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Liar Paradox (Eubulid or Epimenides Paradox)


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220 replies to this topic

#191 physicsgal

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Posted 20 May 2010 - 06:14 AM

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.
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#192 Simms

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Posted 04 June 2010 - 04:13 AM

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.
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#193 Campion

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Posted 16 June 2010 - 11:53 PM

Spoiler for Liar Paradox
Spoiler for

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.


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#194 Juro

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Posted 28 June 2010 - 01:12 PM

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!
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#195 flatline247

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Posted 01 September 2010 - 01:28 AM

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.
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#196 biggie8800

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Posted 17 September 2010 - 09:15 AM

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.
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#197 dorlexat

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Posted 24 October 2010 - 05:16 PM

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?
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#198 Agnosis

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Posted 28 October 2010 - 10:46 PM

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).
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#199 MDK5

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Posted 16 November 2010 - 02:23 PM

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]

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. "All I say is truth" if its is true then statement 1 can't be true so its false
So again, he is lying and the truth is that some Cretans are liars.

3. "
I always lie"
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.

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#200 seanorjohn

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Posted 04 December 2010 - 10:37 PM

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 by seanorjohn, 04 December 2010 - 10:37 PM.

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