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Simplifying the Surprise Exam

Creative Commons 'BY-NC-ND' version 4.0 license

In this paper, I argue for a solution to the surprise exam paradox, designated student paradox, and variations theoreof, based on an analysis of the paradoxes using modal logic. The solution to the paradoxes involves distinguishing between two setups, the Inevitable Event and the Promised Event, and between the two-day and n-day cases of the paradoxes. For the Inevitable Event, the problem in the two-day case is the assumption that the student knows the teacher’s announcement; for more days, the student can know the announcement, and the base case of the student’s backward induction is correct, but there is a mistake in the induction step. For the Promised Event, even the base case is questionable. After defending this analysis, I argue that it also leads to a solution to a modified version of the surprise exam paradox, due to Ayer and Williamson, based on the idea of a conditionally expected exam.

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