A User's Guide to the Surprise Exam Paradoxes

The surprise exam paradox and its variants have achieved zombie-like status in the philosophical literature: despite many attempts to kill them they live on. Some of the most prominent readings of the surprise exam announcement are surveyed. The versions pushed by the logicians are chosen to highlight features of the concept of provability. In this they succeed but at the price of providing contorted self-referential readings of the announcement. The versions pushed by the epistemologists are chosen to provide a stress test for the concepts of knowledge and justified belief. In this they succeed but at the price of entangling the resolution of the paradox with controversies surrounding these concepts. A reading that is free of such controversies and that allows a resolution of the paradox to stand out is offered. This resolution does not provide any deep lessons that could not be learned from other sources. Nevertheless the paradox and its variants deserve to live on as a superb teaching instrument

Reasoning About Justified Belief

Halpern and Pass [2011] introduce a logic of justified belief and go on to prove that strong rationalizability is characterized in this logic in terms of common justified belief of rationality (CJBR). Their paper provides semantics for this logic but no axiomatization. We correct this deficiency by reformulating the definition of justified belief and providing a complete axiomatization of this new system. We then prove a result analogous to the characterization of strong rationalizability in terms of CJBR, and analyze the additional assumptions needed to do so.