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Double Liar Paradox (Jourdain's paradox)
Posted 22 October 2010 - 04:52 PM
Posted 22 December 2010 - 11:00 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?
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.
Posted 02 January 2011 - 03:39 AM
Posted 07 January 2011 - 04:35 AM
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:
Inscription on the other side is true
Inscription on the other side is not true
I like to think outside the box and therefore let me use some wordplay.
The solution: With this predicament, all I see is a loop, a continuous never-ending loop.
You can choose to start with either side both end up in the loop.
Starting with the back side: it is trying to say that the inscription on the other side is true as in the word true. Lets try a different word for a second, the inscription on the other side is dog and you turn it over and see the word dog. So, going back to the original, you expect to see the inscription or the word 'true' but find a sentence that is true in saying that the inscription on the back is not true. you return to the back side and find that it was false and true. False because there wasn't a single word (true) and true because the other inscription was right in saying this one is wrong.[/spoiler]
If you're head is not hurting and you want to start with the front side as is common sense for it to be in front of you.
Starting with the front side: it is trying to say that the phrase on the other side is wrong. You turn it over and find some falseness and some truth. False in the sense that the inscription on the otherside doesn't read 'true', it obviously reads 'Inscription on the other side is not true'. However, it is true in verifying the other side saying that itself is lying.
Just like the liar paradox, if something is solely true than it is honest. However, just as in modern society a liar is known for lying and he can sometimes tell the truth. A mix of truth and false is a lie just as something needs to be completely correct and not half correct for that is incorrect. Therefore, all teachers should not give you a mark out of 100. You should fail if you don't know everything single last and little thing but that is only in technical terms. Positive times negative is negative. Positive times positive is positive. How ever the double negative being a positive doesn't apply.
Edited by GGJT, 07 January 2011 - 04:36 AM.
Posted 02 May 2011 - 08:39 PM
Posted 16 May 2011 - 09:27 PM
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.
Posted 28 August 2011 - 01:29 AM
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>
Posted 05 September 2011 - 12:24 PM
only 1side can be true. It can be any side. Both can't be true or both can't be lies at the same time.
Edited by twilight, 05 September 2011 - 12:26 PM.
Posted 24 June 2012 - 06:45 PM
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?
Posted 07 August 2012 - 07:40 AM
THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.
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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