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Summary Logical Pluralism is the view that there is more than one correct logic. What this claim amounts to depends on a specification both of what a logic is and of what it means for a logic to be correct. One of the strongest and most controversial varieties of logical pluralism is the claim that there is more than one correct account of logical consequence, that is, that multiple distinct logics correctly capture the logical consequence relation of natural language.
Key works The recent flurry of interest in strong forms of logical pluralism was initiated by Beall & Restall 2000, in which Beall and Restall argue that there is no single logical consequence relation in natural language, and so no single correct logic. Beall & Restall 2005 further develops the argument. Carnap 1937 argues for pluralism on linguistic grounds: for Carnap, the correctness of logic is relative to the choice of language, and there is no neutral standpoint from which the choice of language can be made. Shapiro 2006 and Cook 2002 independently argue that we should understand logic as a modelling tool: if this is right, then it is certainly possible that there could be two equally good and incommensurable models of the same unitary phenomena. Field 2009 argues that very few forms of logical pluralism are both interesting and true, and Priest 2005 defends logical monism: the view that there is just one correct logic.
Introductions Cook 2010 Russell forthcoming
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  1. Hércules A. Feitosa & Itala M. Loffredo D'Ottaviano (2001). Conservative Translations. Annals of Pure and Applied Logic 108 (1-3):205-227.
    In this paper we introduce the concept of conservative translation between logics. We present some necessary and sufficient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and translations.
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  2. Andrew Aberdein (2001). Classical Recapture. In V. Fano, M. Stanzione & G. Tarozzi (eds.), Prospettive Della Logica E Della Filosofia Della Scienza. Rubettino 11-18.
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  3. Musa Akrami (2007). From Logical Complementarity and Pluralism to Super-Logic. In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic. 67.
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  4. Patrick Allo (2016). Logic, Reasoning and Revision. Theoria 82 (1):3-31.
    The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this article I first place Harman's challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms (...)
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  5. Patrick Allo (2014). Synonymy and Intra-Theoretical Pluralism. Australasian Journal of Philosophy 93 (1):77-91.
    The starting point of this paper is a version of intra-theoretical pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second (...)
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  6. Patrick Allo (2013). Noisy Vs. Merely Equivocal Logics. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer 57--79.
    Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...)
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  7. Patrick Allo (2012). Information and Logical Discrimination. In S. Barry Cooper (ed.), How the World Computes. 17--28.
    Informational conceptions of logic are barely novel. We find them in the work of John Corcoran, in several papers on substructural and constructive logics by Heinrich Wansing, and in the interpretation of the Routley-Meyer semantics for relevant logics in terms of Barwises and Perrys theory of situations. Allo & Mares [2] present an informational account of logical consequence that is based on the content-nonexpantion platitude, but that also relies on a double inversion of the standard direction of explanation (in- formation (...)
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  8. Patrick Allo (2007). Logical Pluralism and Semantic Information. Journal of Philosophical Logic 36 (6):659 - 694.
    Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore.
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  9. Patrick Allo & Edwin Mares (2012). Informational Semantics as a Third Alternative? Erkenntnis 77 (2):167-185.
    Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...)
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  10. Tomás Barrero (2006). Carnielli, Walter (ed.). Logic and Philosophy of the Formal Sciences: A Festscrift for Itala M. Loffredo D´ Ottaviano. São Paulo: Centro de Lógica, Epistemología e Historia da Ciência, UNICAMP (Número especial de Manuscrito, Revista Internacional de Filosofia, vol. 28, n. 2, jul-dez.) pp. 191-591.(2005). [REVIEW] Ideas Y Valores 55 (132):124-126.
  11. Jeremy Barris (2014). Metaphysics, Deep Pluralism, and Paradoxes of Informal Logic. International Journal of Philosophical Studies 23 (1):59-84.
    The paper argues that metaphysical thought, or thought in whose context our general framework of sense is under scrutiny, involves, legitimates, and requires a variety of informal analogues of the ‘true contradictions’ supported in some paraconsistent formal logics. These are what we can call informal ‘legitimate logical inadequacies’. These paradoxical logical structures also occur in deeply pluralist contexts, where more than one, conflicting general framework for sense is relevant. The paper argues further that these legitimate logical inadequacies are real or (...)
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  12. Neil Barton (2015). Pluralism in Mathematics: A New Position in Philosophy of Mathematics. By Michèle Friend. Logic, Epistemology and the Unity of Science, Springer, 2014. £60. ISBN 978-94-007-7058-4. [REVIEW] Philosophy 90 (4):685-691.
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  13. Jc Beall (2014). Strict-Choice Validities: A Note on a Familiar Pluralism. Erkenntnis 79 (2):301-307.
    My aim here is a modest one: to note another example in which the theory of validity and the theory of ‘inference’ naturally come apart. The setting is multiple-conclusion logic. At least on one philosophy of multiple-conclusion logic, there are very clear examples of where logic qua validity and logic qua normative guide to inference are essentially different things. On the given conception, logic tells us only what follows from what, what our ‘choices’ are given a set of premises; it (...)
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  14. JC Beall & Greg Restall, Defending Logical Pluralism.
    We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logical consequence is to be defined. To quote Jeffrey.
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  15. Jc Beall & Greg Restall (2005). Logical Pluralism. Oxford University Press.
    Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...)
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  16. Jc Beall & Greg Restall (2000). Logical Pluralism. Australasian Journal of Philosophy 78 (4):475 – 493.
    Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...)
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  17. Francesco Berto (2015). A Modality Called ‘Negation’. Mind 124 (495):761-793.
    I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...)
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  18. Francesco Berto (2006). Characterizing Negation to Face Dialetheism. Logique Et Analyse 49 (195):241-263.
  19. Manuel Bremer, What is Logical Pluralism?
    Within the philosophy of logic there has been an old debate about strengths and weaknesses of so-called “deviant” logics, as compared to standard logic (i.e. First Order Logic with Identity). With the development of a multitude of many-valued and modal logical systems and the various ways they can be employed in various fields of philosophy, linguistics and computer science, former “deviant” logics have become well accepted. Nowadays we seem to have a new and almost contrary debate about whether there is (...)
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  20. Manuel Bremer (2014). Restall and Beall on Logical Pluralism: A Critique. Erkenntnis 79 (2):293-299.
    With their book Logical Pluralism, Jc Beall and Greg Restall have elaborated on their previous statements on logical pluralism. Their view of logical pluralism is centred on ways of understanding logical consequence. The essay tries to come to grips with their doctrine of logical pluralism by highlighting some points that might be made clearer, and questioning the force of some of Beall’s and Restall’s central arguments. In that connection seven problems for their approach are put forth: (1) The Informal Common (...)
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  21. Georg Brun (2012). Rival Logics, Disagreement and Reflective Equilibrium. In C. Jaeger W. Loeffler (ed.), Epistemology: Contexts, Values, Disagreements (Proceedings of the 34th International Ludwig Wittgenstein Symposium). 355-368.
    Two challenges to the method of reflective equilibrium have been developed in a dispute between Michael D. Resnik and Stewart Shapiro: because the method itself involves logical notions, it can neither be specified in a logic-neutral way nor can it allow logical pluralism. To analyse and answer these claims, an explicit distinction is introduced between judgements held prior to the process of mutual adjustments and judgements in agreement with the systematic principles, which result from the process. It is then argued (...)
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  22. Otávio Bueno & Scott A. Shalkowski (2009). Modalism and Logical Pluralism. Mind 118 (470):295-321.
    Logical pluralism is the view according to which there is more than one relation of logical consequence, even within a given language. A recent articulation of this view has been developed in terms of quantification over different cases: classical logic emerges from consistent and complete cases; constructive logic from consistent and incomplete cases, and paraconsistent logic from inconsistent and complete cases. We argue that this formulation causes pluralism to collapse into either logical nihilism or logical universalism. In its place, we (...)
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  23. J. A. Burgess (2010). Review of J.C. Beall and Greg Restall, Logical Pluralism. [REVIEW] Philosophy and Phenomenological Research 81 (2):519-522.
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  24. Rudolf Carnap (1937). The Logical Syntax of Language. London, K. Paul, Trench, Trubner & Co., Ltd..
    Available for the first time in 20 years, here is the Rudolf Carnap's famous principle of tolerance by which everyone is free to mix and match the rules of ...
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  25. Nicola Ciprotti & Luca Moretti (2009). Logical Pluralism is Compatible with Monism About Metaphysical Modality. Australasian Journal of Philosophy 87 (2):275-284.
    Beall and Restall 2000; 2001; 2006 advocate a comprehensive pluralist approach to logic, which they call Logical Pluralism, according to which there is not one true logic but many equally acceptable logical systems. They maintain that Logical Pluralism is compatible with monism about metaphysical modality, according to which there is just one correct logic of metaphysical modality. Wyatt 2004 contends that Logical Pluralism is incompatible with monism about metaphysical modality. We first suggest that if Wyatt were right, Logical Pluralism would (...)
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  26. Daniel Cohnitz, Peter Pagin & Marcus Rossberg (2014). Monism, Pluralism and Relativism: New Essays on the Status of Logic. Erkenntnis 79 (2):201-210.
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  27. Roy T. Cook (2010). Let a Thousand Flowers Bloom: A Tour of Logical Pluralism. Philosophy Compass 5 (6):492-504.
    Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent attempts to argue for (...)
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  28. John Corcoran (2010). Peter Hare on the Proposition. Transactions of the Charles S. Peirce Society 46 (1):21-34.
    Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department in (...)
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  29. Bożena Czarnecka-Rej (2013). Czym jest pluralizm logiczny?(stanowisko JC Bealla i Grega Restalla). Roczniki Filozoficzne 61 (1):5-22.
    WHAT IS LOGICAL PLURALISM? (J.C. BEALL’S AND GREG RESTALL’S STANDPOINT) S u m m a r y C. Beall and Greg Restall are advocates of a comprehensive pluralist approach to logic, which they call Logical Pluralism (LP). According to LP, there is not one correct logic, but many equally acceptable logical systems. The authors share Tarski’s conviction and follow the mainstream in thinking about logic as the discipline that investigates the notion of logical consequence. LP is the pluralism about logical (...)
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  30. Bogdan Dicher (2014). Logical Pluralism and the Meaning of the Logical Constants. Dissertation, The University of Melbourne
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  31. Antonino Drago (2012). Pluralism in Logic: The Square of Opposition, Leibniz'Principle of Sufficient Reason and Markov's Principle. In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser 175--189.
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  32. Matti Eklund (2012). Multitude, Tolerance and Language-Transcendence. Synthese 187 (3):833-847.
    Rudolf Carnap's 1930s philosophy of logic, including his adherence to the principle of tolerance, is discussed. What theses did Carnap commit himself to, exactly? I argue that while Carnap did commit himself to a certain multitude thesis—there are different logics of different languages, and the choice between these languages is merely a matter of expediency—there is no evidence that he rejected a language-transcendent notion of fact, contrary to what Warren Goldfarb and Thomas Ricketts have prominently argued. (In fact, it is (...)
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  33. Manuel Carmo Ferreira (1993). A Intersubjectividade Em Kant. Revista Portuguesa de Filosofia 49 (4):571 - 585.
    A convergência de interpretações contemporâneas de Kant (Jacobi) e nossas contemporâneas (Apel e Habermas) na crítica ao monologismo. tanto teorético como prático, inerente à filosofia kantiana, é questionada pela emergência nesta de referências signitlcativas à ordem intersubjectiva, na defesa de um pluralismo lógico. ético e estético que culmina na concepção de uma razão comunicacional. /// La convergence d'interprétations contemporaines de Kant (Jacobi) et nos contemporaines (Apel et Habermas) dans la critique au monologisme. aussi théorétique que pratique, inhérent à la philosophie (...)
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  34. Hartry Field (2009). Pluralism in Logic. Review of Symbolic Logic 2 (2):342-359.
    There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...)
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  35. Michèle Friend, Pluralism in Mathematics: A New Position in Philosophy of Mathematics.
    The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart (...)
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  36. Michèle Friend (2014). Using a Formal Theory of Logic Metaphorically. In Pluralism in Mathematics: A New Position in Philosophy of Mathematics. Springer Netherlands
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  37. Michele Friend & Andrea Pedeferri (2011). An Analysis of the Notion of Rigour in Proofs. Logic and Philosophy of Science 9 (1):165-171.
    We are told that there are standards of rigour in proof, and we are told that the standards have increased over the centuries. This is fairly clear. But rigour has also changed its nature. In this paper we as-sess where these changes leave us today.1 To motivate making the new assessment, we give two illustra-tions of changes in our conception of rigour. One, concerns the shift from geometry to arithmetic as setting the standard for rig-our. The other, concerns the notion (...)
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  38. Dov Gabbay & John Woods (2003). Normative Models of Rational Agency: The Theoretical Disutility of Certain Approaches. Logic Journal of the IGPL 11 (6):597-613.
    Much of cognitive science seeks to provide principled descriptions of various kinds and aspects of rational behaviour, especially in beings like us or AI simulacra of beings like us. For the most part, these investigators presuppose an unarticulated common sense appreciation of the rationality that such behaviour consists in. On those occasions when they undertake to bring the relevant norms to the surface and to give an account of that to which they owe their legitimacy, these investigators tend to favour (...)
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  39. Antonio García Gutiérrez (2007). Desclasificados: Pluralismo Lógico y Violencia de la Clasificación. Feder.
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  40. G. C. Goddu (2002). What Exactly is Logical Pluralism? Australasian Journal of Philosophy 80 (2):218 – 230.
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  41. Susana Gómez (2007). Language and Logical Pluralism: Some Aspects of a Wittgensteinian Perspective on the Nature of Logic. Logic Journal of the IGPL 15 (5-6):603-619.
    This essay examines the importance of some aspects of Wittgenstein's post-Tractatus work in the realm of discussions on the nature of logic. The first part considers a relationship between certain conceptions of language and certain positions on the nature of logical laws and logical pluralism. Supposing the rejection of mentalism in the field of meaning leads to a rejection of psychologism, it presents some alternatives different from psychologism, based on non mentalistic theories of meaning. One is the Platonistic Fregean approach (...)
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  42. José González (2006). Las Lógicas No Clásicas Como Reflejo Del Pluralismo Lógico. Gladis Palau, Introducción Filosófica A Las Lógicas No ClásicasNon-classical Logics As A Reflexion Of Logical Pluralism. Gladis Palau, Introducción Filosófica A Las Lógicas No Clásicas. [REVIEW] Laguna 18.
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  43. Ivor Grattan-Guinness (2011). Was Hugh MacColl a Logical Pluralist or a Logical Monist? A Case Study in the Slow Emergence of Metatheorising. Philosophia Scientiae 15:189-203.
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  44. Ivor Grattan-Guinness (2011). Was Hugh MacColl a Logical Pluralist or a Logical Monist? A Case Study in the Slow Emergence of Metatheorising. Philosophia Scientae 15:189-203.
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  45. Owen Griffiths (2013). Problems for Logical Pluralism. History and Philosophy of Logic 34 (2):170 - 182.
    I argue that Beall and Restall's logical pluralism fails. Beall?Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ?settled core? of consequence: they believe that truth-preservation, necessity, formality and normativity are ?settled? features of logical consequence and that any relation satisfying these criteria is a logical consequence relation. I consider historical evidence and argue that their (...)
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  46. Lucas P. Halpin (2012). Analyticity and Substantive Inquiry. Self-Published.
    In this book, a Grice/Strawson account of analyticity is explained and formalized, and a corresponding account of logic is offered. The implications of these views for science/substantive inquiry are explored and a neo-Carnapian/verificationist meta-theory is presented.
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  47. Geoffrey Hellman (2006). Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis. Journal of Philosophical Logic 35 (6):621-651.
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  48. Ole Hjortland (2014). Verbal Disputes in Logic: Against Minimalism for Logical Connectives. Logique Et Analyse 227:463-486.
    Logic, Logical connectives, Verbal disputes, Proof theory, Non-classical logic.
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  49. Ole Thomassen Hjortland (2013). Logical Pluralism, Meaning-Variance, and VerbalDisputes. Australasian Journal of Philosophy 91 (2):355-373.
    Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and (...)
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  50. Lloyd Humberstone (2009). Logical Pluralism. Australasian Journal of Philosophy 87 (1):162 – 168.
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