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1What is Semantics? A Brief Note on a Huge QuestionSorites 3 43-47. 1995.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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Nouveau regard et nouveaux résultats sur la logique paraconsistante C1Logique Et Analyse 36 45-58. 1993.
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7Neue Forschung zur formalen Logik bei KantIn Michael Lewin (ed.), Klassische Deutsche Philosophie: Wege in die Zukunft, Brill | Mentis. pp. 19-44. 2024.Im Folgenden stellen wir drei aktuelle Forschungsbereiche zur formalen Logik bei Kant allgemeinverständlich dar und greifen dabei auf die trans zendentale Logik nur dann zurück, wenn sie ein besseres Verständnis der formalen Logik ermöglicht: Zunächst wird Kants Beitrag zur Rezeption und Weiterentwicklung von Euler-artigen Diagrammen dargestellt. Diese Diagramme wurden in den 1990er Jahren wiederentdeckt, als formales System interpretiert und werden heute insbes. in der Didaktik, in den Kognitio…Read more
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9Logica Universalis: Towards a General Theory of Logic (edited book)Birkhäuser Verlog. 2005.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 thirty years: there …Read more
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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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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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36To distribute or not to distribute?Logic Journal of the IGPL 19 (4): 466-583. 2011.In 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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64The 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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20The Lvov-Warsaw School: A True MythologyIn Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present, Springer- Birkhauser,. pp. 779-815. 2018.I discuss various aspects of the Lvov-Warsaw School: its past, present and future; its location, evolution, mathematics; the variety of its members. I develop this analysis on the basis of my 25-year experience with Poland.
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99Square of Opposition: A Diagram and a Theory in Historical PerspectiveHistory and Philosophy of Logic 35 (4): 315-316. 2014.We are pleased to present this special issue of the journal History and Philosophy of Logic dedicated to the square of opposition.The square of opposition is a diagram and a theory of opposition re...
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31Editorial: Neurophysiology of Silence: Neuroscientific, Psychological, Educational and Contemplative PerspectivesFrontiers in Psychology 12. 2021.
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The Square of Opposition: Past, Present, and FutureIn Jean-Yves Beziau & Ioannis Vandoulakis (eds.), The Exoteric Square of Opposition., Birkhauser. pp. 1-14. 2022.
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4The Future of LogicFelsefe Arkivi 51 367-374. 2019.In this paper we discuss the recent developments of logic and explain what can be done to promote a bright future for logic. After comments on the contest The Future of Logic that took place during the 5th UNILOG in Istanbul in 2015, we give a general idea of how logic can be practiced and understood, emphasizing in particular the distinction between logic as reasoning and logic as the science of reasoning. And we discuss some projects we have launched: the book series Logic PhDs, series of even…Read more
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58The 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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10Is there an Axiom for Everything?In Oliver Passon & Christoph Benzmüller (eds.), Wider den Reduktionismus -- Ausgewählte Beiträge zum Kurt Gödel Preis 2019, Springer Nature Switzerland. pp. 103-117. 2021.We first start by clarifying what axiomatizing everything can mean. We then study a famous case of axiomatization, the axiomatization of natural numbers, where two different aspects of axiomatization show up, the model-theoretical one and the proof-theoretical one. After that we discuss a case of axiomatization in a sense opposed to the one of arithmetic, the axiomatization of the notion of order, where the idea is not to catch a specific structure, but a notion.
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Is there an axiom for everything?In Oliver Passon & Christoph Benzmüller (eds.), Wider den Reduktionismus -- Ausgewählte Beiträge zum Kurt Gödel Preis 2019, Springer Nature Switzerland. 2021.We first start by clarifying what axiomatizing everything can mean. We then study a famous case of axiomatization, the axiomatization of natural numbers, where two different aspects of axiomatization show up, the model-theoretical one and the proof-theoretical one. After that we discuss a case of axiomatization in a sense opposed to the one of arithmetic, the axiomatization of the notion of order, where the idea is not to catch a specific structure, but a notion. A third mathematical case is the…Read more
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63Logic 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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21Logic and Religion: Special Issue of Logica Universalis (edited book)Springer. 2017.This special issue of Logica Universalis (Springer) deals with the relations between logic and religion, broadly conceived. It 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 Existen…Read more
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51Beyond 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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39The Mystery of the Fifth Logical Notion (Alice in the Wonderful Land of Logical Notions)Studia Humana 9 (3-4): 19-36. 2020.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 the context…Read more
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25An Unexpected Feature of Classical Propositional Logic in the TractatusIn Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium, De Gruyter. pp. 385-396. 2019.