•  5
    The Mystery of the Fifth Logical Notion
    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
  •  1
    Possible 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.
  • Do Sentences Have Identity?
    The Paideia Archive: Twentieth World Congress of Philosophy 8 3-10. 1998.
    We study here equiformity, the standard identity criterion for sentences. This notion was put forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable but if the notion of sentence is taken as a fundamental basis for logic and mathematics, it seems that this principle cannot be maintained without vicious circle. It seems also that equiformity has some semantical features ; maybe this is not so clear for individual signs…Read more
  •  18
    The Cretan Square
    Logica 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.
  •  137
    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.
  • Formal Approaches to the Ontological Argument
    with Ricardo Silvestre
    Journal of Applied Logics 5 (7): 1433-1440. 2018.
    This paper introduces the special issue on Formal Approaches to the Ontological Argument and briefly introduces the ontological argument from the standpoint of logic and philosophy of religion (more specifically the debate on the rationality of theistic belief).
  •  4
    The Contingency of Possibility
    Principia: 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.
  •  22
    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.
  • New Directions in Paraconsistent Logic: 5th WCP, Kolkata, India, February 2014 (edited book)
    with Mihir Chakraborty and Soma Dutta
    . 2016.
  •  15
    1st World Logic Day: 14 January 2019
    Logica 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
  •  1
    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
  • Is Modern Logic Non-Aristotelian?
    In Dmitry Zaitsev & Vladimir Markin (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic, Springer Verlag. 2017.
  •  1
    Being Aware of Rational Animals
    In 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
  •  8
    Logic Prizes et Cætera
    Logica 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
  • Many 1
    Journal of 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.
  •  45
    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.
  •  30
    Universal Logic: Evolution of a Project
    Logica 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.
  •  20
    Trivial Dialetheism and the Logic of Paradox
    Logic 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.
  •  11
    Self-extensional three-valued paraconsistent logics have no implications
    with Arnon Avron
    Logic Journal of the IGPL 25 (2): 183-194. 2017.
    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.
  • The Road to Universal Logic (Studies in Universal Logic) (edited book)
    Springer International Publishing. 2015.
  •  27
    Quine on Identity
    Principia: 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 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, we an…Read more
  • The Square of Opposition: A Cornerstone of Thought (Studies in Universal Logic) (edited book)
    with Gianfranco Basti
    Birkhäuser. 2017.
  •  1
    Hartley Slater and False Contradictions
    SOUTH AMERICAN JOURNAL OF LOGIC 2 (1): 101-107. 2016.
  •  4
    Classical negation can be expressed by one of its halves
    Logic 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
  •  1
    What is Semantics? A Brief Note on a Huge Question
    with Newton da Costa and Otávio Bueno
    Sorites 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.
  •  155
    Professor Newton CA da Costa awarded Nicholas Copernicus University medal of merit
    with Newton C. A. da Costa and Otávio Bueno
    Logic and Logical Philosophy 7 7-10. 1999.