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)

Sven Bernecker develops a theory of propositional memory that is at odds with the received epistemic theory of memory. On Bernecker’s account the belief that is remembered must be true, but it need not constitute knowledge, nor even have been true at the time it was acquired. I examine his reasons for thinking the epistemic theory of memory is false and mount a defense of the epistemic theory.

According to the sensitivity account of knowledge, S knows that p only if S's belief in p is sensitive in the sense that S would not believe that p if p were false. It is widely accepted that the sensitivity condition should be relativized to belief-formation methods to avoid putative counterexamples. A remaining issue for the account is how belief-formation methods should be individuated. In this paper, I argue that while a coarse-grained individuation is still susceptible to counterexamples, a fine-grained (...) individuation makes the target belief trivially insensitive. Therefore, there is no principled way of individuating belief-formation methods that helps the sensitivity account to accommodate different cases. (shrink)

It has been argued that an advantage of the safety account over the sensitivity account is that the safety account preserves epistemic closure, while the sensitivity account implies epistemic closure failure. However, the argument fails to take the method-relativity of the modal conditions on knowledge, viz., sensitivity and safety, into account. In this paper, I argue that the sensitivity account and the safety account are on a par with respect to epistemic closure once the method-relativity of the modal conditions is (...) taken into account. Therefore, epistemic closure is no longer an arbiter in the debate. (shrink)

Amodal completion is the representation of occluded parts of perceived objects. We argue for the following three claims: First, at least some amodal completion-involved experiences can ground knowledge about the occluded portions of perceived objects. Second, at least some instances of amodal completion-grounded knowledge are not sensitive, that is, it is not the case that in the nearest worlds in which the relevant claim is false, that claim is not believed true. Third, at least some instances of amodal completion-grounded knowledge (...) are not safe, that is, it is not the case that in all or nearly all near worlds where the relevant claim is believed true, that claim is in fact true. Thus, certain instances of amodal completion-grounded knowledge refute both the view that knowledge is necessarily sensitive and the view that knowledge is necessarily safe. (shrink)

Vogel, Sosa, and Huemer have all argued that sensitivity is incompatible with knowing that you do not believe falsely, therefore the sensitivity condition must be false. I show that this objection misses its mark because it fails to take account of the basis of belief. Moreover, if the objection is modified to account for the basis of belief then it collapses into the more familiar objection that sensitivity is incompatible with closure.

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)

The topic of this paper may be introduced by fast zooming in and out of the philosophy of information. In recent years, philosophical interest in the nature of information has been increasing steadily. This has led to a focus on semantic information, and then on the logic of being informed, which has attracted analyses concentrating both on the statal sense in which S holds the information that p (this is what I mean by logic of being informed in the rest (...) of this article) and on the actional sense in which S becomes informed that p. One of the consequences of the logic debate has been a renewed epistemological interest in the principle of information closure (henceforth PIC), which finally has motivated a revival of a skeptical objection against its tenability first made popular by Dretske. This is the topic of the paper, in which I seek to defend PIC against the skeptical objection. If I am successful, this means – and we are now zooming out – that the plausibility of PIC is not undermined by the skeptical objection, and therefore that a major epistemological argument against the formalization of the logic of being informed based on the axiom of distribution in modal logic is removed. But since the axiom of distribution discriminates between normal and non-normal modal logics, this means that a potentially good reason to look for a formalization of the logic of being informed among the non-normal modal logics, which reject the axiom, is also removed. And this in turn means that a formalization of the logic of being informed in terms of the normal modal logic B (also known as KTB) is still very plausible, at least insofar as this specific obstacle is concerned. In short, I shall argue that the skeptical objection against PIC fails, so it is not a good reason to abandon the normal modal logic B as a good formalization of the logic of being informed. (shrink)

Sosa, Pritchard, and Vogel have all argued that there are cases in which one knows something inductively but does not believe it sensitively, and that sensitivity therefore cannot be necessary for knowledge. I defend sensitivity by showing that inductive knowledge is sensitive.

One common objection to Dretske’s Information Theoretic Account of Knowledge (ITAK) is that it violates closure. I show that it does not, and that extant arguments attempting to establish that it does rely instead on the KK thesis. That thesis does fail for ITAK. I show moreover that an interesting consequence of ITAK obeying the closure principle after all is that on this view if skepticism is false, we can have a great deal of empirical knowledge, but it is in (...) principle impossible to know that skepticism is false. In short, a proper understanding of how ITAK closes off the KK thesis shows that we can 1) take seriously the skeptic, we can 2) respond to her appropriately that we do have knowledge and we can 3) keep closure. (shrink)

Those of us who have followed Fred Dretske's lead with regard to epistemic closure and its impact on skepticism have been half-wrong for the last four decades. But those who have opposed our Dretskean stance, contextualists in particular, have been just wrong. We have been half-right. Dretske rightly claimed that epistemic status is not closed under logical implication. Unlike the Dretskean cases, the new counterexamples to closure offered here render every form of contextualist pro-closure maneuvering useless. But there is a (...) way of going wrong under Dretske's lead. As the paper argues, Cartesian skepticism thrives on closure failure in a way that is yet to be acknowledged in the literature. The skeptic can make do with principles which are weaker than the familiar closure principles. But I will further claim that this is only a momentary reprieve for the skeptic. As it turns out, one of the weaker principles on which a skeptical modus tollens must rest can be shown false. (shrink)

The conclusive reasons view of knowledge entails the “abominable conjunction” that I know that I have hands but I do not know that I am not a brain in a vat. The argument from abomination takes this as a reason to reject the view. This paper aims to buttress the argument from abomination by adding a new sort to this list: the logical abominations. These include: “I know that argument is sound and that sound arguments have true conclusions but I (...) don’t know whether the conclusion of that argument is true”. Two standard replies to the argument from abomination are raised. It is argued that the logical abominations open new holes in both. (shrink)

Abstract: Luciano Floridi has impressively applied the concept of information to problems in semantics and epistemology, among other areas. In this essay, I briefly review two areas where I think one may usefully raise questions about some of Floridi's conclusions. One area is in the project to naturalize semantics and Floridi's use of the derived versus nonderived notion of semantic content. The other area is in the logic of information and knowledge and whether knowledge based on information necessarily supports closure, (...) in every instance. I suggest that it does not and, thereby, raise a challenge to Floridi's logic of being informed. (shrink)

According to the sensitivity account of knowledge, if one knows that p, then (roughly) were p false, one would not believe that p. One important issue regarding sensitivity is whether or not it preserves inductive knowledge. Critics including Jonathan Vogel, Ernest Sosa, and Duncan Pritchard argue that it does not. Proponents including Kevin Wallbridge insist that it does. In this paper, I first draw attention to an often-neglected distinction between two different versions of sensitivity—a distinction that has important implications for (...) the debate regarding inductive knowledge. In particular, I distinguish between the sensitivity principle originally defended by Robert Nozick and another version that has been the focus of many recent discussions. With the distinction in place, it is shown that a sensitivity theorist cannot preserve inductive knowledge while being unscathed. For neither account can simultaneously preserve inductive knowledge while properly handling the Gettier problem. Overall, sensitivity theorists are in trouble. (shrink)

This article examines the intersection of the theory of extended mind/cognition and theory of knowledge. In the minds of some, it matters to conditions for knowing whether the mind extends beyond the boundaries of body and brain. I examine these intuitions and find no support for this view from tracking theories of knowledge. I then argue that the apparent difference extended mind is supposed to have for ability or credit theories is also illusory.