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 context of epistemic theories of truth, compare Tennant (2000: 829) and Wright (2001: 59-60, n. 17). 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 1 revision of normal modal principles. The result may be taken as a new and improved paradox of knowability and as data for the future analysis of factive concepts of possible knowledge. 2 The puzzle was introduced by Sven Rosenkranz (2004) and threatens to show that a factive interpretation of knowability entails the invalidity of a familiar closure principle. The closure principle says that possibility is closed over necessary implication: ◊ϕ, �(ϕ → ψ) | – ◊ψ. The discussion focuses on instances of the principle where our propositional variables take epistemic propositions of the form 'Kϕ', to be read 'somebody at some time knows that ϕ'. Accordingly the focus is on instances of the closure principle (CL) that have the following form