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14The Contingency of PossibilityPrincipia: An International Journal of Epistemology 20 (1): 99-115. 2016.In this paper we criticize the way possibility is characterized in contemporary modal logic through the diamond operator. We explain that it does not match with the usual notion of possibility and that this notion is better described by the vertex Y of the hexagon of opposition usually called contingency.
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80The Square of Opposition: A Cornerstone of Thought (edited book)Birkhäuser. 2016.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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11New Directions in Paraconsistent Logic: 5th WCP, Kolkata, India, February 2014 (edited book)Springer. 2016.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 …Read more
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37The Square of Opposition: A General Framework for Cognition (edited book)Peter Lang. 2011.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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391st World Logic Day: 14 January 2019Logica Universalis 13 (1): 1-20. 2019.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 presenting and…Read more
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3A Chromatic Hexagon of Psychic DispositionsIn Marcos Silva (ed.), How Colours Matter to Philosophy, Springer. 2017.Colors can be understood in a logical way through the theory of opposition. This approach was recently developed by Dany Jaspers, giving a new and fresh approach to the theory of colors, in particular with a hexagon of colors close to Goethe’s intuitions. On the other hand colors can also be used at a metalogical level to understand and characterize the relations of opposition, including the relations of opposition between colors themselves. In this paper we furthermore develop a theory of psych…Read more
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1Is Modern Logic Non-Aristotelian?In Dmitry Zaitsev & Vladimir Markin (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic, Springer Verlag. 2017.
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20Being Aware of Rational AnimalsIn Gordana Dodig-Crnkovic & Raffaela Giovagnoli (eds.), Representation of Reality: Humans, Other Living Organism and Intelligent Machines, Springer. 2017.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 feat…Read more
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34Logic Prizes et CæteraLogica Universalis 12 (3-4): 271-296. 2018.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 prizes winners from 9 countries. In a third section I discuss …Read more
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3Many 1Journal 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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82Is the Principle of Contradiction a Consequence of $$x^{2}=x$$ x 2 = x?Logica Universalis 12 (1-2): 55-81. 2018.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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55Universal 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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58Trivial 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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33Self-extensional three-valued paraconsistent logics have no implicationsLogic Journal of the IGPL 25 (2): 183-194. 2016.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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The Road to Universal Logic (Studies in Universal Logic) (edited book)Springer International Publishing. 2015.
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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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13The Square of Opposition: A Cornerstone of Thought (Studies in Universal Logic) (edited book)Birkhäuser. 2016.This is a collection of new investigations and discoveries on the theory 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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13Classical negation can be expressed by one of its halvesLogic Journal of the IGPL 7 (2): 145-151. 1999.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 extens…Read more
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175Professor Newton CA da Costa awarded Nicholas Copernicus University medal of meritLogic and Logical Philosophy 7 7-10. 1999.
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1What is a possible worldIn Guido Imaguire & Dale Jacquette (eds.), Possible Worlds: Logic, Semantics and Ontology, Philosophia. pp. 25--37. 2010.
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409Logica Universalis: Towards a General Theory of Logic (edited book)Birkhäuser Basel. 2007.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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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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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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66New Directions in Paraconsistent Logic (edited book)Springer, India. 2015.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 …Read more
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42MANY 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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70The paraconsistent logic Z. A possible solution to Jaśkowski's problemLogic and Logical Philosophy 15 (2): 99-111. 2006.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