-
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.
-
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
-
2Do 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
-
1Is Modern Logic Non-Aristotelian?In Dmitry Zaitsev & Vladimir Markin (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic, Springer Verlag. 2017.
-
1What is a possible worldIn Guido Imaguire & Dale Jacquette (eds.), Possible Worlds: Logic, Semantics and Ontology, Philosophia. pp. 25--37. 2010.
-
Définition, théorie Des objets et paraconsistance (definition, objects' theory and paraconsistance)Theoria 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
-
La Critique Schopenhaurienne de l’Usage de la Logique en MathématiquesO Que Nos Faz Pensar 7 81-88. 1993.
-
The Square of Opposition: Past, Present, and FutureIn Jean-Yves Beziau & Ioannis Vandoulakis (eds.), The Exoteric Square of Opposition., Birkhauser. pp. 1-14. 2022.
-
Transitivity and ParadoxesThe Baltic International Yearbook of Cognition, Logic and Communication 1. 2005.
-
Nouveaux résultats et nouveau regard sur la logique paraconsistante C1Logique Et Analyse 36 45-58. 1993.
-
A Logical Analysis Of Singular TermsSorites 10 6-14. 1999.We analyse the behaviour of definite descriptions and proper names terms in mathematical logic. We show that in formal arithmetic, wether some axioms are fixed or not, proper names cannot be considered rigid designators and have the same behaviour as definite descriptions. In set theory, sometimes two names for the same object are introduced. It seems that this can be explained by the notion of meaning. The meaning of such proper names can be considered as fuzzy sets of equivalent co-designative…Read more
-
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
-
From Paraconsistent Logic to Universal LogicSorites 12 5-32. 2001.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
-
Was Frege Wrong when Identifying Reference with Truth-Value?Sorites 11 15-23. 1999.We discuss Sengupta's argumentation according to which Frege was wrong identifying reference with truth-value.After stating various possible interpretations of Frege's principle of substitution, we show that there is no coherent interpretation under which Sengupta's argumentation is valid.Finally we try to show how Frege's distinction can work in the context of modern mathematics and how modern logic grasps it
-
The Road to Universal Logic (Studies in Universal Logic) (edited book)Springer International Publishing. 2015.