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Double Liar Paradox (Jourdain's paradox)


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What underlies paradoxes of this type is the syntactical rule that a declarative sentence is by its nature an assertion of some particular truth. To use a presumed assertion of truth to deny that

I don't quite understand the fascination with 'paradoxes' of this sort, which basically come down to which of the two statements are true, if any. I am blue. I am red. Am I blue or red? Maybe

just burn the card

The lying example doesn't work. Lying and not telling the truth are entirely different. When you lie, you are telling someone something that you believe is incorrect. When you don't tell the truth, you are still able to say what you believe, be incorrect, and not be lying about it.

The tricky part with this paradox is that one statement means nothing without the other. In any event where the statement can stand alone it's not a paradox. Ex: "This statement is false." The statement that is being called false is false, while the entire sentence is true. What is false does not include the word false itself.

The only circular part about this problem is trying to figure it out. The problem itself isn't circular, they both exist at the same time, in the same space.

Even knowing that, I'm having a hard time getting out of the circle. Can anyone else get out of it?

Bravo for your insight on this paradox. You have reminded me of the "lying by omission" statement. If I do not speak the truth, it may still exist, just not in the realm of hearing it being spoken by me. It may also not exist at all, but that is irrelevant. If I state, "I do not speak the truth," but I know the truth and choose not to speak it, does this mean I am lying? I would suggest that instead of considering this to be a circular reasoning problem, consider the dimensions a paradox exists in. The Grecian spoke ill of all Cretans, "All Cretans are liars." When he returned to the island of Crete for a second time, he spoke it again, then added, "All I say is the truth." The only way through this, is to realize that the absolute word ALL is the one thing that can be proven wrong. It does follow that one truthful Cretan can be found. This nullifies the Grecians words that he speaks only the truth. He can be proven to be a liar, without considering his proclamation that he speaks only the truth. In the realm of evidence to the contrary.

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Double Liar Paradox (Jourdain's paradox) - Back to the Paradoxes

This version of the famous paradox was presented by an English mathematician P. E. B. Jourdain in 1913.

The following inscriptions are on a paper:

Back side

Inscription on the other side is true

Face side

Inscription on the other side is not true

Edited by GGJT
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Very, very simple answer. Both sides are false.

The other side is true

= = = = = = = = = = =

The other side is not true

If both false, wouldn't you get:

The other side is not true = the other side is not true

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

The other side is not not true = the other side is true

Back to where we started.

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<p>this statement is false<br />

synonym to false is incorrect</p>

<p>this statement is incorrect - if the statement is incorrect is it correct in saying its incorrect not really, because it is incorrect the statement is actually true but by saying its false it is wrong. So its basically the concept of a double negative<br />

false * truth = false</p>

<p><br />

</p>

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The sentence on the other side of the card is true that this is false. It is an extreme paradox. There is a point of view.

If you look at the front and then the back, then contradiction comes into play. It means that the back side is true that this is false, but that means both sides are false.

To do this paradox for myself, I used an index card to do it. I came up with "Both sides are false." Any other points?

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hey guys think in this way

let

P:

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.

&

Q:

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE.

now let us assume P is true which means Q is true.Now Q says P is false ,a contradiction,so P is false.

From above we concluded P is false so it means Q is false(what P says of Q is wrong).Now Q being false says wrong about P.Thus, P is true ,again contradiction.

This way we can start with Q and show that it too has no truth value(neither true nor false).

So, these statements mean nonsense although individually they seem to be logical statements.

Hence, it's all paradoxical

I hope i have conveyed it clearly :-)

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In order to truly make this a paradox, you would need to qualify at the beginning that both statements are either true or false.

If both statements are true, it's a paradox because they cannot both be true.

If both statements are false, it's a paradox because they cannot both be false.

There is no such qualifer to this "puzzle"; therefore, it's philosophy.

But it does provoke thought, doesn't it? That's what philosophy does.

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Here are the facts:

Front= "THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE."

Back= "THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE."

You can start with either side, it does not matter. Let's use "-n" to specify deniability, and let's start with BACK:

Back = Front = -nBack = -nFront = -n-nBack = -n-nFront = -n-n-nBack = -n-n-nFront = -n-n-n-nBack = -n-n-n-nFront = etc. = etc.

It is an infinite loop of deniability. By starting with BACK, first, assumes truth until the loop cycles back to BACK and deniability begins, infinitely. Starting with FRONT initiates the infinite loop immediately, but intuition of using the FRONT, first, should call the question of "when did this start in the first place?" (there was no beginning, it has always been), because we could have started with BACK initially... See how this works?

Added:

This problem has two flows: a reverse flow


Edited by ACuriousMind
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The edit rules are very stringent in this forum, and the edit button did not seem to appear after the "10 min rule". Anyway, from my above post, this is supposed to be the finalized edit:

Added:

This problem tends to have a reverse chronological flow, because the mind attempts to unravel the pattern as soon as the illogical loop is recognized, to find any initializing details.

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Whatever value of truth we assign to any of the statements, we'll be trapped in a contradiction. The resolution of such a thing would be to assert that the two statements aren't correlated. It is assumed that the truth value of one statement affects the other one, but we can state that this assumption is wrong and that they are un correlated, and the problem is solved.

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On 3/26/2008 at 11:17 AM, Guest said:

 

Both sides can't define what is true or false, individually and as a whole, but both sides indicate they can define what is true or false, individually and as a whole, so it is giving a false indication.

It is indicating it can define what's true or false, when it is actually attempting to leave what's true or false undefined.

Edited by double 0 zero
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Back side

Inscription on the other side is true

Face side

Inscription on the other side is not true

 

what if we make it like this.

there are 2 person separated by a wall

1st person said, "listen to me. i'm telling you the truth. the person on the other side of this wall is telling the truth."

2nd person said, "listen to me. i'm telling you the truth. the person on the other side of this wall is not telling the truth."

 

which one is telling the truth? which one is telling lies?

are both telling the truth? or are both telling lies?

 

guess that's why they call it window pa,,, uhm... i mean, double liar

cmiiw...

 

temporary sig

"paradox born from our failure on placing matter in a proper context."
- insert some famous name here -

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On 7/19/2007 at 10:48 PM, Guest said:

I don't quite understand the fascination with 'paradoxes' of this sort, which basically come down to which of the two statements are true, if any.

 

I am blue.

I am red.

 

Am I blue or red? Maybe I'm green. Doesn't matter, both cannot be true.

 

The truth is on the other side.

The other side holds no truths.

 

Or is that just it? We enjoy 'trapping' the mind in a room with mirrors on both the wall we are facing and the wall directly behind, and looking at the infinite reflections that result?

 

I just don't get it. Can someone tell me what I am missing?

 

I am reminded of the "bullet that pierces all vs. armour that cannot be pierced" contradiction. Similar situation, both just cannot exist. One is right, the other is wrong, or maybe both are wrong, but the contradictory elements cannot both be right.

In the case of the "bullet that pierces all vs. the armor that cannot be pierced" contradiction, I think some amount of scientific logic can be applied. In a situation where two equally powerful forces clash, the outcome is neutral. The bullet would not pierce the armor and the armor would not damage the bullet. This makes the statement that the bullet can pierce all and that the armor cannot be pierced false. However I don't think it's a true paradox. 

As for what the fun is in paradoxes, it's that they make you think more deeply than the common riddle. While normal riddles make you think outside the box, paradoxes make you throw the box away and start looking under a bowl. It completely changes the game by making it an insolvable riddle that stretches the mind to its limits. Some people don't enjoy puzzles, but for puzzle people, there is no greater puzzle than the paradox.

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Spoiler

once defined the idea of nothing becomes real.

Nothing is for real. ( paradox ( paradox )

Albert  Einstein knew exactly what the scientific method was .  Doing the same thing over and over and expecting different results is reality not crazy and never happens in a changing environment.  - roll a die.    Doing the same thing over and over and expecting a different result IS not the definition of insanity..  In fact saying that silly statement is the ONLY time possible in this reality that this is true every single time.   Every time you say it,  it is nuts.  He purposefully said it as a joke and stupid idiots made it the paradox it is.

Edited by exorb
double paradox
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IS = false.  It IS without perspective or exception, upon further investigation .  Closed notion for closed minds.  Higher intel or quantum communication  would leave such notions open ended for further learning. Don't close the book on this topic.  reinvestage.  don't take my word as fact.

Nothing exists.

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