A Paradox Explained

PARADOX STATEMENT A judge tells a condemned prisoner that he will be hanged at noon on one day in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that if the hanging were on Friday then it would not be a surprise, since he would know by Thursday night that he was to be hanged the following day, as it would be the only day left. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday. He then reasons that the hanging cannot be on Thursday either, because that day would also not be a surprise. On Wednesday night he would know that, with two days left (one of which he already knows cannot be execution day), the hanging should be expected on the following day. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all. The next week, the executioner knocks on the prisoner's door at noon on Wednesday - an utter surprise to him. Everything the judge said has come true. CRITICISM The judge by stating the nature of hanging has removed the surprise factor completely. However he assumes that the prisoner will be intelligent enough to conclude that he cannot be hanged by some simple deductions and at the same time foolish enough not to observe the trap that everyday will be a surprise for him if he so confidently concludes it - the classic case of flawed/implausible inherent assumption. Basically the paradox tries to play around with words. It is as good as a judge pronouncing that You will be hanged tomorrow but it will be complete surprise to you. So the prisoner deduces that he cannot be hanged as he already knows the date of hanging. And then he sleeps peacefully in his cell. When the executioner appears it is a complete surprise for him. But here the flaw is apparent. That is why the paradox is stated in a roundabout way. Try to equate this thing with the Surprise Quizzes conducted in IITs as part of the grading. Everyone knows that there will be a quiz on a day within the four months of the semester. So they should not be a surprise at all considering similar deduction. But the point is since all days are equally likely to have a quiz and no-one wants to remain prepared for the quiz on each day, there is a small surprise factor. But it is by their own choosing. They can very well not be surprised at all. Ditto for our life. We all know that we have to die within our lifetime. Hence it should not be a surprise at all. What makes it surprising is our inherent logic that if we start waiting for our death from the start of our life, we would not gain anything from it. Hence we choose death by surprise by our own volition.