Not sure why you brought this up, but as long as you did, I’d like to share my resolution of this paradox. Basically, it hinges on the definition of a surprise. If the prisoner is spared on Wednesday, he will know that he is doomed on Thursday or Friday, but is ignorant of which of these possibilities is true. So when Thursday dawns, whatever outcome obtains will be surprising. To say we are surprised by an event is simply to say that we cannot predict it in advance. Therefore, you can only reason about surprise looking forward in time, not backward.
Or look at it this way. What if the judge told the prisoner that he was going to draw a slip of paper from a hat contain five slips, labeled Monday thru Friday and execute him on that day. Whatever day is chosen will be a surprise to both judge and prisoner.
Not sure why you brought this up, but as long as you did, I’d like to share my resolution of this paradox. Basically, it hinges on the definition of a surprise. If the prisoner is spared on Wednesday, he will know that he is doomed on Thursday or Friday, but is ignorant of which of these possibilities is true. So when Thursday dawns, whatever outcome obtains will be surprising. To say we are surprised by an event is simply to say that we cannot predict it in advance. Therefore, you can only reason about surprise looking forward in time, not backward. Or look at it this way. What if the judge told the prisoner that he was going to draw a slip of paper from a hat contain five slips, labeled Monday thru Friday and execute him on that day. Whatever day is chosen will be a surprise to both judge and prisoner.