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Principles of Knowledge

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Closure of Knowledge
  • P. Baumann (2006). Information, Closure, and Knowledge: On Jäger's Objection to Dretske. Erkenntnis 64 (3).
    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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  • 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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  • Radu Bogdan, Cognition and Epistemic Closure.
    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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  • Anthony Brueckner (2004). Strategies for Refuting Closure for Knowledge. Analysis 64 (4):333–335.
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  • Claudio de Almeida (2007). Closure, Defeasibility and Conclusive Reasons. Acta Analytica 22 (4).
    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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  • Fred Dretske (2006). Information and Closure. Erkenntnis 64 (3).
    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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  • Fred I. Dretske (1970). Epistemic Operators. Journal of Philosophy 67 (24):1007-1023.
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  • Richard Feldman (1995). In Defence of Closure. Philosophical Quarterly 45 (181):487-494.
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  • 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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  • Christoph Jäger, Skepticism, Information, and Closure.
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  • Christoph Jäger (2004). Skepticism, Information, and Closure: Dretske's Theory of Knowledge. Erkenntnis 61 (2-3).
    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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  • 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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  • 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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  • Steven Luper, The Epistemic Closure Principle. Stanford Encyclopedia of Philosophy.
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  • 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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  • Jonathan Schaffer (2007). Closure, Contrast, and Answer. Philosophical Studies 133 (2):233–255.
    How should the contrastivist formulate closure? That is, given that knowledge is a ternary contrastive state Kspq (s knows that p rather than q), how does this state extend under entailment? In what follows, I will identify adequacy conditions for closure, criticize the extant invariantist and contextualist closure schemas, and provide a contrastive schema based on the idea of extending answers. I will conclude that only the contrastivist can adequately formulate closure.
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  • G. C. Stine (1976). Skepticism, Relevant Alternatives, and Deductive Closure. Philosophical Studies 29 (4).
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  • Jonathan Vogel (2004). Speaking of Knowledge. Philosophical Issues 14 (1):501–509.
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  • Ted A. Warfield (2004). When Epistemic Closure Does and Does Not Fail: A Lesson From the History of Epistemology. Analysis 64 (281):35–41.
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  • Brian Weatherson, Tracking, Closure and Conjunctions.
    Comments on Sherri Rousch’s Tracking Truth for the 2006 Philosophy of Science Association conference.
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  • Matt Weiner, Deductive Closure and the Sorites.
    I argue against unqualified acceptance of the principle of deductive closure (DC): that, if p follows deductively from premises that are already known, we are in a position to know p. DC, I claim, is a sorites premise; it seems intuitively irresistible, but indiscriminate application of it leads to absurd conclusions. Furthermore, a theory on which the application of DC is restricted explains our practice of deriving new knowledge from old knowledge better than a theory on which our application of (...)
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Knowability
  • JC Beall (2000). Fitch's Proof, Verificationism, and the Knower Paradox. Australasian Journal of Philosophy 78 (2):241 – 247.
    I have argued that without an adequate solution to the knower paradox Fitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any honest, non-dogmatic reflection on (...)
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  • John Bigelow (2005). Omnificence. Analysis 65 (287):187–196.
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  • Berit Brogaard (2009). On Keeping Blue Swans and Unknowable Facts at Bay : A Case Study on Fitch's Paradox. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
    (T5) ϕ → ◊Kϕ |-- ϕ → Kϕ where ◊ is possibility, and ‘Kϕ’ is to be read as ϕ is known by someone at some time. Let us call the premise the knowability principle and the conclusion near-omniscience.2 Here is a way of formulating Fitch’s proof of (T5). Suppose the knowability principle is true. Then the following instance of it is true: (p & ~Kp) → ◊K(p & ~Kp). But the consequent is false, it is not possible to know (...)
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  • Berit Brogaard & Joe Salerno (2002). Clues to the Paradoxes of Knowability: Reply to Dummett and Tennant. Analysis 62 (2):143–150.
    Tr(A) iff ‡K(A) To remedy the error, Dummett’s proposes the following inductive characterization of truth: (i) Tr(A) iff ‡K(A), if A is a basic statement; (ii) Tr(A and B) iff Tr(A) & Tr(B); (iii) Tr(A or B) iff Tr(A) v Tr(B); (iv) Tr(if A, then B) iff (Tr(A) Æ Tr(B)); (v) Tr(it is not the case that A) iff ¬Tr(A), where the logical constant on the right-hand side of each biconditional clause is understood as subject to the laws of intuitionistic (...)
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  • Rudolf Carnap (1936). Testability and Meaning. Philosophy of Science 3 (4):419-471.
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  • Roy T. Cook (2006). Knights, Knaves and Unknowable Truths. Analysis 66 (289):10–16.
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  • Alexandre Costa-Leite, Combining Possibility and Knowledge.
    This paper is an attempt to define a new modality with philosophical interest by combining the basic modal ingredients of possibility and knowledge. This combination is realized via product of modal frames so as to construct a knowability modality, which is a bidimensional constructor of arity one defined in a two-dimensional modal frame. A semantical interpretation for the operator is proposed, as well as an axiomatic system able to account for inferences related to this new modality. The resulting logic for (...)
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  • Alexandre Costa-Leite, Paraconsistency and Knowability.
    We propose a modal paraconsistent logic sound and complete in order to create a model where the premisses of the knowability paradox are true except the conclusion.
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  • Cesare Cozzo (1994). What Can We Learn From the Paradox of Knowability? Topoi 13 (2):71--78.
    The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand what (...)
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  • David De Vidi & Graham Solomon (2001). Knowability and Intuitionistic Logic. Philosophia 28 (1-4).
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  • W. Dean & H. Kurokawa (forthcoming). From the Knowability Paradox to the Existence of Proofs. Synthese.
    The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed (...)
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  • David DeVidi & Tim Kenyon (2003). Analogues of Knowability. Australasian Journal of Philosophy 81 (4):481 – 495.
    An interesting recent reply to the Paradox of Knowability is Neil Tennant's proposal: to restrict the anti-realist's knowability thesis to truths the knowing of which is logically consistent. However, this proposal is egregiously ad hoc unless motivated by something other than the wish to save anti-realism from embarrassment. We examine Tennant's argument that his restriction is motivated by parallel considerations in cases that are neutral with respect to debates about realism. We conclude that the cases are not neutral, nor the (...)
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  • Igor Douven (2007). Fitch's Paradox and Probabilistic Antirealism. Studia Logica 86 (2).
    Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.
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  • Igor Douven (2005). A Principled Solution to Fitch's Paradox. Erkenntnis 62 (1).
    To save antirealism from Fitchs Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennants yields a non-ad hoc solution to (...)
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  • Michael Dummett (2001). Victor's Error. Analysis 61 (1):1–2.
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  • Dorothy Edgington (1985). The Paradox of Knowability. Mind 94 (376):557-568.
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  • Michael Fara (2010). Knowability and the Capacity to Know. Synthese 173 (1).
    This paper presents a generalized form of Fitch’s paradox of knowability, with the aim of showing that the questions it raises are not peculiar to the topics of knowledge, belief, or other epistemic notions. Drawing lessons from the generalization, the paper offers a solution to Fitch’s paradox that exploits an understanding of modal talk about what could be known in terms of capacities to know. It is argued that, in rare cases, one might have the capacity to know that p (...)
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  • Frederic B. Fitch (1963). A Logical Analysis of Some Value Concepts. Journal of Symbolic Logic 28 (2):135-142.
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  • Pierdaniele Giaretta (2009). The Paradox of Knowability From a Russellian Perspective. Prolegomena - Journal of Philosophy 8 (2):141-158.
    The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed out.
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  • Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (298):114-120.
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  • M. Hand (2003). Knowability and Epistemic Truth. Australasian Journal of Philosophy 81 (2):216 – 228.
    The so-called knowability paradox results from Fitch's argument that if there are any unknown truths, then there are unknowable truths. This threatens recent versions of semantical antirealism, the central thesis of which is that truth is epistemic. When this is taken to mean that all truths are knowable, antirealism is thus committed to the conclusion that no truths are unknown. The correct antirealistic response to the paradox should be to deny that the fundamental thesis of the epistemic nature of truth (...)
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  • Michael Hand (2010). Antirealism and Universal Knowability. Synthese 173 (1).
    Truth’s universal knowability entails its discovery. This threatens antirealism, which is thought to require it. Fortunately, antirealism is not committed to it. Avoiding it requires adoption (and extension) of Dag Prawitz’s position in his long-term disagreement with Michael Dummett on the notion of provability involved in intuitionism’s identification of it with truth. Antirealism (intuitionism generalized) must accommodate a notion of lost-opportunity truth (a kind of recognition-transcendent truth), and even truth consisting in the presence of unperformable verifications. Dummett’s position cannot abide (...)
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  • Michael Hand & Jonathan L. Kvanvig (1999). Tennant on Knowability. Australasian Journal of Philosophy 77 (4):422 – 428.
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  • W. D. Hart & Colin McGinn (1976). Knowledge and Necessity. Journal of Philosophical Logic 5 (2).
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  • Robert G. Hudson (2009). Faint-Hearted Anti-Realism and Knowability. Philosophia 37 (3).
    It is often claimed that anti-realists are compelled to reject the inference of the knowability paradox, that there are no unknown truths. I call those anti-realists who feel so compelled ‘faint-hearted’, and argue in turn that anti-realists should affirm this inference, if it is to be consistent. A major part of my strategy in defending anti-realism is to formulate an anti-realist definition of truth according to which a statement is true only if it is verified by someone, at some time. (...)
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  • Mark Jago (forthcoming). Closure on Knowability. Analysis.
    The Church-Fitch argument, or ‘paradox’ of knowability, apparently shows that, if all truths are knowable, then all truths are known. As some truths are unknown, anti-realists who hold that truths must be knowable have been at pains to block the argument. Here, I consider two such approaches: denying that knowledge distributes over conjunction, and moving to a typed logic. I argue that neither approach works. I first show that a Church-Fitch argument can be run with an assumption weaker than distribution (...)
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  • Mark Jago (forthcoming). Joe Salerno (Ed): New Essays on the Knowability Paradox. Journal of Logic, Language and Information.
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  • C. S. Jenkins (2007). Anti-Realism and Epistemic Accessibility. Philosophical Studies 132 (3).
    I argue that Fitch’s ‘paradox of knowability’ presents no special problem for the epistemic anti-realist who believes that reality is epistemically accessible to us. For the claim which is the target of the argument (If p then it is possible to know p) is not a commitment of anti-realism. The epistemic anti-realist’s commitment is (or should be) to the recognizability of the states of affairs which render true propositions true, not to the knowability of the propositions themselves. A formal apparatus (...)
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  • Carrie Jenkins (2009). The Mystery of the Disappearing Diamond. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
    Addresses the question of why we find Fitch's knowability 'paradox' argument surprising.
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