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Jean-Yves Beziau
Universidade Federal do Rio de Janeiro
  1. 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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  2.  35
    Logic and Religion.Jean-Yves Beziau & Ricardo Silvestre - 2017 - Logica Universalis 11 (1):1-12.
    This paper introduces the special issue on Logic and Religion of the journal Logica Universalis (Springer). The issue contains the following articles: Logic and Religion, by Jean-Yves Beziau and Ricardo Silvestre; Thinking Negation in Early Hinduism and Classical Indian Philosophy, by Purushottama Bilimoria; Karma Theory, Determinism, Fatalism and Freedom of Will, by Ricardo Sousa Silvestre; From Logic in Islam to Islamic Logic, by Musa Akrami; Leibniz’s Ontological Proof of the Existence of God and the Problem of Impossible Objects, by Wolfgang (...)
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  3.  51
    A New Four-Valued Approach to Modal Logic.Jean-Yves Béziau - 2011 - Logique Et Analyse 54 (213):109.
  4.  15
    Paraconsistent Logic From a Modal Viewpoint.Jean-Yves Béziau - 2005 - Journal of Applied Logic 3 (1):7-14.
  5. Around and Beyond the Square of Opposition.J.-Y. Beziau & Dale Jacquette (eds.) - 2012 - Birkhäuser.
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  6.  11
    Self-Extensional Three-Valued Paraconsistent Logics Have No Implications.Arnon Avron & Jean-Yves Beziau - 2017 - Logic Journal of the IGPL 25 (2):183-194.
    A proof is presented showing that there is no paraconsistent logics with a standard implication which have a three-valued characteristic matrix, and in which the replacement principle holds.
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  7.  49
    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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  8.  35
    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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  9.  28
    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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  10. Is Modern Logic Non-Aristotelian?Jean-Yves Beziau - 2017 - In Dmitry Zaitsev & Vladimir Markin (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic. Springer Verlag.
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  11. 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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  12.  34
    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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  13.  17
    New Directions in Paraconsistent Logic.Jean-Yves Beziau (ed.) - 2015 - New Delhi, India: Springer, India.
    The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions (...)
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  14.  25
    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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  15.  28
    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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  16. Formal Approaches to the Ontological Argument.Ricardo Silvestre & Jean-Yves Beziau - 2018 - Journal of Applied Logics 5 (7):1433-1440.
    This paper introduces the special issue on Formal Approaches to the Ontological Argument of the Journal of Applied Logics (College Publications). The issue contains the following articles: Formal Approaches to the Ontological Argument, by Ricardo Sousa Silvestre and Jean-Yves Béziau; A Brief Critical Introduction to the Ontological Argument and its Formalization: Anselm, Gaunilo, Descartes, Leibniz and Kant, by Ricardo Sousa Silvestre; A Mechanically Assisted Examination of Begging the Question in Anselm’s Ontological Argument, by John Rushby; A Tractarian Resolution to the (...)
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  17.  11
    The Mystery of the Fifth Logical Notion.Jean-Yves Beziau - 2020 - Studia Humana 9 (3-4):19-36.
    We discuss a theory presented in a posthumous paper by Alfred Tarski entitled “What are logical notions?”. Although the theory of these logical notions is something outside of the main stream of logic, not presented in logic textbooks, it is a very interesting theory and can easily be understood by anybody, especially studying the simplest case of the four basic logical notions. This is what we are doing here, as well as introducing a challenging fifth logical notion. We first recall (...)
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  18.  26
    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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  19.  4
    Classical Negation Can Be Expressed by One of its Halves.J.-Y. 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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  20.  69
    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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  21.  8
    Possible Worlds: A Fashionable Nonsense?Jean-Yves Beziau - 2018 - Proceedings of the XXIII World Congress of Philosophy 55:5-9.
    In this paper we discuss the notion of “possible worlds” contrasting a philosophical idea due to Malebranche with a mathematical concept of modern logic due to Kripke from which many pseudo-philosophical discussions have arisen.
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  22. Logic is Not Logic.Jean-Ives Béziau - 2010 - Abstracta 6 (1):73-102.
    In this paper we discuss the difference between (...)
     
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  23.  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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  24. 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.
  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.  36
    Preface.Jean-Yves Beziau & Gillman Payette - 2008 - Logica Universalis 2 (1):1-1.
  27.  32
    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. La Pointure du Symbole.Jean-Yves Beziau (ed.) - 2014 - Petra.
    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 variés que la chimie, la théologie, (...)
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  29.  35
    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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  30.  15
    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.
  31.  17
    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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  32.  1
    Logica Universalis: Towards a General Theory of Logic.Jean-Yves Béziau (ed.) - 2005 - Birkhäuser Verlog.
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last (...)
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  33.  11
    Aspects of Paraconsistent Logic.Newton A. da Costa, Jean-Yves Beziau & Otavio S. Bueno - 1995 - Logic Journal of the IGPL 3 (4):597-614.
  34.  28
    Sequents and Bivaluations.Jean-Yves Béziau - 2001 - Logique Et Analyse 44 (176):373-394.
  35.  24
    The New Rising of the Square of Opposition.Jean-Yves Béziau - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 3--19.
  36. New Dimensions of the Square of Opposition.Jean-Yves Béziau & 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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  37.  40
    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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  38.  38
    13 Questions About Universal Logic.Jean-Yves Béziau - 2006 - Bulletin of the Section of Logic 35 (2/3):133-150.
  39.  80
    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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  40.  5
    The Square of Opposition: A General Framework for Cognition.Jean-Yves Beziau & Gillman Payette (eds.) - 2011 - Peter Lang.
    Papers... "selected from a larger number of contributions most of them based on talks presented at the First World Congress on the Square of Opposition organized in Montreux in June 2007"--Preface, p. 12.
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  41.  1
    Being Aware of Rational Animals.Jean-Yves Beziau - 2017 - In Gordana Dodig-Crnkovic & Raffaela Giovagnoli (eds.), Representation of Reality: Humans, Other Living Organism and Intelligent Machines. Springer.
    Modern science has qualified human beings as homo sapiens. Is there a serious scientific theory backing this nomenclature? And can we proclaim ourselves as wise? The classical rational animals characterization has apparently the same syntactic form but it is not working exactly in the same way. Moreover the semantics behind is more appropriate, encompassing a pivotal ambiguity. In the second part of the paper, we further delve into this ambiguity, relating rationality with three fundamental features of these creatures: ability to (...)
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  42. 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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  43. Logiques construites suivant les méthodes de da Costa.Jean-Yves Béziau - 1990 - Logique Et Analyse 131 (132):259-272.
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  44.  18
    Semantic Computations of Truth Based on Associations Already Learned.Patrick Suppes & Jean-Yves Béziau - 2004 - Journal of Applied Logic 2 (4):457-467.
  45.  50
    Idempotent Full Paraconsistent Negations Are Not Algebraizable.Jean-Yves Béziau - 1998 - Notre Dame Journal of Formal Logic 39 (1):135-139.
  46. 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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  47.  25
    Paraconsistent Logic in a Historical Perspective.Newton Ca da Costa, Jean-Yves Beziau & Otavio Bueno - 1995 - Logique Et Analyse 38:111-125.
  48.  59
    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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  49.  21
    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.
  50. Special Issue on the Square of Opposition.J. Y. Beziau & G. Payette - 2008 - Logica Universalis 2 (1).
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