Safety theorists prefer a strong version of safety over a weak version, in order to account for our intuition that we do not know lottery propositions. I argue that weak safety has advantages that can outweigh our intuitions in lottery cases. First, I argue that for the nonepistemic domain, we should adopt weak safety to account for experts’ claims about cyber security. Second, I argue that a unified account of safety is preferable. Hence, we should adopt weak safety for the (...) epistemic domain as well. My argument can also be put as follows. It is more plausible to suppose that our intuitions about lottery cases are misguided than to suppose either that experts’ judgments about cyber security are misguided or that there are different versions of safety. (shrink)

This paper explores some consequences of Lewis’s (Australas J Philos 74(4):549–567, 1996) understanding of how knowledge is compartmentalized. It argues, first, that he underestimates how badly it impacts his view. When knowledge is compartmentalized, it lacks at least one of two essential features of Lewis’s account: (a) Elusiveness—familiar skeptical possibilities, when relevant, are incompatible with everyday knowledge. (b) Knowledge is a modality—when a thinker knows that p, there is no relevant possibility where p is false. Lewis proposes compartmentalized knowledge to (...) keep treating knowledge as a modality while mitigating one of its unrealistic epistemological implications: In normal modal epistemic logic (and standard possible world semantics), a thinker always counts as knowing the strongest proposition that follows from the set of all the individual propositions that this thinker knows. Lewis’s compartmentalization proposal is that thinkers merely know the conjunctions of propositions that are known in each of, but not across, their compartments. The irony is that in avoiding overblown knowledge the view now allows for thinkers to attend to skeptical error possibilities and yet knowledge is present. The account avoids inflation of knowledge in one sense only to acquire another type of knowledge the view denies subjects can have. This problem motivates an inspection of knowledge accounts whose intra-compartment closure principles are weaker than those that are valid in normal modal-logic. The conclusion is that some formulations of closure can avoid the challenge Lewis’s view faces. Nevertheless, even these closure principles pose a barrier—perhaps an implausible barrier—for knowledge of ignorance. Even when the reasoning supporting the lack of knowledge is sound, a subject cannot always know she doesn’t know. Interestingly, this obstacle is one that knowledge of knowledge doesn’t seem to face. (shrink)

In this paper, I’ll survey a number of closure principles of epistemic justification and find them all wanting. However, it’ll be my contention that there’s a novel closure principle of epistemic justification that has the virtues of its close cousin closure principles, without their vices. This closure principle of epistemic justification can be happily thought of as a multi-premise closure principle and it cannot be used in Cartesian skeptical arguments that employ a closure principle of epistemic justification. In this way, (...) then, it represents marked improvement over other contemporary closure principles of epistemic justification that require both sacrificing multi-premise closure and forcing anti-Cartesian skeptics who reject the closure principle employed in certain Cartesian skeptical arguments to cast aside justification closure. (shrink)

There are few indulgences academics can crave more than to have their work considered and addressed by leading researchers in their field. We have been fortunate to have two outstanding philosophers from whose work we have learned a great deal give ours their thoughtful attention. Grappling with Stephen Yablo’s, and Juan Comesaña’s comments and criticisms has helped us gain a better understanding of our ideas as well as their shortcomings. We are extremely grateful to them for the attentiveness and seriousness (...) with which they have considered our arguments and to philosophical studies for giving us this opportunity. Given the substantive difference between the two response papers, there is not much beyond sincere gratitude that we can covey to them jointly. We will therefore address them in turn. (shrink)

The paper argues that knowledge is not closed under logical inference. The argument proceeds from the openness of evidential support and the dependence of empirical knowledge on evidence, to the conclusion that knowledge is open. Without attempting to provide a full-fledged theory of evidence, we show that on the modest assumption that evidence cannot support both a proposition and its negation, or, alternatively, that information that reduces the probability of a proposition cannot constitute evidence for its truth, the relation of (...) evidential support is not closed under known entailment. Therefore the evidence-for relation is deductively open regardless of whether evidence is probabilistic or not. Given even a weak dependence of empirical knowledge on evidence, we argue that empirical knowledge is also open. On this basis, we also respond to the strongest argument in support of knowledge closure. Finally, we present a number of significant benefits of our position, namely, offering a unified explanation for a range of epistemological puzzles. (shrink)

We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a (...) disjunction. (shrink)

Before the semester begins, a teacher tells his students: “There will be exactly one exam this semester. It will not take place on a day that is an immediate-successor of a day that you are currently in a position to know is not the exam-day”. Both the students and the teacher know – it is common knowledge – that no exam can be given on the first day of the semester. Since the teacher is truthful and reliable, it seems that (...) the students can know that what he says is true. However, in that case, assuming the students can know that they know whatever it is they know (KK) and assuming their knowledge is closed under entailment (closure), the students can reason from what they know to the conclusion that no exam will take place during the semester. This conclusion contradicts what they supposedly know: that there will be an exam. This puzzle, we argue, gives rise to a new consideration for the rejection of KK. We discuss unique features of the argument, especially in comparison to Timothy Williamson's rejection of KK in light of other versions of the surprise exam paradox. (shrink)

When spelled out properly infallibilism is a viable and even attractive view. Because it has long been summary dismissed, however, we need a guide on how to properly spell it out. The guide has to fulfil four tasks. The first two concern the nature of knowledge: to argue that infallible belief is necessary, and that it is sufficient, for knowledge. The other two concern the norm of belief: to argue that knowledge is necessary, and that it is sufficient, for justified (...) certainty. With such a guide in hand infallibilism can be evaluated on its own merits. The most controversial parts are the first and fourth. The idea that knowledge requires infallible belief is thought to be excessively sceptical. The idea that knowledge warrants certainty is thought to be excessively dogmatic. The present paper addresses the first. It argues that knowledge requires infallible belief. (shrink)

Epistemic closure under known implication is the principle that knowledge of "p" and knowledge of "p implies q", together, imply knowledge of "q". This principle is intuitive, yet several putative counterexamples have been formulated against it. This paper addresses the question, why is epistemic closure both intuitive and prone to counterexamples? In particular, the paper examines whether probability theory can offer an answer to this question based on four strategies. The first probability-based strategy rests on the accumulation of risks. The (...) problem with this strategy is that risk accumulation cannot accommodate certain counterexamples to epistemic closure. The second strategy is based on the idea of evidential support, that is, a piece of evidence supports a proposition whenever it increases the probability of the proposition. This strategy makes progress and can accommodate certain putative counterexamples to closure. However, this strategy also gives rise to a number of counterintuitive results. Finally, there are two broadly probabilistic strategies, one based on the idea of resilient probability and the other on the idea of assumptions that are taken for granted. These strategies are promising but are prone to some of the shortcomings of the second strategy. All in all, I conclude that each strategy fails. Probability theory, then, is unlikely to offer the account we need. (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)