logic & reasoning · new to this edition
the surprise exam
a teacher promises an exam you will not see coming, and a student proves it cannot happen.
The surprise exam, also called the unexpected hanging, appeared in conversation in the 1940s and has produced a library of papers without a settled solution. It is a case where an argument that looks airtight leads to a conclusion that is manifestly false. Work through it, then decide for yourself which step to blame.
is the student’s reasoning sound?
On Friday afternoon a teacher announces: “Next week, one day from Monday to Friday, there will be a surprise exam. You will not know which morning it is until that morning arrives.”
The students think it through. Friday is impossible: if no exam had come by Thursday evening, they would know it must be Friday, so it would not be a surprise. With Friday eliminated, Thursday is the last possible day, and by the same reasoning it could not be a surprise either. So Thursday is out. Then Wednesday, and Tuesday, and Monday. The students conclude that no surprise exam is possible at all.
On Wednesday morning, the teacher hands out the exam. Every student is surprised.
So where is the mistake in the students’ reasoning?
further reading
- epistemic paradoxes, including the surprise examination stanford encyclopedia of philosophy
- on a so-called paradox original paper
- the surprise examination or unexpected hanging paradox original paper
- unexpected hanging paradox wikipedia