We represent the well-known surprise exam paradox in constructive and computable mathematics and offer solutions. One solution is based on Brouwer’s continuity principle in constructive mathematics, and the other involves type 2 Turing computability in classical mathematics. We also discuss the backward induction paradox for extensive form games in constructive logic.

This paper offers a new solution to the Surprise Test Paradox. The paradox arises thanks to an ingenious argument that seems to show that surprise tests are impossible. My solution to the paradox states that it relies on a questionable closure principle. This closure principle says that if one knows something and competently deduces something else, one knows the further thing. This principle has been endorsed by John Hawthorne and Timothy Williamson, among others, and I trace its motivation back to (...) work by Alvin Goldman. I provide counterexamples to the principle and explain the flaw in the reasoning of those who defend it. (shrink)

The mooronic solution to the surprise quiz paradox says students know there will be a surprise quiz one day this week but they lose this knowledge on the penultimate day. This is because ‘there will be a surprise quiz one day this week’ then becomes an instance of Moore's paradox. This view has surprising consequences. Furthermore, even though the surprise quiz announcement becomes an instance of Moore's paradox on the penultimate day, this does not prevent the students from knowing the (...) quiz is coming. I conclude that the first stage of the paradoxical argument succeeds and the mooronic solution fails. (shrink)