Often we have coarsely grained knowledge: for example, we know about how many people are present. In possessing such knowledge, we also have finer grained knowledge of what is not: there certainly is nothing like that number of people here. The combination of such knowledge types, through sorites, generates contradiction and bafflement. This paper seeks to resolve the bafflement: it rejects a Timothy Williamson proposal, introduces muddle numbers and inference gaps, and shows how the different grains of knowledge do not (...) always meet. In so doing, the paper identifies a distinctive first‐person inferring. (shrink)

The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...) 'Wright & Sudbury Argument,' and the 'Epistemic Blindspot Argument.' The reason that the Surprise Exam Paradox has persisted this long is not because any of these arguments is problematic. On the contrary, each of them is correct. The reason that it has persisted so long is because each argument is only part of the solution. The correct solution requires all three of them to be combined together. Once they are, we may see exactly why the No Friday Argument fails and therefore why we have a solution to the Surprise Exam Paradox that should stick. (shrink)