I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief (...) Closure. After recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too. (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)

Kripke’s puzzle has puts pressure on the intuitive idea that one can believe that Superman can fly without believing that Clark Kent can fly. If this idea is wrong then many theories of belief and belief ascription are built from faulty data. I argue that part of the proper analysis of Kripke’s puzzle refutes the closure principles that show up in many important arguments in epistemology, e.g., if S is rational and knows that P and that P (...) entails Q, then if she considers these two beliefs and Q, then she is in a position to know that.. (shrink)

Recent views in hinge epistemology rely on doxastic normativism to argue that our attitudes towards hinge propositions are not beliefs. This paper has two aims; the first is positive: it discusses the general normative credentials of this move. The second is negative: it delivers two negative results for No-Belief hinge epistemology such construed. The first concerns the motivation for the view: if we’re right, doxastic normativism offers little in the way of theoretical support for the claim that our attitudes (...) towards hinge propositions are anything but garden-variety beliefs. The second concerns theoretical fruitfulness: we show that embracing a No-Belief view will either get us in serious theoretical trouble, or loose all anti-sceptical appeal. (shrink)

An analysis is presented of the relationships between consumers ethical beliefs, ethical ideology, Machiavellianism, political preference and the individual difference variable "need for closure". It is based on a representative survey of 286 Belgian respondents. Standard measurement tools of proven reliability and robustness are used to measure ethical beliefs (consumer ethics scale), ethical ideology (ethical positioning), Machiavellianism (Mach IV scale) and need for closure. The analysis finds the following. First, individuals with a high need for closure tend (...) to have beliefs that are more ethical as regards possible consumer actions, and score higher on idealism and lower on Machiavellianism, than those with a low need for closure. Second, a correlation exists between political preference and ethical beliefs. Third, a significant relationship exists between ethical ideology and political preference for the two largest political parties. Fourth, individuals with a high and low need for closure have different political preferences for right-wing and left-wing parties. (shrink)

An analysis is presented of the relationships between consumers’ ethical beliefs, ethical ideology, Machiavellianism, political preference and the individual difference variable "need for closure". It is based on a representative survey of 286 Belgian respondents. Standard measurement tools of proven reliability and robustness are used to measure ethical beliefs (consumer ethics scale), ethical ideology (ethical positioning), Machiavellianism (Mach IV scale) and need for closure. The analysis finds the following. First, individuals with a high need for closure tend (...) to have beliefs that are more ethical as regards possible consumer actions, and score higher on idealism and lower on Machiavellianism, than those with a low need for closure. Second, a correlation exists between political preference and ethical beliefs. Third, a significant relationship exists between ethical ideology and political preference for the two largest political parties. Fourth, individuals with a high and low need for closure have different political preferences for right-wing and left-wing parties. (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)

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)

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)

I argue that fallibilism, single-premise epistemic closure, and one formulation of the “knowledge-action principle” are inconsistent. I will consider a possible way to avoid this incompatibility, by advocating a pragmatic constraint on belief in general, rather than just knowledge. But I will conclude that this is not a promising option for defusing the problem. I do not argue here for any one way of resolving the inconsistency.

Most solutions to the skeptical paradox about justified belief assume closure for justification, since the rejection of closure is widely regarded as a non-starter. I argue that the rejection of closure is not a non-starter, and that its problems are no greater than the problems associated with the more standard anti-skeptical strategies. I do this by sketching a simple version of the unpopular strategy and rebutting the three best objections to it. The general upshot for theories (...) of justification is that it is not a constraint on such theories that we must somehow have justification to believe that we are not massively deceived. (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)

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)

The focus of this paper is the prima facie plausible view, expressed by the principle of Counter-Closure, that knowledge-yielding competent deductive inference must issue from known premises. I construct a case that arguably falsifies this principle and consider five available lines of response that might help retain Counter-Closure. I argue that three are problematic. Of the two remaining lines of response, the first relies on non-universal intuitions and forces one to view the case I construct as exhibiting a (...) justified, true belief to which none of the usual diagnoses of knowledge failure in Gettier cases apply. The second line involves claiming that Fake Barns and its ilk are misdiagnosed by epistemological orthodoxy as Gettier cases. We are thus confronted by a trilemma: either the case I discuss undermines the first-blush plausible principle of Counter-Closure; or the case I discuss instantiates a novel kind of Gettier case; or a popular conception of a key range of alleged Gettier cases must be rejected. No matter which horn we choose, the case points to a philosophically curious conclusion. (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)

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)

According to a popular closure principle for epistemic justification, if one is justified in believing each of the premises in set Φ and one comes to believe that ψ on the basis of competently deducing ψ from Φ—while retaining justified beliefs in the premises—then one is justified in believing that ψ. This principle is prima facie compelling; it seems to capture the sense in which competent deduction is an epistemically secure means to extend belief. However, even the single-premise (...) version of this closure principle is in conflict with certain seemingly good inferences involving the epistemic possibility modal ♢. According to other compelling principles concerning competent deduction and epistemic justification, one can competently infer ¬♢φ from ¬φ in deliberation even though there are cases in which one can justifiably believe ¬φ but would be unjustified in believing ¬♢φ. Thus, as we argue, philosophers must choose between unrestricted closure for justification and the validity of these other principles. (shrink)

Many people, such as Adam Smith, Milton Friedman, Irving Fisher, and William Sharpe, assume that free markets full of rational people automatically lead to ethical actions and outcomes. After all, at its equilibrium point, a perfectly competitive free market maximizes utility, respects autonomy, and fulfills justice’s dictates. Unfortunately, in some technology markets, there are a significant number of people who have undergone epistemic closure. Epistemic closure entails that all reliable evidence that would challenge deeply held beliefs is dismissed (...) as corrupted, whereas all supporting evidence, no matter how unreliable, is accepted as incontrovertible. Those who have the condition act irrationally within that domain. As a result, business decisions become much more difficult than they would be in a rational market. In this article, epistemic closure’s ethical issues are developed. First, although they are acting irrationally within the closure’s domain, those with epistemic closure can still be held accountable for their actions. Second, to deal ethically with epistemic closure and its consequences, then it is vital to know what it is and its root causes, as well as to have a practical principle that can assist in making pragmatic decisions. Because some new technologies face epistemic closure, then focusing on a particular representative case of it will help to illustrate the issue’s ethical dimensions. (shrink)

ABSTRACTMany discussions of the ‘preface paradox’ assume that it is more troubling for deductive closure constraints on rational belief if outright belief is reducible to credence. I show that this is an error: we can generate the problem without assuming such reducibility. All that we need are some very weak normative assumptions about rational relationships between belief and credence. The only view that escapes my way of formulating the problem for the deductive closure constraint is (...) in fact itself a reductive view: namely, the view that outright belief is credence 1. However, I argue that this view is unsustainable. Moreover, my version of the problem turns on no particular theory of evidence or evidential probability, and so cannot be avoided by adopting some revisionary such theory. In sum, deductive closure is in more serious, and more general, trouble than some have thought. (shrink)

Crispin Wright has articulated and defended the view that by incorporating non-evidential entitlements into our theory of knowledge, we can achieve a satisfactory reply to key skeptical challenges. Crucial to this view is the thesis that regions of thought are underpinned by ‘cornerstone’ propositions— propositions for which warrant is antecedently required in order for ordinary beliefs in that region to be supported by experiential evidence. Critics have noted that because cornerstone propositions are entailed by ordinary propositions, Closure delivers two (...) unwelcome results: (i) one can acquire evidential justification for cornerstones via deduction (alchemy); and (ii) the epistemic risk involved in accepting cornerstone propositions impugns the evidential justification we are supposed to have for ordinary propositions (leaching). It is argued here that leaching has been misdiagnosed by Wright and his critics as relying essentially on a Closure principle. Instead, it relies on a Counter-Closure-style principle. Once this point is recognized , Wright’s own solution to the leaching problem becomes unsatisfactory. However, a guiding maxim from the extant literature for demarcating true from false Counter-Closure-style principles can be usefully applied to identify a successful resolution to the leaching worry on Wright’s behalf. (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)

Radical scepticism contends that our knowledge of the external world is impossible. Particularly, radical scepticism can be motivated by the closure principle. Several commentators have noted that a straightforward way to respond to such arguments is via externalist strategies, e.g., Goldman, Greco, Bergmann. However, these externalist strategies are not effective against a slightly weaker form of the argument, a closure principle for rationally grounded knowledge, closureRK.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${closure}_{RK.}$$\end{document} The sceptical argument, (...) framed around the closureRK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {closure}_{\mathrm{RK}}$$\end{document} principle, targets rationally grounded knowledge. Although externalist strategies are ineffective against this form of argument, its conclusion can nonetheless be resisted by combining, in a novel way, the resources of Wittgenstein and Davidson. In particular, I argue that the sceptic is assuming an unrestricted way of using the closureRK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {closure}_{\mathrm{RK}}$$\end{document} principle, which is incorrect. Alternatively, I argue for The Conditionality of Rational Support Thesis, i.e., the thesis that rational support via competent deduction is conditional. In particular, rational support must be provided within an evaluative system in which hinge propositions are presupposed and contentful beliefs are being evaluated. In the end, we can resist the closureRK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {closure}_{\mathrm{RK }}$$\end{document}-based sceptical argument while retaining the closureRK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {closure}_{\mathrm{RK}}$$\end{document} principle. (shrink)

According to Fred Dretske's externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretske's epistemology is his denial that knowledge is closed under known entailment. I argue that, given Dretske's construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. Hence, if it is (...) true that, as Dretske also believes, accepting closure leads to skepticism, he must either embrace skepticism or abandon his information theory of knowledge. (shrink)

The problem of closure for the traditional unstructured possible worlds model of attitudinal content is that it treats belief and other cognitive states as closed under entailment, despite apparent counterexamples showing that this is not a necessary property of such states. One solution to this problem, which has been proposed recently by several authors (Schaffer 2005; Yalcin 2018; Hoek forthcoming), is to restrict closure in an unstructured setting by treating propositional attitudes as question-sensitive. Here I argue that (...) this line of response is unsatisfying as it stands because the problem of closure is more general than is typically discussed. A version of the problem recurs for attitudes like wondering, entertaining, considering, and so on, which are directed at questions rather than propositions. For such questioning attitudes, the appeal to question-sensitivity is much less convincing as a solution to the problem of closure. (shrink)

Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole (...) generality. This solution is based on the notion of confidence levels, which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure. (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)

The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less (...) than fully confident in one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (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)

The general principle of epistemic closure stipulates that epistemic properties are transmissible through logical means. According to this principle, an epistemic operator, say ε, should satisfy any valid scheme of inference, such as: if ε(p entails q), then ε(p) entails ε(q). The principle of epistemic closure under known entailment (ECKE), a particular instance of epistemic closure, has received a good deal of attention since the last thirty years or so. ECKE states that: if one knows that p (...) entails q, and she knows that p, then she knows that q. It is widely accepted that ECKE constitutes an important piece of the skeptical argument, but the acceptance of an unrestricted version of ECKE is still a matter of debate. On the side of the defenders of ECKE, one finds Stine (1976), Brueckner (1985), Vogel (1990), and Feldman (1995). Others proposed a refutation or a limitation of the principle, like Dretske (1970), Nozick (1981), Hales (1995), Williams (1996), and Sosa (1999). As it turns out, the relevant alternatives view (RAV) elaborated by Dretske, which restricts the scope of ECKE, has been discussed extensively and acknowledged as one of the most important contributions. There is nonetheless a major unsolved difficulty pertaining to Dretske-RAV: the notion of relevant alternatives is defined in such a way that it is bounded by counterfactual possibilities. This ontological import leaves open the door to the skeptic. Some have tried to give more precision to this notion, like Stine (1976), who appealed to a Gricean approach to define relevant alternatives in conversational contexts. My proposal is in accordance with the gist of Dretske’s strategy, i.e. to restrict the validity of ECKE, and I claim that in order to escape the difficulties inherent to RAV one has to introduce a more robust notion, the notion of epistemic context. Epistemic contexts are a subclass of propositional contexts. In that perspective, the closure property is expressed in terms of a property of a relation between epistemic contexts. ECKE holds when and only when either the epistemic context of the premisses is the same as the epistemic context of the conclusion, or the epistemic context change between the premisses and the conclusion is permissible. Permissibility of epistemic context change is a function of consistency. By means of this epistemic context approach, I will show that: (1) epistemic contexts are defined by basic propositions (unchallenged justified beliefs), (2) ECKE holds only under very specific constraints, and (3) the skeptical argument involves a non-permissible change of epistemic context and, by the same token, cannot rely upon ECKE. (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)

By deduction, we often extend both our knowledge and our justified belief. Moreover, in achieving knowledge or justified belief of some proposition, we commonly acquire justification for believing many of its entailed consequences, such as at least some of those that self-evidently follow from it. These and related facts have led some philosophers to endorse strong closure principles, for instance: If a person, S, is justified in believing a proposition, p, and p entails q, then S is (...) justified in believing q. Others have denied such principles, whether for justification or, with the appropriate additions, for knowledge. The debate continues. There is, however, this much consensus: there are difficult problems about the scope of closure, and epistemology should develop theories that can resolve them. (shrink)

This is a brief review of issues over which Henry Kyburg and I differed concerning the requirement that full beliefs should be closed under deductive consequence.

Este artigo examina a objeção ao fechamento [dedutivo] que surge no contexto de certos paradoxos epistêmicos, paradoxos cuja conclusão é que a crença justificada pode ser inconsistente. É universalmente aceito que, se essa conclusão é correta, o fechamento deve ser rejeitado, para que se evite a crença justificada em enunciados contraditórios (P, ~P). Mas, mesmo que os argumentos desses paradoxos – o paradoxo da falibilidade (do prefácio) e o paradoxo da loteria – sejam mal-sucedidos, eles, ainda assim, sugerem a existência (...) de evidência independente para uma objeção mais direta contra o fechamento. O exame do argumento da falibilidade revela uma exigência de modéstia epistêmica que viola o fechamento a partir de múltiplas premissas. A reflexão sobre o paradoxo da loteria nos confronta com um dilema em que cada alternativa fornece um contra-exemplo ao fechamento a partir de uma única premissa. Seja ou não possível a inconsistência racional, há uma objeção contra o fechamento. PALAVRAS-CHAVE – Fechamento dedutivo. Falibilidade. Paradoxo da Loteria. Paradoxo do Prefácio. Justificação. Inconsistência. ABSTRACT This paper examines the case against closure that arises in the context of certain epistemic paradoxes, paradoxes whose conclusion is that it is possible for justified belief to be inconsistent. It is generally agreed that if this conclusion is correct, closure must be rejected in order to avoid justified belief in contradictory statements (P, ~P). But even if the arguments of these paradoxes – the fallibility (preface) paradox and the lottery paradox – are unsuccessful, they nonetheless suggest independent grounds for a more direct case against closure. Examination of the fallibility argument reveals a requirement of epistemic modesty that violates multiple premise closure. Reflection on the lottery paradox presents us with a dilemma in which each alternative provides a counterexample to single premise closure. Whether or not rational inconsistency is possible, there is a case against closure. KEY WORDS – Closure. Fallibility. Lottery paradox. Preface paradox. Justification. Inconsistency. (shrink)

ABSTRACT 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 is necessary for it to be rational to believe that. The rationality of self-fulfilling beliefs is here defended against the idea that their rationality is incompatible (...) with a compelling closure principle. (shrink)

This paper contributes to the current debate about radical scepticism and the structure of warrant. After a presentation of the standard version of the radical sceptic’s challenge, both in its barest and its more refined form, three anti-sceptical responses, and their respective commitments, are being identified: the Dogmatist response, the Conservativist response and the Dretskean response. It is then argued that both the Dretskean and the Conservativist are right that the anti-sceptical hypothesis cannot inherit any perceptual warrants from ordinary propositions (...) about the environment—and so the Dogmatist response founders. However, if this is so Epistemic Closure lacks any clear rationale. There is therefore good reason to agree with both the Dretskean and the Dogmatist that perceptual warrants for ordinary propositions about the environment are enough in order for those propositions to enjoy a positive epistemic status—and so the Conservativist response founders. However, the Conservativist is nonetheless right that a warrant for the anti-sceptical hypothesis is needed. For contrary to what much of the recent literature suggests, the radical sceptic need not appeal to Epistemic Closure in order to cast doubt on the legitimacy of our beliefs in ordinary propositions about the environment: there is a Pyrrhonian version of scepticism that, though equally radical, is consistent with failure of Epistemic Closure. For this reason, the Dretskean response is insufficient to answer scepticism. (shrink)

The postulate of recovery is commonly regarded to be the intuitively least compelling of the six basic Gärdenfors postulates for belief contraction. We replace recovery by the seemingly much weaker postulate of core-retainment, which ensures that if x is excluded from K when p is contracted, then x plays some role for the fact that K implies p. Surprisingly enough, core-retainment together with four of the other Gärdenfors postulates implies recovery for logically closed belief sets. Reasonable contraction operators (...) without recovery do not seem to be possible for such sets. Instead, however, they can be obtained for non-closed belief bases. Some results on partial meet contractions on belief bases are given, including an axiomatic characterization and a non-vacuous extension of the AGM closure condition. (shrink)

According to the closure-based radical skeptical argument, it is impossible for us to have knowledge of the majority of everyday propositions because we can’t have knowledge of the denials of the skeptical hypotheses they entail (Pritchard 96). In Chapter 6 of his book Epistemology, Duncan Pritchard describes a response to this argument which uses the sensitivity principle to deny the closure principle, thereby defeating the radical skeptic’s argument. Despite Pritchard’s concerns with this solution, denying the closure principle (...) using the sensitivity principle is a plausible method of defeating the skeptic. I respond to each of his three objections in turn. First, I argue that the reason the closure principle seems so intuitively plausible (despite being false) is that we tend to consider obvious entailments, rather than skeptical hypotheses, when considering the closure principle. Unlike the skeptical hypotheses, we can know the denial of the obvious entailments because those beliefs are sensitive. Second, I will explain why not allowing for inductive knowledge is no reason to reject the sensitivity principle, as true belief gained by induction can be considered rational belief, rather than knowledge. Finally, I will argue that the sensitivity principle can, indeed, provide the necessary counterexamples to the closure principle— something Pritchard denies because he thinks the sensitivity principle demands an evaluation process that cannot be applied when considering skeptical scenarios. However, with a proper understanding of what the sensitivity principle requires, we can use it to deny the closure principle. This paper endeavours to demonstrate that Pritchard’s concerns are not sufficient reason to reject the sensitivity principle as a solution to closure-based radical skepticism. (shrink)

The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing “if θ is true then, normally, φ is true” be said to follow from a given set of items of such information. Many answers to this question have been proposed but, surprisingly, virtually none have attempted any explicit connection to belief revision. The aim of (...) this paper is to give an example of how such a connection can be made by showing how the lexicographic closure of a set of defaults may be conceptualised as a process of iterated revision by sets of sentences. Specifically we use the revision method of Nayak. (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.

I present an intractable puzzle for the currently popular view that belief is weak—the view that expressions like ‘S believes p’ ascribe to S a doxastic attitude towards p that is rationally compatible with low credence that p. The puzzle concerns issues that arise on considering beliefs in conditionals. I show that proponents of weak belief either cannot consistently apply their preferred methodology when accommodating beliefs in conditionals, or they must deny that beliefs in conditionals can be used (...) in reasoning. (shrink)

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and (...) indeed nontrivially so) and that the principles are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

In a recent essay, Tasos Kazepides has used the later Wittgenstein’s account of religious beliefs as either ‘superstitions’ or non-rational to condemn such beliefs as ‘doctrines’. By this term he means teachings which close minds to alternative truth-claims. In this paper we criticise his interpretation and use of Wittgenstein and argue that, far from closing minds, an appropriate education in religious beliefs can open minds to possible realms of existence unconsidered in other subjects of the curriculum.

In a recent essay, Tasos Kazepides has used the later Wittgenstein’s account of religious beliefs as either ‘superstitions’ or non-rational to condemn such beliefs as ‘doctrines’. By this term he means teachings which close minds to alternative truth-claims. In this paper we criticise his interpretation and use of Wittgenstein and argue that, far from closing minds, an appropriate education in religious beliefs can open minds to possible realms of existence unconsidered in other subjects of the curriculum.

In a recent essay, Tasos Kazepides has used the later Wittgenstein’s account of religious beliefs as either ‘superstitions’ or non-rational to condemn such beliefs as ‘doctrines’. By this term he means teachings which close minds to alternative truth-claims. In this paper we criticise his interpretation and use of Wittgenstein and argue that, far from closing minds, an appropriate education in religious beliefs can open minds to possible realms of existence unconsidered in other subjects of the curriculum.

There are two ways of representing rational belief: qualitatively as yes-or-no belief, and quantitatively as degrees of belief. Standard rationality conditions are: consistency and logical closure, for qualitative belief, satisfaction of the probability axioms, for quantitative belief, and a relationship between qualitative and quantitative beliefs in accordance with the Lockean thesis. In this paper, it is shown that these conditions are inconsistent with each of three further rationality conditions: fallibilism, open-mindedness, and invariance under independent (...) conceptual expansions. Restrictions of the Lockean thesis that have been suggested in the literature cannot remove the inconsistency. In the outlook we discuss two alternative ways of dealing with this problem: restricting conjunctive closure or going for a dual system account. (shrink)

Topological semantics have proved to be a very fruitful approach in formal epistemology, two noticeable representatives being the interior semantics and topological evidence models. In this paper, we introduce the concept of _quasi-factive evidence_ as a way to account for untruthful evidence in the interior semantics. This allows us to import concepts from topological evidence models, thereby connecting the two frameworks in spite of their apparent disparities. This approach sheds light on the interpretation of belief in the interior semantics, (...) and gives meaning to concepts that used to be essentially technical: the closure-interior semantics can be interpreted as the condition of existence of a _quasi-factive_ justification, while the extremally disconnected spaces are now characterized as those where the available information is always consistent. But our most important result is the equivalence between the interior-closure-interior semantics and what we call the _strengthening condition_, along with a sound and complete axiomatization. Finally, we build on this strengthening condition to introduce a notion of relative plausibility. (shrink)

Reliabilist accounts of knowledge are widely seen as having the resources for blocking sceptical arguments, since these arguments appear to rely on assumptions about the nature of knowledge that are rendered illegitimate by reliabilist accounts. The goal of this book is to assess the main arguments against the possibility of knowledge, and its conclusions challenge this consensus. The book articulates and defends a theory of knowledge that belongs firmly in the truth-tracking tradition, and argues that although the theory has the (...) resources for blocking the main standard lines of sceptical reasoning, there is a sceptical argument against which the theory offers no defence, as it doesn’t rely on any assumptions that the theory would render illegitimate. The book ends with the suggestion that the problem might have a metaphysical solution—that although the sceptical argument may make no illegitimate epistemological assumptions, it does rest on a questionable account of the nature of cognition. (shrink)

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed (...) that this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

Among the bearers of truth or falsity, there are at least some assumptions, beliefs, and claims. At least, this is how we often talk. We commonly say.