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220 replies to this topic

### #1 rookie1ja

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Posted 09 June 2007 - 12:31 PM

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

Spoiler for first part

Spoiler for second part

Spoiler for further reading for interest

Examples of incorrect interpretations from replying posts

Spoiler for

Note that this thread is closed since there have been hundreds of posts and resolution is summarized in this very first post.
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### #2 jayat27

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Posted 17 June 2007 - 06:46 AM

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.
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### #3 brainytrafficlight

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Posted 18 June 2007 - 05:41 AM

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.
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### #4 cpotting

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Posted 19 June 2007 - 09:01 PM

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.

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### #5 davidsparkman

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Posted 20 June 2007 - 03:17 PM

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.
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### #6 MissMaryKathryn

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Posted 21 June 2007 - 12:53 AM

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.
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### #7 brainytrafficlight

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Posted 21 June 2007 - 10:03 AM

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.
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### #8 Cyr|x

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Posted 25 June 2007 - 12:16 PM

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"
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### #9 Querube

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Posted 25 June 2007 - 01:09 PM

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.

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Posted 27 June 2007 - 04:33 AM

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.
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