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Double Liar Paradox (Jourdain's paradox)

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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

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a much simpler liars paradox:

"This statement is a lie"

if its telling the truth then its lying

if its lying then its telling the truth

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 same truth is paradoxical: One cannot

convey usable knowledge by asserting a denial. Nor can one

meaningfully deny a truth: the coin has two paradoxical

sides:

[1] "I am asserting a falsehood." or "I am lying."

[2] "I am not asserting something that is true." or "I am not telling the truth."

Putting it another way, it's physically possible to speak the

words, "I am lying." But when one undertakes a linear

analysis of what has happened when the words are spoken,

one is drawn into the syntactical analogy of a Moebius Strip:

a piece of paper having a physical connection of its two sides.

The circular reasoning forced on the mind by a linear

analysis of such statements creates a pleasantly frustrating

tease, and the desire for consistency and meaning leaves

one in a disturbingly uncomfortable state.

Long live paradoxes...

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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.

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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.

......

Can someone tell me what I am missing?

It's the fact that one statement can be a contradiction.

[1] "I am lying."

Spreading that over two statements does not change the

nature of the paradox:

[2] "I am telling the truth."

[3] "The previous statement is a lie."

Here, one can simply eliminate statement [2],

which carries no information, and change [3] into

[4] "This statement is a lie."

which is equivalent to statement [1].

To my mind the paradox arises from an explicit assertion of something's falseness

using a vehicle [declarative sentence] which implicitly asserts its truth.

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it is just like in math.

rule 1) 0 * anything is.... 0

rule 2) infinity * anything is... infinity

whats 0*infinity?

what is that absence of everything * the fulfilliment of everything?

its impossible to end the problem, unless u know calc.

i do believe that it is an infinit loop. but then again, it could be based on how u read it. and your thought process

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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?

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non of inscriptios are true.

becouse "the truth is absolute definition of an event acordingly to our reality"

retskcah .eht 8.8 2007

*this is not an event but a contradictional statement.*

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absolute truth?

*grins*

depending on culture and education, some people will fight to the death that there is no such thing as any absolute truth about anything, even for things that seem obvious.

"well, that's that's your opinion" or "well, not really, exactly, because of this obscure thing"

for a paradox "this is a lie" .. you have to dig into the definitions of a lie.

and something not being a lie does not make it a truth.

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This reminds me of the movie Labrynth.

"does that sound right to you?"

"I dont know, Ive never understood it!!"

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The bigger picture here is that neither side of the paper provides any useful information, so it isn't important which is true or false. Applying the label of truth or un-truth to either statement causes no effect beyond the piece of paper.

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...unless it labels the other side

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Back side

Inscription on the other side is true

Face side

Inscription on the other side is not true

The other side of this equation is true=The other side of this equation is not true

x=-x

x+x=0

2x=0

x=0

This statement does not exist. The truth nor non-truth are really inexistent, even though the words themselves exist in their order, their meaning is equal to nothing.

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this card is contradicting itself

you cant believe one side without lookin at the other

neither side can be true

if each side is calling the other wrong

therefore this statement cannot be considered into anything

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the side that claims the other side is a lie is false so both mean to say that the other side is true...

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Someone asked what the purpose of such paradoxes is.

One result is that they prove that language isn't completely logical even if you follow all the rules of grammer. It can be shown that no many how many rules of grammer you added, language would still have to have paradoxes like this.

That isn't so interesting but, in fact, it can also be proved that mathematics itself is not logical in a very similar way. There is no set of rules or axioms for mathematics that would make it so that everything true in mathematics could be proved by mathematics. That was a very interesting discovery because mathematics (and geometry) was always devised to be complete that way.

Gess

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Given:

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

Back side

Inscription on the other side is true

Face side

Inscription on the other side is not true

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

The side of the card that faces the evaluator is always A. Is the ticker tape a one-way tape or can the tape go back and forth, allowing the examiner to ratchet back and forth to evaluate at any point in the tape?

At t=0, we see the Face and have

Tape is one way (Unilinear expression) = A[t0] = ^A[t1]

Tape is two-way (Bilinear) = A[t] = ^A[t+1]

At t=1, we see the "Back" and have

Unilinear expression: A[t1] = A[t0] = ^A[t1] = This statement is false

Bilinear expression: A[t] = A[t-1] = ^A[t+1]

The ticker is clicked forward to t=2 for the purposes of our poor Unilinear universe, who are developing gastrointestinal difficulties. (Or Bilinear universe are contentedly munching on Pizza):

Unilinear expression: A[t2] = ^A[t1] = ^A[t0] = A[t1] = ^A[t2] = This statement is false

Bilinear expression: A[t] = ^A[t+1]

Substituting in the Bilinear A[t]=A[t-1], we consistently get A[t-1] = ^A[t+1], which is to say that in the present moment for A[t], the truth of the previous face of the card is equal to the reverse of what the next face of the card will say.

The Bilinear solution shows us that the solution depends on back-and-forth motion to solve the truth, rendering the Unilinear expression irrelevant. The Bilinear solution is in integrity, as it forms a integrous mathematical series shaped as a triangle with a single non-intersecting linear convergence between the past, present, and future. It has no discrete value in the present but rather only momentum within its defined universe.

Eric Mumford

Waterford, NY

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It's clever, but in my opinion it isn't a paradox, because the statements are meaningless.

There is a difference, by the way, between a "lie" and a "false statement". A lie is a statement, usually false, made with the intent to deceive.

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This is the same as the paradox:

Father: 'What your Mother says is true'

Mother: 'What your Father says is false'

I love these ones. XD

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Scenario 1: If 'True' and 'False' are mutually exclusive and exhaustive, this 2 cards situation is a loop.

True vs False => loop

False vs False => loop

True vs True => plausible (This is the possibility).

So we have to change the word "False" to "True".

We can change it because this is a liar paradox, isn't it!

OR

Scenario 2: True and False are not exhaustive. There is something which is 'not true' and 'not false'. This is the solution of this paradox.

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Putting it simply, you cannot assume out of ignorance that either side is true. However, you cannot assume either is false also. In a case like this, you need a third party to verify a fact. If the back was a liar though, you do not know how often it lies, when it lies, what it lies about, etc. Taking that in stride, the front can be true or false depending on the condition. There are many different scenarios: They could also both be liars, their positions can be switched around, etc. Again, you need the third party for verification.

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Very, very simple answer. Both sides are false.

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just burn the card

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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?

I think what I'm reading there is that the statement being referred to is false, not the statement being called false is false, with what was said there's only 1 statement, you can go around in circles if you try and break it down. Theoretically, anything you say can be either condensed or broken down depending on what it is. I am confused by what he means by What is false does not include the word false itself, perhaps implying that the word false in the statement isn't false? Any thoughts?

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Back side

Inscription on the other side is true this is not true

Face side

Inscription on the other side is not true this card is true but if the other card is false it can't be.

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