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)

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

What can we learn from cases of knowledge from falsehood? Critics of knowledge-first epistemology have argued that these cases provide us with good reason for rejecting the knowledge accounts of evidence, justification, and the norm of belief. I shall offer a limited defense of the knowledge-first approach to these matters. Knowledge from falsehood cases should undermine our confidence in like-from-like reasoning in epistemology. Just as we should be open to the idea that knowledge can come from non-knowledge, we should be (...) open to the idea that justified beliefs can come from unjustified beliefs. (shrink)

Recently, a number of cases have been proposed which seem to show that – contrary to widely held opinion – a subject can inferentially come to know some proposition p from an inference which relies on a false belief q which is essential. The standard response to these cases is to insist that there is really an additional true belief in the vicinity, making the false belief inessential. I present a new kind of case suggesting that a subject can inferentially (...) come to know a proposition from an essential false belief where no truth in the vicinity seems to be present. (shrink)

I propose and defend the conjecture that what explains why Gettiered subjects fail to know is the fact that their justified true belief depends essentially on unknown propositions. The conjecture follows from the plausible principle about inference in general according to which one knows the conclusion of one’s inference only if one knows all the premises it involves essentially.

Dretske’s theory of self-knowledge is interesting but peculiar and can seem implausible. He denies that we can know by introspection that we have thoughts, feelings, and experiences. But he allows that we can know by introspection what we think, feel, and experience. We consider two puzzles. The first puzzle, PUZZLE 1, is interpretive. Is there a way of understanding Dretske’s theory on which the knowledge affirmed by its positive side is different than the knowledge denied by its negative side? The (...) second puzzle, PUZZLE 2, is substantive. Each of the following theses has some prima facie plausibility: there is introspective knowledge of thoughts, knowledge requires evidence, and there are no experiences of thoughts. It is unclear, though, that these claims form a consistent set. These puzzles are not unrelated. Dretske’s theory of self-knowledge is a potential solution to PUZZLE 2 in that Dretske’s theory is meant to show how,, and can all be true. We provide a solution to PUZZLE 1 by appeal to Dretske’s early work in the philosophy of language on contrastive focus. We then distinguish between “Closure” and “Transmissibility”, and raise and answer a worry to the effect that Dretske’s theory of self-knowledge runs counter to Transmissibility. These results help to secure Dretske’s theory as a viable solution to PUZZLE 2. (shrink)

According to Duncan Pritchard, there are two kinds of radical sceptical problem; the closure-based problem, and the underdetermination-based problem. He argues that distinguishing these two problems leads to a set of desiderata for an anti-sceptical response, and that the way to meet all of these desiderata is by supplementing a form of Wittgensteinian contextualism with disjunctivist views about factivity. I agree that an adequate response should meet most of the initial desiderata Pritchard puts forward, and that some version of (...) Wittgensteinian contextualism shows the most promise as a starting point for this, but I argue, contra Pritchard, that the addition of disjunctivism is unnecessary and potentially counter-productive. If we draw on lessons from Michael Williams's inferential contextualism then it is both possible, and preferable, to meet the most important of Pritchard's desiderata, undercutting both closure-based and underdetermination-based sceptical problems in a unified way, without the need to resort to disjunctivism. (shrink)

This paper asks how perception becomes racializing and seeks the means for its critical interruption. My aim is not only to understand the recalcitrant and limitative temporal structure of racializing habits of seeing, but also to uncover the possibilities within perception for a critical awareness and destabilization of this structure. Reading Henri Bergson and Maurice Merleau-Ponty in dialogue with Frantz Fanon, Iris Marion Young and race-critical feminism, I locate in hesitation the phenomenological moment where habits of seeing can be internally (...) fractured. Hesitation, I claim, makes visible the exclusionary logic of racializing and objectifying perception, countering its affective closure and opening it to critical transformation. (shrink)

In recent decades, several theories have claimed to explain the teleological causality of organisms as a function of self-organising and self-producing processes. The most widely cited theories of this sort are variations of autopoiesis, originally introduced by Maturana and Varela. More recent modifications of autopoietic theory have focused on system organisation, closure of constraints and autonomy to account for organism teleology. This article argues that the treatment of teleology in autopoiesis and other organisation theories is inconclusive for three reasons: (...) First, non-living self-organising processes like autocatalysis meet the defining features of autopoiesis without being teleological; second, organisational approaches, whether defined in terms of the closure of constraints, self-determination or autonomy, are unable to specify teleological normativity, that is, the individuation of an ultimate beneficiary; third, all self-organised systems produce local order by maximising the throughput of energy and/or material (obeying the maximum entropy production (MEP) principle) and thereby are specifically organised to undermine their own critical boundary conditions. Despite these inadequacies, an alternative approach called teleodynamics accounts for teleology. This theory shows how multiple self-organising processes can be collectively linked so that they counter each other’s MEP principle tendencies to become codependent. Teleodynamics embraces – not ignoring – the difficulties of self-organisation, but reinstates teleology as a radical phase transition distinguishing systems embodying an orientation towards their own beneficial ends from those that lack normative character. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I proffer four novel extensions of the theory, and detail six issues that the theory faces. I provide a counter-example to epistemic closure for reductio proofs.

Aristotle’s Poetics defends the value of tragic poetry, presumably to counter Plato’s critique in the Republic. Can this defense resonate with something larger and rather surprising, that Aristotle’s overall philosophy displays a tragic character? I define the tragic as pertaining to indigenous and inescapable limits on life, knowledge, control, achievement, and agency. I explore how such limits figure in Aristotle’s physics, metaphysics, and biological works. Accordingly I want to disturb the common account of Aristotle’s thought as a neat system (...) of ontological order and metaphysical closure—not to exclude such elements but to place them within a world-view that includes certain limits at the edges of being. (shrink)

As we have seen in the transition form Part I to Part II of this book, the inductive riskiness of doxastic methods applied in testimonial uptake or prescribed as exemplary of religious faith, helpfully operationalizes the broader social scientific, philosophical, moral, and theological interest that people may have with problems of religious luck. Accordingly, we will now speak less about luck, but more about the manner in which highly risky cognitive strategies are correlated with psychological studies of bias studies and (...) human cognitive ecology. Chapter Four is concerned with connections between psychological study of biases and heuristics, and the comparative study of fundamentalism. The first section looks at work by psychologists and philosophers on our bias blind spot. Later sections ask, ‘In what ways might biases and heuristics play a special role in aiding our understanding of, and response to, fundamentalist orientation?’. The judgments we make in ignorance of our own biases Montaigne calls our importunate presumptions, and he suggests a host of practical factors that make them appealing. Montaigne, as I discuss in the first section, associates many of our errors with one or another kind of presumption, often about our similarity or differences from others, or from God. Our obvious psychographic diversity, and the polemical ground dynamics involved in our ‘culture wars’ are compounded on the agential side by the invisibility of our biases to ourselves. A number of person and social biases are described that plausibly affect all of our beliefs in domains of controversial views, religious views included. The second section continues to study of how etiological symmetry (similar patterns of belief-uptake) gives rise to religious contrariety (diverse narratives and theologies) in testimonial faith traditions, and what the implications of this are for philosophy of religion, generally, and for an improved comparative study of fundamentalism, in particular. Utilizing the work of philosophers such as Rachel Fraser and psychologists such as Emily Pronin and her co-authors, I offer a four-step genealogical account for how etiological symmetry so easily gives rise to religious contrariety. This account begins with the narrative nature of testimony in the Abrahamic family of religions, and how narrative content confounds our “source monitoring.” My genealogy also introduces what I term biased-closure inferences (BCI) as one of the key enablers of religious exclusivism and absolutism. These are the seemingly ‘logical’ but actually very self-serving inferences people often make, inferences from their own belief being true, to any belief contrary to it being false. Those who claim unique truth, epistemic access, and/or virtue and religious value for the home religion are no exception to the broad pertinence of bias studies across domains of controversial view. The proximate causes of belief are all that we can study, and in these there may be significant etiological symmetries. Yet those groups themselves, especially to the extent that they are exclusivist, are tunnel-visioned on claims of doctrinal uniqueness: on content differences of a theological sort. Comparative philosophy is met with the puzzlement that symmetric or essentially similar doxastic strategies should give rise not just to cognitive diversity, but to what we can call polarized or polemical contrariety, contrariety of a kind where each view adamantly rejects all others. Arguably, the more that theologies offer explanations of a counter-inductive sort, or profess counter-inductive thinking as exemplary of faith, the better evidential ground there for inferring that bias involved in the acquisition or maintenance of beliefs. This provides more substance to the question of when censure, and etiological challenges to faith-based beliefs are philosophically well-motivated. (shrink)

The acceptance of causal closure has had a profoundly limiting effect on the philosophical treatment of sui generis mental causation in recent decades. Philosophical treatments of special divine action have been likewise hampered by a widespread commitment to closure. If fundamental reality is as closure tells us it is, then nonphysical minds—human and divine— are either causally impotent or redundant. In this paper, I reject this limitation as baseless. Specifically, I will show how Hempel’s dilemma poses a (...) far greater challenge when applied to a causal closure principle than it did to the task of defining physicalism. Reponses to the dilemma can be used to disambiguate closure, but not without significant cost. In light of Hempel’s dilemma, there is no conception of closure that can do all of the following: rule out sui generis mental causation, have a reasonable chance of being true, and avoid problematic circularity. At the end of the day, I maintain that closure, properly understood, is, or ought to be, just one methodological stance among many. If this is correct, it is a stance that a theist can freely reject. (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)

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)

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)

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

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)

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

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)

Within Michel Foucault’s own conceptualization of governmentality, there is little room for something like ‘ungovernable life’. The latter seems to hint at a form of social conduct beyond power-relations, which would offend Foucault’s basic philosophical postulates. I argue that this identification between governmentality and power as such demonstrates a one-sided focus on the history of Western power-relations. By opposing Foucault’s genealogy of governmentality to Ivan Illich’s critical history of government, I delineate indigenous struggles against governmentalization as a form of ungovernable (...) counter-conduct. Throughout his books from the 1970s to 1990s, Illich wrote a critical history of government surprisingly similar to Foucault’s, from the pastorate to modern political economy. However, rather than merely describing this history, Illich argued governmentalization alienated human beings from their autonomy. As a former missionary priest, he criticized the Church’s and modern governments’ attempts to subsume populations under a conduct of conducts. He advocated anticolonial resistance to subsumption under Western governmental regimes. In Illich’s appreciation of decolonized life, an ungovernable form of life can be discovered, which I defend with the example of Zapatismo and indigenous self-government through mandar obedeciendo. (shrink)

We report the results of four empirical studies designed to investigate the extent to which an epistemic closure principle for knowledge is reflected in folk epistemology. Previous work by Turri (2015a) suggested that our shared epistemic practices may only include a source-relative closure principle—one that applies to perceptual beliefs but not to inferential beliefs. We argue that the results of our studies provide reason for thinking that individuals are making a performance error when their knowledge attributions and denials (...) conflict with the closure principle. When we used research materials that overcome what we think are difficulties with Turri’s original materials, we found that participants did not reject closure. Furthermore, when we presented Turri’s original materials to non-philosophers with expertise in deductive reasoning (viz., professional mathematicians), they endorsed closure for both perceptual and inferential beliefs. Our results suggest that an unrestricted closure principle—one that applies to all beliefs, regardless of their source—provides a better model of folk patterns of knowledge attribution than a source-relative closure principle. (shrink)

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)

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 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 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)

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).

In response to the claim that certain epistemically defective inferences such as Moore’s argument lead us to the conclusion that we ought to abandon closure, Crispin Wright suggests that we can avoid doing so by distinguishing it from a stronger principle, namely transmission. Where closure says that knowledge of a proposition is a necessary condition on knowledge of anything one knows to entail it, transmission makes a stronger claim, saying that by reasoning deductively from known premises one can (...) thereby acquire knowledge of or justification for the conclusion. Wright’s thought is that in cases such as Moore what is really going on is a failure of transmission, not a failure of closure. The problem with this claim is that it relies on an outdated formulation of closure which few nowadays would find plausible. Once we stipulate that it is the intuitive closure principle that deserves our attention, it becomes far less obvious that the project of diagnosing what is wrong with arguments such as Moore in terms of transmission failure but not closure failure can be vindicated. In order to demonstrate this claim, I consider intuitive closure of propositional justification vs. transmission of propositional justification and concede that perhaps these can come apart in the way that Wright suggests. I then argue that despite this concession, we also need an answer to the question of whether intuitive closure for doxastic justification and transmission for doxastic justification can come apart. We need an answer to this question because our ultimate interest in these issues stems from our interest in whether knowledge obeys closure, not merely whether propositional justification does. I argue that, even on the assumption that there is transmission failure of propositional justification, there is no transmission failure of doxastic justification. And if this is true, then there is no transmission failure of knowledge either. The transmission failure diagnosis of Moore’s argument and its ilk is thus in trouble. (shrink)

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

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)

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)

In spite of the intuitiveness of epistemic closure, there has been a stubborn stalemate regarding whether it is true, largely because some of the “Moorean” things we seem to know easily seem clearly to entail “heavyweight” philosophical things that we apparently cannot know easily—or perhaps even at all. In this paper, I will show that two widely accepted facts about what we do and don’t know—facts with which any minimally acceptable understanding of knowledge must comport—are jointly inconsistent with the (...) truth of CLR. The proof works by supposing the truth of “Categorialism,” a thesis about the relation between basic categories and common nouns and predicates, which is itself a heavyweight claim that cannot be easily known to be either true or false. (shrink)

Philosophers have long debated ‘substrate’ and ‘bundle’ theories as to how properties hold together in objects ― but have neglected to consider that every chemical entity is defined by closure of relationships among components ― here designated ‘Closure Louis de Broglie.’ That type of closure underlies the coherence of spectroscopic and chemical properties of chemical substances, and is importantly implicated in the stability and definition of entities of many other types, including those usually involved in philosophic discourse (...) ― such as roses, statues, and tennis balls. Characteristics of composites are often presumed to ‘supervene on’ properties of components. This assumption does not apply when cooperative interactions among components are significant. Once correlations dominate, then adequate descriptions must involve different entities and relationships than those that are involved in ‘fundamental-level’ description of similar but uncorrelated systems. That is to say, descriptions must involve different semantics than would be appropriate if cooperative interactions were insignificant. This is termed ‘Closure Henri Poincaré. Networks of chemical reactions that have certain types of closure of processes display properties that make other more-complex coherences possible. This is termed ‘Closure Jacques Cauvin.’ Each of these three modes of closure provides a sufficient basis for warranted recognition of causal interaction, thus each of them has epistemological significance. Other modes of epistemologically-important closure probably exist. It is important to recognize that causal efficacy generally depends on closure of relationships of constituents. (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 topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to (...) restrict it to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction. (shrink)

The physical realm is causally closed, according to physicalists like me. But why is it causally closed, what metaphysically explains causal closure? I argue that reductive physicalists are committed to one explanation of causal closure to the exclusion of any independent explanation, and that as a result, they must give up on using a causal argument to attack mind–body dualism. Reductive physicalists should view dualism in much the way that we view the hypothesis that unicorns exist, or that (...) the Kansas City Royals won the 2003 World Series: false, but not objectionable in any distinctively causal way. My argument turns on connections between explanation, counterfactuals, and inductive confirmation. (shrink)

According to some philosophers, we are “cognitively closed” to the answers to certain problems. McGinn has taken the next step and offered a list of examples: the mind/body problem, the problem of the self and the problem of free will. There are naturalistic, scientific answers to these problems, he argues, but we cannot reach them because of our cognitive limitations. In this paper, we take issue with McGinn's thesis as the most well-developed and systematic one among the so-called “new mysterians”. (...) McGinn aims to establish a strong, representational notion of cognitive closure: a principled inaccessibility of a true theory of certain properties of the world, but he offers arguments that only bear on difficulties with psychologically grasping the correct answers. The latter we label psychological closure. We argue that representational closure does not follow from psychological closure, and that McGinn's case therefore falters. We could very well be able to represent the correct answer to some question, even without being able to grasp that answer psychologically. McGinn's mistake in deriving representational closure from psychological closure rests on a fallacy of equivocation relating to the concept of ‘understanding’. By making this distinction explicit, we hope to improve our thinking about the limits of science in particular and human knowledge in general. (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.

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)

It has been argued that an advantage of the safety account over the sensitivity account is that the safety account preserves epistemic closure, while the sensitivity account implies epistemic closure failure. However, the argument fails to take the method-relativity of the modal conditions on knowledge, viz., sensitivity and safety, into account. In this paper, I argue that the sensitivity account and the safety account are on a par with respect to epistemic closure once the method-relativity of the (...) modal conditions is taken into account. Therefore, epistemic closure is no longer an arbiter in the debate. (shrink)

I 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)

Carter and Pritchard (2016) and Pritchard (2010, 2012, 2016) have tried to reconcile the intuition that perceptual knowledge requires only limited discriminatory abilities with the closure principle. To this end, they have introduced two theoretical innovations: a contrast between two ways of introducing error-possibilities and a distinction between discriminating and favoring evidence. I argue that their solution faces the “sufficiency problem”: it is unclear whether the evidence that is normally available to adult humans is sufficient to retain knowledge of (...) the entailing proposition and come to know the entailed proposition. I submit that, on either infallibilist or fallibilist views of evidence, Carter and Pritchard have set the bar for deductive knowledge too low. At the end, I offer an alternative solution. I suggest that the knowledge-retention condition of the closure principle is not satisfied in zebra-like scenarios. (shrink)

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)

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)

What are the truth conditions of want ascriptions? According to an influential approach, they are intimately connected to the agent’s beliefs: ⌜S wants p⌝ is true iff, within S’s belief set, S prefers the p worlds to the not-p worlds. This approach faces a well-known problem, however: it makes the wrong predictions for what we call (counter)factual want ascriptions, wherein the agent either believes p or believes not-p—for example, ‘I want it to rain tomorrow and that is exactly what (...) is going to happen’ or ‘I want this weekend to last forever, but of course it will end in a few hours’. We solve this problem. The truth conditions for want ascriptions are, we propose, connected to the agent’s conditional beliefs. We substantiate this connection by pursuing a striking parallel between (counter)factual and non-(counter)factual want ascriptions on the one hand and counterfactual and indicative conditionals on the other. (shrink)

Tainted political symbols ought to be confronted, removed, or at least recontextualized. Despite the best efforts to achieve this, however, official actions on tainted symbols often fail to take place. In such cases, I argue that political vandalism—the unauthorized defacement, destruction, or removal of political symbols—may be morally permissible or even obligatory. This is when, and insofar as, political vandalism serves as fitting counter-speech that undermines the authority of tainted symbols in ways that match their publicity, refuses to let (...) them speak in our name, and challenges the derogatory messages expressed through a mechanism I call derogatory pedestalling: the glorification or honoring of certain individuals or ideologies that can only make sense when members of a targeted group are taken to be inferior. (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)

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

Standard definitions of causal closure focus on where the causes in question are. In this paper, the focus is changed to where they are not. Causal closure is linked to the principle that no cause of another universe causes an event in a particular universe. This view permits the one universe to be affected by the other via an interface. An interface between universes can be seen as a domain that violates the suggested account of causal closure, (...) suggesting a view in which universes are causally closed whereas interfaces are not. On this basis, universes are not affected by other universes directly but rather indirectly. (shrink)