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  1. Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • On Propositions: What They Are and How They Mean.Bertrand Russell - 1919 - Aristotelian Society Supplementary Volume 2:1--43.
  • Is 'No' a Force-Indicator? No!M. Textor - 2011 - Analysis 71 (3):448-456.
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  • General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
    Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...)
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  • The Logical Basis of Metaphysics.Michael Dummett, Hilary Putnam & James Conant - 1994 - Philosophical Quarterly 44 (177):519-527.
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  • Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
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  • The Philosophy of Logical Atomism, Lectures 5-6.Bertrand Russell - 1919 - The Monist 29 (2):190-222.
  • Conjunction and contonktion revisited.A. N. Prior - 1964 - Analysis 24 (6):191.
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  • The Philosophy of Logical Atomism.Bertrand Russell - 1940 - Open Court.
    THE PHILOSOPHY which I advocate is generally regarded as a species of realism, and accused of inconsistency because of the elements in it which seem contrary to that doctrine. For my part, I do not regard the issue between realists and their opponents as a funda- mental one; I could alter my view on this issue without changing my mind as to any of the doctrines upon which I wish to lay stress. I hold that logic is what is fundamental (...)
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  • The Philosophy of Logical Atomism.Bertrand Russell (ed.) - 1940 - Routledge.
    Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world’s (...)
     
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  • A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...)
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  • On an Intuitionistic Modal Logic.G. M. Bierman & V. C. V. de Paiva - 2000 - Studia Logica 65 (3):383-416.
    In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4— our formulation has several important metatheoretic properties. In addition, we study models of IS4— not in the framework of Kirpke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models but also (...)
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  • Classical Harmony: Rules of Inference and the Meaning of the Logical Constants.Peter Milne - 1994 - Synthese 100 (1):49 - 94.
    The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified (...)
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  • Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
    According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...)
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  • Harmony and Autonomy in Classical Logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.
    Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration (...)
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  • On the Idea of a General Proof Theory.Dag Prawitz - 1974 - Synthese 27 (1-2):63 - 77.
  • Frege.Michael Dummett - 1973 - Teorema: International Journal of Philosophy 5 (2):149-188.
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  • The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38.
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  • On Propositions: What They Are and How They Mean.Bertrand Russell - 1919 - Aristotelian Society Supplementary Volume 2 (1):1-43.
  • The Logical Basis of Metaphysics.Michael DUMMETT - 1991 - Harvard University Press.
    Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...
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  • The Co-Ordination Principles: A Problem for Bilateralism.Fernando Ferreira - 2008 - Mind 117 (468):1051-1057.
    In "'Yes" and "No'" (2000), Ian Rumfitt proposed bilateralism--a use-based account of the logical words, according to which the sense of a sentence is determined by the conditions under which it is asserted and denied. One of Rumfitt's key claims is that bilateralism can provide a justification of classical logic. This paper raises a techical problem for Rumfitt's proposal, one that seems to undermine the bilateralist programme.
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  • Co-Ordination Principles: A Reply.Ian Rumfitt - 2008 - Mind 117 (468):1059-1063.
    I explain why Fernando Ferreira's interesting formal result does not threaten the bilateralist account of the sense of the connectives.
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  • Sense, Assertion, Dummett and Denial.Huw Price - 1983 - Mind 92 (366):161-173.
  • Yes and No.I. Rumfitt - 2000 - Mind 109 (436):781-823.
    In what does the sense of a sentential connective consist? Like many others, I hold that its sense lies in rules that govern deductions. In the present paper, however, I argue that a classical logician should take the relevant deductions to be arguments involving affirmative or negative answers to yes-or-no questions that contain the connective. An intuitionistic logician will differ in concentrating exclusively upon affirmative answers. I conclude by arguing that a well known intuitionistic criticism of classical logic fails if (...)
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  • Unilateralism Disarmed: A Reply to Dummett and Gibbard.Ian Rumfitt - 2002 - Mind 111 (442):305-322.
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  • [Omnibus Review].Dag Prawitz - 1991 - Journal of Symbolic Logic 56 (3):1094-1096.
    Reviewed Works:Gaisi Takeuti, Proof Theory.Georg Kreisel, Proof Theory: Some Personal Recollections.Wolfram Pohlers, Contributions of the Schutte School in Munich to Proof Theory.Stephen G. Simpson, Subsystems of $\mathbf{Z}_2$ and Reverse Mathematics.Solomon Feferman, Proof Theory: A Personal Report.
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  • Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
  • Price and Rumfitt on Rejective Negation and Classical Logic.Peter Gibbard - 2002 - Mind 111 (442):297-304.
  • A Discussion of a Certain Type of Negative Proposition.Raphael Demos - 1917 - Mind 26 (102):188-196.
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  • Book Reviews. [REVIEW]Dag Prawitz - 1994 - Mind 103 (411):373-376.
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  • Conjunction and Contonktion Revisited.A. N. Prior - 1964 - Analysis 24 (6):191 - 195.
  • The Runabout Inference Ticket.Arthur Prior - 1967 - In Peter Strawson (ed.), Analysis. Oxford University Press. pp. 38-9.
  • What is a Theory of Meaning? (II).Michael Dummett - 1976 - In Gareth Evans & John McDowell (eds.), Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press.
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  • A Discussion of a Certain Type of Negative Proposition.Raphael Demos - 2016 - Philosophical Inquiry 40 (3-4):192-200.
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  • Why ‘Not’?Huw Price - 1990 - Mind 99 (394):221-238.
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  • On an Intuitionistic Modal Logic.G. M. Bierman & V. C. V. De Paiva - 2000 - Studia Logica 65 (3):383 - 416.
    In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4 -- our formulation has several important metatheoretic properties. In addition, we study models of IS4 -- not in the framework of Kripke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models (...)
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  • What is a Theory of Meaning?Michael A. E. Dummett - 1975 - In Samuel Guttenplan (ed.), Mind and Language. Oxford University Press.
  • ‘Yes’, ‘No’ and ‘Can't Say’.Michael Dummett - 2002 - Mind 111 (442):289-296.
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  • On Propositions: What They Are and How They Mean.Bertrand Russell - 1919 - Proceedings of the Aristotelian Society, Supplementary Volumes( 2:1-43.
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  • The Justification of Deduction.Michael A. E. Dummett - 1974 - In Michael Dummett (ed.), Truth and Other Enigmas. Oxford University Press.
  • Die Grundlagen der Arithmetik.Gottlob Frege - 1988 - Felix Meiner Verlag.
    Die "Grundlagen" gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen.
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  • Meaning Theory and Anti-Realism.Dag Prawitz - 1994 - In Brian McGuiness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Kluwer Academic Publishers. pp. 79--89.
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  • The Philosophical Basis of Intuitionistic Logic.Michael Dummett - 1975 - In Truth and Other Enigmas. Cambridge: Harvard UP. pp. 215--247.
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  • Die Widerspruchsfreiheit der Reinen Zahlentheorie.Gerhard Gentzen - 1936 - Journal of Symbolic Logic 1 (2):75-75.
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