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Closure of Knowledge

Edited by Julien Dutant (University of Geneva, University of Michigan, Ann Arbor)
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  1. Fred Adams (2005). Tracking Theories of Knowledge. Veritas 50 (4):1-35.
    As teorias epistemológicas do rastreamento sustentam que o conhecimento é uma relação real entre o agente cognitivo e seu ambiente. Os estados cognitivos de um agente epistêmico fazem o rastreamento da verdade das proposições que são objeto de conhecimento ao embasarem a crença em indicadores confiáveis da verdade (evidência, razões, ou métodos de formação de crença). A novidade nessa abordagem é que se dá pouca ênfase no tipo de justificação epistêmica voltada ao fornecimento de procedimentos de decisão doxástica ou regras (...)
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  2. Marc Alspector-Kelly (2011). Why Safety Doesn't Save Closure. Synthese 183 (2):127-142.
    Knowledge closure is, roughly, the following claim: For every agent S and propositions P and Q, if S knows P, knows that P implies Q, and believes Q because it is so implied, then S knows Q. Almost every epistemologist believes that closure is true. Indeed, they often believe that it so obviously true that any theory implying its denial is thereby refuted. Some prominent epistemologists have nevertheless denied it, most famously Fred Dretske and Robert Nozick. There are closure advocates (...)
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  3. Brian Ball & Michael Blome-Tillmann (forthcoming). Counter Closure and Knowledge Despite Falsehood. Philosophical Quarterly.
    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 (...)
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  4. P. Baumann (2006). Information, Closure, and Knowledge: On Jäger's Objection to Dretske. [REVIEW] Erkenntnis 64 (3):403 - 408.
    Christoph Jäger (2004) argues that Dretske’s information theory of knowledge raises a serious problem for his denial of closure of knowledge under known entailment: Information is closed under known entailment (even under entailment simpliciter); given that Dretske explains the concept of knowledge in terms of “information”, it is hard to stick with his denial of closure for knowledge. Thus, one of the two basic claims of Dretske would have to go. Since giving up the denial of closure would commit Dretske (...)
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  5. Tim Black (2008). Solving the Problem of Easy Knowledge. Philosophical Quarterly 58 (233):597-617.
    Stewart Cohen argues that several epistemological theories fall victim to the problem of easy knowledge: they allow us to know far too easily that certain sceptical hypotheses are false and that how things seem is a reliable indicator of how they are. This problem is a result of the theories' interaction with an epistemic closure principle. Cohen suggests that the theories should be modified. I argue that attempts to solve the problem should focus on closure instead; a new and plausible (...)
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  6. Michael Blome-Tillmann (2006). A Closer Look at Closure Scepticism. Proceedings of the Aristotelian Society 106 (3):381–390.
    The most prominent arguments for scepticism in modern epistemology employ closure principles of some kind. To begin my discussion of such arguments, consider Simple Knowledge Closure (SKC): (SKC) (Kxt[p] ∧ (p → q)) → Kxt[q].1 Assuming its truth for the time being, the sceptic can use (SKC) to reason from the two assumptions that, firstly, we don’t know ¬sh and that, secondly, op entails ¬sh to the conclusion that we don’t know op, where ‘op’ and ‘sh’ are shorthand for ‘ordinary (...)
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  7. Radu Bogdan (1985). Cognition and Epistemic Closure. American Philosophical Quarterly 22 (1):55 - 63.
    JUSTIFICATION and knowledge are thought to be closed under known implication..1 This widely shared assumption is embodied in the following principles of epistemic closure.
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  8. Jochen Briesen (2010). Reconsidering Closure, Underdetermination, and Infallibilism. Grazer Philosophische Studien 80 (1):221-234.
    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 (...)
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  9. Anthony Brueckner (2004). Strategies for Refuting Closure for Knowledge. Analysis 64 (4):333–335.
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  10. Anthony Brueckner (1998). Closure and Context. Ratio 11 (1):78–82.
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  11. Anthony L. Brueckner (1985). Skepticism and Epistemic Closure. Philosophical Topics 13 (3):89-117.
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  12. Christopher Buford (2009). Contextualism, Closure, and the Knowledge Account of Assertion. Journal of Philosophical Research 34:111-121.
    This paper argues that Epistemic Contextualism, Knowledge Closure, and the Knowledge Account of Assertion are inconsistent. The argument is developed by considering an objection to Contextualism that is unsuccessful. Some Contextualist responses are canvassed and rejected. Finally, it is argued that an analogue of the inconsistency arises for those who accept that justification is closed under known entailment.
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  13. J. Adam Carter (2011). Radical Skepticism, Closure, and Robust Knowledge. Journal of Philosophical Research 36:115-133.
    The Neo-Moorean response to the radical skeptical challenge boldly maintains that we can know we’re not the victims of radical skeptical hypotheses; accordingly, our everyday knowledge that would otherwise be threatened by our inability to rule out such hypotheses stands unthreatened. Given the leverage such an approach has against the skeptic from the very start, the Neo-Moorean line is an especially popular one; as we shall see, though, it faces several commonly overlooked problems. An initial problem is that this particular (...)
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  14. John M. Collins, Epistemic Closure Principles. Internet Encyclopedia of Philosophy.
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  15. John M. Collins (2002). Ryan on Epistemic Closure Principles. Philosophia 29 (1-4):371-376.
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  16. C. B. Cross (2012). The Paradox of the Knower Without Epistemic Closure -- Corrected. Mind 121 (482):457-466.
    This essay corrects an error in the presentation of the Paradox of the Knowledge-Plus Knower, which is the variant of Kaplan and Montague’s Knower Paradox presented in C. Cross 2001: ‘The Paradox of the Knower without Epistemic Closure,’ MIND, 110, pp. 319–33. The correction adds a universally quantified transitivity principle for derivability as an additional assumption leading to paradox. This correction does not affect the status of the Knowledge-Plus paradox as a rebuttal to an argument against epistemic closure, since the (...)
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  17. Charles B. Cross (2004). More on the Paradox of the Knower Without Epistemic Closure. Mind 113 (449):109-114.
    In “The Paradox of the Knower without Epistemic Closure”, MIND 110:319-33, 2001, I develop a version of the Knower Paradox which does not assume epistemic closure, and I use it to argue that the original Knower Paradox does not support an argument against epistemic closure. In “The Paradox of the Knower without Epistemic Closure?”, MIND 113:95-107, 2004, Gabriel Uzquiano, using his own result, argues that my rebuttal to the anti-closure argument is not successful. I respond here by arguing that in (...)
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  18. Charles B. Cross (2001). The Paradox of the Knower Without Epistemic Closure. Mind 110 (438):319-333.
    In this essay I present a new version of the Paradox of the Knower and show that this new paradox vitiates a certain argument against epistemic closure. I then prove a theorem that relates the new paradox to epistemological scepticism. I conclude by assessing the use of the Knower in arguments against syntactical treatments of knowledge.
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  19. Claudio de Almeida (2007). Closure, Defeasibility and Conclusive Reasons. Acta Analytica 22 (4):301 - 319.
    It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.
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  20. Marcello Di Bello (2014). Epistemic Closure, Assumptions and Topics of Inquiry. Synthese 191 (16):3977-4002.
    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 (...)
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  21. Fred Dretske (2006). Information and Closure. Erkenntnis 64 (3):409 - 413.
    Peter Baumann and Nicholas Shackel defend me against a serious criticism by Christoph Jäger. They argue that my account of information is consistent with my denial of closure for knowledge. Information isn’t closed under known entailment either. I think that, technically speaking, they are right. But the way they are right doesn’t help me much in my effort to answer the skeptic. I describe a way in which information, like knowledge, fails to be closed in a way that makes an (...)
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  22. Fred Dretske (2005). Is Knowledge Closed Under Known Entailment? The Case Against Closure. In Matthias Steup & Ernest Sosa (eds.), Contemporary Debates in Epistemology. Blackwell. 13-26.
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  23. Fred I. Dretske (1970). Epistemic Operators. Journal of Philosophy 67 (24):1007-1023.
  24. Richard Feldman (1995). In Defence of Closure. Philosophical Quarterly 45 (181):487-494.
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  25. Bryan Frances (1999). Contradictory Belief and Epistemic Closure Principles. Mind and Language 14 (2):203–226.
    Kripke’s puzzle has puts pressure on the intuitive idea that one can believe that Superman can fly without believing that Clark Kent can fly. If this idea is wrong then many theories of belief and belief ascription are built from faulty data. I argue that part of the proper analysis of Kripke’s puzzle refutes the closure principles that show up in many important arguments in epistemology, e.g., if S is rational and knows that P and that P entails Q, then (...)
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  26. Alessandro Giordani (2013). On the Factivity of Implicit Intersubjective Knowledge. Synthese (8):1-15.
    The concept of knowledge can be modelled in epistemic modal logic and, if modelled by using a standard modal operator, it is subject to the problem of logical omniscience. The classical solution to this problem is to distinguish between implicit and explicit knowledge and to construe the knowledge operator as capturing the concept of implicit knowledge. In addition, since a proposition is said to be implicitly known just in case it is derivable from the set of propositions that are explicitly (...)
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  27. Steven D. Hales (1995). Epistemic Closure Principles. Southern Journal of Philosophy 33 (2):185-202.
    This paper evaluates a number of closure principles (for both knowledge and justification) that have appeared in the literature. Counterexamples are presented to all but one of these principles, which is conceded to be true but trivially so. It is argued that a consequence of the failure of these closure principles is that certain projects of doxastic logic are doomed, and that doxastic logic is of dubious merit for epistemologists interested in actual knowers in the actual world.
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  28. John Hawthorne (2005). Contemporary Debates in Epistemology. Malden, Ma: Blackwell.
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  29. John Hawthorne (2004). Knowledge and Lotteries. Oxford University Press.
    Knowledge and Lotteries is organized around an epistemological puzzle: in many cases, we seem consistently inclined to deny that we know a certain class of propositions, while crediting ourselves with knowledge of propositions that imply them. In its starkest form, the puzzle is this: we do not think we know that a given lottery ticket will be a loser, yet we normally count ourselves as knowing all sorts of ordinary things that entail that its holder will not suddenly acquire a (...)
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  30. Wesley H. Holliday (forthcoming). Fallibilism and Multiple Paths to Knowledge. Oxford Studies in Epistemology 5.
  31. Wesley H. Holliday (forthcoming). Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism. Journal of Philosophical Logic:1-62.
    Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do (...)
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  32. Wesley H. Holliday (forthcoming). Epistemic Logic and Epistemology. In Sven Ove Hansson Vincent F. Hendricks (ed.), Handbook of Formal Philosophy. Springer.
    This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...)
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  33. Wesley H. Holliday (2012). Epistemic Logic, Relevant Alternatives, and the Dynamics of Context. Lecture Notes in Computer Science 7415:109-129.
    According to the Relevant Alternatives (RA) Theory of knowledge, knowing that something is the case involves ruling out (only) the relevant alternatives. The conception of knowledge in epistemic logic also involves the elimination of possibilities, but without an explicit distinction, among the possibilities consistent with an agent’s information, between those relevant possibilities that an agent must rule out in order to know and those remote, far-fetched or otherwise irrelevant possibilities. In this article, I propose formalizations of two versions of the (...)
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  34. Michael Huemer (2005). Logical Properties of Warrant. Philosophical Studies 122 (2):171 - 182.
    Trenton Merricks argues that on any reasonable account, warrant must entailtruth. I demonstrate three theses about the properties ofwarrant: (1) Warrant is not unique;there are many properties that satisfy the definition of warrant. (2) Warrant need not entail truth; there are some warrant properties that entailtruthand others that do not. (3) Warrant need not be closed under entailment, even if knowledge is. If knowledge satisfies closure, then some warrant properties satisfy closure while others do not;if knowledge violates closure, then allwarrant (...)
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  35. Michael Hughes (2013). Problems for Contrastive Closure: Resolved and Regained. Philosophical Studies 163 (3):577-590.
    The standard contextualist solution to the skeptical paradox is intended to provide a way to retain epistemic closure while avoiding the excessive modesty of radical skepticism and the immodesty of Moorean dogmatism. However, contextualism’s opponents charge that its solution suffers from epistemic immodesty comparable to Moorean dogmatism. According to the standard contextualist solution, all contexts where an agent knows some ordinary proposition to be true are contexts where she also knows that the skeptical hypotheses are false. It has been hoped (...)
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  36. Christoph Jäger (2004). Skepticism, Information, and Closure: Dretske's Theory of Knowledge. Erkenntnis 61 (2-3):187 - 201.
    According to Fred Dretskes externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretskes epistemology is his denial that knowledge is closed under known logical entailment. I argue that, given Dretskes construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. This has far-reaching consequences. (...)
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  37. Mark Jago (2013). The Problem of Rational Knowledge. Erkenntnis:1-18.
    Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...)
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  38. Peter Klein (2004). ``Closure Matters: Skepticism and Easy Knowledge&Quot;. Philosophical Issues 14:165--184.
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  39. Peter Klein (1995). ``Skepticism and Closure: Why the Evil Genius Argument Fails&Quot;. Philosophical Topics 23 (1):213--236.
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  40. Jonathan Kvanvig (2008). Contrastivism and Closure. Social Epistemology 22 (3):247 – 256.
    This paper argues for a solution to a problem that contrastivism faces. The problem is that contrastivism cannot preserve closure, in spite of claims to the contrary by its defenders. The problem is explained and a response developed.
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  41. Jonathan L. Kvanvig (2008). ``Closure and Alternative Possibilities&Quot. In John Greco (ed.), Oxford Handbook of Skepticism. Oxford: Oxford University Press. 456-484.
  42. Jonathan L. Kvanvig (2006). Closure Principles. Philosophy Compass 1 (3):256–267.
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  43. Jonathan L. Kvanvig (2006). ``Epistemic Closure Principles&Quot. Philosophy Compass 1:256-267.
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  44. Jonathan L. Kvanvig (2004). ``Nozickian Epistemology and the Question of Closure&Quot. Croatian Journal of Philosophy 3 (3):351-364.
    Nozick’s contribution to the epistemology of the last half of the twentieth century includes addressing the question of whether knowledge is closed under known implication. I argue that the question of closure provides a serious obstacle to Nozickian approaches to epistemology.
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  45. Maria Lasonen-Aarnio (2008). Single Premise Deduction and Risk. Philosophical Studies 141 (2):157 - 173.
    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 (...)
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  46. Krista Lawlor (2005). Living Without Closure. Grazer Philosophische Studien 69 (1):25-50.
    Epistemic closure, the idea that knowledge is closed under known implication, plays a central role in current discussions of skepticism and the semantics of knowledge reports. Contextualists in particular rely heavily on the truth of epistemic closure in staking out their distinctive response to the so-called "skeptical paradox." I argue that contextualists should re-think their commitment to closure. Closure principles strong enough to force the skeptical paradox on us are too strong, and closure principles weak enough to express unobjectionable epistemic (...)
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  47. Steven Luper, The Epistemic Closure Principle. Stanford Encyclopedia of Philosophy.
    Most of us think we can always enlarge our knowledge base by accepting things that are entailed by (or logically implied by) things we know. The set of things we know is closed under entailment (or under deduction or logical implication), which means that we know that a given claim is true upon recognizing, and accepting thereby, that it follows from what we know. However, some theorists deny that knowledge is closed under entailment, and the issue remains controversial. The arguments (...)
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  48. Steven Luper (2006). Dretske on Knowledge Closure. Australasian Journal of Philosophy 84 (3):379 – 394.
    In early essays and in more recent work, Fred Dretske argues against the closure of perception, perceptual knowledge, and knowledge itself. In this essay I review his case and suggest that, in a useful sense, perception is closed, and that, while perceptual knowledge is not closed under entailment, perceptually based knowledge is closed, and so is knowledge itself. On my approach, which emphasizes the safe indication account of knowledge, we can both perceive, and know, that sceptical scenarios (such as being (...)
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  49. Guido Melchior (2010). Knowledge-Closure and Inferential Knowledge. Croatian Journal of Philosophy 10 (30):259-285.
    Closure is the principle that a person, who knows a proposition p and knows that p entails q, also knows q. Closure is usually regarded as expressing the commonplace assumption that persons can increase their knowledge through inference from propositions they already know. In this paper, I will not discuss whether closure as a general principle is true. The aim of this paper is to explore the various relations between closure and knowledge through inference. I will show that closure can (...)
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  50. Jennifer Nagel (2011). The Psychological Basis of the Harman-Vogel Paradox. Philosophers' Imprint 11 (5):1-28.
    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 (...)
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