4 ms·

There is a simple resolution to this "paradox": it's only a paradox if you consider the judge's initial statement to be True. If the judge's initial statement i

There is a simple resolution to this "paradox": it's only a paradox if you consider the judge's initial statement to be True. If the judge's initial statement is False (i.e. he's lying) then the whole situation is logically consistent. The truth table for modus ponens helps clarify, both F->T and F->F evaluate as T https://en.wikipedia.org/wiki/Modus_ponens#Justification_via_truth_table https://en.wikipedia.org/wiki/Modus_ponens#Justification_via... The judge is saying he can predict how someone else will feel in the future (i.e. he can predict the future), which unless he is omnipotent is a false premise in my book.

mattdeboard 8y ago
This was convincing at first. But this logic problem is predicated on the notion judges do not conceal their intentions (iow that his initial statement is True). There is just no point in even considering the question if the prisoner isn't actually going to be executed.
- Gormisdomai 8y ago
  The Judge could be lying even if the prisoner is actually executed - in particular he could be lying about the "and it will be a surprise" bit.
- tristanj 8y ago
  I should clarify. The judge is not necessarily "lying" (i.e. making a false statement). He's making a statement which has no bearing on the future. The judge's statement could end up being True or False. Using that interpretation resolves the "paradox". The question encourages you to start from a flawed premise to begin with. Why must the judge's first statement be True? A judge cannot guarantee how someone will feel the future. Further, why must the prisoner be surprised at the date of his execution? If the prisoner is not surprised at his date of execution, that is also a logically consistent situation. The question tries to shoehorn you into an irreconcilable input state and output state. Yes, it is a paradox if you assume the question's implied start and end result. However if you remove the limitations implied by the question, in the bigger picture there is no paradox.
zbentley 8y ago
I think that misinterprets the term "surprise" in the paradox. "Surprise" isn't meant primarily as "the prisoner will feel surprised" (though the ending is more pithy if it is put that way), but rather "the event will not be logically predictable for the prisoner".

mattdeboard 8y ago

This was convincing at first. But this logic problem is predicated on the notion judges do not conceal their intentions (iow that his initial statement is True). There is just no point in even considering the question if the prisoner isn't actually going to be executed.

Gormisdomai 8y ago
The Judge could be lying even if the prisoner is actually executed - in particular he could be lying about the "and it will be a surprise" bit.
tristanj 8y ago
I should clarify. The judge is not necessarily "lying" (i.e. making a false statement). He's making a statement which has no bearing on the future. The judge's statement could end up being True or False. Using that interpretation resolves the "paradox". The question encourages you to start from a flawed premise to begin with. Why must the judge's first statement be True? A judge cannot guarantee how someone will feel the future. Further, why must the prisoner be surprised at the date of his execution? If the prisoner is not surprised at his date of execution, that is also a logically consistent situation. The question tries to shoehorn you into an irreconcilable input state and output state. Yes, it is a paradox if you assume the question's implied start and end result. However if you remove the limitations implied by the question, in the bigger picture there is no paradox.

zbentley 8y ago

I think that misinterprets the term "surprise" in the paradox. "Surprise" isn't meant primarily as "the prisoner will feel surprised" (though the ending is more pithy if it is put that way), but rather "the event will not be logically predictable for the prisoner".