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The KK Principle

Edited by Julien Dutant (University of Geneva, University of Michigan, Ann Arbor)
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  1. 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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  2. Matthew A. Benton (2013). Dubious Objections From Iterated Conjunctions. Philosophical Studies 162 (2):355-358.
    The knowledge account of assertion - roughly: one should not assert what one does not know - can explain a variety of Moorean conjunctions, a fact often cited as evidence in its favor. David Sosa ("Dubious Assertions," Phil Studies, 2009) has objected that the account does not generalize satisfactorily, since it cannot explain the infelicity of certain iterated conjunctions without appealing to the controversial "KK" principle. This essay responds by showing how the knowledge account can handle such conjunctions without use (...)
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  3. Giacomo Bonanno (2000). Common Belief with the Logic of Individual Belief. Mathematical Logic Quarterly 46 (1):49-52.
    The logic of common belief does not always reflect that of individual beliefs. In particular, even when the individual belief operators satisfy the KD45 logic, the common belief operator may fail to satisfy axiom 5. That is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. We identify the intersubjective restrictions on individual beliefs that are incorporated in axiom 5 for common belief.
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  4. Denis Bonnay & Paul Égré (2009). Inexact Knowledge with Introspection. Journal of Philosophical Logic 38 (2):179 - 227.
    Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated (...)
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  5. Eleonora Cresto (2012). A Defense of Temperate Epistemic Transparency. Journal of Philosophical Logic 41 (6):923-955.
    Epistemic transparency tells us that, if an agent S knows a given proposition p , then S knows that she knows that p . This idea is usually encoded in the so-called KK principle of epistemic logic. The paper develops an argument in favor of a moderate version of KK , which I dub quasi-transparency , as a normative rather than a descriptive principle. In the second Section I put forward the suggestion that epistemic transparency is not a demand of (...)
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  6. Simon D'Alfonso (2013). Explicating a Standard Externalist Argument Against the KK Principle. Logos and Episteme (4).
    The KK principle is typically rejected in externalist accounts of knowledge. However, a standard general argument for this rejection is in need of a supportive explication. In a recent paper, Samir Okasha argues that the standard externalist argument in question is fallacious. In this paper I start off with some critical discussion of Okasha’s analysis before suggesting an alternative way in which an externalist might successfully present such a case. I then further explore this issue via a look at how (...)
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  7. Jérôme Dokic & Paul Égré (2009). Margin for Error and the Transparency of Knowledge. Synthese 166 (1):1 - 20.
    In chapter 5 of Knowledge and its Limits, T. Williamson formulates an argument against the principle (KK) of epistemic transparency, or luminosity of knowledge, namely “that if one knows something, then one knows that one knows it”. Williamson’s argument proceeds by reductio: from the description of a situation of approximate knowledge, he shows that a contradiction can be derived on the basis of principle (KK) and additional epistemic principles that he claims are better grounded. One of them is a reflective (...)
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  8. Julien Dutant, Inexact Knowledge, Margin for Error and Positive Introspection. Proceedings of Tark XI.
    Williamson (2000a) has argued that posi- tive introspection is incompatible with in- exact knowledge. His argument relies on a margin-for-error requirement for inexact knowledge based on a intuitive safety prin- ciple for knowledge, but leads to the counter- intuitive conclusion that no possible creature could have both inexact knowledge and posi- tive introspection. Following Halpern (2004) I put forward an alternative margin-for-error requirement that preserves the safety require- ment while blocking Williamson’s argument. I argue that the infallibilist conception of knowledge (...)
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  9. Antony Eagle, The KK Principle.
    relevant alternatives: I take it that a process is reliable in the actual world iff, in the actual set of outcomes (i.e. beliefs being formed), the frequency of successes (those beliefs being true) is much greater than the frequency of failures (those beliefs being false). One may wish to run a more sophisticated kind of reliabilism, where one demands that a reliable process also be reliable in counterfactual situations, but one need not, and I won’t here. If perception is a (...)
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  10. Carl Ginet (1970). What Must Be Added to Knowing to Obtain Knowing That One Knows? Synthese 21 (2):163 - 186.
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  11. Olivier Gossner & Elias Tsakas (2012). Reasoning-Based Introspection. Theory and Decision 73 (4):513-523.
    We show that if an agent reasons according to standard inference rules, the truth and introspection axioms extend from the set of non-epistemic propositions to the whole set of propositions. This implies that the usual axiomatization of partitional possibility correspondences is redundant, and provides a justification for truth and introspection that is partly based on reasoning.
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  12. Patrick Greenough, Duncan Pritchard & Timothy Williamson (eds.) (2009). Williamson on Knowledge. Oxford University Press.
    16 leading philosophers offer critical assessments of Timothy Williamson's ground-breaking work on knowledge and its impact on philosophy today.
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  13. David Hemp, KK (Knowing That One Knows) Principle. Internet Encyclopedia of Philosophy.
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  14. Jaakko Hintikka (1962). Knowledge and Belief. Ithaca, N.Y.,Cornell University Press.
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  15. 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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  16. 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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  17. Mikael Janvid (2012). Knowledge Versus Understanding: The Cost of Avoiding Gettier. Acta Analytica 27 (2):183-197.
    In the current discussion on epistemic value, several philosophers argue that understanding enjoys higher epistemological significance and epistemic value than knowledge—the epistemic state the epistemological tradition has been preoccupied with. By noting a tension between the necessary conditions for understanding in the perhaps most prominent of these philosophers, Jonathan Kvanvig, this paper disputes the higher epistemological relevance of understanding. At the end, on the basis of the results of the previous sections, some alternative comparative contrasts between knowledge and understanding are (...)
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  18. Neil Kennedy (2009). Savoir Que l'On Sait. La Question de la Transparence Dans les Attitudes Épistémiques. Dialogue 48 (03):451-.
    ABSTRACT: In this paper, I revisit arguments for and against various theses concerning higher-order knowledge in order to fully gauge their impact on the principles of positive and negative introspection. I argue that the expression has at least two salient understandings: the more common one, labelled , validates the principle of positive introspection, while the other which is less common, labelled , supports some of the arguments against this principle.
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  19. Steffen Lewitzka (2011). ?K: A Non-Fregean Logic of Explicit Knowledge. Studia Logica 97 (2):233-264.
    We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. ? k (Epsilon-K) is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K i? ? ? and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical (...)
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  20. Berislav Marušić (2013). The Self-Knowledge Gambit. Synthese 190 (12):1977-1999.
    If we hold that perceiving is sufficient for knowing, we can raise a powerful objection to dreaming skepticism: Skeptics assume the implausible KK-principle, because they hold that if we don’t know whether we are dreaming or perceiving p, we don’t know whether p. The rejection of the KK-principle thus suggests an anti-skeptical strategy: We can sacrifice some of our self-knowledge—our second-order knowledge—and thereby save our knowledge of the external world. I call this strategy the Self-Knowledge Gambit. I argue that the (...)
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  21. Conor McHugh (2010). Self-Knowledge and the KK Principle. Synthese 173 (3):231 - 257.
    I argue that a version of the so-called KK principle is true for principled epistemic reasons; and that this does not entail access internalism, as is commonly supposed, but is consistent with a broad spectrum of epistemological views. The version of the principle I defend states that, given certain normal conditions, knowing p entails being in a position to know that you know p. My argument for the principle proceeds from reflection on what it would take to know that you (...)
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  22. T. F. Morris (1989). Knowledge of Knowledge and of Lack of Knowledge in the Charmides. International Studies in Philosophy 21 (1):49-61.
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  23. David Owens (2004). Williamson on Scepticism and Rationality. Philosophical Books 45 (4):306-312.
    We are often in no position to know whether p is true but, it is widely held, where we do know that p, we are always in a position to know that we know that p: knowledge is luminous. In Chapter 4 of Knowledge and Its Limits Williamson argues that knowledge is not luminous and with this conclusion in hand he hopes to see off the sceptic, amongst other things.
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  24. Murali Ramachandran (2012). The KK-Principle, Margins for Error, and Safety. Erkenntnis 76 (1):121-136.
    This paper considers, and rejects, three strategies aimed at showing that the KK-principle fails even in most favourable circumstances (all emerging from Williamson’s Knowledge and its Limits ). The case against the final strategy provides positive grounds for thinking that the principle should hold good in such situations.
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  25. Assaf Sharon & Levi Spectre (2008). Mr. Magoo's Mistake. Philosophical Studies 139 (2):289 - 306.
    Timothy Williamson has famously argued that the (KK) principle (roughly, that if one knows that p, then one knows that one knows that p) should be rejected. We analyze Williamson’s argument and show that its key premise is ambiguous, and that when it is properly stated this premise no longer supports the argument against (KK). After canvassing possible objections to our argument, we reflect upon some conclusions that suggest significant epistemological ramifications pertaining to the acquisition of knowledge from prior knowledge (...)
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  26. Martin Smith (2012). Some Thoughts on the JK-Rule1. Noûs 46 (4):791-802.
    In ‘The normative role of knowledge’ (2012), Declan Smithies defends a ‘JK-rule’ for belief: One has justification to believe that P iff one has justification to believe that one is in a position to know that P. Similar claims have been defended by others (Huemer, 2007, Reynolds, forthcoming). In this paper, I shall argue that the JK-rule is false. The standard and familiar way of arguing against putative rules for belief or assertion is, of course, to describe putative counterexamples. My (...)
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  27. Thomas Studer (2013). Decidability for Some Justification Logics with Negative Introspection. Journal of Symbolic Logic 78 (2):388-402.
    Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.
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  28. Timothy Williamson (2011). Improbable Knowing. In T. Dougherty (ed.), Evidentialism and its Discontents. Oxford University Press.
    Can we turn the screw on counter-examples to the KK principle (that if one knows that P, one knows that one knows that P)? The idea is to construct cases in which one knows that P, but the epistemic status for one of the proposition that one knows that P is much worse than just one’s not knowing it. Of course, since knowledge is factive, there can’t be cases in which one knows that P and knows that one doesn’t know (...)
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  29. Timothy Williamson (2005). Contextualism, Subject-Sensitive Invariantism and Knowledge of Knowledge. Philosophical Quarterly 55 (219):213–235.
    §I schematises the evidence for an understanding of ‘know’ and other terms of epistemic appraisal that embodies contextualism or subject-sensitive invariantism, and distinguishes between those two approaches. §II argues that although the cases for contextualism and sensitive invariantism rely on a principle of charity in the interpretation of epistemic claims, neither approach satisfies charity fully, since both attribute metalinguistic errors to speakers. §III provides an equally charitable anti-sceptical insensitive invariantist explanation of much of the same evidence as the result of (...)
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  30. Timothy Williamson (1996). Self-Knowledge and Embedded Operators. Analysis 56 (4):202–209.
    Queen Anne is dead, and it is a fallacy to substitute a definite description for another designator of the same object in stating the content of someone’s propositional attitudes. The fallacy can take subtle forms, as when Godel’s incompleteness theorems are used to argue against mechanistic views of mind. Some instances of the fallacy exemplify a more general logical phenomenon: the set of principles satisfied by one sentential operator can differ from, and even contradict, the set of principles satisfied by (...)
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  31. Timothy Williamson (1992). Inexact Knowledge. Mind 101 (402):217-242.
    Most of our knowledge is inexact, and known by us to be so. An example of such known inexactness will be described in some detail. The description seems to entail a contradiction. However, the paradoxical reasoning rests on an assumption. It will be suggested that the description is correct and this assumption false. Its failure will be explained by means of a picture of inexact knowledge in which the notion of a margin for error is central. This picture suggests diagnoses (...)
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