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A Multimodal Pragmatic Treatment of the Knowability Paradox.

In Gillman Payette & Rafal Urbaniak (eds.), Applications of Formal Philosophy. The Road Less Travelled. Berlin: Springer International Publishing AG. pp. 195-209 (2017)

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  1. Diamonds are a philosopher's best friends.Heinrich Wansing - 2002 - Journal of Philosophical Logic 31 (6):591-612.
    The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is (...)
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  • Knowability and intuitionistic logic.David Vidi & Graham Solomon - 2001 - Philosophia 28 (1-4):319-334.
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  • Modal logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.
    Modern modal logic originated as a branch of philosophical logic in which the concepts of necessity and possibility were investigated by means of a pair of dual operators that are added to a propositional or first-order language. The field owes much of its flavor and success to the introduction in the 1950s of the “possible-worlds” semantics in which the modal operators are interpreted via some “accessibility relation” connecting possible worlds. In subsequent years, modal logic has received attention as an attractive (...)
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  • Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
    This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much (...)
  • A. S. Troelstra and H. Schwichtenberg. Basic proof theory. Second edition of jsl lxiii 1605. Cambridge tracts in theoretical computer science, no. 43. cambridge university press, cambridge, new York, etc., 2000, XII + 417 pp.Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.
  • Products of modal logics, part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
    The paper studies many-dimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: p-morphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area.
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  • A logical analysis of some value concepts.Frederic Fitch - 1963 - Journal of Symbolic Logic 28 (2):135-142.
  • Some remarks on restricting the knowability principle.Martin Fischer - 2013 - Synthese 190 (1):63-88.
    The Fitch paradox poses a serious challenge for anti-realism. This paper investigates the option for an anti-realist to answer the challenge by restricting the knowability principle. Based on a critical discussion of Dummett's and Tennant's suggestions for a restriction desiderata for a principled solution are developed. In the second part of the paper a different restriction is proposed. The proposal uses the notion of uniform formulas and diagnoses the problem arising in the case of Moore sentences in the different status (...)
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  • Knowability and intuitionistic logic.David De Vidi & Graham Solomon - 2001 - Philosophia 28 (1-4):319-334.
  • A pragmatic interpretation of intuitionistic propositional logic.Carlo Dalla Pozza & Claudio Garola - 1995 - Erkenntnis 43 (1):81-109.
    We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, (...)
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  • Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Cambridge University Press.
    This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
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  • Discovering knowability: a semantic analysis.Sergei Artemov & Tudor Protopopescu - 2013 - Synthese 190 (16):3349-3376.
    In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...)
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  • New Essays on the Knowability Paradox.Joe Salerno (ed.) - 2008 - Oxford, England and New York, NY, USA: Oxford University Press.
    This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox.
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  • Fitch's paradox of knowability.Michael Dummett - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
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  • Fusions of Modal Logics and Fitch’s Paradox.Alexandre Costa-Leite - 2006 - Croatian Journal of Philosophy 6 (2):281-290.
    This article shows that although Fitch’s paradox has been extremely widely studied, up to now no correct formalization of the problem has been proposed. The purpose of this article is to present the paradox front the viewpoint of combining logics. It is argued that the correct minimal logic to state the paradox is composed by a fusion of modal frames, and a fusion of modal languages and logics.
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  • Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
     
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  • Modalities and Multimodalities.Walter Alexandre Carnielli, Claudio Pizzi & Juliana Bueno-Soler - 2008 - Dordrecht, Netherland: Springer.
    In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could (...)
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  • Combining logics.Walter Carnielli & Marcelo E. Coniglio - 2008 - Stanford Encyclopedia of Philosophy.
    Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) as well as methods for decomposing logics, showing their interesting properties (...)
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  • The Knowability Paradox in the light of a Logic for Pragmatics.Massimiliano Carrara & Daniele Chiffi - 2014 - In R. Ciuni, H. Wansing & C. Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Berlin: Springer. pp. 47-58.
    The Knowability Paradox is a logical argument showing that if all truths are knowable in principle, then all truths are, in fact, known. Many strategies have been suggested in order to avoid the paradoxical conclusion. A family of solutions –ncalled logical revision – has been proposed to solve the paradox, revising the logic underneath, with an intuitionistic revision included. In this paper, we focus on so-called revisionary solutions to the paradox – solutions that put the blame on the underlying logic. (...)
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  • On intuitionistic modal epistemic logic.Timothy Williamson - 1992 - Journal of Philosophical Logic 21 (1):63--89.
  • Knowability and possible epistemic oddities.J. C. Beall - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press. pp. 105--125.
     
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  • .Joe Salerno - 2009 - In New Essays on the Knowability Paradox. Oxford University Press.
     
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