Liar Paradox (Eubulid or Epimenides Paradox)

[Guest]

Lets say the Cretan was telling the truth. if so not _all_ Cretan tell lie as he is himself is a Cretan telling the truth.

If he was telling a lie, he is saying that not all (i.e if there were 100 Cretan, 99 may be telling a lie)

In both cases Cretan is telling a lie.

[Guest]

The paradox about lying Cretans isn't a paradox at all. It's just a matter of definitions. If the Cretan said "All Cretans are liars" he was telling the truth. He himself is a liar and so are they BECAUSE a liar is not someone who lies 100% of the time, but someone who has told at least one lie. Therefore, though the Cretan has lied, he is currently telling the truth.

Now, if the Cretan had said "All Cretans lie 100% of the time" it would be different, but still not a paradox. Here is why: the moment the lying rate reaches 100%, untrue statements become the new way of expressing truth; that is to say, if people lie 100% of the time, you never need to worry about whether the truth or a lie is being told. You can assume it's a lie and then determine the truth from the lie statement. Lying is only a problem when it is done less than 100% of the time. THEREFORE, the Cretan, by saying that all Cretans lie 100% of the time, would himself be committing a lie: Cretans in this state would NEVER lie by always saying things that are untrue (lies)- though they are always lying with their words, they would in a second context/instance never be lying with their meanings. In order to be lying all the time, do you have to say something untrue or communicate something untrue? Hmm...

Okay, so let's set some definitions. A lie is an intentional communication of an untruth, regardless of the words/gestures used. A liar is someone who intentionally communicates an untruth. The Cretan:

says "All Cretans are liars"

means "All Cretans intentionally communicate untruth 100% of the time"

... so the problem here is that in order to intentionally communicate untruth, you can't create the "truth state" of always using false words/gestures because that always intentionally communicates truth.

What needs to happen then, in order to have "All Cretans are people who intentionally communicate untruths 100% of the time" be true, is that each individual Cretan must assess his listener(s) individually and craft his statements such that each individual listener will draw untrue conclusions based on his words. As no Cretan is omniscient, this can never be done perfectly and mistakes (true conclusions being drawn) will occur, but it's really not a matter of outcome- it's a matter of intent.

Now... what happens when one Cretan is speaking to two (or more) other Cretans, each of whom will (to the best of his knowledge) draw opposite conclusions from whatever he says? In this case, the Cretan, in order to remain a 100%-liar, would have to remain silent to all such audiences until he could isolate the opposite individuals or groups and speak/lie to them separately, each in their own manner of misunderstanding.

In fact, there could be well more than two groups he'd have to speak to separately for any given untruth statement. There could be X different groups where X is the number of possible ways to infer the truth from the speaker 's statement.

[Guest]

It's clearly a paradox. It is not a problem of definition or something else. You didn't understand. It's logical.

First time, he said :" All cretans are liars "

At this time, we don't know if he tells us the truth. This just have importance for the second quote.

Second time, he said "All cretans are liars and i tell the truth"

If he tells us the truth, all cretans are liars.

By the way, you can understand in two different ways (the first is the good one and the second is almost the same with different view):

1_ He's telling the truth in the second quote. So if he tells the truth and only the truth in the second quote, all cretans are really liars BUT it means that he was lying in the first quote ! (all cretans are liars)

So this is non sense because it means that all cretans are not liars (quote 2 over 1) and they are really liar (quote2).

2_ All cretans are liars (Q1) : if you think he's right, that means that he's lying to you. So you think that cretans are not liars. But in Q2, if he's not a liar, he really told us the truth and cretans are really liars.

Again, this is nonsense because cretans are not liars in Q1 and it means that cretans are liars in Q2.

Possible 3 (but i dont think this one is good because u have to take in consideration the 2 quotes) : just take the first _ If creatans are liars, he's lying and cretans are not liars .. If they re not liars, cretans can't be liars.

[Guest]

the definition of liar is one who tells lies. Yet this is an old laguage therefor one must learn the language and all its aspects before one assumes the liar in that language is not of multiple meanings. Therefor rendering this undecipherable until one learns the original language and reads it in its original language which could be lost due to the wrath of the ages. Also if this paradox was passed down by mouth for some time the phrasing could have been altered somewhat which could have been witten down as the altered version hundreds of years after this paradox was created. This creates possible variables in the paradox which the original did not have. Making the paradox itself impossible to solve due to unlimited possibilities.

The salution to this paradox is this. Liar is one who tells lies therefor making the answer to the paradox is the cretions could all be liars or may not. One cannot tell due to the possiblity that the sailora were at that moment they could be telling the truth or be telling a lie in which not all creations are liars making it inconclusive due to lack of knowlage of the sailors' way of path. (one path is telling a lie another telling the truth)

[Guest]

The Cretan is lying - if he was honest then not all Cretan's would be liars and therefore he would be lying anyway. If he was lying then the whole thing makes sense.

[Guest]

the definition of liar is one who tells lies. Yet this is an old laguage therefor one must learn the language and all its aspects before one assumes the liar in that language is not of multiple meanings. Therefor rendering this undecipherable until one learns the original language and reads it in its original language which could be lost due to the wrath of the ages. Also if this paradox was passed down by mouth for some time the phrasing could have been altered somewhat which could have been witten down as the altered version hundreds of years after this paradox was created. This creates possible variables in the paradox which the original did not have. Making the paradox itself impossible to solve due to unlimited possibilities.

From that crap above, I sort of know what you getting at. Languages and sociality changes. Which I agree, but then if we can't deduce that variable, and as we can only solve problems with the information available.

The Cretan may have after saying the first quote, he realized, that his statement was incorrect, and modified it to the second quote, if so, this isn't a paradox as he just didn't think before he said the first quote.

Although the Cretan may have done this (a week is a long time to think about what has been said), We can not assume this. So the language is out of the question.

The first quote, supports the second quote. In both cases of the second quote, he is telling a lie.

Let assume that he was telling the truth, in which case, as his previous quote was a lie, he is therefore a lier as well. If he was telling a lie, then both quotes support each over.

[Guest]

I think you are all arguing semantics.

The core of the paradox is easier to see if you restate it as

"I am Cretian and everything Cretians say is always a lie".

and if you then assume that before this moment everything every Cretian has ever said actually has been a lie.

Then this statement is true at the same moment it is false. When it is true it is false and when it is false it is true.

This can't be resolved. That's what makes it so interesting.

[Guest]

my question is: did the cretans and greeks understand each other in the first place?

[Guest]

Very, very simple. But first I want to explain why I think no one has said this yet. Fuzzy logic is the name for the ability to think "sort of". It is a concept scientists can't get in robots/computers (but many want to). Many paradoxes can be solved by thinking "yes, but no"

1. A familiar Cretan sails to Greece and says to Greek men, who stand on the waterside: "All Cretans are liars." Did he say the truth or did he lie?

Option A: He told the truth- All Cretans are liars. Which of course can't be true because he would have lied.

Option B: He lied- No Cretans are liars. This can't be true either, because he wouldn't have lied

Option C: He lied- Not all Cretans are liars (but some are). This could be it- he was one of the liars, and his original statement wasn't true.

2. A week later, Cretan was sailing there again and said: "All Cretans are liars and all I say is the truth." Although the Greeks ashore hardly found out, what he said the first time, now they were absolutely puzzled.

That statement is a lie, because it contradicts itself. Using that logic, not all he says is the truth (but some of it is), making his original statement false.

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

It's probably true, who doesn't lie sometimes?

[Guest]

This is an interesting "paradox", but quite simple in my opinion.

Assuming that by saying all Cretans are liars, he means that they tell nothing but lies; this is my solution:

The Cretan is saying that Cretans tell nothing but lies.

The Cretan is saying that his self (a Cretan) tells nothing but the truth.

The Cretan is lying.

Just because something is said to be false, doesn't mean the solution is the exact opposite.

By saying all Cretans are liars, he is lying in terms of the word all. Not all Cretans are liars, but he is one. Therefore, not all Cretans are liars but some are (like his self).

By saying that he tells nothing but the truth, he is lying again.

Unless I missed something, the solution is just that simple.

[Guest]

the cretan is a liar. meaning the statement "all cretans are liars" is false.

This doesnt make them all truth tellers either its just a false generlisation.

some lie and some dont.

[Guest]

Okay this is pretty basic and can be proven the first thing is to establish the statement and then the conclusion and the mathmatecal equasion of S)N =If s then n . Not only are all cretans liars but all men lie. All cretans do lie at one time or another as do all men, Therefore the statement that all cretans are liars is true because although they do not do it all at one time. They all do it.

[Guest]

As I read in "I Touch the Earth, The Earth Touches Me" by Hugh Prather; (Psychologist turned Author) "no matter what we speak about, we speak about ourselves"...The Cretans he dealt w/in his life, had only been Cretan liars...Not meeting actually & totally all Cretans???So I would have to say, "The Sailor Cretan visting Greece was not a liar of mind; so yet is "True"...But the truth of his statement I believe is "False"!!!

[Guest]

They both have to be liars.

[Guest]

He's lying of course! Not all Cretans are liars, but he is. If all Cretans ARE liars, then it would be a lie, therefore it's true - but it can't be true.... <_<

Wait, he's telling the truth! No, he can't be, 'cause that would mean he's a liar, which he is ... wait a minute.. Does that mean he ALWAYS lies? If all Cretans ARE liars (all the TIME? ok, let's assume it's constant, non-stop for the sake of argument)...

Ok, I was sooo confident at first. darn.

[Guest]

Liars don't always tell lies. If he had said something that would translate to him always lying, then there would be a paradox. The part where he said that all Cretins are liars could be the truth, and then when he said that all he said was the truth, he could have been lying, because he had earlier told the truth.

[Guest]

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.

This is my first time on this site. I am now a new member and look forward to solving puzzles with the rest of you. Perhaps we can solve the worlds ills together.

I read through all of the explainations of the liar paradox trying to find the one that best satisfied it for me. Czor's is it. Short, simple and to the point. As far as I'm concerned, this is the answer to the paradox. Thank you, czor, for you simple eloquence.

tenfive64

[Guest]

1. A familiar Cretan sails to Greece and says to Greek men, who stand on the waterside: "All Cretans are liars." Did he say the truth or did he lie?

If he is a Cretan, and he claims that all Cretans are liars, he could not be telling the truth. He must be lying, therefore not all Cretans are liars, but he surely did. His fib does not make all Cretans liars, nor prove his point.

2. A week later, Cretan was sailing there again and said: "All Cretans are liars and all I say is the truth." Although the Greeks ashore hardly found out, what he said the first time, now they were absolutely puzzled.

This is the same basic principle, only he lied twice. All Cretans are not liars, he lied about that; and "...all I says is the truth" is another lie.

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

Case 1: A person proclaiming that he does lie could be either truth or lie. Not enough information is given to prove the validity in his claim.

Case 2: A claim that he is lying about a given statement he'd previously made is either a truth, or just that: a lie.

Case 3: Should he simply be stating "I am lying", this would be a claim with no clear subject as to what he might be lying about, and therefore be an improper or nonsensical statement.

[Guest]

The assumption most people make upon first reading this is that Cretans lie all the time.

li·ar /ˈlaɪər/

–noun

a person who tells lies.

Here we see the fatal error:

A liar is not a person who lies all the time.

A liar is a person who has made a habit of lying. However, this does not mean that every statement out of the person's mouth is a lie.

Therefore, the paradox is flawed. If Chrysippos were to have said "Everything any Cretan says is inevitably a lie," then this would be truly paradoxical.

However, the Cretan's first statement, "All Cretans are liars" is true. All Cretans, himself included are habitual, perhaps even compulsive liars. But they do have the ability to speak the truth.

His second statement, "All Cretans are liars, and all I say is the truth" is a simple lie.

Edited February 4, 2008 by riddle_me_this

[Guest]

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).

1. A familiar Cretan sails to Greece and says to Greek men, who stand on the waterside: "All Cretans are liars." Did he say the truth or did he lie?

2. A week later, Cretan was sailing there again and said: "All Cretans are liars and all I say is the truth." Although the Greeks ashore hardly found out, what he said the first time, now they were absolutely puzzled.

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

The solution is easy. No matter what the Cretan says he is not telling the truth. Here is why.

1) If all Cretan tells lies, then the Cretan was telling the truth, making what he said a lie.

2) If not all Cretan tells lies, then he was not telling the truth making him a liar.

If some one says he lies, it is the truth, but that doesn't mean he is lying right now it just mean he will lie in the future.

Edited February 7, 2008 by eric11

[Guest]

I conclude the answer is it depends. If some one says about himself that he lies, it can be the truth and it can be a lie too.

1. A familiar Cretan sails to Greece and says to Greek men, who stand on the waterside: "All Cretans LIKE DOUBLE WHOPPER" Did he say the truth or did he lie?

2. A week later, Cretan was sailing there again and said: "All Cretans LIKE DOUBLE WHOPPER and I DO NOT LIKE DOUBLE WHOPPER BUT I LIKE BIG MAC." Although the Greeks ashore hardly found out, what he said the first time, now they were absolutely puzzled.

We just have to check whether that person eats whopper or big mac. Timing is also a factor, I remember Batman and Robin when setting up a trap. Robin would say why you set the trap in such an obvious manner. Batman would say : the enemy know that I know that so I come up with something they do not know.

[Guest]

1. A familiar Cretan sails to Greece and says to Greek men, who stand on the waterside: "All Cretans are liars." Did he say the truth or did he lie?

2. A week later, Cretan was sailing there again and said: "All Cretans are liars and all I say is the truth." Although the Greeks ashore hardly found out, what he said the first time, now they were absolutely puzzled.

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

1. If it were true, then he would be a liar, and could not make the statement because it would be the truth; so all Cretans can NOT be liars.

2. So if ALL cretans can NOT be liars, this one IS by stating that ALL he speaks is the truth.

[Guest]

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).

1. A familiar Cretan sails to Greece and says to Greek men, who stand on the waterside: "All Cretans are liars." Did he say the truth or did he lie?

2. A week later, Cretan was sailing there again and said: "All Cretans are liars and all I say is the truth." Although the Greeks ashore hardly found out, what he said the first time, now they were absolutely puzzled.

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

1. A familiar Cretan sails to Greece and says to Greek men, who stand on the waterside: "All Cretans are liars." Did he say the truth or did he lie?

he was telling the truth. just because they lie doesnt meen they never tell the truth.

(everyone lies its human nature and if anyone says they dont. its a lie)

2. A week later, Cretan was sailing there again and said: "All Cretans are liars and all I say is the truth." Although the Greeks ashore hardly found out, what he said the first time, now they were absolutely puzzled.

thats half a lie. "all cretans are liars" is true and "all i say is truth" is a lie

how do i know he is lieing?.....coz he is a man from cretan. he said ALL cretans are liars.

so if he is a man from cretan that doesnt lie it makes him a liar for saying all cretans lie.

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

they are telling the truth if they say they are liars. they just arent lieing at the present time. Not every word that comes out of your mouth has to be a lie for someone to be a liar.

its probably all been said before but i cbf reading the whole thread.

[Guest]

The Cretan made a generilisation. It is very, very unlikely that every Cretan would be a liar.

Also, when one says another is a liar, they never actually mean all the time.

And finally, if one admits tha they are a liar, it would be considered truth. Even if it wasnt true, therefore at that moment, he is a liar, otherwise, he would be an honest person

[Guest]

Well technically at first it is said "A Familiar Cretan". he says all Cretans are liars. if so he is wrong. or he hopes that you understand he is lying and therefore understanding that they are all liars. you really cant tell until the second man comes. This time it does not say "a Cretan" it just says "

 A week later, Cretan was sailing ..." This does not say that this man is a Cretan, or a man, but that his or her NAME is Cretan. therefore the first person could have gone and asked this next person to tell everyone that so that it could be the truth. He is not lying because he is not AA  Cretan, but the person IS Cretan literally. 

you have to not only know you have to think semi hard about this , but WHERE to think semi hard about it.

Who says one's name cannot have other meanings? like Geogia, i knew of a woman by the name, it is one of the United States, and it is also a country in Europe.

Edited March 13, 2008 by Lycanthropy