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197The relativity and universality of logicSynthese 192 (7): 1939-1954. 2015.After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we discuss the emergence of universal logic as a general theory of logical systems, making comparison with universal algebra and the project of mathesis universalis. In a third part we critically present three lines of research connected to universal logic: logical …Read more
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51Many-valued and Kripke semanticsIn Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics, Springer. pp. 89--101. 2006.
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From Paraconsistent Logic to Universal LogicSorites 12 5-32. 2001.For several years I have been developing a general theory of logics that I have called Universal Logic. In this article I will try to describe how I was led to this theory and how I have progressively conceived it, starting my researches about ten years ago in Paris in paraconsistent logic and the broadening my horizons, pursuing my researches in Brazil, Poland and the USA
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Was Frege Wrong when Identifying Reference with Truth-Value?Sorites 11 15-23. 1999.We discuss Sengupta's argumentation according to which Frege was wrong identifying reference with truth-value.After stating various possible interpretations of Frege's principle of substitution, we show that there is no coherent interpretation under which Sengupta's argumentation is valid.Finally we try to show how Frege's distinction can work in the context of modern mathematics and how modern logic grasps it
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56of implication and generalization rules have a close relationship, for which there is a key idea for clarifying how they are connected: varying objects. Varying objects trace how generalization rules are used along a demonstration in an axiomatic calculus. Some ways for introducing implication and for generalization are presented here, taking into account some basic properties that calculi can have.
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83Truth as a Mathematical ObjectPrincipia: An International Journal of Epistemology 14 (1): 31-46. 2010.Neste artigo, discutimos em que sentido a verdade é considerada como um objeto matemático na lógica proposicional. Depois de esclarecer como este conceito é usado na lógica clássica, através das noções de tabela de verdade, de função de verdade, de bivaloração, examinamos algumas generalizações desse conceito nas lógicas não clássicas: semânticas matriciais multi-valoradas com três ou quatro valores, semântica bivalente não veritativa, semânticas dos mundos possiveis de Kripke. DOI:10.5007/1808-…Read more
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17Preface: Scope of Logic Theorems In Memoriam Adolf LindenbaumLogica Universalis 8 (3-4): 283-284. 2014.
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Paraconsistent Logic!Sorites 17 17-25. 2006.We answer Slater's argument according to which paraconsistent logic is a result of a verbal confusion between «contradictories» and «subcontraries». We show that if such notions are understood within classical logic, the argument is invalid, due to the fact that most paraconsistent logics cannot be translated into classical logic. However we prove that if such notions are understood from the point of view of a particular logic, a contradictory forming function in this logic is necessarily a clas…Read more
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58From consequence operator to universal logic: a survey of general abstract logicIn J. Y. Beziau (ed.), Logica Universalis, Birkhäuser Verlog. pp. 3--17. 2005.
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41Semantic computations of truth based on associations already learnedJournal of Applied Logic 2 (4): 457-467. 2004.
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655La Pointure du Symbole (edited book)Petra. 2014.Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente et ce qui est représenté, joue un rôle fondamental dans la plupart des activités humaines, qu’elles soient scientifiques, artistiques ou religieuses. C’est cette dimension symbolique, sa portée, son fonctionnement et sa signification dans des domaines aussi var…Read more
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87Logic may be simple. Logic, congruence and algebraLogic and Logical Philosophy 5 (n/a): 129-147. 1997.This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLane-Curry’s theorem and a discussion about Curry’s algebras). We also examine how these…Read more
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54The New Rising of the Square of OppositionIn J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition, Birkhäuser. pp. 3--19. 2012.
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241What is “Formal Logic”?Proceedings of the Xxii World Congress of Philosophy 13 9-22. 2008.“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science…Read more
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10Ruth Barcan Marcus est-elle la mère du fils de Wittgenstein?(Considerations existencialistes sur la formule de Barcan)Manuscrito: Revista Internacional de Filosofía 22 (2): 11-27. 1999.
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105Many-valued logics are standardly defined by logical matrices. They are truth-functional. In this paper non truth-functional many-valued semantics are presented, in a philosophical and mathematical perspective.
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33O Suicídio segundo Arthur SchopenhauerDiscurso 28 127-144. 1997.Neste artigo examinamos a concepção filosófica do suicídio em Schopenhauer. Mostramos que a razão fundamental pela qual Schopenhauer rejeita o suicídio está intimamente ligada ao fundamento da sua metafísica. Explicamos suas diferenças face às rejeições tradicionais do suicídio, visto que Schopenhauer considera o suicídio um erro mas não um crime, e quais são os casos nos quais o suicídio pode ser aceito
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94In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. A de…Read more
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Définition, théorie Des objets et paraconsistance (definition, objects' theory and paraconsistance)Theoria 13 (2): 367-379. 1998.Trois sortes de définitions sont présentées et discutées: les définitions nominales, les définitions contextuelles et les définitions amplificatrices. On insiste sur le fait que I’elimination des definitions n’est pas forcement un procede automatique en particulier dans le cas de la logique paraconsistante. Finalement on s’int’resse à la théorie des objets de Meinong et l’on montre comment elle peut êrre considéréecomme une théorie des descripteurs.Three kinds of definitions are presented and di…Read more
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19Truth as a Mathematical Object DOI:10.5007/1808-1711.2010v14n1p31Principia: An International Journal of Epistemology 14 (1): 31-46. 2010.In this paper we discuss in which sense truth is considered as a mathematical object in propositional logic. After clarifying how this concept is used in classical logic, through the notions of truth-table, truth-function and bivaluation, we examine some generalizations of it in non-classical logics: many-valued matrix semantics with three and four values, non-truth-functional bivalent semantics, Kripke possible world semantics. • DOI:10.5007/1808-1711.2010v14n1p31.
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107Relativizations of the Principle of IdentityLogic Journal of the IGPL 5 (3): 17-29. 1997.We discuss some logico-mathematical systems which deviate from classical logic and mathematics with respect to the concept of identity. In the first part of the paper we present very general formulations of the principle of identity and show how they can be ‘relativized’ to objects and to properties. Then, as an application, we study the particular cases of physics and logic . In the last part of the paper, we discuss the alphabar logics, that is, those logical systems which violate a formulatio…Read more