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56The Vatican SquareLogica Universalis 10 (2-3): 135-141. 2016.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 o…Read more
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53The Cretan SquareLogica Universalis 14 (1): 1-5. 2020.This special issue is related to the 6th World Congress on the Square of Opposition which took place at the Orthodox Academy of Crete in November 2018. In this introductory paper we explain the context of the event and the topics discussed.
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52Logic and ReligionLogica Universalis 11 (1): 1-12. 2017.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…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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50Trivial Dialetheism and the Logic of ParadoxLogic and Logical Philosophy 25 (1): 51-56. 2016.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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50Beyond Faith and Rationality: Essays on Logic, Religion and Philosophy (edited book)Springer. 2020.This volume deals with the relation between faith and reason, and brings the latest developments of modern logic into the scene. Faith and rationality are two perennial key concepts in the history of ideas. Philosophers and theologians have struggled to bring into harmony these otherwise conflicting concepts. Despite the diversity of approaches about what rationality effectively means, logic remains the cannon of objective and rational thought. The chapters in this volume analyze several issues …Read more
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49Quine on IdentityPrincipia: An International Journal of Epistemology 7 (1-2): 1-15. 2003.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 (or diagonal) identity, Leibniz identity, etc.; and this leads him to commit several mistakes. In a second section, we review Quine’s criticisms to various philosophers (Wittgenstein, Whitehead, Leibniz, etc.), who ac-cording to him made confusion between names and objects in defining identity. We show that in fact only Korzybski can …Read more
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49Disentangling Contradiction from Contrariety via IncompatibilityLogica Universalis 10 (2-3): 157-170. 2016.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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48From 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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48Universal Logic: Evolution of a ProjectLogica Universalis 12 (1-2): 1-8. 2018.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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46The 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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44Around and Beyond the Square of Opposition (edited book)Springer Verlag. 2012.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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43Perspectives on Universal Logic (edited book)Polimetrica. 2007.Universal logic is to logic what universal algebra is to algebra. It is not a specific system of logic that would apply to everything but a general theory of all existing and possible logics. This new field has been slowly emerging through the new directions of research in logic of the past decades and the name was coined 15 years ago. In the Spring of 2005 was organized in Montreux, Switzerland, the First World Congress on Universal Logic. This exciting event gathered more than 200 people from …Read more
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41Universal Logic: An Anthology From Paul Hertz to Dov Gabbay (edited book)Birkhäuser. 2012.A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist …Read more
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41CONCEPTUAL CLARIFICATIONS Tributes to Patrick Suppes (1922-2014) (edited book)College Publication. 2015.This is a volume containing papers honoring Patrick Suppes (1922-2014). All contributors have worked directly with Suppes or/and with his ideas. The book also contains one of the last papers by Suppes (co-authored by two of his collaborators). The work of Suppes touches many different areas, ranging from meteorology to physics, through logic, mathematics, psychology, neuroscience, education, painting, but he was first of all and above all a philosopher, always questioning, but not in vain. There…Read more
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41The Exoteric Square of Opposition. (edited book)Birkhauser. 2022.The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of…Read more
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40of 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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40MANY 1 - A Transversal Imaginative Journey across the Realm of MathematicsJournal of the Indian Council of Philosophical Research 34 (2): 259-287. 2017.We discuss the many aspects and qualities of the number one: the different ways it can be represented, the different things it may represent. We discuss the ordinal and cardinal natures of the one, its algebraic behaviour as a neutral element and finally its role as a truth-value in logic.
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35ForewordJournal of Applied Non-Classical Logics 22 (1-2): 1-1. 2012.(2012). Foreword. Journal of Applied Non-Classical Logics: Vol. 22, SPECIAL ISSUE 1: Uses of Non-Classical Logic: Foundational Issues; SPECIAL ISSUE 2: Formal Models of Norm Change, pp. 1-1. doi: 10.1080/11663081.2012.682433
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35Définition, Théorie des Objets et Paraconsistance (Definition, Objects’ Theory and Paraconsistance)Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 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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33Possible Worlds: A Fashionable Nonsense?Proceedings of the XXIII World Congress of Philosophy 55 5-9. 2018.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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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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32Semantic computations of truth based on associations already learnedJournal of Applied Logic 2 (4): 457-467. 2004.