Liar Paradox (Eubulid or Epimenides Paradox)

[rookie1ja]

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.

1st problem:

A Cretan sails to Greece and says to some Greek men who are standing upon the shore:

"All Cretans are liars."

Is he lying or telling the truth?

2nd problem:

Read after resolving the first as this contains a massive hint.

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

A Cretan states "All Cretans are liars and all I say is the truth."

Is he lying or telling the truth?

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

Rational assumptions:

A liar always tells lies, and a truth-teller always tells the truth.

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

This Cretan is not the only Cretan.

The two problems are of disjoint cases.

Resolution

1. His statement is false (and he is a liar) if there is at least one Cretan who is not a liar.

2. His statement is false (and all Cretans are liars); the "all I say is the truth" part is false.

http://en.wikipedia.org/wiki/Square_of_opposition

Examples of incorrect interpretations from replying posts

He means that everyone has lied, but is not necessarily a liar.

This is an attempt to find a loophole in the wording, which is not an objective response to a logic problem. If you're going to make a semantic argument, you might as well state that words are not universally meaningful. You could be right, but this is no fun and detracts from the idea of a paradox (or really, anything...).

This is not a paradox.

It IS a paradox (the word is just a descriptive label), even if it is not 'truly paradoxical'.

Note that this thread is closed since there have been hundreds of posts and resolution is summarized in this very first post.

[Guest]

Well, if it were true the he says all truth, then it wouldn't make sense that all cretans are liars. Therefore, wouldnt it make sense that he was lying about saying all the truth and not all cretans are liars. I hope I explained myself well.

[Guest]

Well, if it were true the he says all truth, then it wouldn't make sense that all cretans are liars. Therefore, wouldnt it make sense that he was lying about saying all the truth and not all cretans are liars. I hope I explained myself well.

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.

[Guest]

I don't see any paradox here.

The first man says all Cretans are liars. If only some Cretans are liars then he is a liar and what he said is a lie.

The second says all Cretans are liars and he tells the truth. Okay, some Cretans are liars, including him and what he said is a lie.

All this proves to the Greeks is that, as far as they know, all sea-faring Cretans are liars.

Where is the paradox?

[Guest]

The key is that the statements are not totally exclusive. To say that Cretans are liars does is not the same as saying Cretans always lie or that Cretans cannot ever tell the truth. It says that all Cretans have told at least one lie. Moral: never assume you know what the other guy is saying before he explicitly says that - a favorite trick of those in sales and politics.

[Guest]

I think this is just confusing. I think what he is doing is exagerating!

How can you lie ALL the time?

He's just saying they lie a lot.

Or he's lieing and actually saying they tell the truth often.

In the last case, he would be a liar for just a moment.

[Guest]

I think this is just confusing. I think what he is doing is exagerating!

How can you lie ALL the time?

He's just saying they lie a lot.

Or he's lieing and actually saying they tell the truth often.

In the last case, he would be a liar for just a moment.

Exactly. The answer to this paradox is... (drumroll) Time! He means that everyone has lied, but is not necessarily a liar.

[Guest]

The paradox is soo obvious here

cretan1 says : all cretans are liars

now case 1 : "the cretan is a liar"

if the cretan is liar he wouldnt have said all cretans are liars

he would have rather said " all cretans are truth-speakers"

case 2: "the cretan is a truth-speaker"

in such case he would never have said "all cretans are liars"

because all of them speak the truth

and he would have said sumthing like "all cretans are truth-speakers"

there are 2 very important keywords here

"ALL" and "truth-speakers"

[Guest]

Well... I consider that you just need to use math to find the solution.

(-) x (+) = (-)

Or you can use filosophy.

If I say that all the people in a town are liers.

I live in that town.

Im a lier, so, what I say is a lie.

The solution is that not everyone in the town is a lier.

[Guest]

This is not a paradox.

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

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.

[Guest]

dont forget while it is very easy to call him a liar

the paradox is that he can also be telling the truth

remember just because someone is a liar doesn't mean they have to lie all of the time.

he can tell the truth one day and lie the next. as long as he has said one lie he is a liar.

for example i am a liar. i can lie about my age but i can tell the truth about this. but i am still a liar.

and also making the cretan a liar also works.

nice paradox

[Guest]

initally the speak is identified as a Cretian and states that all cretans are liars, yet it is under the discrepency of the greeks ashore to assume or know that this man is truly a cretan. If greeks believe so, the question then arises of the vailidity of his statement if he reports that he belongs to a group of whihc are ALL Liars. tHUS, INITIALLY TWO POSSIBILTIES EXIT: 1. HE IS A LIAR WITH ASSUMPTION THAT HE IS A CRETAN 2. HE IS NOT TRULY A CRETAN AS STATED, THUS NOT COMMITTED TO BEING A MEMBER OF A GROUP OF LIARS, THUS HE MAY SPEAK THE TRUTH.

SO ONE CAN SAY CRETANS ARE OR ARE NOT LIARS.

NEXT, HE STATES THAT HE SPEAKS THE TRUTH, AND HE IS A CRETAN (WHO LIE). DICHOTOMOUS OF COURSE. BUT IONE CANNOT TRUST THE VAIDILTY OF HIS INITIAL STATEMENT THAT ALL CRETANS ARE LIARS IF HE IS A LIAR, SO PERHAPS HE IS LYING ABOUT ALL THE CRETANS BEING LIARS AS WELL AS HHIS SPEAKING THE TRUTH,. ON THE OTHER HAND,

IF HES A CRETAN AND HES LYING THEN THERE IS NO WAY TO DEPEND ON HIS STATEMENTS; THUS LYING AND TRUTH LOSE SIGNIFICANCE AND IDENTITY BECOMES THE FOCUS.

AND WHO TRUSTS THAT GREEKS TRULY KNEW THIS MAN WAS A CRETAN AT ALL.

[Guest]

Ok, so first the speaker is identified as a cretan

automatically discrepency arises for who trusts that the identifier is of truth.

Next, this so called "Cretan" proclaims that all cretans are liars,

yet it is under the discrepancy of the Greeks ashore to assume or know that this man is truly a Cretan.Upon determination of this truth, we must again decide between two possibilites.

If we trust the Greeks that he is truly a Cretan the question then arises of the validity of his statement if he reports that he belongs to a group of which are ALL Liars.

Again, two possibilities:

1. HE IS A LIAR WITH ASSUMPTION THAT HE IS A CRETAN , yet some cretans can be liars and some not for if he lies, then how do we know that there truthful parts of he or the Cretans exist.

2. Or HE IS NOT TRULY A CRETAN AS STATED, thus he is not a member of a group of questionable liars, yet his character is far from elucidated. Who is to say he is not a lying Greek?

So we can have a lying greek, a truth telling man of unknown descend, a liar of unknown descent, a Cretan who lies at times, but may be telling the truth, or a cretan who is lying now.

NEXT, HE STATES THAT HE SPEAKS THE TRUTH, AND HE IS A CRETAN (WHO LIE). DICHOTOMOUS OF COURSE. BUT ONE CANNOT TRUST THE his initial statement *we dont know if hes lying anyway*, here presents the same issues in a different light

1. if indeed the first man is a Cretan, there is no substance to his statement because we cannot trust whether he lies or speaks the truth.

2. If we believe he is indeed a liar, then what realm does this word lie' include? all words, some words. and has he the Cretan been lied to if indeed he is surrounded by others of deception.

i believe that the truth and a lie cannot be defined by one who generalizes that ALL of people are such a way, for a speaker of pure truth would know that it is impossible for ALL to be liars without defining the parameters of the term lie, thus i begin to wonder whether this man is a Cretan at all and the Greek who determined these men are Cretans is of knowledge, has been deceived, or is a Cretan himself.

In addition what man can exist in ENTIRETY as a liar or truth speaker? and what human has the true ability to know how existence is present as ONLY and ALL of one ethical and moral being. It is beyond the realm of human thinking. Thus, the paradox reveals itself in that even the words truth and lie are not concrete, rather depdendent upon others' understanding of such states that exist in spectrums far too broad to earn explanation with one word.

[Guest]

The man is a liar, he lies about all Cretans being liars but in fact he is a liar.

That is why he lies about what he says is always the truth.

[Guest]

It's curious how many times a good answer was given, then someone else came along and obscured it with their bad answer.

Anyway, the man may or may not be a liar, but he is certainly a fool.

The first word you (well, most of you) should look up is "liar". While you're doing that, I'll continue.

In order for the Cretan (there was only ONE in this story, and his nationality was clearly established by the dialog - READ CAREFULLY) to make a logical assertion about ALL Cretans, he would have to know it was true in ALL cases.

Now, assuming that Crete had more people than just his immediate family, do you propose that he personally verified each and every Cretan alive (even the babies) to have told at least one lie? Very unlikely.

If you've finished looking up "liar" now, please explain where it says a liar always lies. (If you attempt to do that, then you'd better go back and look up "always".)

In short, the Cretan most likely could not have known if his statement was true or not. In real life, everyone would just assume he was a bitter man who had been lied to by many of his countrymen. (Unless they believed in the gods and felt Crete had been magically cursed to lie.)

In shorter, there is no paradox here. But Filetos seems like an idiot.

[Guest]

Fear not it has been solved!!!

Seriously though. Logically, this guy probably has know idea what he's talking about. The chances of his words being consistant in his honesty aren'y very good so I've come up with three likely reasons he talked the way he did.

1. He knew all pure-blood Cretans lied but he himself was only half Cretan (his father was a very rich Egyptian who died mysteriously one night, leaving the mother and her boy very rich indeed) whose appearance was more similar to that his mother. He said all Cretans lie (for at that time he was the only half-blood Cretan due to high travel costs) then realized that he himself appeared to be a Cretan and so returned to inform them that all Cretans are liars except himself!

2. He was just trying to confuse the Greeks so the Cretans could overtake their land in war.

3. He was drunk.

[Guest]

I think that that you need to prove someone a liar instead of making a statement that they are liars. It would not be fair if without any fault I called you a liar for no reason. For example, If you did steal something and there is no witnesses to prove you stole and you lie to protect yourself you are not considered a liar until proven guilty.

[Guest]

The first time he says all Cretans are liars, which is therefore a lie because he himself is a cretan thus, properly interpreted the real message is: all cretans speak the truth or something close to that.

Next he says all Cretans are liars except me, I speak the truth. If properly interpreted this means: All cretans speak the truth but I am a liar.

*Note- (This is my opinion however the answer may be somewhat different)

It is not nessesary that whom ever speaks of himself is a liar but whoever considers himself supirior to others is in most cases a liar.

[Guest]

Well if he is saying that all cretans are liars then wouldnt he be lying about them all being liars so therfore what he is saying is false! I think that made sense!!!

[Guest]

He said all cretins are liars AND I tell the truth all the time. Because of that AND, for the entire sentence to be a lie, only one of the two things needs to be false.

So he can assumably be telling the truth about the first part and lying about the second part, making the sentence as a whole a lie, making him a "liar" and doing away with the paradox there. It's the first part I'm wondering about...

[Guest]

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

any.

Becouse:

He can be a lier and tell the truth in that particular sentence. so therefore he told the truth

And if he was not a lier but sad that he is lier then he become a lier , but he was not in the past.so therefor he told a lie.

[Guest]

being a liar does not at all necessarily mean you only lie and never tell the truth, it just means that you lie sometimes, and therefore is able to tell the truth,

in my definition a liar is more of someone who can lie shamelessly if it seems to lead to better consequences than telling truth.

so this cretan was lieing when he said everything i say is true. this is a paradox for people who cannot find themselves to be openminded

SO, if someone says about themself that they lie, it is definitely the truth, it cant be a lie since an honest person cant say that they lie without lieing, making them a liar

if you dont get it, too bad idontfeel like rephrasing.

[Guest]

it's true,

outside of honestants and swindlecants,

people can be lyers without lying ALL the time.

Or,

maybe he's not a pure Cretan, maybe his father was grecian fugitive or something.

[Guest]

The point of this and all paradox is that there is not finite answer.

With the statement "I am a liar"

If I were a liar the statement "I am a liar" would be a lie, in other words the statement should read, "I am not a liar". If that were true than I could have never stated that "I am a liar" because that in itself be a lie. The same is true for the Cretian, If all Cretians were liars he would have to lie in that statement. Again making the statement read "All Cretians are not liars". With that being said then again the Cretian lied about not being a liar and telling a lie at the same time.

[Guest]

This is simple. The two phrases are: "All Cretans are Liars" and "All Cretans are Liars. I tell the truth." The simplest way to think of this is reality. As a fact, no one group of people are liars. Some are. Therefore the men who say all cretans are liars are liars themselves. The truth would be that some cretans are liars including the cretans that said it. Ofcourse when the second man said that he was telling the truth, he was lying at that time also.