The Unexpected Execution -- You Bet Your Life

Quote: MathExtremist

Not really. The original problem statement was taken from a factual announcement by the Swedish civil authorities. They simply said "A civil defense exercise will be held this week. In order to make sure that the civil defense units are properly prepared, no one will know in advance on what day this exercise will take place".

But the statement was rather different. Imagine, rather, if they announced "One of next week's mornings we will conduct a boot inspection for submitting to the International Chrome Boot Award Commission. In order to ensure the results honestly represent the average boot shininess level, we guarantee that no one will be able to expect this inspection the day before it."

Two things are clear here: first, that the guarantee will be broken anyway, as average boot shininess level will not be represented.
Second, that if the inspection is held on Friday, everyone has to expect it the day before, and the award will be guaranteed invalid.
It's even possible to predict that (if the inspection never takes place) the shiniest boots will be seen on Thursday, because, seeing how doing it on Friday invalidates the award automatically, everyone will shine his boots the most on Wednesday.

Quote: MathExtremist

There's a limit to what you can deduce or predict if you simply don't know something. In my counting-up-to-5 example, you simply cannot deduce whether I'll keep counting or whether I'll stop until after I've stopped. By then it's too late.

The difference comes from the Judge giving a guarantee, which positively prevents an execution from taking place, making the event and the decision not independent. If I say "you'll stop counting", you can't stop counting. But as said, the issue still hinges on how the problem is formulated rather than on its merits per se.

P90: Please help me understand your position more clearly by answering just a few questions:

(1) Do you believe that sound logic leads to the conclusion that the execution cannot be held on any day that week without violating the judge's statements?

(2) If so, would you still advise the prisoner to make predictions about the execution occurring on one or more days?

(3a) If so, why bother to predict the timing of something you have already decided cannot occur?

(3b) If not, what solace would you offer the prisoner when the executioner shows up one morning, with the day of his arrival not having been predicted logically?

If "deduce" is taken to mean "determined using sound formal logic and correct", no. If "deduce" is taken to mean "determined by mental exercise and correct", a more casual interpretation, yes.

I have to maintain that the latter interpretation is possible. For instance, if in NLH someone makes a min-raise on the turn after raising big on the flop, you can say you have deduced that he's got nothing, even though the logic behind your deduction is weak and based on long-reaching assumptions. Ironically, trying to formalize poker judgments often leads to the "it looks like he wants me to think he has aces, but he knows I will think he wants me to think he has aces, so he wants me to think I think he wants me to think he has aces..." infinite sequence.

I don't really want to get this thread going again, but I thought that maybe the folks who like this executioner puzzle/paradox would find some humor in this comic strip.