Questions, topics and restricted closure

Single-premise epistemic closure is the principle that: if one is in an evidential position to know that φ where φ entails ψ, then one is in an evidential position to know that ψ. In this paper, I defend the viability of opposition to closure. A key task for such an opponent is to precisely formulate a restricted closure principle that remains true to the motivations for abandoning unrestricted closure but does not endorse particularly egregious instances of closure violation. I focus on two brands of epistemic theory (each the object of sustained recent interest in the literature) that naturally incorporate closure restrictions. The first type holds that the truth value of a knowledge ascription is relative to a relevant question. The second holds that the truth value of a knowledge ascription is relative to a relevant topic. For each approach, I offer a formalization of a leading theory from the literature (respectively, that of Jonathan Schaffer and that of Stephen Yablo) and use this formalization to evaluate the theory's adequacy in terms of a precise set of desiderata. I conclude that neither theory succeeds in meeting these desiderata, casting doubt on the viability of the underlying approaches. Finally, I offer a novel variant of the topic-sensitive approach that fares better.