On Two Paradoxes of Knowledge*

This chapter focuses on the paradox of the surprise examination. A teacher announces that he will give an examination within the month. Examinations are always given at noon. He also announces that the exam will be a surprise exam: no student will know on the day before the exam is given that it will be given the next day. A student can then reason as follows: The teacher, if he intends to fulfill his announced promise, cannot give the exam on the very last day. If he did, after noon had passed on the previous day, we (the students) would know that only the last day was left and that it had to be the day of the examination. This would be a plain contradiction of the announcement that it was to be a surprise exam, so that day can be crossed off the calendar. But then it cannot be given on the second-to-last day either because, after noon of the day before has passed and the exam still has not been given, we will realize that only two days are left, and that since the last day is ruled out, the exam must be given on the second-to-last day. But then we would know in advance that that is the day of the exam, which is again a contradiction. It is interesting that this kind of problem is discussed as if it were a philosophical problem at all. How philosophical it actually is depends on whatever philosophical morals we may draw from it.