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the following paradox is a variation of the Barber Paradox, I don't quite understand why this is a paradox so I'd like to hear you tell why, please.

There was a philosopher who had committed a crime (for example, he stared at a King's espouse) and he will be executed. The Benevolent King, though, allows the philosopher to choose if he wants be hanged up or beheaded, he only needs to tell a truth or a lie. The philosopher, then, says: I'll be beheaded.

I'm lost, read this several times and couldn't find the paradox. I appreciate any help.

rodrigoalves
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  • I'm pretty sure you don't have the full version of the problem. Some stuff are missing, I believe. Do you have a link to where you got that problem? – Git Gud Feb 10 '13 at 13:35
  • I see. Actually I translated it from pt-BR. But I sincerely think if there is something missing, it is missing in the original source. Which is located here http://pt.wikipedia.org/wiki/Paradoxo_do_barbeiro#Variante:_morte_por_enforcamento_ou_decapita.C3.A7.C3.A3o – rodrigoalves Feb 10 '13 at 13:37
  • The king paradox isn't there, just the barber's. EDIT: Nevermind, found it. – Git Gud Feb 10 '13 at 13:37
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    The original source is badly written, it should be "se quer ser enforcado ou decapitado, desde que ele diga uma verdade ou uma mentira, $\textbf{respectivamente}$". – Git Gud Feb 10 '13 at 13:42
  • Thanks Git! What an awesome thing that you know portuguese! – rodrigoalves Feb 10 '13 at 13:46
  • No problem. ${}{}$ – Git Gud Feb 10 '13 at 13:52
  • He should have said something like "There are infinitely many twin primes". – hmakholm left over Monica Feb 10 '13 at 16:28
  • Where's the paradox? This seems to be an illustration of the fact that one can have well-defined logical propositions yet not know the truth function. One might well have said ``God exists.'' That also is a proposition -- it is either True or False. (As @HenningMakholm said -- one could also have stated any currently unsolved mathematical conjecture: Continuum Hypothesis, Twin Primes, etc.) – Assad Ebrahim Oct 27 '13 at 09:55

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The full story should contain something like this: The King said: "If your statement is true, you will be hanged; if it is false, you will be beheaded instead."

Will he be hanged? If so, the statement turns out to be true, but then he will not be hanged according to the King's promise. Will he be beheaded? If so, that would make his prediction correct, so that he should be hanged, not beheaded.

Hagen von Eitzen
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