Half a century later, a Dretskean stance on epistemic closure remains a minority view. Why? Mainly because critics have successfully poked holes in the epistemologies on which closure fails. However, none of the familiar pro-closure moves works against the counterexamples on display here. It is argued that these counterexamples pose the following dilemma: either accept that epistemic closure principles are false, and steal the thunder from those who attack classical logic on the basis of similarly problematic cases—specifically, relevance logicians and (...) like-minded philosophers—or stick with closure and surrender to relevantist claims of failure in truth-preservation aimed at classical rules of inference. Classicist closure advocates find the promise of a way out of the dilemma in the works of Roy Sorensen and John Hawthorne. The paper argues against their pro-closure move and renews Robert Audi’s call for a theory of closure-failure. (shrink)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty in (...) known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (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)

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)

Safety, as discussed in contemporary epistemology, is a feature of true beliefs. Safe beliefs, when formed by the same method, remain true in close-by possible worlds. I argue that our beliefs being safely true serves no recognisable epistemic interest and, thus, that this notion of safety should play no role in epistemology. Epistemologists have been misled by failing to distinguish between a feature of beliefs — being safely true — and a feature of believers, namely being safe from error. The (...) latter is central to our epistemic endeavours: we want to be able to get right answers, whatever they are, to questions of interest. I argue that we are sufficiently safe from error (in some relevant domain) by being sufficiently sensitive (to relevant distinctions). (shrink)