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

It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for (...) rejecting single premise closure. Because of the symmetry between the principles, they come as a package: either both will have to be rejected or both will have to be revised. (shrink)

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)

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)

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)

John Hawthorne has two forceful arguments in favour of:Single-Premise Closure Necessarily, if S knows p, competently deduces q from p, and thereby comes to believe q, while retaining knowledge of p throughout, then S knows q.Each of Hawthorne's arguments rests on an intuitively appealing principle which Hawthorne calls the Equivalence Principle. I show, however, that the opponents of SPC with whom he's engaging - namely Fred Dretske and Robert Nozick - have independent reason to reject this principle, (...) and resultantly conclude that Hawthorne's arguments in favour of SPC are not knock-down. (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)

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.

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)

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

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)

According to the principle of Knowledge Counter-Closure , knowledge-yielding single-premise deduction requires a known premise: if S believes q solely on the basis of deduction from p, and S knows q, then S must know p. Although prima facie plausible, widely accepted, and supported by seemingly compelling motivations, KCC has recently been challenged by cases where S arguably knows q solely on the basis of deduction from p, yet p is false or p is true but (...) not known . I explore a view that resolves this tension by abandoning KCC in the light of these challenges, and which acknowledges their force but also their limits. Adopting this view helps identify the epistemic constraints that operate on the premises of knowledge-yielding deduction, clarifies the epistemic role of deduction, and allows us to distil the kernel of truth in the motivations that are standardly taken to support KCC. (shrink)

Harman’s lottery paradox, generalized by Vogel to a number of other cases, involves a curious pattern of intuitive knowledge ascriptions: certain propositions seem easier to know than various higher-probability propositions that are recognized to follow from them. For example, it seems easier to judge that someone knows his car is now on Avenue A, where he parked it an hour ago, than to judge that he knows that it is not the case that his car has been stolen and driven (...) away in the last hour. Contextualists have taken this pattern of intuitions as evidence that ‘knows’ does not always denote the same relationship; subject-sensitive invariantists have taken this pattern of intuitions as evidence that non-traditional factors such as practical interests figure in knowledge; still others have argued that the Harman Vogel pattern gives us a reason to abandon the principle that knowledge is closed under known entailment. This paper argues that there is a psychological explanation of the strange pattern of intuitions, grounded in the manner in which we shift between an automatic or heuristic mode of judgment and a controlled or systematic mode. Understanding the psychology behind the pattern of intuitions enables us to see that the pattern gives us no reason to abandon traditional intellectualist invariantism. The psychological account of the paradox also yields new resources for clarifying and defending the single premise closure principle for knowledge ascriptions. (shrink)

Despite their substantial appeal, closure principles have fallen on hard times. Both anti-luck conditions on knowledge and the defeasibility of knowledge look to be in tension with natural ways of articulating single-premise closure principles. The project of this paper is to show that plausible theses in the epistemology of testimony face problems structurally identical to those faced by closure principles. First I show how Lasonen-Aarnio’s claim that there is a tension between single premise (...) closure and anti-luck constraints on knowledge can be extended to make trouble for transmission theses. Second, I show how Schechter’s claim that there is a tension between single premise closure and the thought that knowledge is defeasible can be extended to make trouble for transmission theses. I end the paper by sketching the consequences of this trouble for the dialectic in the epistemology of testimony. (shrink)

In ‘Single premise deduction and risk’ (2008) Maria Lasonen-Aarnio argues that there is a kind of epistemically threatening risk that can accumulate over the course of drawing single premise deductive inferences. As a result, we have a new reason for denying that knowledge is closed under single premise deduction—one that mirrors a familiar reason for denying that knowledge is closed under multiple premise deduction. This sentiment has more recently been echoed by others (see (...) Schechter 2011). In this paper, I will argue that, although there is a kind of risk that can accumulate over the course of drawing single premise deductive inferences, it is importantly different to the kind of risk that multiple premise deductive inferences can introduce. Having distinguished these two kinds of risk, I shall offer some reasons for thinking that the kind associated with single premise deductions is, in fact, epistemically benign—it poses no threat, in and of itself, to the knowledge status of a belief. If this is right, then Lasonen-Aarnio’s argument against single premise closure is unsuccessful. (shrink)

John Hawthorne’s recent monograph Knowledge and Lotteries1 is centred on the following puzzle: Suppose you claim to know that you will not be able to afford to summer in the Hamptons next year. Aware of your modest means, we believe you. But suppose you also claim to know that a ticket you recently purchased in a multi-million dollar lottery is a loser. Most of us have the intuition that you do not know that your ticket is a loser. However, your (...) alleged knowledge of not being able to afford to summer in the Hamptons puts you in a position to know that your ticket is a loser. For the proposition that you will not be able to afford to summer in the Hamptons entails the proposition that you will lose the lottery. And the following principle, what Hawthorne calls ‘Single Premise Closure’ ( p. 34), is very plausible: If you know that p, p entails q, and you competently deduce q from p thereby coming to believe that q (all the while retaining your knowledge of p), then you come to know q. (shrink)

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

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.

The principle of Counter-Closure embodies the widespread view that when a proposition is believed solely as the conclusion of single-premise deduction, it can be known only if the premise is also known. I raise a problem for the compatibility of Jason Stanley's Interest-Relative Invariantism (IRI) with Counter-Closure. I explore the landscape of options that might help Stanley resolve this tension and argue that a trilemma confronts Stanley: he must either (i) renounce a key intuition that (...) lies at the foundation of his view; or (ii) admit into his epistemology an IRI-specific novel brand of Gettier case; or (iii) abandon Counter-Closure. (shrink)

In this paper we investigate some families of decision problems associated with a restricted class of Post canonical forms, specifically, those defined over one-letter alphabets whose productions have single premises and contain only one variable. For brevity sake, we call any such form an RPCF (Restricted Post Canonical Form). Constructive proofs are given which show, for any prescribed nonrecursive r.e. many-one degree of unsolvability D, the existence of an RPCF whose word problem is of degree D and an RPCF (...) with axiom whose decision problem is also of degree D. Finally, we show that both of these results are best possible in that they do not hold for one-one degrees. (shrink)

This paper argues that the agent concerned to have accurate (outright) beliefs will have a consistent and multi-premise closed belief set, and not a (merely) single-premise closed and (merely) pairwise consistent belief set, as has often been thought. This argument rests on the fact that we need a notion of accuracy coherence for belief that is belief-sensitive; sensitive to one's perspective, in a way that the standard belief-insensitive notion of accuracy coherence is not. The choice of the (...) belief-sensitive over belief-insensitive notion is defended, as is the choice of this particular belief-sensitive kind of accuracy coherence over other belief-sensitive rivals. Our conclusion is that accurate believers are deductively cogent. (shrink)

While globalization is largely theorized in terms of trans-border flows, this article suggests an exploratory sociological framework for analyzing globalization as consisting of systemic processes of closure and containment. The suggested framework points at the emergence of a global mobility regime that actively seeks to contain social movement both within and across borders. The mobility regime is theorized as premised upon a pervasive “paradigm of suspicion” that conflates the perceived threats of crime, immigration, and terrorism, thus constituting a conceptual (...) blueprint for the organization of global risk-management strategies. The article draws on multiple examples, singling out some elementary forms of the mobility regime, emphasizing the sociological affinity between guarded borders on the one hand and gated communities on the other. In particular, the article aims at theorizing the translation of the paradigm of suspicion into actual technologies of social screening designed to police the mobility of those social elements that are deemed to belong to suspect social categories. Specifically, the article points at biosocial profiling as an increasingly dominant technology of intervention. Biosocial profiling, in turn, is theorized in juxtaposition to other modalities of power, namely, legal and disciplinary measures. (shrink)

The primary objective of this paper is to introduce a new epistemic paradox that puts pressure on the claim that justification is closed under multi premise deduction. The first part of the paper will consider two well-known paradoxes—the lottery and the preface paradox—and outline two popular strategies for solving the paradoxes without denying closure. The second part will introduce a new, structurally related, paradox that is immune to these closure-preserving solutions. I will call this paradox, The Paradox (...) of the Pill. Seeing that the prominent closure-preserving solutions do not apply to the new paradox, I will argue that it presents a much stronger case against the claim that justification is closed under deduction than its two predecessors. Besides presenting a more robust counterexample to closure, the new paradox also reveals that the strategies that were previously thought to get closure out of trouble are not sufficiently general to achieve this task as they fail to apply to similar closure-threatening paradoxes in the same vicinity. (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)

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

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)

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)

I argue against unqualified acceptance of the principle of deductive closure (DC): that, if p follows deductively from premises that are already known, we are in a position to know p. DC, I claim, is a sorites premise; it seems intuitively irresistible, but indiscriminate application of it leads to absurd conclusions. Furthermore, a theory on which the application of DC is restricted explains our practice of deriving new knowledge from old knowledge better than a theory on which our (...) application of DC is unrestricted. This restriction on the application of DC allows contextualists to meet an argument of Hawthorne’s that contextualism must lead either to absurd knowledge attributions or to constant shifting of the standards for knowledge. Even if the standard of knowledge remains constant, the absurd knowledge attribution is the conclusion of a sorites argument and should be rejected. (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)

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)

In this paper, I’ll survey a number of closure principles of epistemic justification and find them all wanting. However, it’ll be my contention that there’s a novel closure principle of epistemic justification that has the virtues of its close cousin closure principles, without their vices. This closure principle of epistemic justification can be happily thought of as a multi-premise closure principle and it cannot be used in Cartesian skeptical arguments that employ a closure (...) principle of epistemic justification. In this way, then, it represents marked improvement over other contemporary closure principles of epistemic justification that require both sacrificing multi-premise closure and forcing anti-Cartesian skeptics who reject the closure principle employed in certain Cartesian skeptical arguments to cast aside justification closure. (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)

Transmission arguments against closure of knowledge base the case against closure on the premise that a necessary condition for knowledge is not closed. Warfield argues that this kind of argument is fallacious whereas Brueckner, Murphy and Yan try to rescue it. According to them, the transmission argument is no longer fallacious once an implicit assumption is made explicit. I defend Warfield’s objection by arguing that the various proposals for the unstated assumption either do not avoid the fallacy (...) or turn the central premise of the transmission argument, namely that a necessary condition is not closed, into a redundant and superfluous premise. I conclude that Warfield’s advice is still to be heeded: Arguments against closure must not rely essentially on the premise that a necessary condition for knowledge is not closed. (shrink)

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

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)

Anthony Brueckner argues for a strong connection between the closure and the underdetermination argument for scepticism. Moreover, he claims that both arguments rest on infallibilism: In order to motivate the premises of the arguments, the sceptic has to refer to an infallibility principle. If this were true, fallibilists would be right in not taking the problems posed by these sceptical arguments seriously. As many epistemologists are sympathetic to fallibilism, this would be a very interesting result. However, in this paper (...) I will argue that Brueckner’s claims are wrong: The closure and the underdetermination argument are not as closely related as he assumes and neither rests on infallibilism. Thus even a fallibilist should take these arguments to raise serious problems that must be dealt with somehow. (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)

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)

I examine the meaning and merits of a premise in the Exclusion Argument, the causal closure principle that all physical effects have physical causes. I do so by addressing two questions. First, if we grant the other premises, exactly what kind of closure principle is required to make the Exclusion Argument valid? Second, what are the merits of the requisite closure principle? Concerning the first, I argue that the Exclusion Argument requires a strong, “stringently pure” version (...) of closure. The latter employs two qualifications concerning the physical sufficiency and relative proximity of the physical cause required for every physical effect. The second question is addressed in two steps. I begin by challenging the adequacy of the empirical support offered by David Papineau for closure. Then I assess the merits of “level” and “domain” versions of stringently pure closure. I argue that a domain version lacks adequate and non-question-begging support within the context of the Exclusion Argument. And I argue that the level version leads to a puzzling metaphysics of the physical domain. Thus, we have grounds for rejecting the version of closure required for the Exclusion Argument. This means we can resist the Exclusion Argument while avoiding the implausible implications that come with rejecting one of its other premises. That is, because there are grounds to reject causal closure, one can reasonably affirm the non-overdeterminative causal efficacy of conscious mental states while denying that the latter are identical with physical states. (shrink)

For over 2000 years our culture has believed in the possibility of a single true account of the world. Now this age is coming to a close. As a result there is a deep unease. We are lost both as individuals, and as a culture. In the new relativistic, post-modern era, we have no history, no right or moral action, and no body of knowledge. In their place is a plethora of alternative, and sometimes incompatible theories from 'fuzzy logic' (...) to 'consilience' proposing a theory of everything. _Closure_ is a response to this crisis. It is a radically new story about the nature of ourselves and of the world. _Closure_ exposes the central questions of contemporary philosophy: language and meaning, of the individual and identity, of truth and reality, but it is also philosophical in the broader everyday sense that it enables us to make sense of where and who we are. A central principle, the process of closure, is shown to be at the heart of experience and language. As a theory of knowledge it has dramatic consequences for our understanding of the sciences, involving a reinterpretation of what science does and how it is able to do it. It similarly proposes a profound shift in the role of art and religion. But, above all, it reshapes our understanding of ourselves and the organisation of society, our goals and our capacity to achieve them. A superb new account of how order is created out of disorder, _Closure_ is an exhilarating work of conceptual geography. (shrink)

Non-reductive physicalism is the view that mental events cause other events in virtue of their mental properties and that mental properties supervene on, without being identical to, physical properties. Jaegwon Kim has presented several much-discussed arguments against this view. But the much simpler causal closure argument, which purports to establish that every mental property is identical to a physical property, has received less attention than Kim’s arguments. This paper aims to show how a non-reductive physicalist should rebut the causal (...) closure argument. A crucial premise in the argument is a principle stating that the physical world is causally closed. It states, roughly, that every physical event has a physical sufficient cause. I argue that when the principle is formulated in this way, the causal closure argument is invalid. Less frequently, the causal closure principle is formulated in terms of a difference-making conception of causation so that it states that every physical effect has a physical difference-making cause. I argue that the principle, so formulated, is false and the causal closure argument unsound. Either way the argument lacks the apodeictic force to compel acceptance of its conclusion. (shrink)

Malformations concerning the ventral body wall constitute one of the leading categories of human birth defects and are present in about one out of every 2000 live births. Although the occurrence of these defects is relatively common, few detailed experimental studies exist on the development and closure of the ventral body wall in mouse and human. This field is further complicated by the array of theories on the pathogenesis of body wall defects and the likelihood that there is no (...) single cause for these abnormalities. In this review, we summarize what is known concerning the mechanisms of normal ventral body wall closure in humans and mice. We then outline the theories that have been proposed concerning human body wall closure abnormalities and examine the growing number of mouse mutations that impact normal ventral body wall closure. Finally, we speculate how studies in animal models such as mouse and Drosophila are beginning to provide a much‐needed mechanistic framework with which to identify and characterize the genes and tissues required for this vital aspect of human embryogenesis. BioEssays 26:1307–1321, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

Fred Dretske notoriously claimed that knowledge closure sometimes fails. Crispin Wright agrees that warrant does not transmit in the relevant cases, but only because the agent must already be warranted in believing the conclusion in order to acquire her warrant for the premise. So the agent ends up being warranted in believing, and so knowing, the conclusion in those cases too: closure is preserved. Wright's argument requires that the conclusion's having to be warranted beforehand explains transmission failure. (...) I argue that it doesn't, and that the correct explanation does not imply that the agent will end up warranted in believing the conclusion when transmission fails. Those who agree that transmission does fail in those cases, therefore, might as well follow Dretske in denying knowledge closure too. (shrink)

A causal argument for physicalism is widely held to pose a problem for dualism. This view has an unobvious presupposition, namely that the causal closure of the physical has a special sort of ground. The requisite sort of ground must distinguish the causal argument for physicalism from many defective causal arguments. On behalf of physicalists, I develop an account of the ground for the causal closure of the physical, thereby putting the causal argument for physicalism back in the (...) business of causally problematizing dualism. One consequence of my account is that physicalists can pose a causal problem for dualism using a much weaker closure premise than is generally assumed. (shrink)

We present a semi-formal foundational theory of sorts, akin to sets, named librationism because of its way of dealing with paradoxes. Its semantics is related to Herzberger’s semi inductive approach, it is negation complete and free variables (noemata) name sorts. Librationism deals with paradoxes in a novel way related to paraconsistent dialetheic approaches, but we think of it as bialethic and parasistent. Classical logical theorems are retained, and none contradicted. Novel inferential principles make recourse to theoremhood and failure of theoremhood. (...) Identity is introduced à la Leibniz-Russell, and librationism is highly non-extensional. Π 1 1 -comprehension with ordinary Bar-Induction is accounted for (to be lifted). Power sorts are generally paradoxical, and Cantor’s Theorem is blocked as a camouflaged premise is naturally discarded. (shrink)

Focusing on Crispin Wright, I try in Chapter One to show that semantic antirealism cannot stably be combined with either communitarianism or constructivism about meaning. I also argue that the rational tenability of communitarianism is threatened by a powerful argument of Wright's own devising in "What Could Anti-Realism About Ordinary Psychology Possibly Be?" In Chapters Two and Three, I defend the individualist idea that the meaning of an expression in an agent's idiolect is correlative with her understanding of its use. (...) I try to show that individualism, so conceived, is fully compatible with natural-kind externalism and that none of the familiar and widely accepted arguments for social externalism are cogent. I also argue that there is no incompatibility between externalism and self-knowledge in matters of meaning. In Chapters Four and Five, I criticize a transcendental argument developed by Donald Davidson and recently defended by Robert Brandom that a creature cannot properly be credited with language or thought unless it is in communication with at least one other creature. Neither philosopher, I argue, provides a cogent case for the argument's crucial premise that the concept of objectivity is unavailable to a creature outside of a social, linguistic setting. The thesis that meaning is normative has widespread currency in the philosophy of language and does much to motivate the social, deontological approach to meaning taken in Making it Explicit. However, I argue in Chapter Six that central arguments for the thesis rest on confusions about the relation between the concepts of meaning, truth, use and intention. In Chapter Seven, I conclude, by connecting Davidson and Brandom's social account of the concept of objectivity with a certain "non-individualist" theory of perception. Following John McDowell, I argue that the theory renders the empirical contentfulness language and thought unintelligible. (shrink)

Contextualists claim two important virtues for their view. First, contextualism is a non-skeptical epistemology, given the plausible idea that not all contexts invoke the high standards for knowledge needed to generate the skeptical conclusion that we know little or nothing. Second, contextualism is able to preserve closure concerning knowledge – the idea that knowledge is extendable on the basis of competent deduction from known premises. As long as one keeps the context fixed, it is plausible to think that some (...) closure principle can be articulated that will survive scrutiny. Opponents of contextualism often try to gain an advantage over it by claiming that their view mimics these virtues of contextualism as well as having other virtues. A recent example of the same is termed ‘contrastivism," as presented by Jonathan Schaffer. I will argue that the representation made is chimerical, that in fact contrastivism has no hope of mirroring these twin virtues of contextualism. (shrink)

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

Arguments with what are called "independent" or "convergent" premises are typically diagrammed by using an arrow between each premise and the conclusion. This makes diagramming objections to the reasoning difficult. It also obscures differences in argument structure. I suggest that a single arrow should be used for such arguments and that this is so even in the extreme form of independent premises when the argument is entirely unstructured. I then discuss the diagramming of objections.