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)

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)

Harman and Lewis credit Kripke with having formulated a puzzle that seems to show that knowledge entails dogmatism. The puzzle is widely regarded as having been solved. In this paper we argue that this standard solution, in its various versions, addresses only a limited aspect of the puzzle and holds no promise of fully resolving it. Analyzing this failure and the proper rendering of the puzzle, it is suggested that it poses a significant challenge for the defense of epistemic closure.

Timothy Williamson has famously argued that the principle should be rejected. We analyze Williamson's argument and show that its key premise is ambiguous, and that when it is properly stated this premise no longer supports the argument against. After canvassing possible objections to our argument, we reflect upon some conclusions that suggest significant epistemological ramifications pertaining to the acquisition of knowledge from prior knowledge by deduction.

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)