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Double Liar Paradox (Jourdain's paradox)


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#1 rookie1ja

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Posted 09 June 2007 - 12:44 PM

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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#2 unreality

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Posted 03 July 2007 - 02:24 AM

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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#3 bonanova

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Posted 20 July 2007 - 06:22 AM

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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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#4 Babers-san

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Posted 20 July 2007 - 06:48 AM

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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#5 bonanova

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Posted 20 July 2007 - 07:49 AM

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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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 wsguede

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Posted 28 July 2007 - 02:53 PM

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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#7 Linewalker

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Posted 31 July 2007 - 07:01 PM

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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#8 retskcah .eht

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Posted 08 August 2007 - 11:02 AM

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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#9 bptdude

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Posted 22 August 2007 - 02:08 AM

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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#10 impact504

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Posted 28 August 2007 - 09:16 PM

This reminds me of the movie Labrynth.

"does that sound right to you?"

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