Traditionally, sensitivity theorists deny closure. In the last post I suggested that some anti-sceptical beliefs (e.g. I am not a BIV) which are often taken to be non-sensitive, are in fact sensitive, when the sensitivity condition is parsed so as to take into account belief-forming methods. This though doesn’t mean that there might not be some, more elaborately contrived, beliefs in which closure would fail, even given a version of sensitivity that takes into account belief-forming methods.
But closure failure could be avoided if we adopted a disjunctive account of knowledge, whereby knowledge is either sensitively formed true belief, or belief that is soundly inferred from a sensitively formed true belief. Oftentimes disjunctive explanations (or disjunctive proofs) are seen as being less explanatory than non-disjunctive counterparts (as they are less unifying), but there is some virtue in this disjunctive account of knowledge. It does justice to the holistic nature of our beliefs. Beliefs, taken individually, may lack sensitivity or responsiveness to the world, but may constitute knowledge because of the way they are apperceptively integrated into a wider whole, of which some parts are appropriately responsive to the world. It is well-known that coherentist constraints on knowledge, taken on their own, leave out the important thought that beliefs that constitute knowledge must in some sense be responsive to reality (“frictionless spinning in the void” and all that); but modal constraints on knowledge, taken on their own, may also leave out the important role that coherence-making relationships have with respect to knowledge. It may be that both kinds of consideration must be built into an account of knowledge, but that neither can be understood in terms of the other. In which case, a disjunctive account of knowledge would be in order.
