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Natural Deduction for Diagonal Operators

In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Cham: Birkhäuser. pp. 39-51 (2017)

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  1. Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.
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  • Demonstratives: An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and other Indexicals.David Kaplan - 1989 - In Joseph Almog, John Perry & Howard Wettstein (eds.), Themes From Kaplan. Oxford University Press. pp. 481-563.
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  • A cut-free sequent system for two-dimensional modal logic, and why it matters.Greg Restall - 2012 - Annals of Pure and Applied Logic 163 (11):1611-1623.
    The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...)
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  • Actuality, Tableaux, and Two-Dimensional Modal Logics.Fabio Lampert - 2018 - Erkenntnis 83 (3):403-443.
    In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate (...)
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  • Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
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  • Metaphysics Without Conceptual Analysis.Robert Stalnaker - 2001 - Philosophy and Phenomenological Research 62 (3):631-636.
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  • What is the correct logic of necessity, actuality and apriority?Peter Fritz - 2014 - Review of Symbolic Logic 7 (3):385-414.
    This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...)
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  • A logic for epistemic two-dimensional semantics.Peter Fritz - 2013 - Synthese 190 (10):1753-1770.
    Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...)
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  • Symbolic logic.Frederic Brenton Fitch - 1952 - New York,: Ronald Press Co..
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  • Symbolic Logic. An Introduction.Wilhelm Ackermann - 1952 - Journal of Symbolic Logic 17 (4):266-268.
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  • Symbolic Logic, An Introduction.R. M. Martin - 1953 - Philosophy and Phenomenological Research 14 (2):260-261.
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  • Reference and contingency.Gareth Evans - 1979 - The Monist 62 (2):161-189.
    ‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...)
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  • Reference and Contingency.Gareth Evans - 1979 - The Monist 62 (2):161-189.
    ‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...)
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  • Two notions of necessity.Martin Davies & Lloyd Humberstone - 1980 - Philosophical Studies 38 (1):1-31.
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  • Epistemic Two-Dimensional Semantics.David J. Chalmers - 2004 - Philosophical Studies 118 (1-2):153-226.
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  • The eliminability of the actuality operator in propositional modal logic.Allen Hazen - 1978 - Notre Dame Journal of Formal Logic 19 (4):617-622.
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  • The Conscious Mind: In Search of a Fundamental Theory (2nd edition).David J. Chalmers - 1996 - Oxford University Press.
    The book is an extended study of the problem of consciousness. After setting up the problem, I argue that reductive explanation of consciousness is impossible , and that if one takes consciousness seriously, one has to go beyond a strict materialist framework. In the second half of the book, I move toward a positive theory of consciousness with fundamental laws linking the physical and the experiential in a systematic way. Finally, I use the ideas and arguments developed earlier to defend (...)
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  • From Metaphysics to Ethics: A Defence of Conceptual Analysis.Frank Jackson - 1998 - New York: Oxford University Press.
    Frank Jackson champions the cause of conceptual analysis as central to philosophical inquiry. In recent years conceptual analysis has been undervalued and widely misunderstood, suggests Jackson. He argues that such analysis is mistakenly clouded in mystery, preventing a whole range of important questions from being productively addressed. He anchors his argument in discussions of specific philosophical issues, starting with the metaphysical doctrine of physicalism and moving on, via free will, meaning, personal identity, motion, and change, to ethics and the philosophy (...)
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  • Naming and Necessity.Saul Kripke - 1980 - Philosophy 56 (217):431-433.
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  • Assertion.Robert Stalnaker - 1978 - In Maite Ezcurdia & Robert J. Stainton (eds.), The Semantics-Pragmatics Boundary in Philosophy. Broadview Press. pp. 179.
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  • From Metaphysics to Ethics: A Defence of Conceptual Analysis.Frank Jackson - 1999 - Philosophical Quarterly 49 (197):539-542.
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  • Assertion.Robert Stalnaker - 1978 - Syntax and Semantics (New York Academic Press) 9:315-332.
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