Knowability and a Modal Closure Principle

Does a factive conception of knowability figure in ordinary use? There is some reason to think so. 'Knowable' and related terms such as 'discoverable', 'observable', and 'verifiable' all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn't say that we were. A's remarks sound contradictory. In this context the factivity of 'someone might discover that' explains this fact. So there is some reason to believe that knowability and related modalities are factive in ordinary use. For factive treatments of knowability in the The factivity of knowability will not be questioned herein, since the paper is concerned to examine some problems that arise in connection with factive knowability. In particular, the paper examines a clutch of issues concerning principles of modal epistemic logic and the knowability of truth. It begins with a puzzle, a closure paradox of knowability, that threatens to show that a factive interpretation of knowability entails the invalidity of a modest modal closure principle. The negative argument is that the puzzle in its original form does not tell against the joint validity of closure and factivity. That is because the puzzle rests on contingent assumptions whose compossibility is doubtful. The positive argument is that there is a formulation of the puzzle that does prescribe