cretans lie. it doesn't mean that they only lie and are incapable of speaking truth.

in the second instance it's harder to believe that he speaks the truth.

he tells them that all cretans are liars but then contradicts himself by saying that all he speaks is truth. Which, i feel, is what caused the greeks confusion. how can one person claim that his race lies but then exclude himself from that generalization.

or you could look at it this way: he believes in both cases that what he speaks stands as a fact and so to him it is truth and he isn't lying. which goes back to the idea that he says "all cretans are liars" meaning that they lie but are also capable of speaking truth.

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I think this cannot be resolved because there is never a declaration of the truth. If as an axiom you state that all Cretans are liars, then you can proceed with logical consequences but in this narrative, all you have is a Cretans declaring that Cretans are liars- so it can't be resolved logically.

In the second question someone states "I always lie" is still just a statement. Until you establish an axiom, you are wasting your time trying to figure it out.

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Key question is what is a lie? See it's based on what makes a liar. But a lie is only a lie based on the facts that surround it. So this means that at both times the same cretin was saying both the truth and a lie.

(example:If you say the universe is in chaos, the components are in chaos but the events aren't because it has to follow the laws of science.)

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>>It's safe to say that everyone sometime in their life has told a lie. Which makes everyone a liar.<<

Case 1. The man is telling the truth. All Cretons are liars. A liar doesn't lie all the time, just when it suits him/her. Even if they only lie sometimes, they are still liars.

Case 2. The man is lying about always telling the truth. He cant always tell the truth, because all Cretons are liars. This is the perfect example for one of those times when a Creton lies. His lie being that he always tells the truth.

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  • 4 weeks later...

He can't be saying the truth, because if he was (suposedly) saying it, it would mean that he is lying, it would be more a confession than a fact,,, whereas if he is lying it would mean that not all the cretans are liars, but that he is ;)

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If someone says "Everything I say is a lie", are they telling the truth? Or are they lying?

It can't be true cause it contradicts itself: 'everything I tell you is a lie' and hes telling the truth.

The reason it can be a lie is - If he's lieing about saying 'everything he says is a lie', it doesn't mean that everything he says is the truth. It just means that maybe half the things he says is a lie. So if he only lies about half of things, than saying he lies about everything would be a lie.

Im confusing myself.. hope it made sense lol.

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depends on top view, it is 2 system. Attacker (Crete) want defender (Greece) to become in state attacker want - him ready to faith for truth about Crete. That is fastest way attacker to attract defender power for his use.

in way that you are defender - answer is simple (trivial - that is lay) and not much addition information for you, but for attacker is much more.

on that paradox are based some divide and conquer strategies.

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

This is a well known paradox written by the great stoical logician Chrysippos. The poet, grammarian and critic Philetus of Cos was said to have died of exhaustion attempting to resolve it.

1. A Cretan sails to Greece and says to some Greek men who are standing upon the shore: "All Cretans are liars." Did he speak the truth, or did he lie?

2. 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 on the shore weren't aware of what he had said the first time, they were truly puzzled.

If someone says "I always lie", are they telling the truth? Or are they lying?

Sentence 1 is an obvious paradox. But sentence 2 is not a paradox. My explanation:

Sentence 2 is "All Cretans are liars and all I say is the truth." I contains 2 statements- Statement p= All cretans are liars, statement q= all I say is the truth. Since statement 'p' and 'q' are joined with 'and' co statement 2 is true only if both the statements 'p' and 'q' are true. In all other case it is false.

Truth table:

Statement 'p' Statement 'q' Statement '2'





Here take the case where statement p is true and statement q is false. Since staement q is false so the speaker(cretan) is a liar. statement q is true, which again says cretans are liar. Overall statement 2 is false (since q is false), so it proves that he, a cretan, is a liar.

So I do not find any paradox in that.

Edited by HereICome
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  • 1 year later...
  • 8 months later...

He is saying that Cretans are liars. However, he is not saying that they lie all the time. if you lied all the time, you would probably be unemployed/homeless. E.G; your boss: complete this assignment by tomorrow. I f you always lie, than you can either say"no" and get fired or say "yes Sir" and not be able to do it because you lied. And get fired. This is really more of a puzzle then a paradox. You just have to think. :thumbsup:

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  • 4 months later...
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On 9/6/2007 at 6:31 PM, rookie1ja said:

2. Now assume that either all Cretans are liars or all Cretans tell the truth.

If a person is not a liar, then they are a truth-teller, and vice versa.

hai, newbie here.

i don't know about the answer, but i see some problem in the preliminary statement there (in bold)


imhl, i would say

either all Cretans are liars (one who 100% tell lies) or Not all Cretans are liars.

if a person not a L, the they are LT or T (T for Truth teller -> one who 100% tell truth)




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"paradox born from our failure on placing matter in a proper context."
- insert some famous name here -

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  • 3 years later...

His first statement that all Cretans are liars is based on a premise that he knows all Cretans.  The probability of this is extremely low as there are likely Cretans that have moved from his home who he may not know or cannot verify that they are indeed liars. Therefore his statement that all Cretans are liars are based on a false statement that makes his claim suspect.  He may be telling the truth that he perceives because of his limited sample size, but this is not likely a universal truth. 

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