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  1. (2 other versions)The Collected Papers of Gerhard Gentzen.K. Schütte - 1972 - Journal of Symbolic Logic 37 (4):752-753.
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  • (1 other version)The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • A proof-theoretic defence of meaning-invariant logical pluralism.Bogdan Dicher - 2016 - Mind 125 (499):727-757.
    In this paper I offer a proof-theoretic defence of meaning-invariant logical pluralism. I argue that there is a relation of co-determination between the operational and structural aspects of a logic. As a result, some features of the consequence relation are induced by the connectives. I propose that a connective is defined by those rules which are conservative and unique, while at the same time expressing only connective-induced structural information. This is the key to stabilizing the meaning of the connectives across (...)
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  • Harmony in a sequent setting: a reply to Tennant.F. Steinberger - 2011 - Analysis 71 (2):273-280.
    In my Steinberger 2009 I argued that Neil Tennant’s Harmony requirement is untenable because of its failure to account for the standard quantifier rules.1 Instead of justifying the customary rules for the existential and universal quantifiers, Tennant’s account appears to sanction only wholly unrestricted – and so patently disharmonious – quantifier rules. In his characteristically thoughtful response Tennant 2010, Tennant offers a sequent calculus version of his Harmony requirement that rules out such pathological would-be quantifiers. While I agree with Tennant (...)
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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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  • Anything Goes.David Ripley - 2015 - Topoi 34 (1):25-36.
    This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.
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  • Pluralism and Proofs.Greg Restall - 2014 - Erkenntnis 79 (S2):279-291.
    Beall and Restall’s Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical (...)
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  • Rule-Circularity and the Justification of Deduction.Neil Tennant - 2005 - Philosophical Quarterly 55 (221):625 - 648.
    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 of Disquotation and (...)
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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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  • Stable Harmony.Nils Kurbis - 2008 - In Peliš Michal (ed.), Logica Yearbook 2007.
    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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  • Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
    This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends classical (...)
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  • Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
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  • (1 other version)The runabout inference ticket.Arthur Prior - 1967 - In Peter Frederick Strawson (ed.), Philosophical logic. London,: Oxford University Press. pp. 38-9.
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  • The Geometry of Non-Distributive Logics.Greg Restall & Francesco Paoli - 2005 - Journal of Symbolic Logic 70 (4):1108 - 1126.
    In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...)
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  • Rule-circularity and the justification of deduction.By Neil Tennant - 2005 - Philosophical Quarterly 55 (221):625–648.
    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 of Disquotation and (...)
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  • A natural extension of natural deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
    The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved.
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  • Basic logic: Reflection, symmetry, visibility.Giovanni Sambin, Giulia Battilotti & Claudia Faggian - 2000 - Journal of Symbolic Logic 65 (3):979-1013.
    We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with (...)
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  • What Harmony Could and Could Not Be.Florian Steinberger - 2011 - Australasian Journal of Philosophy 89 (4):617 - 639.
    The notion of harmony has played a pivotal role in a number of debates in the philosophy of logic. Yet there is little agreement as to how the requirement of harmony should be spelled out in detail or even what purpose it is to serve. Most, if not all, conceptions of harmony can already be found in Michael Dummett's seminal discussion of the matter in The Logical Basis of Metaphysics. Hence, if we wish to gain a better understanding of the (...)
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  • The structure of logical consequence : proof-theoretic conceptions.Ole T. Hjortland - unknown
    The model-theoretic analysis of the concept of logical consequence has come under heavy criticism in the last couple of decades. The present work looks at an alternative approach to logical consequence where the notion of inference takes center stage. Formally, the model-theoretic framework is exchanged for a proof-theoretic framework. It is argued that contrary to the traditional view, proof-theoretic semantics is not revisionary, and should rather be seen as a formal semantics that can supplement model-theory. Specifically, there are formal resources (...)
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  • On a Generality Condition in Proof‐Theoretic Semantics.Bogdan Dicher - 2017 - Theoria 83 (4):394-418.
    In the recent literature on proof-theoretic semantics, there is mention of a generality condition on defining rules. According to this condition, the schematic formulation of the defining rules must be maximally general, in the sense that no restrictions should be placed on the contexts of these rules. In particular, context variables must always be present in the schematic rules and they should range over arbitrary collections of formulae. I argue against imposing such a condition, by showing that it has undesirable (...)
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  • A Robust Non-transitive Logic.Alan Weir - 2015 - Topoi 34 (1):1-9.
    Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and surreal-valued (...)
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  • The taming of the true.Michael Glanzberg - 2000 - Philosophical Review 109 (2):290-293.
    The Taming of the True continues the project Neil Tennant began in Anti-realism and Logic of investigating and defending anti-realism. Tennant’s earlier book anticipated a second volume, in which issues related to empirical discourse would be addressed in greater detail. The Taming of the True provides this sequel. It also attempts a ground-clearing project, by addressing challenges to some of the presuppositions and implications of Tennant’s anti-realist position. Finally, it takes an opportunity to revisit some of the issues examined in (...)
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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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  • The Connectives.Ian Humberstone - unknown
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  • Logical constants as punctuation marks.Kosta Došen - 1989 - Notre Dame Journal of Formal Logic 30 (3):362-381.
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  • Not so stable.Florian Steinberger - 2009 - Analysis 69 (4):655-661.
    According to Michael Dummett, we may think of the meaning of an expression as given by the principles governing the use we make of it. The principles regulating our linguistic practices can then be grouped into two broad categories (Dummett 1973: 396, 1991: 211). We might state them as follows: I-principles: state the circumstances under which an assertion of a sentence containing the expression in question is warranted. E-principles: state the consequences of asserting a sentence containing the expression. In the (...)
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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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  • Investigations into a left-structural right-substructural sequent calculus.Lloyd Humberstone - 2007 - Journal of Logic, Language and Information 16 (2):141-171.
    We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we (...)
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  • (2 other versions)Elements of Intuitionism.Nicolas D. Goodman - 1979 - Journal of Symbolic Logic 44 (2):276-277.
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  • What’s Wrong with Tonk.Roy T. Cook - 2005 - Journal of Philosophical Logic 34 (2):217 - 226.
    In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence.
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  • On the Equivalence Conjecture for Proof-Theoretic Harmony.Florian Steinberger - 2013 - Notre Dame Journal of Formal Logic 54 (1):79-86.
    The requirement of proof-theoretic harmony has played a pivotal role in a number of debates in the philosophy of logic. Different authors have attempted to precisify the notion in different ways. Among these, three proposals have been prominent in the literature: harmony–as–conservative extension, harmony–as–leveling procedure, and Tennant’s harmony–as–deductive equilibrium. In this paper I propose to clarify the logical relationships between these accounts. In particular, I demonstrate that what I call the equivalence conjecture —that these three notions essentially come to the (...)
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  • Are Uniqueness and Deducibility of Identicals the Same?Alberto Naibo & Mattia Petrolo - 2014 - Theoria 81 (2):143-181.
    A comparison is given between two conditions used to define logical constants: Belnap's uniqueness and Hacking's deducibility of identicals. It is shown that, in spite of some surface similarities, there is a deep difference between them. On the one hand, deducibility of identicals turns out to be a weaker and less demanding condition than uniqueness. On the other hand, deducibility of identicals is shown to be more faithful to the inferentialist perspective, permitting definition of genuinely proof-theoretical concepts. This kind of (...)
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  • (2 other versions)Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
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  • Book reviews. [REVIEW]Dag Prawitz - 1994 - Mind 103 (411):373-376.
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  • Conservativeness and uniqueness.Peter Schroeder-Heister - 1985 - Theoria 51 (3):159-173.
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  • Conservativeness and uniqueness.Kosta Došen - 1985 - Theoria 51 (3):159.
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