---------------------------------

Rose asked:

I am doing an essay on the surprise examination paradox. I know what it is, and how the argument
goes, but I would like to know: is it a genuine paradox? why or why not? what has 'vagueness' got to
do with it? what is the answer?!

Where should my essay take me, and where can I find decent arguments on the web?

============

A teacher tells her class: "You will have a logic exam at 10 am one day next week. I'm not telling you
which day. It will be a surprise." One bright student reasons as follows. "Teacher can't wait until
Friday to give the exam, because by then we will know that it has to be on Friday, so it won't be a
surprise. However, if Friday is ruled out, then by the same reasoning the exam can't be on Thursday
either, because by then we will know that the exam has to be on that day. The same reasoning
proves that the exam can't be on Wednesday, Tuesday or Monday. Therefore, our teacher can't give
us a surprise logic exam!"

Confident that there will be no logic exam, the bright student doesn't bother to revise. The following
Wednesday, the teacher hands out examination scripts. Boy, was the student surprised!

I know that some philosophers make a lot of this paradox. (Richard Montague in Formal Philosophyis
one who takes the paradox seriously. I don't recommend that you attempt to read that inpenetrable
book.) In my view it is not, in fact, a genuine paradox.

First, let's get rid of the magician's hand waving. The specious plausibility of the paradox derives from
the fact that the students are given a choice of five days. Watch what happens, however, if we reduce
the number of days to just two. "You will have a logic exam at 10 am either tomorrow or the day after
tomorrow. I'm not telling you which day. It will be a surprise."

Now things are a lot clearer. It is true that the teacher is still able to surprise her class. Tomorrow 10
am comes, and the teacher either gives the exam or doesn't give the exam. Either way, the students
'are surprised'. They didn't know whether they would get the exam on that day or not. However, it is
also clear that when the teacher said, "It will be a surprise," she could not have meant, "WheneverI
give you the exam, you will be surprised." This is something she knows can't be true. They can be
surprised by the exam's notbeing given tomorrow. They can'tbe surprised by the exam's being given
the day after tomorrow.

In my view, therefore, the surprise examination paradox comes into the same category as the
infamous barber paradox. Suppose I tell you that there is a barber in Sheffield who shaves all and
only those Sheffielders who do not shave themselves. Does the barber shave himself? Answering
either "yes" or "no" leads to a contradiction. If he does, he doesn't. If he doesn't, he does. This is not a
genuine paradox because the response is simply to say that the statement, "There is a barber in
Sheffield who shaves all and only those Sheffielders who do not shave themselves" cannot be true.
The statement is self-contradictory. End of story. We should say the same thing about the surprise
examination paradox. The statement, "You will be given an exam one day next week and whichever
day it isyou will be surprised" cannot be true. Only on the assumption of its truth could the bright, but
easily suckered student have reasoned as he did. That reasoning is what shows the teacher's
statement to be self-contradictory.

I don't know where you would find material on the surprise examination on the web. Try a search for
the exact phrase "surprise examination paradox" with Alltheweb. I have found that particular search
engine to be extremely accurate with text string searches. If there is just one page on the web with
that phrase, Alltheweb will find it.

Geoffrey Klempner