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The following thought-experiment was put forward by a 20th century analytic philosopher. Unfortunately I cannot remember the exact context in which it was proposed. Does anybody know how may have come up with this experiment, or where it might come from?

One day a court jester, who also happens to be a logician, ends up making too much fun of his king. Consequently the monarch sentences the poor fool to death. But to make things worse, he tells the condemned: "For your impertinent criticism, not only do I sentence you to die, but I will further punish you with the terror of uncertainty. Your death will take place before Monday in one week [it's Sunday now], but at no point in time will you have logical certainty about which day it will be." The jester-logician, after thinking about it for a minute looks up delighted and answers: "In that case, I thank your majesty for it's infinite mercy, for according to your own royal degree, you cannot kill me."

His thinking of course goes along these lines: if I made it through Saturday I would know with certainty that I get killed on Sunday (as I have to die before Monday), thus I cannot get killed on Sunday. But if I cannot get killed on Sunday, I also cannot get killed on Saturday, as I would know with certainty that I get killed on Saturday if I made it through Friday. And by mathematical induction, I cannot get killed on any of the previous days. Thus, on the conditions given by the king, I cannot get killed at all.

The apparent paradox is of course that the jester's reasoning seem perfectly valid (or does it?), and yet he would be completely surprised if they killed him on, say, Wednesday.

  • This may belong on puzzling... – Joseph Weissman Jan 19 '16 at 0:19
  • Perhaps, but this is an argument put forward by some more or less important analytic philosopher. Furthermore, it does raise some interesting questions concerning the nature of formal, determinate systems, and their relation to an indeterminate world. I would be more than happy if somebody could point me out which philosopher designed this experiment. – mar_cel Jan 19 '16 at 0:21
  • I have a vague recollection of reading a problem like this. The style (jesters and kings) sounds like something that Raymond Smullyan might have written. But this is an old problem that is just as often formulated as a professor promising a pop quiz the following week. The students reason similarly to the jester and similarly are surprised when the pop quiz happens on Wednesday. – A.Ellett Jan 19 '16 at 1:04
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    You might look at the references at the wiki page for Unexpected hanging paradox to find the source you're looking for: in particular TY Chow's article in the AMM publication may be of interest. – A.Ellett Jan 19 '16 at 1:08
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    To others, I would say this is not a puzzle. It is a paradox which rightly belongs on a page dedicated to philosophy. – A.Ellett Jan 19 '16 at 1:12
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This puzzle has been discussed by many philosophers, mostly under two different names: the surprise examination, and the unexpected hanging.

A search for "surprise examination paradox" at philpapers.org shows dozens of papers. Unexpected hanging is the name of the Wikipedia article on the subject.

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