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)

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

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)

In this article, “Narrative Closure,” a theory of the nature of narrative closure is developed. Narrative closure is identified as the phenomenological feeling of finality that is generated when all the questions saliently posed by the narrative are answered. The article also includes a discussion of the intelligibility of attributing questions to narratives as well as a discussion of the mechanisms that achieve this. The article concludes by addressing certain recent criticisms of the view of narrative expounded (...) by this article. (shrink)

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)

Tracking theories of knowledge are widely known to have the consequence that knowledge is not closed. Recent arguments by Vogel and Hawthorne claim both that there are no legitimate examples of knowledge without closure and that the costs of theories that deny closure are too great. This paper considers the tracking theories of Dretske and Nozick and the arguments by Vogel and Hawthorne. We reject the arguments of Vogel and Hawthorne and evaluate the costs of closure denial (...) for tracking theories of knowledge. (shrink)

Classical neo-Darwinian explanations do not fully account for changes in biological forms, and new theories have emerged, primarily in maths and physics, that offer new approaches to the problem of the origin of life and phenomena of order in evolution. This volume focuses on the role of closure at various hierarchical levels as the catalyst between self-organization and selection. Participants addressed special areas of the closure problem such as autopoiesis and autocatalysis and function and selection, and semiosis. Presentations (...) on physical and mathematical modelling are included. The book seeks to clarify the role closure plays in explaining the emergence, development and evolution of structurally stable systems at the thermodynamic, chemical and biochemical, biological, psychological and cultural levels. (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)

Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact (...) that agents do not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. (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)

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)

Christoph Jäger (2004) argues that Dretske's information theory of knowledge raises a serious problem for his denial of closure of knowledge under known entailment: Information is closed under known entailment (even under entailment simpliciter); given that Dretske explains the concept of knowledge in terms of "information", it is hard to stick with his denial of closure for knowledge. Thus, one of the two basic claims of Dretske would have to go. Since giving up the denial of closure (...) would commit Dretske to skepticism, it would most probably be better to rather give up the information-theoretic account of knowledge. But that means that one of the best externalist views of knowledge has to be given up. I argue here that Jäger is mistaken and that there is no problem for Dretske. There is a rather easy way out of Jäger’s problem. (shrink)

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

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)

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

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 argument from causal closure of the physical is usually considered the most powerful argument in favor of the ontological doctrine of physicalism. Many authors, most notably Papineau, assume that CCP implies that physicalism is supported by physics. I demonstrate, however, that physical science has no bias in the ontological debate between proponents of physicalism and dualism. I show that the arguments offered for CCP are effective only against the accounts of mental causation based on the action of the (...) mental forces of a Newtonian nature, i.e. those which manifest themselves by causing accelerations. However, it is conceivable and possible that mental causation is manifested through the redistribution of energy, momentum and other conserved quantities in the system, brought about by altering the state probability distribution within the living system and leading to anomalous correlations of neural processes. After arguing that a probabilistic, interactionist model of mental causation is conceivable, which renders the argument from causal closure of the physical ineffective, I point to some basic features that such a model must have in order to be intelligible. At the same time, I indicate the way that conclusive testing of CCP can be done within the theoretical framework of physics. (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)

The argument from causal closure of the physical is usually considered the most powerful argument in favor of the ontological doctrine of physicalism. Many authors, most notably Papineau, assume that CCP implies that physicalism is supported by physics. I demonstrate, however, that physical science has no bias in the ontological debate between proponents of physicalism and dualism. I show that the arguments offered for CCP are effective only against the accounts of mental causation based on the action of the (...) mental forces of a Newtonian nature, i.e. those which manifest themselves by causing accelerations. However, it is conceivable and possible that mental causation is manifested through the redistribution of energy, momentum and other conserved quantities in the system, brought about by altering the state probability distribution within the living system and leading to anomalous correlations of neural processes. After arguing that a probabilistic, interactionist model of mental causation is conceivable, which renders the argument from causal closure of the physical ineffective, I point to some basic features that such a model must have in order to be intelligible. At the same time, I indicate the way that conclusive testing of CCP can be done within the theoretical framework of physics. (shrink)

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

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)

Deduction is important to scientific inquiry because it can extend knowledge efficiently, bypassing the need to investigate everything directly. The existence of closure failure—where one knows the premises and that the premises imply the conclusion but nevertheless does not know the conclusion—is a problem because it threatens this usage. It means that we cannot trust deduction for gaining new knowledge unless we can identify such cases ahead of time so as to avoid them. For philosophically engineered examples we have (...) “inner alarm bells” to detect closure failure, but in scientific investigation we would want to use deduction for extension of our knowledge to matters we don’t already know that we couldn’t know. Through a quantitative treatment of how fast probabilistic sensitivity is lost over steps of deduction, I identify a condition that guarantees that the growth of potential error will be gradual; thus, dramatic closure failure is avoided. Whether the condition is fulfilled is often obvious, but sometimes it requires substantive investigation. I illustrate that not only safe deduction but the discovery of dramatic closure failures can lead to scientific advances. (shrink)

Closure is the epistemological thesis that if S knows that P and knows that P implies Q, then if S infers that Q, S knows that Q. Fred Dretske acknowledges that closure is plausible but contends that it should be rejected because it conflicts with the plausible thesis: Conclusive reasons (CR): S knows that P only if S believes P on the basis of conclusive reasons, i.e., reasons S wouldn‘t have if it weren‘t the case that P. Dretske (...) develops an analysis of knowing that centers on CR, and argues that the requirement undermines skepticism by implying the falsity of closure. We develop a Dretske-style analysis of knowing that incorporates CR, and we argue that this analysis not only accords with closure, but also implies it. In addition, we argue that the analysis accounts for the prima facie plausibility of closure-invoking skeptical arguments, and nonetheless implies that they are fallacious. If our arguments turn out to be sound, the acceptability of Dretske‘s analysis of knowing will be significantly enhanced by the fact that, despite implying closure, it undermines closure-based skepticism. (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.

How should the contrastivist formulate closure? That is, given that knowledge is a ternary contrastive state Kspq (s knows that p rather than q), how does this state extend under entailment? In what follows, I will identify adequacy conditions for closure, criticize the extant invariantist and contextualist closure schemas, and provide a contrastive schema based on the idea of extending answers. I will conclude that only the contrastivist can adequately formulate closure.

In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look (...) for a formalization of the logic of “ $S$ is informed that $p$ ” among the non-normal modal logics, which reject the axiom, is also removed. This is not to argue that the logic of “ $S$ is informed that $p$ ” should be a normal modal logic, but that it could still be insofar as the objection that it could not be, based on the sceptical objection against pic, has been removed. In other word, I shall argue that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B (also known as KTB) as a formalization of “ $S$ is informed that $p$ ”, which remains plausible insofar as this specific obstacle is concerned. (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.

Epistemic closure refers to the assumption that humans are able to recognize what entails or contradicts what they believe and know, or more accurately, that humans’ epistemic states are closed under logical inferences. Epistemic closure is part of a larger theory of mind ability, which is arguably crucial for downstream NLU tasks, such as inference, QA and conversation. In this project, we introduce a new automatically constructed natural language inference dataset that tests inferences related to epistemic closure. (...) We test and further fine tune the model RoBERTa-large-mnli on the new dataset, with limited positive results. (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)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty (...) in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

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)

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)

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)

K-axiom-based epistemic closure for explicit knowledge is rejected for even the most trivial cases of deductive inferential reasoning on account of the fact that the closure axiom does not extend beyond a raw consequence relation. The recognition that deductive inference concerns interaction as much as it concerns consequence allows for perspectives from logics of multi-agent information flow to be refocused onto mono-agent deductive reasoning. Instead of modeling the information flow between different agents in a communicative or announcement setting, (...) we model the information flow between different states of a single agent as that agent reasons deductively. The resource management of the database of agent states for the deductive reasoning fragment in question is covered by the residuated structure that encodes the nonassociative Lambek Calculus with permutation, bottom, and identity: NLP01. (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)

According to the principle of epistemic closure, knowledge is closed under known implication. The principle is intuitive but it is problematic in some cases. Suppose you know you have hands and you know that ‘I have hands’ implies ‘I am not a brain-in-a-vat’. Does it follow that you know you are not a brain-in-a-vat? It seems not; it should not be so easy to refute skepticism. In this and similar cases, we are confronted with a puzzle: epistemic closure (...) is an intuitive principle, but at times, it does not seem that we know by implication. In response to this puzzle, the literature has been mostly polarized between those who are willing to do away with epistemic closure and those who think we cannot live without it. But there is a third way. Here I formulate a restricted version of the principle of epistemic closure. In the standard version, the principle can range over any proposition; in the restricted version, it can only range over those propositions that are within the limits of a given epistemic inquiry and that do not constitute the underlying assumptions of the inquiry. If we adopt the restricted version, I argue, we can preserve the advantages associated with closure, while at the same time avoiding the puzzle I’ve described. My discussion also yields an insight into the nature of knowledge. I argue that knowledge is best understood as a topic-restricted notion, and that such a conception is a natural one given our limited cognitive resources. (shrink)

In this paper, we advocate the idea that an adequate explanation of biological systems requires appealing to organizational closure as an emergent causal regime. We first develop a theoretical justification of emergence in terms of relatedness, by arguing that configurations, because of the relatedness among their constituents, possess ontologically irreducible properties, providing them with distinctive causal powers. We then focus on those emergent causal powers exerted as constraints, and we claim that biological systems crucially differ from other natural systems (...) in that they realize a closure of constraints, i.e. a second-order emergent regime of causation such that the constituents, each of them acting as a constraint, realize a mutual dependence among them, and are collectively able to self-maintain. Lastly, we claim that closure can be justifiably taken as an emergent regime of causation, without admitting that it inherently involves whole-parts causation, which would require to commit to stronger ontological and epistemological assumptions. (shrink)

Information processing in neural systems can be described and analysed at multiple spatiotemporal scales. Generally, information at lower levels is more fine-grained but can be coarse-grained at higher levels. However, only information processed at specific scales of coarse-graining appears to be available for conscious awareness. We do not have direct experience of information available at the scale of individual neurons, which is noisy and highly stochastic. Neither do we have experience of more macro-scale interactions, such as interpersonal communications. Neurophysiological evidence (...) suggests that conscious experiences co-vary with information encoded in coarse-grained neural states such as the firing pattern of a population of neurons. In this article, we introduce a new informational theory of consciousness: Information Closure Theory of Consciousness (ICT). We hypothesise that conscious processes are processes which form non-trivial informational closure (NTIC) with respect to the environment at certain coarse-grained scales. This hypothesis implies that conscious experience is confined due to informational closure from conscious processing to other coarse-grained scales. ICT proposes new quantitative definitions of both conscious content and conscious level. With the parsimonious definitions and a hypothesise, ICT provides explanations and predictions of various phenomena associated with consciousness. The implications of ICT naturally reconcile issues in many existing theories of consciousness and provides explanations for many of our intuitions about consciousness. Most importantly, ICT demonstrates that information can be the common language between consciousness and physical reality. (shrink)

This note shows that for the proof of the existence and uniqueness of the algebraic closure of a field one needs only the Boolean Ultrafilter Theorem.

This article is a response to an important objection that Sherrilyn Roush has made to the standard closure-based argument for skepticism, an argument that has been studied over the past couple of decades. If Roush's objection is on the mark, then this would be a quite significant finding. We argue that her objection fails.

This paper argues against common views that at least in many cases Robert Nozick is not forced to deny common closure principles. More importantly, Nozick does not – despite first (and second) appearances and despite his own words – deny closure. On the contrary, he is defending a more sophisticated and complex principle of closure. This principle does remarkably well though it is not without problems. It is surprising how rarely Nozick’s principle of closure has been (...) discussed. He should be seen not so much as a denier of closure than as someone who’s proposing an alternative, more complex principle of closure. (shrink)

This paper argues that if knowledge is defined in terms of probabilistic tracking then the benefits of epistemic closure follow without the addition of a closure clause. (This updates my definition of knowledge in Tracking Truth 2005.) An important condition on this result is found in "Closure Failure and Scientific Inquiry" (2017).

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or epistemic rationality ) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.

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)

D’Aquino et al. (J Symb Log 75(1):1–11, 2010) have recently shown that every real-closed field with an integer part satisfying the arithmetic theory IΣ4 is recursively saturated, and that this theorem fails if IΣ4 is replaced by IΔ0. We prove that the theorem holds if IΣ4 is replaced by weak subtheories of Buss’ bounded arithmetic: PV or $${\Sigma^b_1-IND^{|x|_k}}$$. It also holds for IΔ0 (and even its subtheory IE 2) under a rather mild assumption on cofinality. On the other hand, it (...) fails for the extension of IOpen by an axiom expressing the Bézout property, even under the same assumption on cofinality. (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)

Lawson provides a comprehensive look at the history of western thought, the evolution of science and its attempts to provide us with a "theory of everything" and an evaluation of the relativist multiple truths. He discusses why this scientific mind-set no longer works and why relativist truths are no longer sustainable. He then offers a new theory to help us better understand ourselves and our world.