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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: Revista de Filosofia da PUCRS 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. Fred Adams, John A. Barker & Julia Figurelli (2012). Towards Closure on Closure. Synthese 188 (2):179-196.
    Tracking theories of knowledge are widely known to have the consequence that knowledge is not closed. Recent arguments by Vogel and Hawthorne claim both that there are no legitimate examples of knowledge without closure and that the costs of theories that deny closure are too great. This paper considers the tracking theories of Dretske and Nozick and the arguments by Vogel and Hawthorne. We reject the arguments of Vogel and Hawthorne and evaluate the costs of closure denial for tracking theories (...)
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  3. Patrick Allo (2013). The Many Faces of Closure and Introspection. Journal of Philosophical Logic 42 (1):91-124.
    In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.
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  4. Claudio Almeida (2012). Epistemic Closure, Skepticism and Defeasibility. Synthese 188 (2):197-215.
    Those of us who have followed Fred Dretske's lead with regard to epistemic closure and its impact on skepticism have been half-wrong for the last four decades. But those who have opposed our Dretskean stance, contextualists in particular, have been just wrong. We have been half-right. Dretske rightly claimed that epistemic status is not closed under logical implication. Unlike the Dretskean cases, the new counterexamples to closure offered here render every form of contextualist pro-closure maneuvering useless. But there is a (...)
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  5. Claudio 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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  6. 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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  7. Marc Alspector‐Kelly (2015). Wright Back to Dretske, or Why You Might as Well Deny Knowledge Closure. Philosophy and Phenomenological Research 90 (3):570-611.
    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 (...)
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  8. Philip Atkins & Ian Nance (2014). A Problem for the Closure Argument. International Journal for the Study of Skepticism 4 (1):36-49.
    Contemporary discussions of skepticism often frame the skeptic’s argument around an instance of the closure principle. Roughly, the closure principle states that if a subject knows p, and knows that p entails q, then the subject knows q. The main contention of this paper is that the closure argument for skepticism is defective. We explore several possible classifications of the defect. The closure argument might plausibly be classified as begging the question, as exhibiting transmission failure, or as structurally inefficient. Interestingly, (...)
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  9. Robert Audi (1995). Deductive Closure, Defeasibility and Scepticism: A Reply to Feldman. Philosophical Quarterly 45 (181):494-499.
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  10. Robert Audi (1991). Justification, Deductive Closure and Reasons to Believe. Dialogue 30 (1-2):77-.
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  11. Yuval Avnur (2012). Closure Reconsidered. Philosophers' Imprint 12 (9).
    Most solutions to the skeptical paradox about justified belief assume closure for justification, since the rejection of closure is widely regarded as a non-starter. I argue that the rejection of closure is not a non-starter, and that its problems are no greater than the problems associated with the more standard anti-skeptical strategies. I do this by sketching a simple version of the unpopular strategy and rebutting the three best objections to it. The general upshot for theories of justification is that (...)
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  12. Brian Ball & Michael Blome-Tillmann (201). Counter Closure and Knowledge Despite Falsehood. Philosophical Quarterly 64 (257):552-568.
    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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  13. J. A. Barker & F. Adams (2010). Epistemic Closure and Skepticism. Logos and Episteme 1 (2):221-246.
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  14. P. Baumann (2012). Nozick's Defense of Closure. In Kelly Becker & Tim Black (eds.), The Sensitivity Principle in Epistemology. Cambridge University Press 11--27.
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  15. 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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  16. Sven Bernecker (2012). Sensitivity, Safety, and Closure. Acta Analytica 27 (4):367-381.
    It is widely thought that if knowledge requires sensitivity, knowledge is not closed because sensitivity is not closed. This paper argues that there is no valid argument from sensitivity failure to non-closure of knowledge. Sensitivity does not imply non-closure of knowledge. Closure considerations cannot be used to adjudicate between safety and sensitivity accounts of knowledge.
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  17. Sven Bernecker (2008). Skepticism, Externalism, and Closure. In The Metaphysics of Memory. Springer 105--133.
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  18. Sven Bernecker (1998). Self-Knowledge and Closure. In Peter Ludlow & N. Martin (eds.), Externalism and Self-Knowledge. Csli
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  19. Tim Black (2009). What We Can Learn From the Skeptical Puzzle. Iris 1 (2):439-447.
    There is reason to think that a familiar and frequently used epistemic closure principle is false. Given this, the relevant instance of that principle should be removed from a familiar skeptical argument, and replaced with an instance of a more plausible epistemic closure principle. Once this has been done, however, we see that even if the resulting skeptical argument is unsound, we need deny neither closure nor the claim that we know the things we ordinarily take ourselves to know. Nothing (...)
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  20. 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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  21. 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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  22. 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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  23. Radu J. Bogdan (1985). ``Cognition and Epistemic Closure". American Philosophical Quarterly 22:55--63.
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  24. R. Booth & J. B. Paris (1998). A Note on the Rational Closure of Knowledge Bases with Both Positive and Negative Knowledge. Journal of Logic, Language and Information 7 (2):165-190.
    The notion of the rational closure of a positive knowledge base K of conditional assertions | (standing for if then normally ) was first introduced by Lehmann (1989) and developed by Lehmann and Magidor (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice, however, one might expect a knowledge base to consist not just of positive conditional assertions, | , but (...)
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  25. Yves Bouchard (2011). Deductive Closure and Epistemic Context. Logique Et Analyse 216:439-451.
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  26. Yves Bouchard, Epistemic Closure in Context.
    The general principle of epistemic closure stipulates that epistemic properties are transmissible through logical means. According to this principle, an epistemic operator, say ε, should satisfy any valid scheme of inference, such as: if ε(p entails q), then ε(p) entails ε(q). The principle of epistemic closure under known entailment (ECKE), a particular instance of epistemic closure, has received a good deal of attention since the last thirty years or so. ECKE states that: if one knows that p entails q, and (...)
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  27. Cameron Boult (2013). Epistemic Principles and Sceptical Arguments: Closure and Underdetermination. Philosophia 41 (4):1125-1133.
    Anthony Brueckner has argued that claims about underdetermination of evidence are suppressed in closure-based scepticism (“The Structure of the Skeptical Argument”, Philosophy and Phenomenological Research 54:4, 1994). He also argues that these claims about underdetermination themselves lead to a paradoxical sceptical argument—the underdetermination argument—which is more fundamental than the closure argument. If Brueckner is right, the status quo focus of some predominant anti-sceptical strategies may be misguided. In this paper I focus specifically on the relationship between these two arguments. I (...)
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  28. 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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  29. A. L. Brueckner (2000). Klein on Closure and Skepticism. Philosophical Studies 98 (2):139-151.
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  30. Anthony Brueckner (2008). Reply to Coffman on Closure and Skepticism. Synthese 162 (2):167–171.
    E. J. Coffman defends Peter Klein’s work on epistemic closure against various objections that I raised in an earlier paper. In this paper, I respond to Coffman.
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  31. Anthony Brueckner (2004). Strategies for Refuting Closure for Knowledge. Analysis 64 (4):333–335.
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  32. Anthony Brueckner (1998). Closure and Context. Ratio 11 (1):78–82.
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  33. Anthony L. Brueckner (1985). Skepticism and Epistemic Closure. Philosophical Topics 13 (3):89-117.
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  34. 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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  35. James Cargile (1999). On an Argument Against Closure. Noûs 33 (2):239-246.
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  36. 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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  37. 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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  38. E. J. Coffman (2006). Defending Klein on Closure and Skepticism. Synthese 151 (2):257 - 272.
    In this paper, I consider some issues involving a certain closure principle for Structural Justification, a relation between a cognitive subject and a proposition that’s expressed by locutions like ‘S has a source of justification for p’ and ‘p is justifiable for S’. I begin by summarizing recent work by Peter Klein that advances the thesis that the indicated closure principle is plausible but lacks Skeptical utility. I then assess objections to Klein’s thesis based on work by Robert Audi and (...)
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  39. E. J. Coffman (2006). Defending Klein on Closure and Skepticism. Synthese 151 (2):257-272.
    In this paper, I consider some issues involving a certain closure principle for Structural Justification, a relation between a cognitive subject and a proposition that's expressed by locutions like 'S has a source of justification for p' and 'p is justifiable for S'. I begin by summarizing recent work by Peter Klein that advances the thesis that the indicated closure principle is plausible but lacks Skeptical utility. I then assess objections to Klein's thesis based on work by Robert Audi and (...)
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  40. John M. Collins, Epistemic Closure Principles. Internet Encyclopedia of Philosophy.
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  41. John M. Collins (2002). Ryan on Epistemic Closure Principles. Philosophia 29 (1-4):371-376.
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  42. 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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  43. Charles B. Cross (2015). A Logical Transmission Principle for Conclusive Reasons. Australasian Journal of Philosophy 93 (2):353-370.
    Dretske's conclusive reasons account of knowledge is designed to explain how epistemic closure can fail when the evidence for a belief does not transmit to some of that belief's logical consequences. Critics of Dretske dispute the argument against closure while joining Dretske in writing off transmission. This paper shows that, in the most widely accepted system for counterfactual logic , conclusive reasons are governed by an informative, non-trivial, logical transmission principle. If r is a conclusive reason for believing p in (...)
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  44. 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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  45. 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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  46. Marian David & Ted A. Warfield (2008). Knowledge-Closure and Skepticism. In Quentin Smith (ed.), Epistemology: New Essays. Oxford University Press
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  47. 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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  48. 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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  49. 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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  50. 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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