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Double Liar Paradox (Jourdain's paradox)


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63 replies to this topic

#11 jettisoned

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Posted 30 August 2007 - 08:58 PM

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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#12 unreality

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Posted 31 August 2007 - 06:22 AM

...unless it labels the other side
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#13 ericabrauer

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Posted 02 September 2007 - 08:13 PM

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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#14 falling_apart

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Posted 16 October 2007 - 01:57 AM

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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#15 einsteinsdumbcousin

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Posted 10 November 2007 - 04:03 PM

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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#16 Gess

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Posted 11 November 2007 - 06:20 AM

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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#17 biostrategem

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Posted 13 November 2007 - 09:33 PM

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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#18 callumny

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Posted 15 November 2007 - 04:04 AM

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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#19 PlayTheMindGame

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Posted 17 November 2007 - 10:58 PM

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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#20 Naing

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Posted 18 November 2007 - 09:48 AM

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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