How are your opinions on a supposition related to your unconditional opinions? One simple answer is Material Coincidence: when you are not sure that not q, you are sure that p on the supposition that q just in case you are sure that either not q or p (◇q ⊃ (□^qp ≡ □(q ⊃ p))). I give a novel argument against Material Coincidence: given weak side-conditions, it entails the implausible claim that being sure implies being sure that you are sure (□p ⊃ □□p).

You are higher-order ignorant when you fail to know whether you know something. I show that ordinary people sometimes say that they are higher-order ignorant, and use this to undermine the claim that knowing implies knowing that one knows (KK: □p ⊃ □□p), and the thought that taking seriously the possibility that one does not know something raises the standards for the application of the word “know” to the point where one fails to satisfy them.

According to reliabilism, whether a belief is justified, or amounts to knowledge, depends on whether similar beliefs are, or would be, true. We consider familiar arguments that reliabilism is incompatible with defeat, and show how reliabilists can respond to them by understanding similarity in a flexible way. This alternative conception of similarity also allows reliabilists to provide a unified treatment of defeat, including higher-order defeat. However, it also over-generates justification when you learn but ignore excellent evidence for an otherwise unjustified belief. We argue that this problem is much harder, and calls for a structural revision of reliabilism. We propose what we take to be the best such revision.

You generally should and do coordinate your beliefs about logically related questions fairly well, but you in general need not and do not coordinate your beliefs with your beliefs about those beliefs very well at all. I propose an explanation of this contrast from the assumption that belief coordination processes are noisy. Using the tools of accuracy first epistemology, I show that logical and probabilistic coherence are robust ideals — the closer you come to these ideals, the better — but introspection is a fragile ideal — it is only good to realize this ideal perfectly.

According to accuracy-first epistemology, epistemic norms for credences can be derived from considerations of accuracy, or “closeness to the truth”. The standard way of precisifying it leads to collapse results in cases involving epistemic modals. In particular, the accuracy-first view seems to say that you should assign the same credence to sentences A, ‘might A’, and ‘must A’. If you don't, then your credences are accuracy-dominanted, in the sense that there's some other system of credences that's more accurate than yours, no matter how the world turns out to be. We propose a modification of the accuracy-first framework which avoids such collapse results. All of the arguments which made the frameowrk seem attractive in the first place are preserved, and some new desirable constraints derived, such as that you should assign zero credence to so-called epistemic contradictions — i.e., sentences of the form ‘A and might not A’ (or similar).

I explore the combination of epistemic decision theory, which says that we must do what's best in expectation given our knowledge, with optimistic theories of knowledge, according to which we can know all sorts of things that aren't certain on our evidence. I argue that plausible optimistic theories of knowledge make knowledge defeasible and “know” heavily context-dependent in ways that cause problems for epistemic decision theory.