The Bradwardine-Read multiple-meanings solution to paradoxes invented in 1320s and formally reconstructed and developed in 2000s is based on the so-called “closure principle for signification”, in particular, for sentential meaning. According to this principle, sentences are assumed to signify whatever they imply. As a consequence, paradoxical sentences are proved to signify their own truth and thereby are reduced to simply false self-contradictions. One of the problems of this solution to paradoxes is that the closure principle (...) over-generates if sentences are closed under unrestricted entailment. The present proposal will introduce a restriction based on what will be called the “dynamic closure principle”: sentential meaning will be regarded as closed under the inference steps performed in the (actual or optimal) process of evaluating the respective sentence’s truth-value. (shrink)

Causal closure arguments against interactionist dualism are currently popular amongst physicalists. Such an argument appeals to some principles of the causal closure of the physical, together with certain other premises, to conclude that at least some mental events are identical with physical events. However, it is crucial to the success of any such argument that the physical causal closure principle to which it appeals is neither too strong nor too weak by certain standards. In this paper, (...) it is argued that various forms of naturalistic dualism, of an emergentist character, are consistent with the strongest physical causal closure principles that can plausibly be advocated. (shrink)

Todd and Rabern (2021) have argued that if we assume that future contingents are untrue and if we accept the Retro-closure principle (???? → PF(????)), then the existence of a temporal omniscient entity becomes metaphysically impossible. Since the truth of a metaphysical and theological theory should not be dependent on questions of temporal semantics, Todd and Rabern conclude that, if one wishes to maintain that future contingents are untrue, one must abandon the Retro-closure principle. The aim (...) of this paper is to propose a temporal semantics system in which future contingents are untrue, the Retro-closure principle is valid, and the possibility of the existence of an omniscient and temporal being is guaranteed. (shrink)

Sharon Ryan (2000) argues against one epistemic closure principle but defends another one. I argue that the phenomenon of blameless propositional recognition failure provides a counter-example to this closure principle. I suggest a revision to the closure principle to make it immune to this sort of counter-example.

This paper evaluates a number of closure principles (for both knowledge and justification) that have appeared in the literature. Counterexamples are presented to all but one of these principles, which is conceded to be true but trivially so. It is argued that a consequence of the failure of these closure principles is that certain projects of doxastic logic are doomed, and that doxastic logic is of dubious merit for epistemologists interested in actual knowers in the actual world.

Most of us think we can always enlarge our knowledge base by accepting things that are entailed by (or logically implied by) things we know. The set of things we know is closed under entailment (or under deduction or logical implication), which means that we know that a given claim is true upon recognizing, and accepting thereby, that it follows from what we know. However, some theorists deny that knowledge is closed under entailment, and the issue remains controversial. The arguments (...) against closure include the following. (shrink)

A dispute in epistemology has arisen over whether some class of things epistemic (things known or justified, for example) is closed under some operation involving the notion of what follows deductively from members of this class. Very few philosophers these days believe that if you know that p, and p entails q, then you know that q. But many philosophers think that something weaker holds, for instance that if you know that p, and p entails q, then you are in (...) a position to know that p, or if you know that p and you competently deduce p from q, then you know that q. However there are some considerations tracing back to Wittgenstein’s On Certainty and some early work by Fred Dretske that suggests even these weaker principles are false. (shrink)

The conservation laws do not establish the central premise within the argument from causal overdetermination – the causal completeness of the physical domain. Contrary to David Papineau, this is true even if there is no non-physical energy. The combination of the conservation laws with the claim that there is no non-physical energy would establish the causal completeness principle only if, at the very least, two further causal claims were accepted. First, the claim that the only way that something non-physical (...) could affect a physical system is by affecting the amount of energy or momentum within it, or redistributing the energy and momentum within it. Second, the claim that redistribution of energy and momentum cannot be brought about without supplying energy or momentum. Both of these claims, however, are exceedingly difficult to defend in the context of the argument. (shrink)

This is an encyclopedia article about epistemic closure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.

When people learn normative systems, they do so based on limited evidence. Many of the possible actions that are available to an agent have never been explicitly permitted or prohibited. But people will often need to figure out whether those unspecified actions are permitted or prohibited. How does a learner resolve this incompleteness? The learner might assume if an action-type is not expressly forbidden, then acts of that type are permitted. This closure principle is one of Liberty. Alternatively, (...) the learner might assume that if an action-type is not expressly permitted, then acts of that type are prohibited. This closure principle would be one of Residual Prohibition (Mikhail, 2011). On the basis of principles of pedagogical sampling (e.g., Shafto, Goodman, & Griffiths, 2014), we predicted that participants would infer the Liberty Principle (LP) when trained on prohibitions, and they would infer the Residual Prohibition Principle when trained on permissions. This is exactly what we found across several experiments. We also found a bias in favor of Liberty insofar as participants trained on both a prohibition and a permission rule tended still to infer the LP. However, we also found that if an action is potentially harmful, this diminishes the tendency to infer the LP. (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)

We plead for a fluid margin, or mixed/indeterminate buffer zone, between Physical and Non-Physical Causal Closures, and for a Neutrosophic Causal Closure Principle claiming that the chances of all physical effects are determined by their prior partially physical and partially non-physical causes.

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)

Does a factive conception of knowability figure in ordinary use? There is some reason to think so. ‘Knowable’ and related terms such as ‘discoverable’, ‘observable’, and ‘verifiable’ all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn’t say that we were. A’s remarks (...) sound contradictory. In this context the factivity of ‘someone might discover that’ explains this fact. So there is some reason to believe that knowability and related modalities are factive in ordinary use. For factive treatments of knowability in the context of epistemic theories of truth, compare Tennant (2000: 829) and Wright (2001: 59-60, n. 17). (shrink)

Is there a plausible argument for external world skepticism? Robert Nozick’s well-known discussion focuses upon arguments which utilize the Sensitivity Requirement and the Closure Principle. Nozick claims, correctly, that no such argument succeeds. But he gets almost all the details wrong. The Sensitivity Requirement and the Closure Principle are compatible; the Sensitivity Requirement is incorrect; and even if true, the Closure Principle is structurally incapable of generating a plausible and valid global skeptical argument. It (...) is therefore a mistake to take the Closure Principle as central in discussions of skepticism. The paper concludes by examining the prospects for a plausible skeptical argument. (shrink)

The canonical version of external world scepticism has the following structure: Premise1: If P knows that she is not a brain in a vat, then P does not have knowledge of the external world. Premise2: P does not know that she is not a brain in a vat. Conclusion: Therefore, P does not have knowledge of the external world. Some philosophers attack premise1 by denying the underlying closure principle. I will investigate possible argumentations for and against premise2. I (...) will show that premise2 is only true if additional internalistic conditions are fulfilled. I will conclude that the canonical version of the argument is inadequate and that premise1 must be replaced by a stronger internalistic premise. After presenting the adequate argument, I will argue that this internalistic premise contradicts the closure principle underlying premise1. I will conclude that external world scepticism can only hold if the closure principle is rejected. (shrink)

This paper focuses on a potential problem with Sosa’s theory of default assumption, viz., the alleged incompatibility of this theory with the closure principle. Given the similarity between the notion of default assumption and Wittgenstein’s notion of hinge commitment, I suggest that two influential hinge epistemologies including Wright’s entitlement theory and Pritchard’s non-belief theory provide resources for possible solutions to the problem. I argue that default assumption should be classified as acceptance and hence as a non-doxastic propositional attitude. (...) Sosa’s theory can deal with the apparent incompatibility with the closure principle by adopting the solution of the non-belief theory, while also avoiding problems affecting the latter view. (shrink)

Anthony Brueckner has argued that claims about underdetermination of evidence are suppressed in closure-based scepticism (“The Structure of the Skeptical Argument”, Philosophy and Phenomenological Research 54:4, 1994). He also argues that these claims about underdetermination themselves lead to a paradoxical sceptical argument—the underdetermination argument—which is more fundamental than the closure argument. If Brueckner is right, the status quo focus of some predominant anti-sceptical strategies may be misguided. In this paper I focus specifically on the relationship between these two (...) arguments. I provide support for Brueckner’s claim that the underdetermination argument is the more fundamental sceptical argument. I do so by responding to a challenge to this claim put forward by Stewart Cohen (“Two Kinds of Skeptical Argument”, Philosophy and Phenomenological Research 58:1, 1998). Cohen invokes an alternative epistemic principle which he thinks can be used to challenge Brueckner. Cohen’s principle raises interesting questions about the relationship between evidential considerations and explanatory considerations in the context of scepticism about our knowledge of the external world. I explore these questions in my defence of Brueckner. (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)

Closure principles loom large in recent internalist critiques of epistemic externalism. Cohen (Philos Phenomenol Res 65:309–329, 2002, Philos Phenomenol Res 70:417–430, 2005), Vogel (J Philos 97:602–623, 2000), and Fumerton (Meta-Epistemology and skepticism. Rowman and Littlefield, Lanham, 1995) argue that, given closure, epistemic externalism is committed to the possibility of implausibly easy knowledge. By contrast, Zalabardo (Philos Rev 114:33–61, 2005) proposes that epistemic closure actually precludes the possibility of easy knowledge, and appeals to closure principles to solve (...) the problem of easy knowledge. In my view, disagreement over closure’s bearing on externalism and the problem of easy knowledge is rooted in a failure to bear in mind the familiar distinction between ex ante and ex post forms of epistemic justification and warrant. When this distinction is kept in focus, the result is clear: epistemic closure provides no relief from the problem of easy knowledge. (shrink)

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

It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset (...) of the natural numbers. (shrink)

Contemporary discussions of skepticism often frame the skeptic's argument around an instance of the closure principle. Roughly, the closure principle states that if a subject knows p, and knows that p entails q, then the subject knows q. The main contention of this paper is that the closure argument for skepticism is defective. We explore several possible classifications of the defect. The closure argument might plausibly be classified as begging the question, as exhibiting transmission (...) failure, or as structurally inefficient. Interestingly, perhaps, each of these has been proposed as the correct classification of Moore's proof of an external world. (shrink)

Those of us who have followed Fred Dretske’s lead with regard to epistemic closure and its impact on skepticism have been half-wrong for the last four decades. But those who have opposed our Dretskean stance, contextualists in particular, have been just wrong. We have been half-right. Dretske rightly claimed that epistemic status is not closed under logical implication. Unlike the Dretskean cases, the new counterexamples to closure offered here render every form of contextualist pro-closure maneuvering useless. But (...) there is a way of going wrong under Dretske’s lead. As the paper argues, Cartesian skepticism thrives on closure failure in a way that is yet to be acknowledged in the literature. The skeptic can make do with principles which are weaker than the familiar closure principles. But I will further claim that this is only a momentary reprieve for the skeptic. As it turns out, one of the weaker principles on which a skeptical modus tollens must rest can be shown false. (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 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)

Single-premise epistemic closure is the principle that: if one is in an evidential position to know that P where P entails Q, then one is in an evidential position to know that Q. In this paper, I defend the viability of opposition to closure. A key task for such an opponent is to precisely formulate a restricted closure principle that remains true to the motivations for abandoning unrestricted closure but does not endorse particularly egregious (...) instances of closure violation. I focus on two brands of epistemic theory that naturally incorporate closure restrictions. The first type holds that the truth value of a knowledge ascription is relative to a relevant question. The second holds that the truth value of a knowledge ascription is relative to a relevant topic. For each approach, I offer a formalization of a leading theory from the literature and use this formalization to evaluate the theory’s adequacy in terms of a precise set of desiderata. I conclude that neither theory succeeds in meeting these desiderata, casting doubt on the viability of the underlying approaches. Finally, I offer a novel variant of the topic-sensitive approach that fares better. (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)

The topic of this paper may be introduced by fast zooming in and out of the philosophy of information. In recent years, philosophical interest in the nature of information has been increasing steadily. This has led to a focus on semantic information, and then on the logic of being informed, which has attracted analyses concentrating both on the statal sense in which S holds the information that p (this is what I mean by logic of being informed in the rest (...) of this article) and on the actional sense in which S becomes informed that p. One of the consequences of the logic debate has been a renewed epistemological interest in the principle of information closure (henceforth PIC), which finally has motivated a revival of a skeptical objection against its tenability first made popular by Dretske. This is the topic of the paper, in which I seek to defend PIC against the skeptical objection. If I am successful, this means – and we are now zooming out – that the plausibility of PIC is not undermined by the skeptical objection, and therefore that a major epistemological argument against the formalization of the logic of being informed based on the axiom of distribution in modal logic is removed. But since the axiom of distribution discriminates between normal and non-normal modal logics, this means that a potentially good reason to look for a formalization of the logic of being informed among the non-normal modal logics, which reject the axiom, is also removed. And this in turn means that a formalization of the logic of being informed in terms of the normal modal logic B (also known as KTB) is still very plausible, at least insofar as this specific obstacle is concerned. In short, I shall argue that the skeptical objection against PIC fails, so it is not a good reason to abandon the normal modal logic B as a good formalization of the logic of being informed. (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)

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)

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)

Closure is the central premise in one of the best arguments for physicalism—the argument from causal overdetermination. According to Closure, at every time at which a physical event has a sufficient cause, it has a sufficient physical cause. This principle is standardly defended by appealing to the fact that it enjoys empirical support from numerous confirming cases (and no disconfirming cases) in physics. However, in recent literature on mental causation, attempts have been made to provide a stronger (...) argument for it. This essay argues that, insofar as these attempts are successful, they actually establish a far stronger closure principle. Worryingly, the acceptance of this stronger principle presents a new problem for the most popular form of physicalism, that of nonreductive physicalism. The problem shall be referred to as the 'Problem of Strong Closure.'. (shrink)

Physicalism is the idea that everything either is physical or is nothing over and above the physical. For this formulation of physicalism to have determinate content, it should be identified what the “physical” refers to; i.e. the body problem. Some other closely related theses, especially the ones employed in the causal arguments for different versions of physicalism, and more especially the causal closure thesis, are also subject to the body problem. In this paper, I do two things. First, I (...) explore the structure of causal arguments for physicalism that represents a general argument. To do this, the premises and the conclusion of the general argument are given exact formulations. Second, drawing on those premises, especially the causal closure thesis, I propose a naturalistic formulation of the physical that satisfies the requirements any formulation of the physical is expected to fulfill. Following this proposal, we also have a recursive algorithm to recognize the set of all physical events. (shrink)

Bradwardine’s solution to the the logical paradoxes depends on the idea that every sentence signifies many things, and its truth depends on things’ being wholly as it signifies. This idea is underpinned by his claim that a sentence signifies everything that follows from what it signifies. But the idea that signification is closed under entailment appears too strong, just as logical omniscience is unacceptable in the logic of knowledge. What is needed is a more restricted closure principle. A (...) clue can be found in speech act pluralism, whereby indirect speech reports are closed under intersubstitutivity of co-referential terms. The conclusion is that solving the semantic paradoxes does not require revision of logic, thus saving logic from paradox. (shrink)

Ever since Fred Dretske (1970) questioned closure, a denial of this principle has been among the standard options for a resolution of epistemological paradoxes such as the skeptical paradox (Cohen 1988) and the lottery paradox (Harman 1973). In this article, the author shall argue that all possible solutions of the latter paradox can only be defended if Multi-Premise Closure is rejected. These possible solutions are contextualism and both simple and sensitive moderate invariantism. It will be shown that (...) skepticism and the denial of Single-Premise Closure are not possible solutions of the lottery paradox. The upshot of the discussion here will be that while Single-Premise Closure is beyond reasonable doubt, resolving the lottery paradox forces one to abandon Multi-Premise Closure. (shrink)

In contemporary epistemology, sceptical arguments are motivated either by the closure principle or the underdetermination principle. Therefore, it is very important to figure out the structure of the sceptical argument before coming up with an anti-sceptic strategy. With a review of the debate on the relationship between the two principles from Anthony Brueckner to Kevin McCain, it is argued that while maintaining the weak closed justification , closure and underdetermination are not logically equivalent. As a result, (...) two independent responses are needed to answer the sceptical problem satisfactorily. Also, in order to secure a philosophically significant notion of justification and evidence, reasons are given to hold WCJ*, as opposed to rejecting it. This understanding of the sceptical argument would help to focus the real challenge of scepticism. (shrink)

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)

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)

Those of us who have followed Fred Dretske's lead with regard to epistemic closure and its impact on skepticism have been half-wrong for the last four decades. But those who have opposed our Dretskean stance, contextualists in particular, have been just wrong. We have been half-right. Dretske rightly claimed that epistemic status is not closed under logical implication. Unlike the Dretskean cases, the new counterexamples to closure offered here render every form of contextualist pro-closure maneuvering useless. But (...) there is a way of going wrong under Dretske's lead. As the paper argues, Cartesian skepticism thrives on closure failure in a way that is yet to be acknowledged in the literature. The skeptic can make do with principles which are weaker than the familiar closure principles. But I will further claim that this is only a momentary reprieve for the skeptic. As it turns out, one of the weaker principles on which a skeptical modus tollens must rest can be shown false. (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)

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)

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)

Graham and Maitzen think my CORNEA principle is in trouble because it entails “intolerable violations of closure under known entailment.” I argue that the trouble arises from current befuddlement about closure itself, and that a distinction drawn by Rudolph Carnap, suitably extended, shows how closure, when properly understood, works in tandem with CORNEA. CORNEA does not obey Closure because it shouldn’t: it applies to “dynamic” epistemic operators, whereas closure principles hold only for “static” ones. (...) What the authors see as an intolerable vice of CORNEA is actually a virtue, helping us see what closure principles should—and shouldn’t—themselves be about. (shrink)