The paradox thread.

Anyone up for discussing this paradox? I'm reading a book on a paradoxes and I think this is my favorite... and I can't figure it out!

OK, so let's say a teacher tells her students that on the following week there will be an unexpected test on the topics covered on the course so far. She emphasizes that the test will be unexpected, and that no one will be able to predict (with certainty) the day on which it will be set, until that day comes. The teacher has done this every year, so there is no question than the test take place on the week that the she announced.

Here's the paradoxical part: The students may reason: "Well, the test cannot take place on Friday, since that would be the only possibility if it hasn't happened by Thursday. Come Thursday evening, we would be certain that the test would take place the next day, and then it wouldn't be unexpected." So it can't be on Friday. But then the same argument could be made to rule out Thursday as well: "Friday is out. If the test hasn't happened by Wednesday evening, the only possibility is the next day (Thursday), but then..." and so on until we get to Monday. So following this line of reasoning, the test cannot be set on any day of the week. But this is absurd, since obviously the teacher can give a surprise test.

What's the deal then?

...no question that the test will take place...

There's a lengthy discussion of that particular paradox in this thread:

In a small town where everyone is clean-shaven, the barber shaves everybody who does not shave himself. Who shaves the barber?

http://en.wikipedia.org/wiki/Unexpected_hanging_paradox

I am sorta glad that wikipedia refers to this as a 'significant problem" for philosophy' cause I was having some major mind spasms.

Thanks Tuomas. That thread is looool!