This article aims to provide a structural analysis of the problems related to the easy knowledge problem. The easy knowledge problem is well known. If we accept that we can have basic knowledge via a source without having any prior knowledge about the reliability or accuracy of this source, then we can acquire knowledge about the reliability or accuracy of this source too easily via information delivered by the source. Rejecting any kind of basic (...) class='Hi'>knowledge, however, leads into an infinite regress and, plausibly, to skepticism. The article argues that the third alternative, accepting basic knowledge but rejecting easy knowledge, entails closure failure. This is obviously the case for deductive bootstrapping, but, notably, the problem also arises for inductive bootstrapping. Hence, the set of problems related to the easy knowledge problem has the structure of a trilemma. We are forced to accept easy knowledge, closure failure, or skepticism. (shrink)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might (...) appear that all that stands between knowing the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

Certain puzzling cases have been discussed in the literature recently which appear to support the thought that knowledge can be obtained by way of deduction from a falsehood; moreover, these cases put pressure, prima facie, on the thesis of counter closure for knowledge. We argue that the cases do not involve knowledge from falsehood; despite appearances, the false beliefs in the cases in question are causally, and therefore epistemologically, incidental, and knowledge is achieved despite falsehood. (...) We also show that the principle of counter closure, and the concomitant denial of knowledge from falsehood, is well motivated by considerations in epistemological theory--in particular, by the view that knowledge is first in the epistemological order of things. (shrink)

Carter and Pritchard (2016) and Pritchard (2010, 2012, 2016) have tried to reconcile the intuition that perceptual knowledge requires only limited discriminatory abilities with the closure principle. To this end, they have introduced two theoretical innovations: a contrast between two ways of introducing error-possibilities and a distinction between discriminating and favoring evidence. I argue that their solution faces the “sufficiency problem”: it is unclear whether the evidence that is normally available to adult humans is sufficient to retain (...) class='Hi'>knowledge of the entailing proposition and come to know the entailed proposition. I submit that, on either infallibilist or fallibilist views of evidence, Carter and Pritchard have set the bar for deductive knowledge too low. At the end, I offer an alternative solution. I suggest that the knowledge-retention condition of the closure principle is not satisfied in zebra-like scenarios. (shrink)

In this paper I argue in favor of the compatibility of semantic externalism with privileged self-knowledge by showing that an argument for incompatibilism from switching scenarios fails. Given the inclusion theory of self-knowledge, the hypothesis according to which I am having twater thoughts while thinking that I have water thoughts simply isn't a (entertainable) possibility. When I am on Earth thinking earthian concepts, I cannot believe that I am thinking that twater is wet for I don't have the (...) concept of twater available; so this concept cannot figure in any of my mental states. Analogously, when I am on Twin Earth, I cannot mistakenly believe that I am entertaining water thoughts. No matter how often I am switched between Earth and Twin Earth, I will never erroneously think that I am having water thoughts while in fact I am having twater thoughts and vice versa. Privileged self-knowledge is therefore immune to skeptical arguments from switching and twinning scenarios. (shrink)

The Neo-Moorean response to the radical skeptical challenge boldly maintains that we can know we’re not the victims of radical skeptical hypotheses; accordingly, our everyday knowledge that would otherwise be threatened by our inability to rule out such hypotheses stands unthreatened. Given the leverage such an approach has against the skeptic from the very start, the Neo-Moorean line is an especially popular one; as we shall see, though, it faces several commonly overlooked problems. An initial problem is that this (...) particular brand of anti-skeptical strategy is available only to a theory of knowledge that will compromise itself to especially weak epistemic standards—indeed, standards as weak as our epistemic grounds are for accepting the denials of skeptical hypotheses. With this said, the aim here is to investigate whether the Neo-Moorean line could be advanced against the skeptic in a way that wouldn’t require wholesale lowering of epistemic standards. Unfortunately, as we’ll see, Sosa’s (2007; 2009) view as well as what I argue to be the other two most plausible contender-views for maintaining a Neo-Moorean line—Greco’s and Pritchard’s—run (for similar reasons) into dead ends. The way forward, I’ll argue, is to take on board a unique variety of robust virtue epistemology accord­ing to which knowledge is thought to be situated a certain way within a gradient balance between ability and luck. (shrink)

Recent research has identified a tension between the Safety principle that knowledge is belief without risk of error, and the Closure principle that knowledge is preserved by competent deduction. Timothy Williamson reconciles Safety and Closure by proposing that when an agent deduces a conclusion from some premises, the agent’s method for believing the conclusion includes their method for believing each premise. We argue that this theory is untenable because it implies problematically easy epistemic access to one’s (...) methods. Several possible solutions are explored and rejected. (shrink)

In response to the claim that certain epistemically defective inferences such as Moore’s argument lead us to the conclusion that we ought to abandon closure, Crispin Wright suggests that we can avoid doing so by distinguishing it from a stronger principle, namely transmission. Where closure says that knowledge of a proposition is a necessary condition on knowledge of anything one knows to entail it, transmission makes a stronger claim, saying that by reasoning deductively from known premises (...) one can thereby acquire knowledge of or justification for the conclusion. Wright’s thought is that in cases such as Moore what is really going on is a failure of transmission, not a failure of closure. The problem with this claim is that it relies on an outdated formulation of closure which few nowadays would find plausible. Once we stipulate that it is the intuitive closure principle that deserves our attention, it becomes far less obvious that the project of diagnosing what is wrong with arguments such as Moore in terms of transmission failure but not closure failure can be vindicated. In order to demonstrate this claim, I consider intuitive closure of propositional justification vs. transmission of propositional justification and concede that perhaps these can come apart in the way that Wright suggests. I then argue that despite this concession, we also need an answer to the question of whether intuitive closure for doxastic justification and transmission for doxastic justification can come apart. We need an answer to this question because our ultimate interest in these issues stems from our interest in whether knowledge obeys closure, not merely whether propositional justification does. I argue that, even on the assumption that there is transmission failure of propositional justification, there is no transmission failure of doxastic justification. And if this is true, then there is no transmission failure of knowledge either. The transmission failure diagnosis of Moore’s argument and its ilk is thus in trouble. (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)

We report the results of four empirical studies designed to investigate the extent to which an epistemic closure principle for knowledge is reflected in folk epistemology. Previous work by Turri (2015a) suggested that our shared epistemic practices may only include a source-relative closure principle—one that applies to perceptual beliefs but not to inferential beliefs. We argue that the results of our studies provide reason for thinking that individuals are making a performance error when their knowledge attributions (...) and denials conflict with the closure principle. When we used research materials that overcome what we think are difficulties with Turri’s original materials, we found that participants did not reject closure. Furthermore, when we presented Turri’s original materials to non-philosophers with expertise in deductive reasoning (viz., professional mathematicians), they endorsed closure for both perceptual and inferential beliefs. Our results suggest that an unrestricted closure principle—one that applies to all beliefs, regardless of their source—provides a better model of folk patterns of knowledge attribution than a source-relative closure principle. (shrink)

Duncan Pritchard recently proposed a Wittgensteinian solution to closure-based skepticism. According to Wittgenstein, all epistemic systems assume certain truths. The notions that we are not disembodied brains, that the Earth has existed for a long time and that one’s name is such-and-such all function as “hinge commitments.” Pritchard views a hinge commitment as a positive propositional attitude that is not a belief. Because closure principles concern only knowledge-apt beliefs, they do not apply to hinge commitments. Thus, from (...) the fact that a subject knows that he is sitting in a room, and the fact that the subject’s sitting in a room entails his bodily existence, it does not follow that the subject also knows that he is not an envatted brain. This paper rejects Pritchard’s non-belief reading of hinge commitments. I start by showing that the non-belief reading fails to solve the skeptical paradox because the reasons that Pritchard uses to support the non-belief reading do not exempt hinge propositions from closure principles. I then proceed to argue that the non-belief reading is false as it claims that hinge commitments, unlike ordinary beliefs, are rationally unresponsive—with the help of a scenario in which a subject’s experience is internally chaotic, we can safely conclude that the hinge commitment that one is not systematically mistaken about the world is equally responsive to one’s evidential situations. (shrink)

This article gives an overview over different principles of epistemic closure, their attractions and their problems.

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 (...) class='Hi'>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)

In spite of the intuitiveness of epistemic closure, there has been a stubborn stalemate regarding whether it is true, largely because some of the “Moorean” things we seem to know easily seem clearly to entail “heavyweight” philosophical things that we apparently cannot know easily—or perhaps even at all. In this paper, I will show that two widely accepted facts about what we do and don’t know—facts with which any minimally acceptable understanding of knowledge must comport—are jointly inconsistent with (...) the truth of CLR. The proof works by supposing the truth of “Categorialism,” a thesis about the relation between basic categories and common nouns and predicates, which is itself a heavyweight claim that cannot be easily known to be either true or false. (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)

It is received wisdom that the skeptic has a devastating line of argument in the following. You probably think, he says, that you know that you have hands. But if you knew that you had hands, then you would also know that you were not a brain in a vat, a brain suspended in fluid with electrodes feeding you perfectly coordinated impressions that are generated by a supercomputer, of a world that looks and moves just like this one. You would (...) know you weren’t in this state if you knew you had hands, since having hands implies you are no brain in a vat. You obviously don’t know you’re not a brain in a vat, though—you have no evidence that would distinguish that state from the normal one you think you’re in. Therefore, by modus tollens, you don’t know you have hands. At least, the skeptic has a devastating argument, it is thought, if we grant him closure of knowledge under known implication, which many of us are inclined to do: roughly, if you know p, and you know that p implies q, then you know q. (shrink)

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).

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)

The most prominent arguments for scepticism in modern epistemology employ closure principles of some kind. To begin my discussion of such arguments, consider Simple Knowledge Closure (SKC): (SKC) (Kxt[p] ∧ (p → q)) → Kxt[q].1 Assuming its truth for the time being, the sceptic can use (SKC) to reason from the two assumptions that, firstly, we don’t know ¬sh and that, secondly, op entails ¬sh to the conclusion that we don’t know op, where ‘op’ and ‘sh’ are (...) shorthand for ‘ordinary proposition’ and ‘sceptical hypothesis’ respectively. (SKC), however, fails for familiar reasons: since knowledge entails belief (KB), we can derive the falsity (F) from (SKC) by hypothetical syllogism, and thus reduce (SKC) to absurdity: (KB) Kxt[p] → Bxt[p]. (F) (Kxt[p] ∧ (p → q)) → Bxt[q]. (shrink)

Ernest Sosa and others have proposed a safety condition on knowledge: If S knows p, then in the nearest (non-actual) worlds in which S believes p, p is true.1 Colloquially, this is the idea that knowing requires not being easily mistaken. Here, I will argue that like another condition requiring a counterfactual relation between a subject’s belief and the world, viz. Robert Nozick’s sensitivity condition, safety leads, in certain cases, to the unacceptable result that knowledge is not closed (...) under known implication. (shrink)

In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has some extra (...) advantages. First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

Generally, an epistemic fallibilist considers it reasonable to claim, “I know that P, but I may be wrong.” An epistemic infallibilist, on the other hand, would consider this claim absurd. I argue initially that infallibilism presents more advantages in its assertion of the claim’s absurdity than fallibilism does in making the claim. One, infallibilism is not faulted with the propensity for violations of epistemic closure that beleaguers some fallibilist accounts, due in part to the latter’s problematic shunting of fallible (...) epistemic standards across inferential chains. Two, infallibilism is more easily modelled doxastically than fallibilism, as the former’s understanding of certainty is more tractable than the latter’s idea of what counts as a viable standard of fallibility. A rectification of these fallibilist issues may then be called upon to motivate gradualist variants of fallibilism. For epistemic gradualism, the problematic modellability and shunting of standards is curtailed via an awareness that the standard for knowledge is just one out of many along a gradient that includes, at one extreme, the infallibilist standard of certainty. Specifically, first, gradualism, along with infallibilism, can be modelled doxastically through elucidating upon an obtaining relation between doubt and knowledge; next, the problem with violating closure, although not generally applicable to infallibilism, can be answered by gradualism with a reasonable denial of closure altogether that makes precise which epistemic standard is relevant for which part of an inferential chain; lastly, these modelling resources can be appropriated, by both gradualism and infallibilism, to successfully address a doxastically pertinent form of closure violation called rational self-doubt. (shrink)

According to some philosophers, we are “cognitively closed” to the answers to certain problems. McGinn has taken the next step and offered a list of examples: the mind/body problem, the problem of the self and the problem of free will. There are naturalistic, scientific answers to these problems, he argues, but we cannot reach them because of our cognitive limitations. In this paper, we take issue with McGinn's thesis as the most well-developed and systematic one among the so-called “new mysterians”. (...) McGinn aims to establish a strong, representational notion of cognitive closure: a principled inaccessibility of a true theory of certain properties of the world, but he offers arguments that only bear on difficulties with psychologically grasping the correct answers. The latter we label psychological closure. We argue that representational closure does not follow from psychological closure, and that McGinn's case therefore falters. We could very well be able to represent the correct answer to some question, even without being able to grasp that answer psychologically. McGinn's mistake in deriving representational closure from psychological closure rests on a fallacy of equivocation relating to the concept of ‘understanding’. By making this distinction explicit, we hope to improve our thinking about the limits of science in particular and human knowledge in general. (shrink)

Skeptical puzzles and arguments often employ knowledge-closure principles . Epistemologists widely believe that an adequate reply to the skeptic should explain why her reasoning is appealing albeit misleading; but it’s unclear what would explain the appeal of the skeptic’s closure principle, if not for its truth. In this paper, I aim to challenge the widespread commitment to knowledge-closure. But I proceed by first examining a new puzzle about failing to know—what I call the New Ignorance (...) Puzzle . This puzzle resembles to the Old Ignorance Puzzle , although it does not involve a closure principle. It instead centers on the standard view of ignorance, a highly intuitive principle stating that ignorance is merely a failure to know. In Sects. 2 and 3, I argue that the best way to solve the New Ignorance Puzzle is to reject the standard view of ignorance and to explain away its appeal via conversational implicature. I then use this solution to the New Ignorance Puzzle as a way of explaining why knowledge-closure principles would seem true, and why abominable conjunctions would seem abominable, even if such principles were false . The upshot is a new way of explaining why the skeptic’s reasoning is appealing albeit misleading. (shrink)

This paper looks at an argument strategy for assessing the epistemic closure principle. This is the principle that says knowledge is closed under known entailment; or (roughly) if S knows p and S knows that p entails q, then S knows that q. The strategy in question looks to the individual conditions on knowledge to see if they are closed. According to one conjecture, if all the individual conditions are closed, then so too is knowledge. I (...) give a deductive argument for this conjecture. According to a second conjecture, if one (or more) condition is not closed, then neither is knowledge. I give an inductive argument for this conjecture. In sum, I defend the strategy by defending the claim that knowledge is closed if, and only if, all the conditions on knowledge are closed. After making my case, I look at what this means for the debate over whether knowledge is closed. (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)

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)

The epistemic closure principle says that knowledge is closed under known entailment. The closure principle is deeply implicated in numerous core debates in contemporary epistemology. Closure’s opponents claim that there are good theoretical reasons to abandon it. Closure’s proponents claim that it is a defining feature of ordinary thought and talk and, thus, abandoning it is radically revisionary. But evidence for these claims about ordinary practice has thus far been anecdotal. In this paper, I report (...) five studies on the status of epistemic closure in ordinary practice. Despite decades of widespread assumptions to the contrary in philosophy, ordinary practice is ambivalent about closure. Ordinary practice does not endorse an unqualified version of the epistemic closure principle, although it might endorse a source-relative version of the principle. In particular, whereas inferential knowledge is not viewed as closed under known entailment, perceptual knowledge might be. (shrink)

In my 1991 paper, AAnti-Individualism and Privileged Access,@ I argued that externalism in the philosophy of mind is incompatible with the thesis that we have privileged , nonempirical access to the contents of our own thoughts.¹ One of the most interesting responses to my argument has been that of Martin Davies (1998, 2000, and Chapter _ above) and Crispin Wright (2000 and Chapter _ above), who describe several types of cases to show that warrant for a premise does not always (...) transmit to a known deductive consequence of that premise, and who contend that this fact under-mines my argument for incompatibilism. I will try to show here that the Davies/Wright point about transmission of warrant does not adversely affect my argument. (shrink)

Why do our intuitive knowledge ascriptions shift when a subject's practical interests are mentioned? Many efforts to answer this question have focused on empirical linguistic evidence for context sensitivity in knowledge claims, but the empirical psychology of belief formation and attribution also merits attention. The present paper examines a major psychological factor (called ?need-for-closure?) relevant to ascriptions involving practical interests. Need-for-closure plays an important role in determining whether one has a settled belief; it also influences the (...) accuracy of one's cognition. Given these effects, it is a mistake to assume that high- and low-stakes subjects provided with the same initial evidence are perceived to enjoy belief formation that is the same as far as truth-conducive factors are concerned. This mistaken assumption has underpinned contextualist and interest-relative invariantist treatments of cases in which contrasting knowledge ascriptions are elicited by descriptions of subjects with the same initial information and different stakes. The paper argues that intellectualist invariantism can easily accommodate such cases. (shrink)

The focus of this article is the question whether the notion of being in a position to know is closed under modus ponens. The question is answered negatively.

It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure. But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter argues that single-premise (...) closure succumbs to risk aggregation outright. For he thinks that there could be a long sequence of competent single-premise deductions such that, even though we are justified in believing the initial premise of the sequence, intutively, we are not justified in believing the final conclusion. This intuition, Schechter thinks, vitiates single-premise closure. In this paper, I defend single-premise closure against the arguments offered by Lasonen-Aarnio and Schechter. (shrink)

I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true, then S knows that all analytic parts of p are true as well. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox. I close (...) by arguing that contextualists who maintain that knowledge attributions are closed within—but not between—linguistic contexts are tacitly committed to this principle’s truth. (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)

The Preface Paradox is often discussed for its implications for rational belief. Much less discussed is a variant of the Preface Paradox for knowledge. In this paper, I argue that the most plausible closure-friendly resolution to the Preface Paradox for Knowledge is to say that in any given context, we do not know much. I call this view “Socraticism”. I argue that Socraticism is the most plausible view on two accounts—(1) this view is compatible with the claim (...) that most of our knowledge ascriptions are true, and (2) provided that (1) is true, the costs of accepting Socraticism are much less than the costs of accepting any other resolution to the Paradox. I argue for (1) in Section 2 by developing a question-sensitive contextualist model for knowledge that shows how Socraticism is compatible with the claim that most of our knowledge ascriptions are true. I also argue how this contextualist model can achieve this result where other contextualist models fail. I then consider other closure-friendly solutions to the paradox in Section 3 and show how accepting those solutions forces us to give up a number of plausible epistemic principles. (shrink)

Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...) FDE worlds (Berto and Jago, 2019) with a Lewisian (1988) understanding of subject matters as partitions. By doing so, I show how subject matters impose some order in the anarchic space of FDE worlds, while the worlds allow for distinctions between contents which would not otherwise be available. Combining the two approaches, then, brings us closer to the desired closure principles for knowledge of minimally rational agents. (shrink)

ABSTRACT Drawing inspiration from Fred Dretske, L. S. Carrier, John A. Barker, and Robert Nozick, we develop a tracking analysis of knowing according to which a true belief constitutes knowledge if and only if it is based on reasons that are sensitive to the fact that makes it true, that is, reasons that wouldn’t obtain if the belief weren’t true. We show that our sensitivity analysis handles numerous Gettier-type cases and lottery problems, blocks pathways leading to skepticism, and validates (...) the epistemic closure thesis that correct inferences from known premises yield knowledge of the conclusions. We discuss the plausible views of Ted Warfield and Branden Fitelson regarding cases of knowledge acquired via inference from false premises, and we show how our sensitivity analysis can account for such cases. We present arguments designed to discredit putative counterexamples to sensitivity analyses recently proffered by Tristan Haze, John Williams and Neil Sinhababu, which involve true statements made by untrustworthy informants and strange clocks that sometimes display the correct time while running backwards. Finally, we show that in virtue of employing the paradox-free subjunctive conditionals codified by Relevance Logic theorists instead of the paradox-laden subjunctive conditionals codified by Robert Stalnaker and David Lewis. (shrink)

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal characterisations of (...) the surprise notion, crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

This paper argues that a necessary condition on inferential knowledge is that one knows all the propositions that knowledge depends on. That is, I will argue in support of a principle I call the Knowledge from Knowledge principle: (KFK) S knows that p via inference or reasoning only if S knows all the propositions on which p depends. KFK meshes well with the natural idea that (at least with respect to deductively valid or induc- tively strong (...) arguments) the epistemic status of one’s belief in the conclusion of an argument is a function of the epistemic status of the attitudes one has to the premises of that argument. One gets what one puts in: S’s belief in the conclusion C of an argument A has epistemic status E for S only if S’s belief in each of the premises C depends on also has epistemic status E.1 This is compatible, of course, with the epistemic status of S’s conclusion being greater than the epistemic status of the premises on which the conclusion of her reasoning depends. Furthermore, even though KFK applies more straightforwardly to non-suppositional inferences, we can also plausibly apply the principle to sup- positional reasoning if we treat S’s assuming for the sake of argument that p,2 as S assuming for the sake of argument that she knows that p.3 Although extremely plausible, philosophers have failed to present a concerted case in support of KFK. Most of their energy goes to articulating and/or defending some form of closure principle for knowledge.4 What is more, recently versions of this principle have been dismissed as problematic but I think without the reasons in its support been fully appreciated. This paper is an e fort to change the current state of affairs. Its focus is positive, however: my goal is to make the best case I can in support of KFK.5 To that end, the paper presents the reasons we have to accept KFK (§1), consid- ers an objection to the principle (§2), and situates the principle in the broader normative context of knowledge norms (§3). (shrink)

I propose and defend the conjecture that what explains why Gettiered subjects fail to know is the fact that their justified true belief depends essentially on unknown propositions. The conjecture follows from the plausible principle about inference in general according to which one knows the conclusion of one’s inference only if one knows all the premises it involves essentially.

Dretske’s theory of self-knowledge is interesting but peculiar and can seem implausible. He denies that we can know by introspection that we have thoughts, feelings, and experiences. But he allows that we can know by introspection what we think, feel, and experience. We consider two puzzles. The first puzzle, PUZZLE 1, is interpretive. Is there a way of understanding Dretske’s theory on which the knowledge affirmed by its positive side is different than the knowledge denied by its (...) negative side? The second puzzle, PUZZLE 2, is substantive. Each of the following theses has some prima facie plausibility: there is introspective knowledge of thoughts, knowledge requires evidence, and there are no experiences of thoughts. It is unclear, though, that these claims form a consistent set. These puzzles are not unrelated. Dretske’s theory of self-knowledge is a potential solution to PUZZLE 2 in that Dretske’s theory is meant to show how,, and can all be true. We provide a solution to PUZZLE 1 by appeal to Dretske’s early work in the philosophy of language on contrastive focus. We then distinguish between “Closure” and “Transmissibility”, and raise and answer a worry to the effect that Dretske’s theory of self-knowledge runs counter to Transmissibility. These results help to secure Dretske’s theory as a viable solution to PUZZLE 2. (shrink)

Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...) FDE worlds (Berto and Jago, 2019) with a Lewisian (1988) understanding of subject matters as partitions. By doing so, I show how subject matters impose some order in the anarchic space of FDE worlds, while the worlds allow for distinctions between contents which would not otherwise be available. Combining the two approaches, then, brings us closer to the desired closure principles for knowledge of minimally rational agents. (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.

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop (...) a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based (...) and structure-based notions of representation from contemporary mathematical logic. It is argued that the theory-based versions of such logicism are either too liberal (the plethora problem) or are committed to intuitively incorrect closure conditions (the consistency problem). Structure-based versions must on the other hand respond to a charge of begging the question (the circularity problem) or explain how one may have a knowledge of structure in advance of a knowledge of axioms (the signature problem). This discussion is significant because it gives us a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the philosophy of mathematics. (shrink)

A core historical narrative about anthropological knowledge is that it is created in relations with others, with fieldwork seen as ‘a series of apprenticeships’ whose success is determined by the quality of those relations. An ethnographer connects with the conditions of those studied in ‘circulating exchange’; but on leaving the field a degree of closure is needed to formulate and communicate anthropological knowledge. These obligations and requirements in the creation of knowledge entail attachment and detachment, carrying (...) the seeds of betrayal that can compromise that knowledge. Each epistemological enquiry has its own core ethical imperatives, but as long as knowledge posits a knower, ‘the self of the knower will be at epistemological issue’. In discussing the ethics of knowledge creation I consider the following questions, among others: To what extent is the creation of a particular kind of ethical and epistemic person required for knowledge? How can ethnography produce knowledge about others without betraying them? Can relations of knowledge exchange confer or withhold ‘rights to speak’? Is it possible that unethical relations may destroy or hold up the unfolding of knowledge? And are there circumstances in which it is unethical to disclose knowledge? (shrink)

One disturbing but telling demonstration of how definitions of knowledge can go wrong is due to Hawthorne.[1] Although properly intended as an attack on Dretske’s theory of conclusive reasons, it also works against Nozick’s conditional theory. Hawthorne provides a simple example: suppose, he declaims, that salmon induces hallucinations if eaten in great amounts. Suppose that, to be more precise, were you to eat it in amounts greater than 14 pounds at one go (never mind how that is humanly possible), (...) it could cause you to believe that you’ve only had a few tidbits of the savoury fish. Then, on Dretske’s account, if P is the proposition I ate less than 1 pound of salmon, I could know P. On the other hand, let Q be the proposition I ate less than 14 pounds of salmon. Q is not knowable, because were Q to be false, I might still experience the hallucination that I’ve eaten less than a pound of salmon, and therefore I do not have conclusive reasons for Q. (shrink)

Here, I shall be examining the viability of a Moorean response to the Argument from Ignorance; i.e., one that tries to rebut the argument by denying its first premise that we cannot have knowledge that we are not BIVs. After first explicating the Argument from Ignorance in detail, I then go on to try and motivate this approach by critically examining two alternative approaches to dealing with radical scepticism: closure-denial, and attributer contextualism. Finding them wanting, I then turn (...) to a Moorean 'argument from knowledge', and diagnose why as it stands such an approach is ineffective, before going on to explore whether one can wed such an argument to an externalist framework in order to provide a more satisfying answer to the question of how one can know the denials of sceptical hypotheses, one that does not simply beg the question against the sceptic. Finding such a neo-Moorean approach to be initially promising, I then conclude by arguing that ultimately it winds up saving knowledge simpliciter only at the cost of losing rationally-grounded knowledge to the sceptic's grasp, and such a result is highly unpalatable. (shrink)

The multi premise closure principle states that the logical conjunction of known facts yields again a known fact. For absolute knowledge this principle holds. We show that for fallible knowledge, assuming knowing requires a minimum level of statistical certainty (whatever else it requires), and that there is a sufficient number of known facts above a given level of uncertainty, it does not hold, for simple statistical reasons. We present a modified version, the dependent conjunctive closure principle, (...) that does hold. (shrink)

By using the general investigation framework offered by the cognitive science of religion (CSR), I analyse religion as a necessary condition for the evolutionary path of knowledge. The main argument is the "paradox of the birth of knowledge": in order to get to the meaning of the part, a sense context is needed; but a sense of the whole presupposes the sense (meaning) of the parts. Religion proposes solutions to escape this paradox, based on the imagination of sense (...) (meaning) contexts, respectively closures of these contexts through meta-senses. What is important is the practical effectiveness of solutions proposed by religion, taking into account the costs of faith and the costs of the absence of religious belief. The hypothesis has the following consequences: religion is a necessary condition for the initial evolution of knowledge and the emergence of religion is determined by the evolution of knowledge. The continuation of the solving of paradox is a Bayesian one, using explorations: a sense of the whole allows cognitive arrangements of the parties, which in turn open the possibility of a rearrangement of the whole. The contribution of religion to the emergence of sense (meaning) could be governed by the rule: any map of the world is more useful than no map; any meaning (of life) is better than no meaning. The human mind fills the perceptual and cognitive gaps, some (religious) filling solutions being true vault keys of the entire cognitive construction called the world. Knowledge is conditioned by the existence of an organized context, as the cosmos created by religion by means of explanatory meta-theories supports knowledge by closing the cognitive context and using meaning networks. The proposed analysis is consistent with a redefinition of rationality from the perspective of evolution: the importance and relevance of knowledge is determined by its practical outcome - survival. In the context of useful fictions, it does not matter what God actually does, but what we have done by believing in God. Existence has provided a pragmatic verification of the cognitive solutions that underlie the survival strategies promoted by religions. (shrink)