Single-premise epistemic closure is the principle that: if one is in an evidential position to know that P where P entails Q, then one is in an evidential position to know that Q. 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 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 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. (shrink)

Closure principles say that if you know some proposition which entails a second and you meet further conditions then you know the second. In this paper I construct an argument against closure principles which turns on the idea that knowing a proposition requires that one’s belief-forming process be reliable. My argument parallels an influential argument offered by Timothy Williamson against KK principles–principles that say that if you know some proposition and you meet further conditions then you know that you know (...) the proposition. After offering my argument, I provisionally assess its damage to closure principles and also look at how responses to my argument against closure principles can be used to generate responses to Williamson’s argument against KK principles. (shrink)

Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do (...) not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. (shrink)

According to the principle of epistemic closure, knowledge is closed under known implication. The principle is intuitive but it is problematic in some cases. Suppose you know you have hands and you know that ‘I have hands’ implies ‘I am not a brain-in-a-vat’. Does it follow that you know you are not a brain-in-a-vat? It seems not; it should not be so easy to refute skepticism. In this and similar cases, we are confronted with a puzzle: epistemic closure is an (...) intuitive principle, but at times, it does not seem that we know by implication. In response to this puzzle, the literature has been mostly polarized between those who are willing to do away with epistemic closure and those who think we cannot live without it. But there is a third way. Here I formulate a restricted version of the principle of epistemic closure. In the standard version, the principle can range over any proposition; in the restricted version, it can only range over those propositions that are within the limits of a given epistemic inquiry and that do not constitute the underlying assumptions of the inquiry. If we adopt the restricted version, I argue, we can preserve the advantages associated with closure, while at the same time avoiding the puzzle I’ve described. My discussion also yields an insight into the nature of knowledge. I argue that knowledge is best understood as a topic-restricted notion, and that such a conception is a natural one given our limited cognitive resources. (shrink)

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

Some incompatibilists about free will or moral responsibility and determinism would abandon their incompatibilism were they to learn that determinism is true. But is it reasonable to flip-flop in this way? In this article, we contend that it is and show what follows. The result is both a defense of a particular incompatibilist strategy and a general framework for assessing other cases of flip-flopping.