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Jean-Yves Beziau
Universidade Federal do Rio de Janeiro
  1.  30
    Logic and Philosophy of Religion.Ricardo Silvestre & Jean-Yves Beziau - 2017 - Sophia 56 (2):139–145.
    This paper introduces a special issue on logic and philosophy of religion in this journal (Sophia). After discussing the role played by logic in the philosophy of religion along with classical developments, we present the basic motivation for this special issue accompanied by an exposition of its content.
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  2. The Power of the Hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
    The hexagon of opposition is an improvement of the square of opposition due to Robert Blanché. After a short presentation of the square and its various interpretations, we discuss two important problems related with the square: the problem of the I-corner and the problem of the O-corner. The meaning of the notion described by the I-corner does not correspond to the name used for it. In the case of the O-corner, the problem is not a wrong-name problem but a no-name (...)
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  3.  26
    Logic and Religion.Jean-Yves Beziau & Ricardo Silvestre - 2017 - Logica Universalis 11 (1):1-12.
    We first start by describing the happening of the 1st World Congress on Logic and Religion. We then explain the motivation for developing the interaction between logic and religion. In a third part we discuss some papers presented at this event published in the present special issue.
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  4.  44
    Is the Principle of Contradiction a Consequence of $$X^{2}=X$$ X 2 = X?Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):55-81.
    According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as \. We examine in which framework this makes sense and up to which point it depends on notation. This leads us to make various comments on the history and philosophy of modern logic.
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  5.  8
    Paraconsistent Logic From a Modal Viewpoint.Jean-Yves Béziau - 2005 - Journal of Applied Logic 3 (1):7-14.
  6.  23
    Universal Logic: Evolution of a Project.Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):1-8.
    We discuss the origin and development of the universal logic project. We describe in particular the structure of UNILOG, a series of events created for promoting the universal logic project, with a school, a congress, a secret speaker and a contest. We explain how the contest has evolved into a session of logic prizes.
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  7.  24
    Disentangling Contradiction From Contrariety Via Incompatibility.Jean-Yves Beziau - 2016 - Logica Universalis 10 (2-3):157-170.
    Contradiction is often confused with contrariety. We propose to disentangle contrariety from contradiction using the hexagon of opposition, providing a clear and distinct characterization of three notions: contrariety, contradiction, incompatibility. At the same time, this hexagonal structure describes and explains the relations between them.
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  8.  12
    Trivial Dialetheism and the Logic of Paradox.Jean-Yves Beziau - 2016 - Logic and Logical Philosophy 25 (1):51-56.
    In this paper we explain that the paraconsistent logic LP promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.
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  9.  47
    A New Four-Valued Approach to Modal Logic.Jean-Yves Béziau - 2011 - Logique Et Analyse 54 (213):109.
  10.  75
    New Dimensions of the Square of Opposition.Jean-Yves Beziau & Stamatios Gerogiorgakis (eds.) - 2017 - Munich: Philosophia.
    The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has recently (...)
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  11.  8
    Logic Prizes Et Cætera.Jean-Yves Beziau - 2018 - Logica Universalis 12 (3-4):271-296.
    I discuss the origin and development of logic prizes around the world. In a first section I describe how I started this project by creating the Newton da Costa Logic Prize in Brazil in 2014. In a second section I explain how this idea was extended into the world through the manifesto A Logic Prize in Every Country! and how was organized the Logic Prizes Contest at the 6th UNILOG in Vichy in June 2018 with the participation of 9 logic (...)
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  12.  17
    The Square of Opposition: A Cornerstone of Thought.Jean-Yves Beziau & Gianfranco Basti (eds.) - 2016 - Basel, Switzerland: Birkhäuser.
    This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.
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  13.  25
    The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem.Jean-Yves Béziau - 2006 - Logic and Logical Philosophy 15 (2):99-111.
    We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem.
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  14. The Relativity and Universality of Logic.Jean-Yves Beziau - 2015 - Synthese 192 (7):1939-1954.
    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 pluralism, (...)
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  15.  63
    Classical Negation Can Be Expressed by One of its Halves.Jean-Yves Beziau - 1999 - Logic Journal of the IGPL 7 (2):145-151.
    We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an extension of (...)
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  16.  22
    The Vatican Square.Jean-Yves Beziau & Raffaela Giovagnoli - 2016 - Logica Universalis 10 (2-3):135-141.
    After explaining the interdisciplinary aspect of the series of events organized around the square of opposition since 2007, we discuss papers related to the 4th World Congress on the Square of Opposition which was organized in the Vatican at the Pontifical Lateran University in 2014. We distinguish three categories of work: those dealing with the evolution and development of the theory of opposition, those using the square as a metalogical tool to give a better understanding of various systems of logic (...)
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  17.  24
    From Consequence Operator to Universal Logic: A Survey of General Abstract Logic.Jean-Yves Beziau - 2005 - In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlog. pp. 3--17.
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  18.  34
    Preface.Jean-Yves Beziau & Gillman Payette - 2008 - Logica Universalis 2 (1):1-1.
  19. Professor Newton CA da Costa Awarded Nicholas Copernicus University Medal of Merit.Newton C. A. da Costa, Jean-Yves Béziau & Otávio Bueno - 1999 - Logic and Logical Philosophy 7:7-10.
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  20.  71
    Non Truth-Functional Many-Valuedness.Jean-Yves Beziau - manuscript
    Many-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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  21. Malinowski and Suszko on Many-Valued Logics: On the Reduction of Many-Valuedness to Two-Valuedness.Newton da Costa, Jean-Yves Béziau & Otávio Bueno - 1996 - Modern Logic 6 (1):272--299.
  22.  33
    13 Questions About Universal Logic.Jean-Yves Béziau - 2006 - Bulletin of the Section of Logic 35 (2/3):133-150.
  23. What is “Formal Logic”?Jean-Yves Béziau - 2008 - Proceedings of the Xxii World Congress of Philosophy 13:9-22.
    “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, (3) Formal (...)
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  24.  35
    Truth as a Mathematical Object.Jean-Yves Béziau - 2010 - Principia: An International Journal of Epistemology 14 (1):31-46.
    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:10.5007/1808-1711.2010v14n1p31.
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  25. Théorie de la Valuation.Newton Ca da Costa & Jean-Yves Béziau - 1994 - Logique Et Analyse 146 (146):95-117.
     
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  26.  22
    Sequents and Bivaluations.Jean-Yves Béziau - 2001 - Logique Et Analyse 44 (176):373-394.
  27.  28
    Square of Opposition: A Diagram and a Theory in Historical Perspective.Jean-Yves Beziau & Stephen Read - 2014 - History and Philosophy of Logic 35 (4):315-316.
  28.  11
    1st World Logic Day: 14 January 2019.Jean-Yves Beziau - 2019 - Logica Universalis 13 (1):1-20.
    We assess the celebration of the 1st World Logic Day which recently took place all over the world. We then answer the question Why a World Logic Day? in two steps. First we explain why promoting logic, emphasizing its fundamental importance and its relations with many other fields. Secondly we examine the sense of a one-day celebration: how this can help reinforcing logic day-to-day and why logic deserves it. We make a comparison with other existing one-day celebrations. We end by (...)
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  29.  20
    Around and Beyond the Square of Opposition.Jean-Yves Béziau & Dale Jacquette (eds.) - 2012 - Springer Verlag.
    Jean-Yves Béziau Abstract In this paper I relate the story about the new rising of the square of opposition: how I got in touch with it and started to develop new ideas and to organize world congresses on the topic with subsequent publications.
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  30.  26
    Logic May Be Simple. Logic, Congruence and Algebra.Jean-Yves Béziau - 1997 - Logic and Logical Philosophy 5:129-147.
    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 concepts are related to such notions as (...)
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  31. What is Semantics? A Brief Note on a Huge Question.Newton da Costa, Otávio Bueno & Jean-Yves Béziau - 1995 - Sorites 3:43-47.
    After mentioning the cogent connection between pure semantics and the particular set theoretical framework in which it is formulated, some issues regarding the conceptual status of semantics itself, as well as its relationship to logic, are concisely raised.
     
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  32.  8
    Semantic Computations of Truth Based on Associations Already Learned.Patrick Suppes & Jean-Yves Béziau - 2004 - Journal of Applied Logic 2 (4):457-467.
  33.  18
    Non Truth-Functional Many-Valuedness.Buchsbaum Arthur & Jean-Yves Béziau - unknown
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  34. The Square of Opposition: A General Framework for Cognition.Jean-Yves Beziau & Gillman Payette (eds.) - 2011
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  35.  40
    BookReview.Jean-Yves Beziau - 2012 - Studia Logica 100 (3):653-657.
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  36.  16
    A Sequent Calculus for Lukasiewicz's Three-Valued Logic Based on Suszko's Bivalent Semantics.Jean-Yves Béziau - 1999 - Bulletin of the Section of Logic 28 (2):89-97.
  37.  7
    Aspects of Paraconsistent Logic.Newton C. A. da Costa, Jean-Yves Béziau & Otávio A. S. Bueno - 1995 - Logic Journal of the IGPL 3 (4):597-614.
  38.  8
    Aspects of Paraconsistent Logic.Newton A. da Costa, Jean-Yves Beziau & Otavio S. Bueno - 1995 - Logic Journal of the IGPL 3 (4):597-614.
  39.  48
    Introduction of Implication and Generalization in Axiomatic Calculi.Arthur Buchsbaum & Jean-Yves Beziau - unknown
    of 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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  40.  21
    Paraconsistent Logic in a Historical Perspective.Newton Ca da Costa, Jean-Yves Beziau & Otavio Bueno - 1995 - Logique Et Analyse 38:111-125.
  41. From Paraconsistent Logic to Universal Logic.Jean-Yves Béziau - 2001 - Sorites 12:5-32.
    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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  42. Paraconsistent Logic!Jean-Yves Béziau - 2006 - Sorites 17:17-25.
    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 classical negation. In view (...)
     
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  43.  29
    Théorie Legislative de la Négation Pure.Jean-Yves Béziau - 1994 - Logique Et Analyse 147 (148):209-225.
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  44.  6
    Preface of This Special Issue: The Challenge of Combining Logics.Jean-Yves Béziau - 2011 - Logic Journal of the IGPL 19 (4):543-543.
  45. Sentence, Proposition and Identity.Jean-Yves Béziau - 2007 - Synthese 154 (3):371 - 382.
    In this paper we discuss the distinction between sentence and proposition from the perspective of identity. After criticizing Quine, we discuss how objects of logical languages are constructed, explaining what is Kleene’s congruence—used by Bourbaki with his square—and Paul Halmos’s view about the difference between formulas and objects of the factor structure, the corresponding boolean algebra, in case of classical logic. Finally we present Patrick Suppes’s congruence approach to the notion of proposition, according to which a whole hierarchy of congruences (...)
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  46. Identity, Structure and Logic.Jean-Yves Beziau - 1996 - Bulletin of the Section of Logic 25:89-9.
  47.  64
    Relativizations of the Principle of Identity.Décio Krause & Jean-Yves Béziau - 1997 - Logic Journal of the IGPL 5 (3):17-29.
    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 (...)
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  48. Logiques construites suivant les méthodes de da Costa.Jean-Yves Béziau - 1990 - Logique Et Analyse 131 (132):259-272.
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  49.  19
    Quine on Identity.Jean-Yves Béziau - 2003 - Principia: An International Journal of Epistemology 7 (1-2):1-15.
    In a first section, we discuss Quine’s claim according to which identity is a logical notion. We point out that Quine mixes up various types of identities: trivial identity, Leibniz identity, etc.; and this leads him to commit several mistakes. In a second section, we review Quine’s criticisms to various philosophers, who ac-cording to him made confusion between names and objects in defining identity. We show that in fact only Korzybski can be accused of such confusion. In a third section, (...)
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  50.  41
    Yaroslav Shramko and Heinrich Wansing, Truth and Falsehood - An Inquiry Into Generalized Logical Values.Jean-Yves Beziau - 2014 - Studia Logica 102 (5):1079-1085.
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