unexpected
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Swedish civil defense authorities announced that a civil defense drill would be held one day the following week, but the actual day would be a surprise. However, we can prove by induction that the drill cannot be held. Clearly, they cannot wait until Friday, since everyone will know it will be held that day. But if it cannot be held on Friday, then by induction it cannot be held on Thursday, Wednesday, or indeed on any day. What is wrong with this proof?

+y

Let's simplify the paradox a bit- we don't need a
whole week to cause a problem, two days will work just as well. If the judge tells the prisoner he is to be hanged either tomorrow or the next day, and he won't know until the day of the execution, we have a problem. After tomorrow, the prisoner will know the day, which violates the rule. So it must tomorrow. But if it must be tomorrow, then the prisoner knows the day. Which violates the rule. Must make the prisonner's head spin.

Which is fortunate for the judge, because it is this paradox he has constructed which makes the judge's sentence valid. He has created a logical system which traps the prisoner from being able to know the truth.

This even works if the judge had said: "You will be hanged tomorrow and you will not know that you will be hanged tomorrow." Think about it- from the prisonner's perspective he cannot know that sentence to be true. If he could, it would be false.