This paper argues that if knowledge is defined in terms of probabilistic tracking then the benefits of epistemic closure follow without the addition of a closure clause. (This updates my definition of knowledge in Tracking Truth 2005.) An important condition on this result is found in "Closure Failure and Scientific Inquiry" (2017).

Contemporary discussions of epistemological skepticism - the view that we do not and cannot know anything about the world around us - focus very much on a certain kind of skeptical argument involving a skeptical scenario (a situation familiar from Descartes’ First Meditation). According to the argument, knowing some ordinary proposition about the world (one we usually take ourselves to know) requires knowing we are not in some such skeptical scenario SK; however, since we cannot know that we are not (...) in SK we also cannot know any ordinary proposition. One of the most prominent skeptical scenarios is the brain-in-the-vat-scenario: An evil scientist has operated on an unsuspecting subject, removed the subject’s brain and put it in a vat where it is kept functioning and is connected to some computer which feeds the brain the illusion that everything is “normal”. This paper looks at one aspect of this scenario after another – envatment, disembodiment, weird cognitive processes, lack of the right kind of epistemic standing, and systematic deception. The conclusion is that none of these aspects (in isolation or in combination) is of any relevance for a would-be skeptical argument; the brain-in-the-vat-scenario is irrelevant to and useless for skeptical purposes. Given that related scenarios (e.g., involving evil demons) share the defects of the brain-in-the-vat-scenario, the skeptic should not put any hopes on Cartesian topoi. (shrink)

We present a formal semantics for epistemic logic, capturing the notion of knowability relative to information (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB (‘B is knowable on the basis of information A’) as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutness-preservation models (...) the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions. (shrink)

Deduction is important to scientific inquiry because it can extend knowledge efficiently, bypassing the need to investigate everything directly. The existence of closure failure—where one knows the premises and that the premises imply the conclusion but nevertheless does not know the conclusion—is a problem because it threatens this usage. It means that we cannot trust deduction for gaining new knowledge unless we can identify such cases ahead of time so as to avoid them. For philosophically engineered examples we have “inner (...) alarm bells” to detect closure failure, but in scientific investigation we would want to use deduction for extension of our knowledge to matters we don’t already know that we couldn’t know. Through a quantitative treatment of how fast probabilistic sensitivity is lost over steps of deduction, I identify a condition that guarantees that the growth of potential error will be gradual; thus, dramatic closure failure is avoided. Whether the condition is fulfilled is often obvious, but sometimes it requires substantive investigation. I illustrate that not only safe deduction but the discovery of dramatic closure failures can lead to scientific advances. (shrink)

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)

Contemporary discussions of skepticism often frame the skeptic's argument around an instance of the closure principle. Roughly, the closure principle states that if a subject knows p, and knows that p entails q, then the subject knows q. The main contention of this paper is that the closure argument for skepticism is defective. We explore several possible classifications of the defect. The closure argument might plausibly be classified as begging the question, as exhibiting transmission failure, or as structurally inefficient. Interestingly, (...) perhaps, each of these has been proposed as the correct classification of Moore's proof of an external world. (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)

A hyperintensional epistemic logic would take the contents which can be known or believed as more fine-grained than sets of possible worlds. I consider one objection to the idea: Williamson’s Objection from Overfitting. I propose a hyperintensional account of propositions as sets of worlds enriched with topics: what those propositions, and so the attitudes having them as contents, are about. I show that the account captures the conditions under which sentences express the same content; that it can be pervasively applied (...) in formal and mainstream epistemology; and that it is left unscathed by the objection. (shrink)

This paper introduces and defends the paradigm response to external world skepticism. To understand it, consider an analogy. One of the hallmarks of being a bird is an ability to fly. A penguin lacks this hallmark and thus fails to be a paradigm bird. Likewise, there are various hallmarks of knowledge. Some of your external world beliefs lack some of these hallmarks, and thus fail to be paradigm cases of knowledge. Just as the inability of penguins to fly doesn’t prevent (...) them from being birds, likewise the lack of these hallmarks doesn’t prevent your beliefs from being knowledge. It just prevents them from being paradigm cases thereof. (shrink)

What is the role of sceptical scenarios—dreams, evil demons, brains in a vat—in scep- tical arguments? According to the error view, sceptical scenarios illustrate the possibil- ity of massive falsity in one’s beliefs, whereas according to the ignorance view, they illustrate the possibility of massive ignorance not necessarily due to falsity. In this paper, the ignorance view is defended by surveying the arguments in favour of it and by replying to two pressing objections against it. According to the first objection, (...) the ignorance view illicitly introduces the kk-principle into sceptical arguments. In reply I argue that kk is not less plausible than its main rival, the closure principle. According to the second objection, relying on veridical ignorance-possibilities contradicts the transparency of belief. In reply I introduce a version of transparency that is consistent with the ignorance view. (shrink)

John Hawthorne has two forceful arguments in favour of:Single-Premise Closure Necessarily, if S knows p, competently deduces q from p, and thereby comes to believe q, while retaining knowledge of p throughout, then S knows q.Each of Hawthorne's arguments rests on an intuitively appealing principle which Hawthorne calls the Equivalence Principle. I show, however, that the opponents of SPC with whom he's engaging - namely Fred Dretske and Robert Nozick - have independent reason to reject this principle, and resultantly conclude (...) that Hawthorne's arguments in favour of SPC are not knock-down. (shrink)

I argue that to know that a proposition is true one must have justification for being certain that the proposition is true. That is, one must have infallible epistemic justification for believing the proposition. It is widely accepted among epistemologists that we rarely, if ever, have such strong justification for our beliefs. It follows that there is precious little that we know. That conclusion is unacceptable to many philosophers. I argue that the positions that lead to the skeptical conclusion are (...) well-motivated and that the skeptical conclusion is implicitly accepted by ordinary speakers. My dissertation has three main components: a metaphilosophical position, an epistemological position, and an error theory. First, the metaphilosophical position. One very important part of philosophy is the analysis of our ordinary concepts. Analysis of our concepts begins with reflecting on what we are inclined to say about various actual and possible cases when considered under specific descriptions. This traditional method has recently come under attack, due in part to the rise of semantic externalism. I agree with externalists that if ‘meaning is reference’ then there is little reason to think reflecting on our concepts from the armchair will provide insight to the nature of the concepts we investigate. I defend a version of semantic internalism which grounds meaning in factors with which subjects are directly acquainted. That view supports the traditional methodology. Furthermore, as the goal of philosophical analysis is to accurately describe concepts of philosophical interest, the only kind of objection that could be decisive against a proposed analysis is that it does not correctly describe our concept. That opens the door to a skeptical analysis of knowledge. Second, the epistemological position. I argue that the unacceptability of sentences of the form “S knows that p but it is possible for S that not-p” is best explained by the hypothesis that our concept of knowledge requires having justification for being certain that what one believes is true. I offer as a criterion of justified certainty the idea that when one knows a proposition is true, one is in a position to decisively answer questions about one’s knowledge of that proposition. I survey a number of competing theories of knowledge and show that they allow for the possibility of knowledge when one fails my criterion of decisive answerability. Those views fail my criterion because according to those views there is nothing the subject is aware of that guarantees for the subject that the allegedly known proposition is true. On that basis, I contend that knowledge is direct awareness of the factors that constitute the truth of the proposition one believes. Third, the error theory. Of course, we rarely have direct awareness of the factors that constitute the truth of the propositions we believe. So, our knowledge attributions are generally false. Yet, they are overwhelmingly natural to make. I argue that competent speakers are often quick to recognize knowledge attributions as a kind of ‘loose talk’ akin to the way we loosely ascribe geometric properties to ordinary objects. We regularly call objects ‘square’ that are not even close to being square, and we are quick to recognize this when challenged. I argue that we do this because we are so accustomed to communicating using strict language to make false claims that we often do not attend to the literal falsity of what we are saying. While we accept very demanding standards for knowledge, the phenomenon of recognizing that our knowledge claims are regularly false is as pervasive as our use of loose speech. (shrink)