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  1. Stephen Barker, Expressivism About Truth-Making.score: 90.0
    My goal is to illuminate truth-making by way of illuminating the relation of making. My strategy is not to ask what making is, in the hope of a metaphysical theory about is nature. It's rather to look first to the language of making. The metaphor behind making refers to agency. It would be absurd to suggest that claims about making are claims about agency. It is not absurd, however, to propose that the concept of making somehow emerges from some feature (...)
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  2. Nissim Francez & Roy Dyckhoff (2012). A Note on Harmony. Journal of Philosophical Logic 41 (3):613-628.score: 90.0
    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 (...)
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  3. Peter Achinstein (ed.) (2004). Science Rules: A Historical Introduction to Scientific Methods. Johns Hopkins University Press.score: 78.0
    Is there a universal set of rules for discovering and testing scientific hypotheses? Since the birth of modern science, philosophers, scientists, and other thinkers have wrestled with this fundamental question of scientific practice. Efforts to devise rigorous methods for obtaining scientific knowledge include the twenty-one rules Descartes proposed in his Rules for the Direction of the Mind and the four rules of reasoning that begin the third book of Newton's Principia , and continue today in debates (...)
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  4. Deborah C. Smith (2001). Introduction and Elimination Rules Vs. Equivalence Rules in Systems of Formal Logic. Teaching Philosophy 24 (4):379-390.score: 72.0
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  5. Niels Öffenberger (1977). Logical Rules of Language. An Introduction to Logic. Philosophy and History 10 (2):165-166.score: 72.0
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  6. Richard Stoneman (1978). The Rules of Epinician Mary R Lefkowitz: The Victory Ode: An Introduction. Pp. 186. Park Ridge, N.J.: Noyes Press, 1976. Cloth, $18. [REVIEW] The Classical Review 28 (02):211-213.score: 72.0
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  7. James M. DuBois (1993). An Introduction to Adolf Reinach's 'The Supreme Rules of Rational Inference According to Kant'. Aletheia 6:94.score: 72.0
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  8. Giuseppina Mecchia (2007). Introduction to Christian Marazzi's "Rules for The Incommensurable". Substance 36 (1):10-11.score: 72.0
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  9. Peter Schroeder-Heister (forthcoming). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica:1-32.score: 60.0
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational (rather than reductive) account of proof-theoretic harmony. With (...)
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  10. L. Humberstone & D. Makinson (2012). Intuitionistic Logic and Elementary Rules. Mind 120 (480):1035-1051.score: 48.0
    The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and intuitionistic (...)
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  11. Ruy J. G. B. de Queiroz (2008). On Reduction Rules, Meaning-as-Use, and Proof-Theoretic Semantics. Studia Logica 90 (2):211-247.score: 48.0
    The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that (...)
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  12. Wagner de Campos Sanz & Thomas Piecha (2009). Inversion by Definitional Reflection and the Admissibility of Logical Rules. Review of Symbolic Logic 2 (3):550-569.score: 48.0
    The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister (1990, 1991) proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister (2007). Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the (...)
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  13. William P. Bechtel (1988). Connectionism and Rules and Representation Systems: Are They Compatible? Philosophical Psychology 1 (1):5-16.score: 46.0
    The introduction of connectionist or parallel distributed processing (PDP) systems to model cognitive functions has raised the question of the possible relations between these models and traditional information processing models which employ rules to manipulate representations. After presenting a brief account of PDP models and two ways in which they are commonly interpreted by those seeking to use them to explain cognitive functions, I present two ways one might relate these models to traditional information processing models and so (...)
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  14. J. Philip Wogaman (2009). Moral Dilemmas: An Introduction to Christian Ethics. Westminster John Knox Press.score: 42.0
    Introduction -- Part I: Starting points -- Some decisions are easier than others -- Easy decisions -- More difficult decisions -- Moral dilemmas -- The deep basis of the moral life -- Practical decision making -- Why ethics is ultimately religious -- Acceptable and unacceptable forms of revelation -- The useful incomplete ness of religious tradition -- Moral virtue and character -- Intuition and deliberation in moral decision-making -- The absolute and the relative in moral life -- Have we (...)
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  15. Kazuo Tanaka (1997). An Introduction to Fuzzy Logic for Practical Applications. Springer.score: 42.0
    Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of (...)
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  16. Peter Milne (1994). Classical Harmony: Rules of Inference and the Meaning of the Logical Constants. Synthese 100 (1):49 - 94.score: 42.0
    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 (...)
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  17. Gordon P. Baker (2010). Wittgenstein-- Rules, Grammar, and Necessity: Essays and Exegesis of 185-242. Wiley-Blackwell.score: 42.0
    Analytical commentary -- Fruits upon one tree -- The continuation of the early draft into philosophy of mathematics -- Hidden isomorphism -- A common methodology -- The flatness of philosophical grammar -- Following a rule 185-242 -- Introduction to the exegesis -- Rules and grammar -- The tractatus and rules of logical syntax -- From logical syntax to philosophical grammar -- Rules and rule-formulations -- Philosophy and grammar -- The scope of grammar -- Some morals -- (...)
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  18. Mark Alfano (forthcoming). Moral Psychology: An Introduction. Polity.score: 42.0
    This book provides a rich, systematic, and accessible introduction to moral psychology, aimed at undergraduate philosophy and psychology majors. There are eight chapters, in addition to a short introduction, prospective conclusion, and extensive bibliography. The recipe for each chapter will be: a) to introduce a philosophical topic (e.g., altruism, virtue, preferences, rules) and some prominent positions on it, without assuming prior acquaintance on the part of the reader b) to canvass and explain the relevance of a particular (...)
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  19. Robert May, Notes on Frege on Rules of Inference.score: 42.0
    1. There is only one rule of inference, modus ponens. This is true both in the presentations of Begriffsschrift and Grundgesetze. (But cf. note regarding the latter.) There are other ways of making transitions between propositions in proofs, but these are never labeled by Fregerules of inference.” These pertain to scope of quantification, parsing of formulas (bracketing), introduction of definitions, conventions for the use and replacement of the various letters(variables), and certain structural reorganizations, (e.g. amalgamation of (...)
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  20. Frederic B. Fitch (1973). Natural Deduction Rules for English. Philosophical Studies 24 (2):89 - 104.score: 42.0
    A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, (...)
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  21. Richard Bornat (2005). Proof and Disproof in Formal Logic: An Introduction for Programmers. New Yorkoxford University Press.score: 42.0
    Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages and modern-day programming. (...)
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  22. Nissim Francez (2014). Harmony in Multiple-Conclusion Natural-Deduction. Logica Universalis 8 (2):215-259.score: 42.0
    The paper studies the extension of harmony and stability, major themes in proof-theoretic semantics, from single-conclusion natural-deduction systems to multiple-conclusions natural-deduction, independently of classical logic. An extension of the method of obtaining harmoniously-induced general elimination rules from given introduction rules is suggested, taking into account sub-structurality. Finally, the reductions and expansions of the multiple-conclusions natural-deduction representation of classical logic are formulated.
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  23. Tomasz Furmanowski (1983). The Logic of Algebraic Rules as a Generalization of Equational Logic. Studia Logica 42 (2-3):251 - 257.score: 42.0
    In this paper we start an investigation of a logic called the logic of algebraic rules. The relation of derivability of this logic is defined on universal closures of special disjunctions of equations extending the relation of derivability of the usual equational logic. The paper contains some simple theorems and examples given in justification for the introduction of our logic. A number of open questions is posed.
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  24. Pablo E. Navarro (1993). Promulgation and Derogation of Legal Rules. Law and Philosophy 12 (4):385 - 394.score: 42.0
    In this paper, I consider some problems concerning the structure of legal systems. In order to do this, I basically analyze the promulgation and derogation of legal rules. Frequently, promulgation has been referred to as the introduction of a rule into, and derogation as the removal of a rule from, a normative system. I try to show that there is more to it than that. One of the main ideas of the paper is that the enactment or derogation (...)
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  25. Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.score: 42.0
    A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that (...)
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  26. Bartosz Więckowski (2011). Rules for Subatomic Derivation. Review of Symbolic Logic 4 (2):219-236.score: 42.0
    In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from (...)
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  27. Thomas E. Hill (2012). Virtue, Rules, and Justice: Kantian Aspirations. Oxford University Press.score: 42.0
    General introduction -- I. Basic themes. Kant's ethical theory : an overview ; Kantian normative ethics ; Kantian constructivism as normative ethics -- II. Virtue. Finding value in nature ; Kant on weakness of will ; Kantian virtue and "virtue ethics" ; Kant's Tugendlehre as normative ethics -- III. Moral rules and principles. The dignity of persons : Kant, problems, and a proposal ; Assessing moral rules : utilitarian and Kantian perspectives ; The importance of moral (...) and principles ; Moral construction as a task : sources and limits -- IV. Practical questions. Questions about Kant's opposition to revolution ; Treating criminals as ends in themselves ; Kant and humanitarian intervention ; Moral responsibilities of bystanders. (shrink)
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  28. David C. Makinson, Intelim Rules for Classical Connectives.score: 42.0
    We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also (...)
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  29. Amos Witztum (2008). Corporate Rules, Distributive Justice, and Efficiency. Business Ethics Quarterly 18 (1):85-116.score: 42.0
    The question whether corporations should be used as a means for administering distributive justice is crucial. There are two fundamental issues associated with this. Firstly, would the introduction of rules have any distributional effect? Secondly, what would be the efficiency cost? In this paper, we explore both questions with reference to a job-security corporate rule. We show that the job-security rule will always produce distributional consequences which are consistent with its objectives. However, whether or not it is a (...)
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  30. Kunjumon I. Vadakkan (2013). A Supplementary Circuit Rule-Set for the Neuronal Wiring. Frontiers in Human Neuroscience 7.score: 42.0
    Limitations of known anatomical circuit rules necessitate the identification of supplementary rules. This is essential for explaining how associative sensory stimuli induce nervous system changes that generate internal sensations of memory, concurrent with triggering specific motor activities in response to specific cue stimuli. A candidate mechanism is rapidly reversible, yet stabilizable membrane hemi-fusion formed between the closely apposed postsynaptic membranes of different neurons at locations of convergence of sensory inputs during associative learning. The lateral entry of activity from (...)
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  31. Östen Dahl (1988). The Role of Deduction Rules in Semantics. Journal of Semantics 6 (1):1-18.score: 42.0
    The distinction between ‘partial’ and ‘total’ interpretations (models) is discussed and related to the distinction between proof-theoretical and model-theoretical treatments of logic. It is claimed that there is a parallel between the construction of a proof based on a set of premises and e.g. the production of a natural-language text which is based on information in some kind of data-base. The main part of the paper is devoted to a discussion of the relations between the deduction rules traditionally associated (...)
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  32. Helen Frowe (2011). The Ethics of War and Peace: An Introduction. Routledge.score: 42.0

    When is it right to go to war? When is a war illegal? What are the rules of engagement? What should happen when a war is over? How should we view terrorism?

    The Ethics of War and Peace is a fresh and contemporary introduction to one of the oldest but still most relevant ethical debates. It introduces students to contemporary Just War Theory in a stimulating and engaging way, perfect for those approaching the topic for the first time. (...)

    Helen Frowe explains the core issues in Just War Theory, and chapter by chapter examines the recent and ongoing philosophical? debates on:

    • theories of self defence and national defence
    • Jus ad Bellum, Jus in Bello, and Jus post Bellum
    • the moral status of combatants
    • the principle of non-combatant immunity
    • the nature of terrorism and the moral status of terrorists.

    Each chapter concludes with a useful summary, discussion questions and suggestions for further reading, to aid student learning and revision. The Ethics of War and Peace is the ideal textbook for students studying philosophy, politics and international relations.

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  33. Robert Nola (2007). Theories of Scientific Method: An Introduction. Acumen.score: 42.0
    What is it to be scientific? Is there such a thing as scientific method? And if so, how might such methods be justified? -/- Robert Nola and Howard Sankey seek to provide answers to these fundamental questions in their exploration of the major recent theories of scientific method. Although for many scientists their understanding of method is something they just “pick up” in the course of being trained, Nola and Sankey argue that it is possible to be explicit about what (...)
     
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  34. Peter Schroeder-Heister (2011). Implications-as-Rules Vs. Implications-as-Links: An Alternative Implication-Left Schema for the Sequent Calculus. [REVIEW] Journal of Philosophical Logic 40 (1):95 - 101.score: 42.0
    The interpretation of implications as rules motivates a different left-introduction schema for implication in the sequent calculus, which is conceptually more basic than the implication-left schema proposed by Gentzen. Corresponding to results obtained for systems with higher-level rules, it enjoys the subformula property and cut elimination in a weak form.
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  35. Rico Franses (2000). Introduction to "Iconic Space and the Rule of Lands," by Marie-José Mondzain. Hypatia 15 (4):55-57.score: 40.0
    : This introduction highlights two of Mondzain's contributions in the chapter reproduced here, "Iconic Space and the Rule of Lands." The first is her discussion of a link between images and power, which stresses the formal characteristics of paintings rather than their narratives. The second is her examination of the specific task which representation is called on to perform in religious as opposed to secular contexts, where spiritual, otherworldly figures are given physical shape and form.
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  36. Gerald F. Thomas (2012). The Emancipation of Chemistry. Foundations of Chemistry 14 (2):109-155.score: 36.0
    In his classic work The Mind and its Place in Nature published in 1925 at the height of the development of quantum mechanics but several years after the chemists Lewis and Langmuir had already laid the foundations of the modern theory of valence with the introduction of the covalent bond, the analytic philosopher C. D. Broad argued for the emancipation of chemistry from the crass physicalism that led physicists then and later—with support from a rabblement of philosophers who knew (...)
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  37. Heinrich Wansing (2002). A Rule-Extension of the Non-Associative Lambek Calculus. Studia Logica 71 (3):443-451.score: 36.0
    An extension L + of the non-associative Lambek calculus Lis defined. In L + the restriction to formula-conclusion sequents is given up, and additional left introduction rules for the directional implications are introduced. The system L + is sound and complete with respect to a modification of the ternary frame semantics for L.
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  38. Peter Schroeder-Heister (2012). Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning. Topoi 31 (1):77-85.score: 34.0
    From the point of view of proof-theoretic semantics, it is argued that the sequent calculus with introduction rules on the assertion and on the assumption side represents deductive reasoning more appropriately than natural deduction. In taking consequence to be conceptually prior to truth, it can cope with non-well-founded phenomena such as contradictory reasoning. The fact that, in its typed variant, the sequent calculus has an explicit and separable substitution schema in form of the cut rule, is seen as (...)
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  39. Stephen Read (2010). General-Elimination Harmony and the Meaning of the Logical Constants. Journal of Philosophical Logic 39 (5):557-76.score: 30.0
    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, (...)
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  40. Thomas Kroedel (2012). Implicit Definition and the Application of Logic. Philosophical Studies 158 (1):131-148.score: 30.0
    The paper argues that the theory of Implicit Definition cannot give an account of knowledge of logical principles. According to this theory, the meanings of certain expressions are determined such that they make certain principles containing them true; this is supposed to explain our knowledge of the principles as derived from our knowledge of what the expressions mean. The paper argues that this explanation succeeds only if Implicit Definition can account for our understanding of the logical constants, and that fully (...)
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  41. Nils Kürbis (2012). How Fundamental is the Fundamental Assumption? Teorema 2 (2):5-19.score: 30.0
    The fundamental assumption of Dummett’s and Prawitz’ proof-theoretic justification of deduction is that ‘if we have a valid argument for a complex statement, we can construct a valid argument for it which finishes with an application of one of the introduction rules governing its principal operator’. I argue that the assumption is flawed in this general version, but should be restricted, not to apply to arguments in general, but only to proofs. I also argue that Dummett’s and Prawitz’ (...)
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  42. Dag Prawitz (2006). Meaning Approached Via Proofs. Synthese 148 (3):507 - 524.score: 30.0
    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 (...)
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  43. Nils Kürbis (2008). Stable Harmony. In Peliš Michal (ed.), Logica Yearbook 2007.score: 30.0
    In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.
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  44. Stephen Read (2000). Harmony and Autonomy in Classical Logic. Journal of Philosophical Logic 29 (2):123-154.score: 30.0
    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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  45. By Neil Tennant (2005). Rule-Circularity and the Justification of Deduction. Philosophical Quarterly 55 (221):625–648.score: 30.0
    I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules (...)
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  46. Jon Litland, Topics in Philosophical Logic.score: 30.0
    In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the logical constants to be given by their elimination rules. I then consider the question: given a set of introduction (elimination) rules \(\mathcal{R}\), what are the strongest elimination ( (...)) rules that are validated by an assertability (consequence) conditional meaning-theory based on \(\mathcal{R}\)? I prove that the intuitionistic introduction (elimination) rules are the strongest rules that are validated by the intuitionistic elimination (introduction) rules. I then prove that intuitionistic logic is the strongest logic that can be given either an assertability-conditional or consequence-conditional meaning-theory. In “Grounding Grounding” I discuss the notion of grounding. My discussion revolves around the problem of iterated grounding-claims. Suppose that \(\Delta\) grounds \(\phi\); what grounds that \(\Delta\) grounds that \(\phi\)? I argue that unless we can get a satisfactory answer to this question the notion of grounding will be useless. I discuss and reject some proposed accounts of iterated grounding claims. I then develop a new way of expressing grounding, propose an account of iterated grounding-claims and show how we can develop logics for grounding. In “Is the Vagueness Argument Valid?” I argue that the Vagueness Argument in favor of unrestricted composition isn’t valid. However, if the premisses of the argument are true and the conclusion false, mereological facts fail to supervene on non-mereological facts. I argue that this failure of supervenience is an artifact of the interplay between the necessity and determinacy operators and that it does not mean that mereological facts fail to depend on non-mereological facts. I sketch a deflationary view of ontology to establish this. (shrink)
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  47. Enrico Moriconi & Laura Tesconi (2008). On Inversion Principles. History and Philosophy of Logic 29 (2):103-113.score: 30.0
    The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still (...)
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  48. Ross Thomas Brady (2010). Free Semantics. Journal of Philosophical Logic 39 (5):511 - 529.score: 30.0
    Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic (...)
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  49. Arnon Avron, Tonk- A Full Mathematical Solution.score: 30.0
    There is a long tradition (See e.g. [9, 10]) starting from [12], according to which the meaning of a connective is determined by the introduction and elimination rules which are associated with it. The supporters of this thesis usually have in mind natural deduction systems of a certain ideal type (explained in Section 3 below). Unfortunately, already the handling of classical negation requires rules which are not of that type. This problem can be solved in the framework (...)
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  50. Heinrich Wansing (2006). Connectives Stranger Than Tonk. Journal of Philosophical Logic 35 (6):653 - 660.score: 30.0
    Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. (...)
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