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Liar Paradox (Eubulid or Epimenides Paradox)


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#61 Miburo

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Posted 04 November 2007 - 11:42 PM

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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#62 redindian

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Posted 08 November 2007 - 12:07 AM

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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#63 redindian

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Posted 08 November 2007 - 12:11 AM

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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#64 redhot

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Posted 09 November 2007 - 08:20 PM

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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#65 Gess

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Posted 11 November 2007 - 05:54 AM

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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#66 Awesmazing

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Posted 12 November 2007 - 05:25 AM

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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#67 KoboKo

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Posted 13 November 2007 - 07:10 PM

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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#68 biostrategem

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Posted 13 November 2007 - 08:05 PM

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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#69 biostrategem

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Posted 13 November 2007 - 08:25 PM

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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#70 callumny

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Posted 15 November 2007 - 03:53 AM

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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