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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.

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  • $\begingroup$ 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? $\endgroup$
    – Git Gud
    Feb 10, 2013 at 13:35
  • $\begingroup$ 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 pt.wikipedia.org/wiki/… $\endgroup$
    – rodrigoalves
    Feb 10, 2013 at 13:37
  • $\begingroup$ The king paradox isn't there, just the barber's. EDIT: Nevermind, found it. $\endgroup$
    – Git Gud
    Feb 10, 2013 at 13:37
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    $\begingroup$ The original source is badly written, it should be "se quer ser enforcado ou decapitado, desde que ele diga uma verdade ou uma mentira, $\textbf{respectivamente}$". $\endgroup$
    – Git Gud
    Feb 10, 2013 at 13:42
  • $\begingroup$ Thanks Git! What an awesome thing that you know portuguese! $\endgroup$
    – rodrigoalves
    Feb 10, 2013 at 13:46

1 Answer 1

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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.

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  • $\begingroup$ As long as I remember there was a very similar one with this. The logic behind should be the same I guess. $\endgroup$
    – Seyhmus Güngören
    Feb 10, 2013 at 13:46

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