Brandeis University, Philosophy Department
Fall 2003
Brandeis University Web Stite

The Surprise

Professor Andreas Teuber
Prof. Teuber

The Surprise Exam.

Professor Jeffrey D. Sachs announces at the end of class on a Friday (the class meets five days a week) that he is going to give a surprise examination next week. Rachel who is taking Professor Sachs's Economics class: History and Theory of Developmentas well as Professor Teuber's Introductory Philosophy class is somewhat concerned. She has a paper for the Philosophy class to complete and she will (now) have to study for the surprise exam in Economics as well. She has her work cut out for her.

But she then has a brainstorm. She hits upon an argument that shows beyond a doubt that no such exam can be given next week and so she will not have to study for the exam at least. She still has her Philosophy paper to write. Here is how she reasons:

Professor Sachs cannot give the exam next Friday because she will know once class is over on Thursday that the exam will have to be on Friday since once Friday comes there will be no more days in the week and Professor Sachs did say he was going to give the exam on one of the days next week. So if there is no exam on Monday, Tuesday, Wednesday or Thursday, he would have to give the exam on Friday. But then it would not be a surprise because she would know he has to give the exam on Friday. So, she reasons, the exam cannot be (won't be) next Friday.

But Professor Sachs cannot give the exam on Thursday either. For, if he does not give the exam on Monday, Tuesday, or Wednesday, he would have to give the exam on Thursday since he cannot give it on Friday. So she would know after class on Wednesday that the exam had to be given on Thursday and it would not be a surprise.

But then if the exam cannot be on Thursday and it cannot be on Friday by the same argument, she reasons, it cannot be on Wednesday either. And indeed, by the same argument, it cannot be on Tuesday or on Monday. So, she concludes, there will be no surprise exam in Economics next week. She is greatly relieved. She knew there was a reason that she took both Philosophy and Economics.

So now fast-forward in time. Over the weekend Rachel does not study for the Economics exam and works exclusively on her Philosophy paper.

Then next Wednesday Professor Sachs hands out an exam at the beginning of class. Rachel is surprised and does not do very well. She had reasoned that Professor Sachs could not give the exam.

Rachel's reasoning was impeccable, no?

Or is there something wrong about Rachel's reasoning? But what's wrong with it? Professor Sachs says he did exactly what he said he was going to do. Rachel reasoned that if he gave the exam on Wednesday, he would not be able to honor his commitment to give an exam during the week and have it be a surprise.

Who's right?



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