Closure of Knowledge

In this paper it will be attempted to dissolve the lottery problem based on fallibilism, probabilism and the introduction of a so far widely neglected second context of knowledge. First, it will be argued that the lottery problem is actually an exemplification of the much wider Humean "future knowledge problem" (ch. 1). Two types of inferences and arguments will be examined, compared and evaluated in respect to their ability to fittingly describe the thought processes behind lottery/future knowledge propositions (ch. 2). (...) A second context of knowledge that underlines the importance of fallibilism and probabilism in a somewhat different manner will be introduced (ch. 3) and, based on that "two-context probabilism," the lottery/future knowledge problem will be dissolved (ch. 4). Lastly, it will be hinted at the necessity of adopting not just fallibilism including and two context minding probabilism, but, beyond that, also the even more encompassing position of both ontological and epistemological "gradualism" (ch. 5). (shrink)

Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles.

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)

Self-fulfilling beliefs are, in at least some cases, a kind of belief that is rational to form and hold in the absence of evidence. The rationality of such beliefs have significant implications for a range of debates in epistemology. Most startlingly, it undermines the idea that having sufficient evidence for the truth of p is necessary for it to be rational to believe p. The rationality of self-fulfilling beliefs is here defended against the idea that their rationality is incompatible with (...) a compelling closure principle. (shrink)

In this paper I defend the claim that justification is closed under conjunction, and confront its most alarming consequence – that one can have justification for believing propositions that are unlikely to be true, given one’s evidence.

In this paper, I offer reasons for thinking that two prominent sceptical arguments in the literature – the underdetermination-based sceptical argument and the closure-based sceptical argument – are less philosophically interesting than is commonly supposed. The underdetermination-based argument begs the question against a non-sceptic and can be dismissed with little fanfare. The closure-based argument, though perhaps not question-begging per se, does rest upon contentious assumptions that a non-sceptic is under no pressure to accept.

This paper replies to the comments made in Acta Analytica by Peter Baumann, Kelly Becker, Marian David, Nenad Miščević, Wes Siscoe, and Danilo Šuster on my Knowing and Checking: An Epistemological Investigation (Routledge 2019), hereinafter abbreviated as KC. These papers resulted from a workshop organized by the department of philosophy of the University of Maribor. I am very thankful to the organizers of the workshop and to the authors for their comments.

In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and belief on which (...) these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible-worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible-worlds account of mathematical content, knowledge, and inquiry. (shrink)

Epistemologists understand radical skepticism as arising from two principles: Closure and Underdetermination. Both possess intuitive prima facie support for their endorsement. Understanding how they engender skepticism is crucial for any reasonable anti-skeptical attempt. The contemporary discussion has focused on elucidating the relationship between them to ascertain whether they establish distinct skeptical questions and which of the two constitutes the ultimately fundamental threat. Major contributions to this debate are due to Brueckner, Cohen, and Pritchard. This contribution aims at defending Brueckner’s contention (...) that underdetermination expresses the fundamental skeptical threat and that the closure-based argument can ultimately be reduced to it, at least concerning skeptical contexts. This will be achieved by undermining Cohen’s objections to Brueckner on both counts. Cohen’s argument endorses a picture of evidential underdetermination, which, while apt for non-skeptical contexts, cannot be applied to radical skepticism. A comparison with a case of scientific underdetermination is developed to argue for this idea. Our argument is then applied to the principle equivalence issue and to objections against it. It is then shown how this analysis possesses a distinctive effect on our understanding of the skeptical threat and the assessment of successful anti-skeptical strategies. (shrink)

The Cartesian arguments for external world skepticism are usually considered to be significant for at least two reasons: they seem to present genuine paradoxes and that providing an adequate response to these arguments would reveal something epistemically important about knowledge, justification, and/or our epistemic position to the world. Using only premises and reasoning the skeptic accepts, I will show that the most common Cartesian argument for external world skepticism leads to a previously unrecognized self-undermining dilemma: it either leads to a (...) reductio ad absurdum, or to avoid this reductio the skeptic must accept that this argument is epistemically idle—it does not provide any support for external world skepticism. Either way, this Cartesian argument cannot legitimately threaten or even call into question our beliefs about the external world. And thus, either way, this Cartesian argument for external world skepticism is not epistemically significant—it is not a genuine paradox and adequately responding to it need not reveal anything epistemically important. (shrink)

In this Précis, I provide an overview of my Monograph Knowing and Checking: An Epistemological Investigation (Melchior 2019), which is subject to a book symposium organized by the University of Maribor. This volume in Acta Analytica contains contributions by Peter Baumann, Kelly Becker, Marian David, Nenad Miščević, Robert Weston Siscoe, and Danilo Šuster along with my replies.

This volume features new perspectives on the topic of epistemic closure. It connects epistemic closure principles to related themes in epistemology such as scepticism, dogmatism, evidentialism, epistemic logic, and modal epistemology.

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...) of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

In this paper I argue that two claims usually included in any minimally detailed presentation of the epistemic closure principle are inconsistent, namely, that closure explains how we extend our knowledge through deduction and that it is different from another epistemic principle, to wit, transmission. The attempt to offer a correct diagnosis of reasonings such as the one involved in Dretke’s zebra case is an instance of a discussion in which the distinction takes part. My argument has the following structure. (...) First, I introduce the distinction between closure and transmission following the standard presentation. Second, I introduce the main motivations behind the principles; in particular, I establish that the main motivation behind closure consists in explaining the phenomenon of the advancement of knowledge through deductive reasoning. Third, based on the identification of a restriction on any plausible formulation of closure capable of explaining the phenomenon aforementioned, I cast doubts on the distinction between this principle and transmission. I conclude that any formulation of the epistemic principle of closure which satisfies its main motivation collapses into the epistemic principle of transmission. (shrink)

According to the safety account of knowledge, one knows that p only if one's belief could not easily have been false. An important issue for the account is whether we should only examine the belief in the target proposition when evaluating whether a belief is safe or not. In this paper, it is argued that if we only examine the belief in the target proposition, then the account fails to account for why beliefs in necessary truths could fall short of (...) knowledge. But, if we also examine beliefs in other relevant propositions, then the account fails to preserve epistemic closure. Therefore, the safety account cannot find a safe path between epistemic closure and necessary truths. (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)

I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: -/- (1) There is a qualitative difference between knowledge and non-knowledge. (2) Knowledge is valuable in a way that non-knowledge is not. (3) Subjects in Gettier cases do not have knowledge. (4) If S knows that P, P is part of S’s evidence. (5) If S knows (...) that P, ~P is epistemically impossible for S. (6) If S knows that P, S can rationally act as if P. (7) If S knows that P, S can rationally stop inquiring whether P. (8) If S knows each of {P1, P2, … Pn}, and competently deduces Q from these propositions, S knows that Q. -/- I then argue that the skeptical costs of this thesis are outweighed by its explanatory power. (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)

A certain brand of skeptical argument appeals to the thought that our inability to subjectively discriminate between competing hypotheses means that we are unwarranted in believing in either. Externalists respond by pointing out that such arguments depend on an internalist conception of warrant that we would do well to reject. This strategy has been criticised by Crispin Wright who argues that if we pursue the implications of externalism sufficiently far we find that it is ultimately unstable or incoherent. I first (...) rehearse the simple externalist anti-skeptical position. I then present Wright’s argument for the externalist instability, offering a clearer way of understanding its central claim. Finally, I show that the instability in fact arises due to hidden internalist assumptions about evidence and that rid of these assumptions the externalist position is stable after all. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (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)

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 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)

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: an intension, taking care of truth conditions; and a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of (...) knowledge per se for arbitrary agents, and isolate three explanatory factors for them: the topic-sensitivity of content; the fragmentation of knowledge states; the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. (shrink)

Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know, 309–338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is not provable (...) in minimal arithmetic or that the negation of that sentence is not provable in minimal arithmetic. This serves as the formal background for an example that calls into question the correctness of Rosenkranz’s logic of justification. (shrink)

Closure principles say that if you know some proposition which entails a second and you meet further conditions then you know the second. In this paper I construct an argument against closure principles which turns on the idea that knowing a proposition requires that one’s belief-forming process be reliable. My argument parallels an influential argument offered by Timothy Williamson against KK principles–principles that say that if you know some proposition and you meet further conditions then you know that you know (...) the proposition. After offering my argument, I provisionally assess its damage to closure principles and also look at how responses to my argument against closure principles can be used to generate responses to Williamson’s argument against KK principles. (shrink)

The purpose of this paper is to provide a new solution to the radical sceptical paradox. A sceptical paradox purports to indicate the inconsistency within our fundamental epistemological commitments that are all seemingly plausible. Typically, sceptics employ an intuitively appealing epistemic principle (e.g., the closure principle, the underdetermination principle) to derive the sceptical conclusion. This paper will reveal a dilemma intrinsic to the sceptical paradox, which I refer to as the self-hollowing problem of radical scepticism. That is, on the one (...) hand, if the sceptical conclusion turns out to be true, then the epistemic principle employed by sceptics would lose its foundation of plausibility; on the other hand, if the sceptical conclusion does not follow, then the sceptical problem would not arise. In either case, the so-called sceptical paradox cannot be a genuine paradox. This new solution has three theoretical merits: it is undercutting, less theory-laden, and widely applicable. (shrink)

Sensitivity is a modal epistemic principle. Modal knowledge accounts are externalist in nature and claim that the knowledge yielding connection between a true belief and the truthmaker must be spelled out in modal terms. The sensitivity condition was introduced by Robert Nozick. He suggests that if S knows that p, then S’s belief that p tracks truth. Nozick argues that this truth-tracking relation can be captured by subjunctive conditionals. As a first approximation, he provides the following modal analysis of knowledge: (...) S knows that p iff (1) p is true; (2) S believes that p; (3) if p were false, S wouldn’t believe that p and (4) if p were true, S would believe that p. The dominant terminology in the literature, also adopted here, is to call condition (3) the sensitivity condition and condition (4) the adherence condition. The sensitivity condition is intuitively appealing since it states that a subject does not know that p if she would believe that p even if p were false. Nozick used the sensitivity condition to accomplish two major tasks. First, he provided a solution to the Gettier problem by arguing that in Gettier cases subjects do not know since the sensitivity condition is violated. Second, he presented a controversial solution to the skeptical problem according to which we have external world knowledge but do not know that the skeptical hypothesis is false. This solution is available because sensitivity is not closed under known entailment. Quickly, criticism of the sensitivity condition emerged. First, most epistemologists regarded the price of abandoning knowledge closure as a price too high to pay. Second, it was noted that sensitivity leads to the counterintuitive consequence of precluding us from inductive knowledge since induction typically yields insensitive beliefs. The most dominant reaction to these problems was to replace sensitivity by the modal principle of safety, nowadays the most popular modal principle. However, sensitivity is not only important as a starting point of modal epistemology. Because of its intuitive attractiveness, many authors aimed at refining the original sensitivity account in order to avoid well-known problems. This has led to a second wave of sensitivity accounts. As of today, various sensitivity-based theories are on the market, including accounts that avoid closure failure, probabilistic interpretations of sensitivity and adherence, and contextualist approaches. There is thus a vivid and ongoing debate about the sensitivity principle in epistemology. (shrink)

In this essay, I discuss the analogy of the mind as a sponge, the issues of cognitive artifacts, and being a mind in the 21st century.

Knowledge closure is the claim that, if an agent S knows P, recognizes that P implies Q, and believes Q because it is implied by P, then S knows Q. Closure is a pivotal epistemological principle that is widely endorsed by contemporary epistemologists. Against Knowledge Closure is the first book-length treatment of the issue and the most sustained argument for closure failure to date. Unlike most prior arguments for closure failure, Marc Alspector-Kelly's critique of closure does not presuppose any particular (...) epistemological theory; his argument is, instead, intuitively compelling and applicable to a wide variety of epistemological views. His discussion ranges over much of the epistemological landscape, including skepticism, warrant, transmission and transmission failure, fallibilism, sensitivity, safety, evidentialism, reliabilism, contextualism, entitlement, circularity and bootstrapping, justification, and justification closure. As a result, the volume will be of interest to any epistemologist or student of epistemology and related subjects. (shrink)

Two epistemic principles are Knowledge Exclusion and Belief Exclusion. Knowledge Exclusion says that it is necessarily the case that if an agent knows that p, then she does not believe that ∼p, and Belief Exclusion says that it is necessarily the case that if an agent believes that q, then she does not believe that ∼q. Many epistemologists find it reasonable to reject the latter principle and accept the former. I argue that this is in fact not reasonable by proposing (...) a case in which an agent can use that she has contradictory beliefs towards a proposition as decisive evidence for that proposition. A natural response is that this case conflicts with common assumptions about the relation between knowledge, contradictory beliefs and rationality. I reply by drawing ideas from Lasonen-Aarnio’s remarks on unreasonable knowledge to explain why these common assumptions do not threaten my argument. (shrink)

Duncan Pritchard’s Epistemic Angst promises a novel solution to the closure-based sceptical problem that, unlike more traditional solutions, does not entail revising our fundamental epistemological commitments. In order to do this, it appeals to a Wittgensteinian account of rational evaluation, the overarching theme of which is that it neither makes sense to doubt nor to believe in our anti-sceptical hinge commitments. The purpose of this paper is to show that the argument for the claim that there can be no rational (...) basis to believe our anti-sceptical hinge commitments relies upon an implicit assumption about rational support that I label The Pritchensteinian Rational Grounds Principle. I argue that, insofar as this principle is intended to apply to closure-style inferences, it leads to irrational doxastic attitudes. I consider a seemingly plausible modification of the principle that would avoid this result but show that this modified principle faces serious problems of its own. -/- . (shrink)

An orthodox sceptical hypothesis claims that one’s belief that “I am not a brain-in-a-vat (BIV)” (or any other ordinary anti-sceptical belief) is insensitive. A form of sensitivity-based scepticism, can thus be constructed by combining this orthodox hypothesis with the sensitivity principle and the closure principle. Unlike traditional solutions to the sensitivity-based sceptical problem, this paper will propose a new solution—one which does not reject either closure or sensitivity. Instead, I argue that sceptics’ assumption that one’s ordinary anti-sceptical beliefs are insensitive (...) will give rise to self-contradiction. The orthodox sceptical hypothesis is thus revealed to be incoherent and arbitrary. Given that there is no coherent reason to presuppose our ordinary anti-sceptical beliefs to be insensitive, the argument for sensitivity-based scepticism can thus be blocked at a lower epistemological cost. (shrink)

All standard epistemic logics legitimate something akin to the principle of closure, according to which knowledge is closed under competent deductive inference. And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. One might think that serious concerns about closure point us away from epistemic logic altogether—away from the very idea that the knowledge relation could be fruitfully treated as a kind of modal operator. This, however, need not be so. The (...) abandonment of closure may yet leave in place plenty of formal structure amenable to systematic logical treatment. In this paper we describe a family of weak epistemic logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled. One of these—which we term plurality semantics—is relatively unfamiliar. We explore under what conditions plurality frames validate certain much-discussed principles of epistemic logic. It turns out that plurality frames can be interpreted in a very natural way in light of one motivation for rejecting closure, adding to the significance of our technical work. The second framework that we employ—neighbourhood semantics—is much better known. But we show that it too can be interpreted in a way that comports with a certain motivation for rejecting closure. (shrink)

This book is primarily about checking and only derivatively about knowing. Checking is a very common concept for describing a subject’s epistemic goals and actions. Surprisingly, there has been no philosophical attention paid to the notion of checking. In Part I, I develop a sensitivity account of checking. To be more explicit, I analyze the internalist and externalist components of the epistemic action of checking which include the intentions of the checking subject and the necessary externalist features of the method (...) used. Crucially, successfully checking whether p is true requires using a method that is sensitive with respect to p, i.e. a method that would not indicate that p, if p were false. In Part II, I use the distinction between knowing and checking to explain central puzzles about knowledge, particularly puzzles centering on knowledge closure, puzzles concerning bootstrapping and the skeptical puzzle. Moreover, the book clarifies a dispute about modal epistemology, concerning the application of the sensitivity principle. By arguing that sensitivity is necessary for checking but not knowing, I explain where our persisting intuitions about sensitivity have their place in epistemology. (shrink)

It is well-known that versions of the lottery paradox and of the preface paradox show that the following three principles are jointly inconsistent: (Sufficiency) very probable propositions are justifiably believable; (Conjunction Closure) justified believability is closed under conjunction introduction; (No Contradictions) propositions known to be contradictory are not justifiably believable. This paper shows that there is a hybrid of the lottery and preface paradoxes that does not require Sufficiency to arise, but only Conjunction Closure and No Contradictions; and it argues (...) that, given any plausible solution to this paradox, if one is not ready to deny Conjunction Closure (and analogous consistency principles), then one must endorse the thesis that justified believability is factive. (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)

An important question in epistemology is whether the KK principle is true, i.e., whether an agent who knows that p is also thereby in a position to know that she knows that p. We explain how a “transparency” account of self-knowledge, which maintains that we learn about our attitudes towards a proposition by reflecting not on ourselves but rather on that very proposition, supports an affirmative answer. In particular, we show that such an account allows us to reconcile a version (...) of the KK principle with an “externalist” or “reliabilist” conception of knowledge commonly thought to make that principle particularly problematic. (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)

Descartes’s Evil Demon argument has been the subject of many reconstructions in recent analytic debates. Some have proposed a reconstruction with a principle of Infallibility, others with a principle of Closure of Knowledge, others with more original principles. In this paper, I propose a new reconstruction, which relies on the combination of two principles, namely the Meta-Coherence principle and the principle of Closure of Justification. I argue that the argument construed in this way is the best interpretation of what is (...) really at play in the Evil Demon intuition, and also that this argument is dialectically much stronger than previous reconstructions. If this is right, then the “Closure plus Meta-Coherence” argument is what anti-sceptics should really be attacking. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...) and recommended readings provide gateways for further exploration. (shrink)

Arguments from "easy knowledge" are meant to refute a class of epistemological views, including foundationalism about perceptual knowledge. I present arguments from easy knowledge in their strongest form, and explain why other formulations in the literature are inferior. I criticize two features of Stewart Cohen's presentation, namely his focus on knowing that one's faculties are reliable, and his use of a Williamson-style closure principle. Rather, the issue around easy knowledge must be understood using a notion of epistemic priority. Roger White's (...) presentation is contaminated by the so-called lottery puzzle, which is best kept separate. Distinguishing basic from non-basic visual contents limits the force of the examples discussed by Cohen, White, and Crispin Wright. Finally, I present a new strategy for resisting even the best-formulated arguments from easy knowledge. (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 lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties encountered by those (...) approaches. (shrink)

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including (...) a recent one advanced by Hannes Leitgeb (Analysis 74.1). (shrink)

This paper offers a new solution to the Surprise Test Paradox. The paradox arises thanks to an ingenious argument that seems to show that surprise tests are impossible. My solution to the paradox states that it relies on a questionable closure principle. This closure principle says that if one knows something and competently deduces something else, one knows the further thing. This principle has been endorsed by John Hawthorne and Timothy Williamson, among others, and I trace its motivation back to (...) work by Alvin Goldman. I provide counterexamples to the principle and explain the flaw in the reasoning of those who defend it. (shrink)