Liar Paradox (Eubulid or Epimenides Paradox)

[Guest]

This is not a paradox.

The opposite of "All Cretans always tell lies" is not "All Cretans always tell the truth", it is "Not all Cretans always tell lies."

So by saying it he IS implying that he is telling a lie, so he is therefore saying "Not all Cretans always tell lies.". And there it stops!

A better one (which is truly a paradox) is: "This statement is false".

[Guest]

Maybe this deserves a deeper look into the nature of things. The statement, in its simplest interpretation, is a hypocritical stand. It is a run around, a yin yang if you want to call it that. Now, you cant disassemble this situation without taking into account its environment(ie our universe), because you cannot look at an individual without respect to his surroundings. With this you can see that there is a "whole", that all things are interconnected in a dual nature-good and evil, positive and negative. For there to be experience, there needs be polar opposites-and in of themselves, these opposites are not the truth nor lie. The more we dissect things, the more we realize that nothing is really set-there is no "truth". You look at what we believed 30 years ago-that the universe was made up of protons, neutrons and electrons; and you take a look at today's theories: quantum mechanics, string theory, superstring theory. The more complicated you make it, the more you run around in a circle to reach the beginning. On top of this, human nature itself is hypocritical. We are one way one day, another the next. Our biological cells replace themselves every 6 years, there are people with varying conditions such as schizophrenia, bipolar and split personality. Whats to say this Cretan did not have a split personality? A liar and a prick, rolled into one. Personality is not set, people are subject to changes-so anything and everything we say is a lie, but it may have been truth for the MOMENT. So my answer is this: there is only one truth, and that is absolute zero-which in itself is indefinable by us. So paradoxical sayings such as this one go to the "heart" of the matter, and show us the very basis of our own universe. We never tell the truth, we just say what we BELIEVE is the truth. All logic is built upon prior logic, but inherently NOTHING is known apriori. The only reason why we believe the sun will rise tommorow is because it has always risen during our lifetimes-but you cannot guarantee it. You can think of it metaphorically as mirrors within mirrors-it is infinite, but we can only see the first few reflections of the nature of things.

Xin

Edited October 30, 2009 by Xin

[Guest]

Nice answer Xin The question is then, why do you think that you are 'Able' to define: there is only one truth, and that is absolute zero-which in itself is indefinable by us. In this case (as you tell us yourself) you contradicted yourself by defining what can't be defined. Defining the set in which cannot be a part of it self, must be a part of the set which is not a part of it self - again a paradox. You just have to change the way you ask the question about this - change the interpretation and use of the symbols you use in the paradox-formula. It's to complicated to give a proper answer right now, but Bertrand Russell comes with a great analyses about this in his essay from 1908 'Mathematical Logic as based on the theory of Types', if you're interested

[Guest]

Nice answer Xin The question is then, why do you think that you are 'Able' to define: there is only one truth, and that is absolute zero-which in itself is indefinable by us. In this case (as you tell us yourself) you contradicted yourself by defining what can't be defined. Defining the set in which cannot be a part of it self, must be a part of the set which is not a part of it self - again a paradox. You just have to change the way you ask the question about this - change the interpretation and use of the symbols you use in the paradox-formula. It's to complicated to give a proper answer right now, but Bertrand Russell comes with a great analyses about this in his essay from 1908 'Mathematical Logic as based on the theory of Types', if you're interested

Haha thanks. Ill take a look at the essay, it just seems that words are sometimes not enough to describe "it". We do our best, no?

Xin

[Guest]

There is a 50/50 chance that the statement would be true or false. There could be a plethora of reasoning behind a lie, or not. You might guess by the nature of the person or suggestions based on their body language whether you would accept or contest the statement.

[Guest]

The real paradox is not the one in the story!

It goes: is I say "I always lie" - am i telling the truth or not?

I can't be telling truth because then my phrase is true and I am telling lie.

If I am lying - it can mean two things:

1) I am always speaking the truth - which makes the paradox

2)I sometimes lie - no paradox - so not interesting at all

So let us lend at axiom that people can either tell only lie or only truth and never speak some of one and some of other!

And now who am I when i tell "I always lie" - lier or no lier???

[Guest]

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?

Answer: He couldn't be telling the truth, since he is a Cretan himself. So he lied - all Cretans are not liars, just this one so far!

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.

Answer: We have established that not all Cretans are liars from his last visit. Could the Greeks have met the only Cretan liar?!

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

Answer: They can't be telling the truth. They don't ALWAYS lie, just on this particular occassion!!

[Guest]

What the cretan is basically saying in both scenarios is that he speaks the truth. If he's lying about all cretans lying then he's clearly telling the truth. he says the same thing in the second statement but confirms that he speaks the truth which is what was implied in the first scenario.

[Guest]

I say to some the truth is a lie and to some a lie is the truth, therefore, regardless of who says what to whom how and when, the matter lie solely in the definition of the words!!

[Guest]

I just thought of something random:

There are two people. I ask the first person a question (it doesn't matter what) and he nods his head.

Then, the second person interrupts by saying that whenever the first person nods, he actually means 'no,' and when he shakes his head, he means 'yes.'

I ask the first person: 'Is this true?'

He responds by nodding.

What does that mean?

[Guest]

if that's the truth, then he's lying. if he's lying, then that's the truth. there you have it, a paradox. hope I made myself clear. (This is my first post.)

[Guest]

The sucker way:

"all" is such a dangerous word. There are individuals among Cretans who are infants and their bodies aren't even able to gesture, let alone speak. Thus this statement is irrational. Therefore the Cretan who said this statement, is wrong. We can't however say he was lying, he might have not taken in consideration the babies, it's not lying if your unconscious of all the facts.

The orthodox way:

The trick is in the "time". Simply stating X is a liar doesn't translate to X being unable to tell the truth, ever. It merely states that X has a vice of telling lies. Therefore both possibilities can non/simultaneously be in/correct.

[Guest]

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.

"All Cretans are liars" - could be true...All Cretans could have the capacity to lie. I agree with other members that the accepted meaning of "being a liar" is that they sometimes tell lies. If this is the way you read it then there is no paradox...The statement could be true and all Cretans could be able to lie...the sailor may just not be lying at that point in time. The statement could also be untrue and only some Cretans have the ability to lie - of which he would be one!

I prefer the more "puzzling" interpretation of "liar"...i.e. All Cretans are incapable of telling the truth. If this were true then the Cretan would be physically unable to announce the fact - it cannot therefore be true. The statement must be a lie - the truth of the matter being that only some Cretans are incapable of telling the truth - this one at least!

You could of course tease yourself further by interpreting this lie as necessarily meaning "All Cretans are incapable of lying" - which would bring you back round into a painful circle...if Cretan's cannot lie then the sailors statement must be true - but how can it be? etc etc etc!

[Guest]

if he's telling the truth it means he's a lier which doesnt make sense at all.

so he must be lieing therefore not all cretans are liers, just because he's a lier doesnt mean they all are...

[Guest]

The paradox is not the riddle. The fact that in the second statement the Cretan words it slightly differently, "All Cretans are liars and all I say is the truth.", doesn't settle anything.

The riddle is in the statement following the paradox: '"I always lie." Is he lying or telling the truth.' The statement "I always lie." is an emphatic statement meant to reveal a truth. But since he says "I always lie" gives the lie to his statement. So, he's lying.

[Guest]

I think the statement "All Cretans are liars" is a lie..i think some Cretans are liars,others speak the truth while others alternate truth and lie.

The Cretan in question is a liar.

[Guest]

He is lying in either of these cases. Your automatically assuming that anything he says is a statement that is an absolute constant, instead of a variable. It is not stated the possibility that his statement changes in each instance. He may only lie half the time.

[Guest]

Ok. So the first guy says that all Cretians are liars, which means that they have lied at some point in their lives. This does not mean that everything they say is a lie. When he returns he says that all Cretians are liars but all he SAYS is true. This statement is the truth also, seeing as he could lie by writing false words, or something of the sort besides speaking.

Ok. So the first guy says that all Cretians are liars, which means that they have lied at some point in their lives. This does not mean that everything they say is a lie. When he returns he says that all Cretians are liars but all he SAYS is true. This statement is the truth also, seeing as he could lie by writing false words, or something of the sort besides speaking.

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.

[Guest]

A very clever friend of mine once explained this to me. If a person tells you they are lying when they are, then that means they are telling the truth because they told you they were lying. So if they are telling the truth (because they told you that they were lying) but said that they weren't telling the truth, then they are in fact lying - and that is the paradox!

[Guest]

At the bottom of this it says:

[if someone says "I always lie", are they telling the truth? Or are they lying?]

suppose every word was a lie ,you just told the truth by admitting you always lie.

[Guest]

The first statement is what governs this paradox. In the second statement, he states that all cretans are liars but he only tells the truth. In this situation if he were telling the truth he would be lying about all cretans being liars thus he would be lying so cant be telling the truth. However as stated previous, the first statement by the cretan states simply that all cretans are liars. This is a contradictive statement because if he is in fact telling the truth then all cretans are liars which means he cant be telling the truth but would instead be lying. However, if he were lying when he stated that all cretans are liars, then that would mean that at least some tell the truth. Thus when deciphered together, the two statements can only result in the fact that not all cretans are liars, but the one making the statements in fact is.

[Guest]

A person who always lies can't say "im lying" because therefore they would be telling the truth. So, the first Cretian man can't be telling the truth by saying that Cretian men always lie because then he would say that he always lies, but he can't be lying because then he would be saying that Cretian men tell the truth.

Right?

[Guest]

This might have been said before, I didnt read all 20 pages of comments.

I dont see the paradox in this scenario. The case, which basically consists of:

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

wouldnt necessarily be a paradox unless you assume that he always tells the truth or always lies.

"I always lie" could obviously not have been the statement of a truth-teller,

but as far as I can see, nothing contradicts the fact that he may be a liar.

Thus negating the statement, making it "I do not always lie" (instead of "I always tell the truth).

However, if the riddle went something like this:

"On an island there are two kinds of people; those who always tell the truth, and those who always lie.

You encounter an inhabitant who tells you, "I always lie". Did he lie or tell the truth?"

In such a case the paradox becomes more obvious, to me at least. You could, as stated 1000 times before,

not tell the truth if you said that you were always lying. Nor could you be lying, as the negation would

be "I always tell the truth" (which couldnt be the statement of a liar).

[Guest]

yeah, I might not have read all the pages up in here and it might have come before what I am about to say, but whatever....

1. "All Cretans are liars."

Now lets try to negate this, this can be negated as "all Cretans are not liar" or "none Cretans are liar" .

But consider he said, "some Cretans are liars", now if that's the case he is either telling the truth or lie. If he is lying, then that would mean either all Cretans are liar, or none Cretans are liar. If it means that all Cretans are liars then he could not be lying, but if it means none Cretans are liars then that would mean he aint lying thus contradicting our assumption. so in that case he is not lying, thus he is telling the truth, meaning some Cretans tell truth and is he one of 'em.

But he said "All Cretans are liars." and not the above considered statement, first let's assume he's telling the truth, this obviously contradicts the statement, ergo he aint telling the truth, now if he is lying that would mean either "some Cretans are liars" or "none Cretans are liars" is true. Now if none Cretans are liars, he can't be lying, thus the only reasonable choice is "some Cretans are liars".

Thus, he is lying and the truth is that some Cretans are liars.

2. "All Cretans are liars and all I say is the truth."

Let's split the statement from and so we have 2 statement. Let's come to binary and treat 1 as true and 0 as false.

so there can be 4 possibilities.

[pre][b]

 	Statement 1                         		statement 2                   		statement1 AND statement2


i)             		1                               		0   	                                              	0

ii)                    0                               		1                                                 		0

iii)           		1                               		1                                                 		1

iv)           		0                                    	0                                                 		0

[/b][/pre][/html]

Now the third is obviously out of the way, so let's focus on 1, 2 and 4.

Now from previous point I found that only 2nd or 4th case is possible, as statement 1 is false.

so, we just focus on statement 2. [i][color=#0000ff]"All I say is truth"[/color][/i] if its is [color=#0000ff]true[/color] then statement 1 can't be true so its [color=#0000ff]false[/color][color=#ff0000][color=#000000][b][u]

So again, he is lying and the truth is that some Cretans are liars.

[/u]3. [color=#ff0000]"[/color][/b][color=#ff0000]I always lie"

[color=#000000]Yeah, Its a bit tricky, I don't know... whatever. I gotta go now. I might come back tomorrow or some, and try to put a little thought into this.

Good day everyone.

[/color][/color][/color][/color]

[Guest]

He is lying. His intention is to deceive. If he announced he always lies, he knows people could suss him out by doing the opposite. He lies selectively, sometimes helies and sometimes he tells the truth. So he is successfully lying when he says he always lies.

seanorjohn google me.

Edited December 4, 2010 by seanorjohn