Welcome to BrainDen.com - Brain Teasers Forum
|Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.
Of course, you can also enjoy our collection of amazing optical illusions and cool math games.
If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.
Thanks and enjoy the Den :-)
Liar Paradox (Eubulid or Epimenides Paradox)
Posted 09 September 2007 - 01:29 AM
Posted 09 September 2007 - 05:23 PM
The Cretan then says "All Cretans are liars but he always tells the truth", again we can deduce nothing from this using my earlier reasoning.
The real paradox to me is how one's initial answer to the paradox leads onto another answer and then another. A sort of "circular answer"
Posted 11 September 2007 - 04:19 AM
Here's my try...
First, note: In 'Statement 1' he does not follow the language usage of 'Statement 2' - "all I say is the truth." This is an explicit statement, and if he followed the same language usage in 'Statement 1' to say "All Cretans say are lies," it would be the same as saying "All I say is a lie." But he does NOT say this. It is easy to make this mistake.
Statement 1: The Cretan says "All Cretans are liars." This means that all Cretans have lied at least once (and/or make a habit of it,) according to his statement. Therefore, since he is a Cretan, the Greeks cannot trust the statement (he is a liar, because he is a Cretan.) It is also unlikely he is speaking the truth since he is unlikely to know if ALL Cretans have lied.
Therefore: "All Cretans are liars" may or may not be true... though unlikely.
Statement 2: The same Cretan says "All Cretans are liars and all I say is the truth." Here he is explicit in the statement about himself, but we must pay attention to how it's joined to the statement about "All Cretans." If he had said "except" or "but" (exluding himself from the other Cretans,) it would have made the statement about himself valid; however, he says "and."
Therefore: The statement about himself is an untruth - again, he is a liar because he is a Cretan, so "all (he) says is the truth" is untrue.
Note: Here we have paradox - following the statements the other way around, read it as "all (he) says is the truth" so his other statement must be true (he's not excluded himself from it,) so it's true that "All Cretans lie" - but since he is a Cretan he is a liar. Therefore he is a liar and "all (he) says is the truth" at the same time. Paradox!
The question "If someone says about himself that he always lies, is this the truth or a lie?" is related but not exactly what the Statements were all about.
If I say "I always lie," it's an explicit expression; therefore my statement about lying must be false (since I am lying,) and so "I do not always lie." Thus, the statement is untrue- because I do not always lie (if we accept that a lie and an untruth are the same.)
Have to pay attention to grammar, and some logic here.
Posted 14 September 2007 - 04:18 AM
First of all, could we all be clear on what a paradox is.
Paradox (according to dictionary.com): a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.
Some paradoxes turn out to be just amusing and mind-bending yet completely possible and consistent. Others turn out to hold a contradiction. I think this particular paradox is an example of the latter.
(I am assuming that if a Cretan is a liar then they never tell the truth, otherwise it's hardly a paradox, is it?)
The Cretan said "All Cretans are liars." This statement has many implications, like "the next statement I make will be false", "the last statement a Cretan made was a false", etc. But the most problematic of the implications, the one at the heart of this paradox, is "this statement is false".
1. Let the statement "this statement is false" be referred to as A.
A: this statement is false
2. Now we can replace A's reference to itself (the words this statement) with its letter.
A: A is false.
3. Or equivalently to 2.:
A: not A
4. The Cretan's claim was:
5. Which is the same as claiming (i.e., the truth-value would be the same if he had claimed):
A and A
6. Expand the second instance of A in 5., using our knowledge from 3., that 'A: not A'
A and not A
Statements in the form 'A and not A' are contradictions. We have discovered that the Cretan's statement implies a statement of this form. This means his original statement was also contradictory. Contradictory statements are false, so the Cretan's statement was false.
Posted 17 September 2007 - 09:45 AM
Liar Paradox (Eubulid or Epimenides Paradox)
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. Or at least he was so engrossed in it that he wandered under a tree and fell asleep without noticing the oncoming thunder storm. So:
1) A Cretan sails to Greece and proclaims to the 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 sails to Greece again and cries: "All Cretans are liars and everything I say is the truth." Although these Greeks weren't the same Greeks as last week, they are still unsure exactly at whom this whacko is shouting, regardless of whether or not he's telling the truth.
3) If someone says about himself that he always lies, is this the truth or a lie?
4) Why are all these Greek guys standing around on the beach? Shouldn't they be beating their sons into fit warriors or inventing democracy so it can be ignored for the next 2600 years or so?
5) If he thinks Cretans are so God-awful and he's so high-and-mighty, why does this jerk keep going back to Crete and when will he learn his lesson?
6) If a Cretan sets sail in a trireme from his homeland in 727 B.C. headed for Greece at a rate of 4 knots, and the Sirens live 87.6% of the way between Crete and Sicily, what is the probability that Odysseus will finish his thick-crusted pizza before you're done reading this and log out of Facebook only to lie awake in bed confused until you're late for work tomorrow?
In order for this to even begin to be considered a paradox the wording would have to be changed so that assumption doesn’t come into play. “All Cretans are liars,” is likely a truism, simply because it is nearly impossible for a person to live out their entire life speaking only the truth and nothing else. Note that I said "nearly". But any argument using superlatives (every, all, always, never, worst, most, etc) is bound to fail on the basis that there is always (ha, get it) an exception, such as, say, the person who doesn’t talk until someone asks, “Can you speak?” and he replies “Yes.” Then by some cruel fate he is struck dumb (mute) for the rest of his life having never learned sign language. (i.e. he’s struck dead by lightning while still hissing the “s” in “Yes”).
However, if the Cretan says, “All Cretans lie all the time,” then you have a problem because either A) It’s true, which means that the man saying it isn’t actually a Cretan (i.e. he was lying about his heritage and Zeus should smite him with a well aimed lightningbolt, even though Zeus himself was actually born in South Central Crete and is therefore a liar of worst degree) or B it’s a lie; which is most likely because he’s a Cretan using superlatives and we all know them to be liars so why would we believe him in the first place?
But in the case we’re presented, there is no paradox because though all Cretans may be liars; that doesn’t mean that everything they say is a lie.
So this Cretan arrives on the shore and announces to all who will listen, “All Cretans are liars!!” But no one IS listening because he’s telling the truth, which means he's a liar, and no one takes heed of the words of liar even if he's telling the truth a.k.a. the Boy Who Cried Wolf.
When he adds "...everything I say is the truth," it doesn't change the scenario in the least. We already know he's a liar, because he's a Cretan, and once again he's using superlatives. This a** is never going to learn that no matter how many times a liar tells the truth there's still the chance that he's lying. Even the poor schmuck who got struck by lightning (never, ever spoke an untruth in his life, remember?) could have said "No," right before he got struck... there's got to be that possibility. God! A lying mute! I mean s***! His entire life he was even lying about being a mute!! There's no way we can trust that guy! He deserved what he got.
Peter Griffin said it best when he said, "Everything I say is a lie. Except that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that. And that..."
Posted 17 September 2007 - 11:04 PM
If somebody says about himself, that he lies, is it truth or lie?
 It is truth. Everyone lies.
If you recast the question as:
If somebody says about himself, that he is lying, as he speaks, is it truth or lie?
 It is a contradiction. Here's why:
[a.] every declarative sentence, say "I am 66 years old." carries the implicit assertion
"It is true that ... I am 66 years old." equivalently,
"I speak the truth when I say that ... I am 66 years old.".
[b.] To pair that assertion with the assertion "I am lying as I speak"
transforms the statement into the contradiction
"I speak the truth when I tell you that ... I lie as I speak."
This need not be viewed as a paradox.
But it is inescapably a contradiction, of the same form, for example, as the statement
"It is raining heavily as I tell you that ... the skies are perfectly clear."
Vidi vici veni.
Posted 18 September 2007 - 05:37 PM
Posted 21 September 2007 - 01:15 PM
But it is inescapably a contradiction, of the same form, for example, as the statement
"It is raining heavily as I tell you that ... the skies are perfectly clear."[/quote]
this isn't necessarily a contradiction. that's more an assumption. he doesn't say WHERE it is raining heavily even though his skies where he is could be perfectly clear.
Posted 21 September 2007 - 02:02 PM
A Cretan sails to Greece and says to Greek men who stands upon the shore: "All Cretans are liars." Did he speak the truth or did he lie?
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 ashore weren't aware of what he said the first time, they were truly puzzled.
If someone says about himself that he always lies, is this the truth or a lie?
i find it funny reading some of the other posts that do not take the words as they are, but add to them, such as saying 'a second cretan' or 'all sea-faring' to replace 'all', etc.
and since much greater minds than my own have wrapped their heads around this i doubt this simpleton is going to solve this. but i do see one thing amiss -- the paradox about the cretan is not the same paradox as the ending statement.
The first paradox is 'All Cretans are liars' vs 'All Cretans are liars and all i say is the truth'.
The second paradox is the last statement 'if someone says about himself that he always lies is this the truth or a lie'
The difference between the two is the first one states someone lies, the second one states ALWAYS lies' Big Difference!
the second one to me is easier. if you ALWAYS lie then everything you say, including this statement, must be a lie, which cannot be, therefore it is NOT true that you always lie. this does not mean you always tell the truth. just that you do not always lie, therefore sometimes you tell the truth and sometimes you lie.
The first one is indeed more the paradox. A Cretan states ALL Cretans are liars and everything that he says is the truth. He is a liar therefore the first statement he is saying he, too, lies. NOT that he or all Cretans lie ALL the time. Just that they (sometimes, but without a doubt) lie.
The second trip's additional phrase of 'all he speaks is the truth' can be taken at least two ways. Is he saying 'ALL he speaks is truth'? as if ALL the time everything he says is true? which canNOT be because it's similar to saying HE NEVER LIES and Cretans lie at least some of the time. so he contradicted himself.
But if his 'All I'm saying is truth' could be speaking for the moment. Similar to saying, 'hey, i'm just telling you like it is' which is more a moment in time, then this could indeed make sense and be a true statement. ALL Cretans lie (at least sometimes, but not always) and 'shrug' what can i say, it's the truth, including myself (but i'm not lying at this moment in time).
it's like the following>>>An English professor wrote the words, “Woman without her man is nothing” on the blackboard and directed his students to punctuate it correctly.
The men wrote: “Woman, without her man, is nothing.”
The women wrote: “Woman: Without her, man is nothing.”
Posted 24 September 2007 - 08:25 PM
His statement that "all cretans are liars" was indeed a lie. The truth is that SOME cretan's are liars.
His second statement that "all cretan's except himself are liars" would in turn also be a lie because he is one of the liars.
0 user(s) are reading this topic
0 members, 0 guests, 0 anonymous users