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.

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.

It is tempting to consider Girard Desagues’ mathematical work, more precisely his Brouillon project on conics, as a work of mathematics applied to perspective. We would like to show in this text that it is probably more pertinent to consider that Desargues does mathematics as a practitionner of the art of perspective. We shall analyse a few extracts of Desargues’ work with this point of view in mind so as to shed light on his innovative ideas that could be hard (...) to understand in his sometimes obscure style. We shall show how this way of doing geometry can be also be found in the works Philippe de la Hire and Jacques-Francois le Poîvre, leading them to consider a transformation of the plane into itself as an explicited mathematical object. (shrink)

This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will (...) be essential reading for all those working in logic & computer science. (shrink)

Using methods of abstract logic and the theory of valuation, we prove that there is no paraconsistent negation obeying the law of double negation and such that $\neg(a\wedge\neg a)$ is a theorem which can be algebraized by a technique similar to the Tarski-Lindenbaum technique.

(4) Jean apprécie ce livre-là. (‘Jean appreciates ce book-there’) (5) Jean apprécie ce livre-ci. (‘Jean appreciates ce book-here’) in a way that recalls in part non-standard English: (6) John is reading that there book. (7) John is reading this here book. with (6) akin to (4) and with (7) akin to (5). The difference in word order, whereby English has there/here prenominal in (6)/(7) and French has - là/-ci postnominal in (4)/(5), was analyzed by Bernstein (1997) (...) in terms of a movement operation that in French moves the noun to the left of -là/-ci, starting from an English-like order, in a way that recalls the difference between French and English adjective position, as in Cinque (2005; to appear). English allows that and this to occur without any visible noun present, as in. (shrink)

The hexagon of opposition is an improvement of the square of opposition due to Robert Blanché. After a short presentation of the square and its various interpretations, we discuss two important problems related with the square: the problem of the I-corner and the problem of the O-corner. The meaning of the notion described by the I-corner does not correspond to the name used for it. In the case of the O-corner, the problem is not a wrong-name problem but a no-name (...) problem and it is not clear what is the intuitive notion corresponding to it. We explain then that the triangle of contrariety proposed by different people such as Vasiliev and Jespersen solves these problems, but that we don’t need to reject the square. It can be reconstructed from this triangle of contrariety, by considering a dual triangle of subcontrariety. This is the main idea of Blanché’s hexagon. We then give different examples of hexagons to show how this framework can be useful to conceptual analysis in many different fields such as economy, music, semiotics, identity theory, philosophy, metalogic and the metatheory of the hexagon itself. We finish by discussing the abstract structure of the hexagon and by showing how we can swing from sense to non-sense thinking with the hexagon. (shrink)

Resumo A problemática na relação entre Filosofia e Cinema dá origem a duas questões: a primeira, sobre as condições que os filmes têm de satisfazer a fim de poderem ser devidamente tratados por uma compreensão filosófica; a segunda, sobre os requisitos, que os discursos sobre os filmes têm de satisfazer, em ordem a serem legitimamente considerados como filosóficos. Respondendo à primeira pergunta, através de uma análise ao debate entre Paisley Livingston e Aaron Smuts, acerca da “Filosofia do Cinema”, será afirmado (...) que, embora os filmes em si mesmos não façam filosofia, é possível fazer filosofia a partir deles, desde que estes expressem ideias estéticas. Respondendo à segunda questão, através da leitura crítica de Days of Being Wild, In the Mood of Love e 2046 de Wong Kar-wai, com referência aos conceitos de Kierkegaard, Girard e Deleuze, será argumentado que uma análise filosófica implica a renovação de conceitos filosóficos centrais e o alargamento da compreensão da natureza das imagens cinematográficas. Palavras-chave : Deleuze, emoção-imagem, filosofia do cinema, Kierkegaard, repetição, Wong Kar-waiThe problem of the relationships between Philosophy and Films raises two questions: first, the conditions that films have to fulfill in order to be rightly concerned by a philosophical understanding; second the requirements that discourses about films have to fulfill in order to be truly considered as philosophical ones. Answering to the first question through a survey of the debate between Paisley Livingston and Aaron Smuts about “Film-Philosophy”, I will affirm that, though films in themselves are not doing philosophy, it is possible to do philosophy out of them provided they express aesthetical ideas. Answering to the second question through a critical reading of Wong Kar-wai’s Days of Being Wild, In the Mood for Love, and 2046 referring to the concepts of Kierkegaard, Girard and Deleuze, I will argue that a philosophical analysis implies to renew core philosophical concepts and to extend our understanding of the nature of cinematographic images. Keywords : Deleuze, film-philosophy, image-emotion, Kierkegaard, repetition, Wong Kar-wai. (shrink)

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 of logic (...) and those related with applications of the theory of opposition to conceptual analysis and pedagogy. (shrink)

In some situations, a decision is best represented by an incompletely analyzed act: conditionally on a given event A, the consequences of the decision on sub-events are perfectly known and uncertainty becomes probabilizable, whereas the plausibility of this event itself remains vague and the decision outcome on the complementary event ${\bar{A}}$ is imprecisely known. In this framework, we study an axiomatic decision model and prove a representation theorem. Resulting decision criteria aggregate partial evaluations consisting of (i) the conditional expected utility (...) associated with the analyzed part of the decision, and (ii) the best and worst consequences of its non-analyzed part. The representation theorem is consistent with a wide variety of decision criteria, which allows for expressing various degrees of knowledge on ( ${A, \bar{A}}$ ) and various types of attitude toward ambiguity and uncertainty. This diversity is taken into account by specific models already existing in the literature. We exploit this fact and propose some particular forms of our model incorporating these models as sub-models and moreover expressing various types of beliefs concerning the relative plausibility of the analyzed and the non-analyzed events ranging from probabilities to complete ignorance that include capacities. (shrink)

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.

The first volume presents a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including (...) combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, MacColl). This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic. (shrink)

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.

Sont réexaminées plusieurs inscriptions agonistiques d’Athènes. 1. Le texte IG II3 4, 624 pour un héraut périodonique doit certainement être attribué à Valerius Eklektos de Sinope, déjà connu par un long texte d’Athènes, une base à Olympie et un piédestal retrouvé à Delphes resté inédit et publié ici. L’ensemble permet de reconstituer le parcours d’un artiste hors norme connu par quatre textes gravés à des moments différents de sa carrière. 2. Les fragments IG II3 4, 616 et 617 appartiennent au (...) même palmarès du second tiers du IIIe s. et peuvent vraisemblablement être reliés l’un à l’autre. Si IG II3 4, 618 ne provient pas du même monument, il pourrait lui être en revanche contemporain. 3. La base SEG 58, 185 honore non un agonothète mais un épistate, dont sont vantés les succès lors d’une longue carrière. 4. IG II² 2772 est une dédicace funéraire faite par un boxeur et xystarque pour un parent ou un ami. (shrink)

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 and the Problem of Impossible Objects, (...) by Wolfgang Lenzen; A Logical Analysis of the Anselm’s Unum Argumentum (from Proslogion), by Jean-Pierre Desclés; Monotonic and Non-monotonic Embeddings of Anselm’s Proof, by Jacob Archambault; Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy, by C. Benzmüller, L. Weber and B. Woltzenlogel Paleo. (shrink)

Jean-Jacques Rousseau est l'auteur de l'entrée "économie politique" dans l'Encyclopédie en 1755. A ce titre, il aurait pu être l'un des fondateurs de cette discipline. Pourtant, la définition qu'il en donne est à l'encontre de la pensée libérale des physiocrates, puis des classiques, et constitue une véritable "anti-économique". En hypertrophiant le rôle de l'Etat et en niant l'intérêt personnel, Rousseau est au contraire l'un des pères du socialsme. En niant la liberté humaine, il nie aussi l'existence de choix éthiques.

Le comte Joseph de Maistre fut un ennemi radical des Lumières.

qui y recense ses nombreuses victoires. Une brève histoire des choraules et de leur participation aux concours peut ainsi être esquissée : malgré sa popularité, surtout en Occident, la discipline n'a été acceptée que tardivement dans les concours, et aux Pythia sans doute seulement à la fin du Ier siècle. Un premier appendice évoque rapidement les catalogues du personnel cultuel conservés à Olym- pie ; un second établit le texte d'une inscription de Nîmes (IG XIV 2499), où l'on doit reconnaître (...) un acte de l'association universelle des artistes dionysiaques. (shrink)

Que la musique soit faite pour etre ecoutee semble une evidence, et pourtant... C'est pour guider les melomanes et les aider a passer d'une audition passive a une ecoute active que Jean-Yves Bras partage ici son experience d'ecouteur. Apres avoir defini ce qu'est la musique, il s'interroge ensuite sur la nature de l'ecoute: que faut-il entendre par ecouter? Sur quoi porter notre attention? Comment ecouter? Les conditions materielles dans lesquelles nous consommons la musique, notre comportement au concert ou (...) a l'ecoute d'un disque, ont egalement une incidence importante sur la qualite de notre ecoute. Puis il analyse ces liens si mysterieux et si essentiels tisses entre compositeurs, interpretes et nous-memes, auditeurs. Enfin, il trace a grands traits l'histoire de nos oreilles de l'Antiquite a nos jours, pour conclure sur les differentes categories d'auditeurs actuels. Parallelement, l'auteur a cree un site Internet, www.artdecouter.fr, qui apporte un complement d'information agremente d'exemples sonores. Ce chemin d'initiation se parcourt sous forme de dialogue: une jeune personne souhaitant s'instruire, Mademoiselle Croche, nous permet par ses questions d'entendre s'ouvrir pour nous le langage de la musique. Jean-Yves Bras a ete directeur de la Documentation musicale de Radio France et a participe a de nombreuses emissions. Responsable artistique du Festival Chopin a Paris, il est l'auteur des Courants musicaux du XXe siecle et d'un ouvrage sur le chef d'orchestre Carlo Maria Giulini. (shrink)

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.

Ή επιφανειακή έρευνα πού αποσκοπούσε στην ανεύρεση εργαστηρίων παραγωγής αμφορέων στην Δυτική Κρήτη, μας επέτρεψε νά διακρίνουμε 4 τύπους αμφορέων ρωμαϊκής περιόδου. Τήν άνθιση πού παρατηρούμε στην παραγωγή καί εξαγωγή του κρητικού κρασιού, μαρτυρούν επίσης καί οί αρχαίες πηγές. Έκτος από μιά πρώτη τυπολογία θά βρούμε επίσης καί μιά λεπτομερή περιγραφή των εργαστηριακών εγκαταστάσεων καί τής κεραμεικής παραγωγής πού βρέθηκαν κατά τή διάρκεια τής ανασκαφής στό Καστέλλι Κισσάμου.

t.l. Introduction à une anthropologie philosophique.

Le but de cet article est, à travers l’histoire des relations entre science et philosophie du temps, de retracer l’archéologie épistémologique du temps pensé comme progrès linéaire. Nous voudrions montrer : 1. que la pensée du « temps » évolue avec le temps, 2. que cette évolution peut se lire en même temps en science et en philosophie sans qu’il soit nécessaire d opposer l’une à l’autre, 3. qu’elle n’est pas réductible à une opposition entre réversibilité ou irréversibilité ; 4. (...) qu’elle s’exprime à travers trois « métaphores épistémiques » distinctes : cercle, ligne ou réseau — à l’intérieur desquels l’antinomie entre conception « idéaliste » ou « réaliste » de la temporalité ne cesse de se rejouer ; 5. qu’il est possible de dépasser cette antinomie par l’idée régulatrice d’une fonction cosmologique de la temporalité définie comme la forme de l’interaction entre événements physiques et lois naturelles. (shrink)

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 constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions (...) is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics. (shrink)

In his Brouillon Project on conic sections, Girard Desargues studies the notion of traversale, which generalizes that of diameter introduced by Apollonius. One often reads that it is equivalent to the notion of polar, a concept that emerged in the beginning of 19th century. In this article we shall study in great detail the developments around that notion in the middle part of the Brouillon project. We shall in particular show, using the notes added by Desargues after the first draft (...) was written, how here arises a new theory, that of the polarity associated to a conic section. We shall show that besides a natural correspondance between points and lines, Desargues has understood that a conic induces on every line in its plane an involution, and how he progressively handles the considerable conceptual difficulties he has to deal with when trying to explain clearly his novative ideas. (shrink)

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 how this project will develop in the future with the creation of more logic prizes, an Encyclopædia of Logic, the book series Logic PhDs, as well as the creation of a World Logic Day, January 14, day of birth of Alfred Tarski and of death of Kurt Gödel. (shrink)

Le terme de catallaxie a été forgé par F. Hayek pour exprimer l’ordre spontané du marché. Hayek a créé ce terme à partir du mot catallactique, ressorti peu avant de l’oubli par L. Mises, mot venu du verbe grec signifiant « échanger », pour éviter les ambigüités du mot « économie ». Ce papier a pour objet de rechercher la généalogie du terme « catallactique », depuis Richard Whately, qui a été le premier auteur, en 1831, à vouloir rebaptiser « (...) l’économie politique » en « catallactique ». Ce terme était connu et utilisé tout au long du XIX° siècle et on le trouve encore au début du XX° siècle dans divers manuels. L’utilisation de ce terme par Mises, puis Hayek, est donc la reprise d’une tradition remontant à Richard Whately. C’est l’occasion aussi de se pencher sur la vie de Richard Whately, professeur d’économie politique à Oxford jusqu’en 1831, puis archevêque anglican de Dublin. Il a notamment joué un grand rôle dans l’enseignement de cette discipline, en créant 4 000 cours d’économie politique. Un personnage intéressant, un peu trop ignoré aujourd’hui, qui a joué un rôle non négligeable dans la pensée économique. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Heidegger and Dao: Things, Nothingness, Freedom by Eric S. NelsonJean-Yves Heurtebise (bio)Heidegger and Dao: Things, Nothingness, Freedom. Eric S. Nelson. London: Bloomsbury, 2024. Pp. viii + 256. Paper $103.50, ISBN 978-1-350411-90-6.On the Way: from Heidegger to Nagarjuna via Lao-ZhuangAfter having reviewed Eric S. Nelson’s 2017 Chinese and Buddhist Philosophy in Early Twentieth-Century German Thought (for the Journal of Chinese Philosophy) and his 2020 Daoism and Environmental Philosophy (...) (for Monde Chinois Nouvelle Asie), reviewing now, for Philosophy East & West, Nelson’s 2024 Heidegger and Dao: Things, Nothingness, Freedom, which develops on the insights of his two previous opuses, is both a real pleasure and a true challenge. It’s a pleasure to read again Eric S. Nelson’s scholarly prose with its own specific conceptual style and distinctive philosophical rhythm. It’s a challenge to give a meaningful and fair overview of a conceptually complex, scholarly rich, and thought-provoking book.No one can speak better about the aim and goals of Nelson’s book than the author himself--following the wayist way of spontaneous ziranity, we will thus let the book speak for itself:Its primary thesis is that, entangled with Daoist and other intercultural sources, Heidegger’s path proceeds from the paradigmatic Occidental philosophy of available givenness and mere presence--which conceals the open spacing of things and seeks to logically exclude and dialectically subordinate negativity and the nothing--to nothingness, emptiness, and the clearing in their coming to presence and withdrawal in absence or, to accentuate its mutable verbal sense, presencing-absencing. […] Zhuangzi’s vision of free and easy wandering indicates ways of practicing philosophy as contesting and unraveling fixations. These practices allow rethinking Heidegger’s pathways and reimagining for ourselves things, nothingness, and world in the specificity of our existential condition.(p. 10)These lines can give already a good indication about what the reader will be provided with: a Heideggerian reading of Daoism nurturing and enriching a Daoist reading of Heidegger; a Daoist reinterpretation of the late Heidegger feeding and complexifying a Heideggerian Pre-Socratic reinterpretation of early Daoism; a continuous feedback loop leading to a process of mutual symbiosis and multiple conceptually creative hybridizations. Ziran and Dao are used to unlock the concealed potentialities of overdetermined Western concepts such as Nature and Ethos while the Heideggerian deconstruction of “Western metaphysics” is [End Page 1] used to de-Eurocentricize our understanding of Daoist and Buddhist thoughts about Thing and Nothingness.The book is divided in two parts: the first part deals with the concept of Thing, the second with the concept of Nothingness. Thing and Nothingness seem to be the perfect antithesis but the magic of Nelson’s reading of their tri-cultural Daoist, Buddhist and Heideggerian conceptualization is to dissipate the classical, ontological antinomy between Being and Non-Being to explore what’s both beyond and below: the natural source of life emergence, coming and returning to a Nothing that is Everything via a Thing that is never Anything (a ready-made and exchangeable object in the universal trading scheme of capitalist general equivalence) but always Something (this and that in particular, in their own specific rhythm of coming back and forth, from and to their source of un-nothingity).The first five chapters evoke the issue of the encounter of Heidegger and Daoist thinking in relation to the deconstruction of Thingness. In the first chapter, Nelson proposes a cross-cultural perspective about the Nature of the Thing linking Heidegger’s critique of the reduction of Things’ Presence to Functional Tools to the Daoist extended conception of Things in terms of Multitude (wanwu 萬物), in which objects, living beings, and spirits participate in the fabric of reality. Chapter 2 examines the connection between Heidegger’s and Daoism’s understanding of “nature” as manifesting a distinct yet similar attention to things’ autopoiesis: following the natural disclosing and unfolding of “things” entails a specific way to think and be in the world. In chapter 3, a comparison is established between Heidegger and Laozi with respect to the notion of void and emptiness: the fact that what powers the utility of a thing is what... (shrink)

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 (...) psychic dispositions, using the hexagon of opposition of colors. We present a hexagon of psychic dispositions based on colors that we compare in particular with Plutchick’s wheel of emotions. (shrink)

Nous ne pouvons nous dispenser d'un concept linguistique du vrai. Nous ne pouvons pas davantage nous dispenser d'un concept phénoménologique du vrai. Et nous ne pouvons enfin nous dispenser de recourir à l'un et à l'autre, car le vrai se dit et le vrai se donne à l'intuition. Ces affirmations sont élémentaires. Mais les prendre au sérieux, c'est-à-dire considérer l'expérience entière de la vérité, requiert d'élargir le concept de vérité, de telle manière que : le vrai ne soit pas seulement (...) affaire de savoir mais, plus largement, affaire de connaissance ; le vrai puisse être dit dans une multiplicité de langages (philosophique, poétique, scientifique(; le vrai soit indissociable de la question de l'être-dans-le-monde ; le vrai soit à la mesure du logos, dont on montre qu'il excède la ratio sous ses formes modernes. Le vrai doit à nouveau être pensé. La pensée n'est rien de neuf. Mais son intervention dans les débats sur le vrai, au temps du nihilisme, est plus urgente que jamais. (shrink)

Résumé Le but de cet article est de montrer que la manière dont à été posée la question de la scolarisation du créole trahit une sorte d’aveuglement sur ce que peut signifier le fait de parler créole - quelque chose comme l’oubli d’une de ses dimensions. Je dis qu’en réfléchissant à ce que pourrait être une institution (comme l’école ou autre chose) tirée de la vie créole étudiée dans sa manière de dire les choses, on pourrait porter remède à cet (...) oubli. (shrink)

In this article, I attempt to draw as many possible consequences from this fact : in the Mascareignes islands, the use of the word « Creole » is regulated by criteria that limit its application to subgroups of the Creole world. The use of this word is not “cognitive”, it does not refer to the inhabitant of the islands, the “native” : it marks that from which one must separate oneself within the Creole language itself, possibly through the evocation of (...) back-languages, of customs, beliefs and attitudes inherited from somewhere else. A crucial defining feature of Creole life thus appears to consist in a distance between forms of experience that coexist but that strive to be as separated and watertight as possible. Sensitivities are deeply trained in measuring this distance, which leads hybridization to be conceived as subtractions to the norms inherited from colonial times. Distance and hybridization are the main terms through which I have attempted to describe the Creole world in the Mascareignes ; but I tried to do so “from a distance”, in the spirit with which Derek Walcott described fragments of epics in the Caribbean. (shrink)