Conclusion

Abstract

The hangman/surprise-examination/prediction paradox is solved. It is not solved by denying knowledge closure (although knowledge closure is false). It is not solved by denying KK or denying that knowing p implies other iterated knowing attitudes (although these are false). It is not solved by misleading evidence causing the students to lose knowledge because students cannot lose knowledge this way. It is solved by showing that a tacit assumption (what is being said to the students/prisoner is informative) is overlooked and that inferences by contradiction are invalid if assumptions are left out. The phenomenology of the surprise-exam paradox is explored to explain why this solution has been missed. Crucial is that in many cases the students/prisoner know(s) there will be a surprise exam/execution because of an inference from what the teacher/judge meant to say, and not directly by the literal application of what he did say.