A professor tells his class that he will give them a surprise examination sometime next week.

For our purposes, an examination is considered a "surprise" if on that day, the class is not 100% sure that they will get an examination. (If they only suspect it, the examination can still be a surprise.)

Having given the class this warning, is it still possible for the professor to give them a surprise examination next week? (Assume that he will not give them an exam if it will not be a surprise.)

to say it can be given on any day because we have deduced it cannot be given on any day is wrong. that a surprise can still occur is totally unrelated to our logic. the statement by the teacher that the test will be a surprise is nonsensical and must be ignored (you can't tell someone when you will surprise them). now we are only left with the information that there will be a test the following week. it may still be a surprise (if it happens mon-thur), or it might not be a surprise (if it happens on friday). and if, instead, the teacher tells the students there will be a "surprise test" (instead of conveying the information in two parts) then the whole statement must be disregarded. so now it is just as if the teacher told us nothing, so any test given will be a surprise (even if it occurs friday).

we have now decided that there may still be a surprise test the following week, but that is the null assumption (there may always be a surprise test the following week no matter what a teacher might tell you) and that conclusion was not derived from anything the teacher told us.

Posted by donnmike on 2003-12-03 19:07:23