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.

In the middle part of his Brouillon Project on conics, Girard Desargues develops the theory of the traversale, a notion that generalizes the Apollonian diameter and allows to give a unified treatment of the three kinds of conics. We showed elsewhere that it leads Desargues to a complete theory of projective polarity for conics. The present article, which shall close our study of the Brouillon Project, is devoted to the last part of the text, in which Desargues puts his theory (...) of the traversal into practice by giving a very elegant tratment of the classical theory of parameters and foci. This will lead us to show that Desargues’ proofs can only be understood if one accepts that he reasons in a resolutely projective framework, completely assimilating elements at infinity to those at finite distance in his proofs. (shrink)

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)

(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)

Linear logic, introduced in 1986 by J.-Y. Girard, is based upon a fine grain analysis of the main proof-theoretical notions of logic. The subject develops along the lines of denotational semantics, proof nets and the geometry of interaction. Its basic dynamical nature has attracted computer scientists, and various promising connections have been made in the areas of optimal program execution, interaction nets and knowledge representation. This book is the refereed proceedings of the first international meeting on linear logic held at (...) Cornell University, in June 1993. Survey papers devoted to specific areas of linear logic, as well as an extensive general introduction to the subject by J.-Y. Girard, have been added, so as to make this book a valuable tool both for the beginner and for the advanced researcher. (shrink)

Jean-Yves Strasser The Olympia of Alexandria and the Pancratiast M. Aur. Asklepiades p.421-468 The Alexandrian Olympia are known thanks to inscriptions and especially papyri. The latter mention the olympionikoi, who may have been victors not in the great competition at Pisa, but in the Olympia of the Egyptian city. These competitions, created under Marcus Aurelius, became eiselastikoi under Gallien; they were first celebrated in 268. Like the majority of the great competitions in Egypt, they took place in the (...) winter of even years divisible by four. That was the case already in the 2nd century AD: the first Olympia were organised in 180. In 200, at the time of the sixth celebration, the periodonikes M. Aur. Asklepiades won the Olympia pancration in the presence of Septimius Severus and Caracalla. An inscription at Coptus (I. Portes 88) mentions a hellanodikes of Alexandria: he could have been serving at the time of the seventeenth Olympiad in 244; in 246-247 he had a statue of Sarapis Polieus erected under the prefect of Egypt Valerius Firmus. (shrink)

This paper discusses the development of the Logic and Religion project and the various events organized within this framework, particularly the 3rd and 4th editions, with this volume including papers presented at both.

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 pancratiaste périodonique Markos Aurèlios Dèmostratos Damas de Sardes est connu par de nombreux témoignages trouvés dans sa patrie, à Rome, à Éphèse, à Delphes et en Egypte. Leur réexamen permet de reconstruire avec précision la carrière du champion, comme d'éclairer certains points de l'histoire des concours qu'il a remportés. Deux inscriptions d'Éphèse qui lui ont été rapportées ne doivent sans doute pas l'être. On peut proposer de nouveaux suppléments aux palmarès de Sardes et de Delphes ; un autre texte (...) delphique est identifié comme une nouvelle liste chronologique des victoires de Dèmostratos Damas. Le pancratiaste, dont le floruit se situe sous le règne de Marc Aurèle, a brillé en fin de carrière dans la boxe. Les statues dont on a retrouvé les bases ont été érigées essentiellement après sa carrière sportive, lorsqu'il exerce, sous Septime Sévère, les plus hautes charges au sein de l'association des athlètes. (shrink)

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.

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)

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 extension of (...) K. (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)

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 are not many philosophers (...) who can be proud of having written influential math textbooks, contributed decisively to the philosophical foundations of science, helped to develop research in real labs, promoted new forms o education (computer-assisted learning and the EGPY – Education Program for Gifted Youth). -/- Since the range of interest of Suppes was very broad, so is the variety of topics dealt with in this volume. The work of a researcher is certainly not limited to his own writings, but also has to be appreciated through the work of the people he has been working with and influenced. From this point of view the work of Suppes is very impressive, and the present book contributes to show that. -/- This is a follow up of a special issue of the journal Synthese, New Directions in the Foundations of Science, edited by Béziau and Krause, after a meeting they organized with Suppes in Florianópolis (Brazil) in 2002 for his 80th birthday. -/- Jean-Yves Béziau worked with Suppes at Stanford University for two years (2000 and 2001) and has been continuously working in the Suppes tradition of logic, methodology and philosophy of science, which emphasizes structures and models. -/- Décio Krause has used Suppes’ approach to the axiomatization of scientific theories in many fields. With J.C.M. Magalhães, he presented a ``Suppes predicate” for genetics and natural selection and with S. French he developed a Suppes predicate for quantum field theories via Fock spaces. (shrink)

Nous tentons dans cet article de proposer une thèse cohérente concernant la formation de la notion d’involution dans le Brouillon Project de Desargues. Pour cela, nous donnons une analyse détaillée des dix premières pages dudit Brouillon, comprenant les développements de cas particuliers qui aident à comprendre l’intention de Desargues. Nous mettons cette analyse en regard de la lecture qu’en fait Jean de Beaugrand et que l’on trouve dans les Advis Charitables.

My paper concerns a rather extraordinary generation which arose in France in the 1930s, reacting against Action française which had long infected French Catholic political and social thought. Action française was a line of thought — and a political movement — inspired by Charles Maurras, himself an agnostic, basing his political thinking on a form of naturalism and positivism which clearly divorced politics from religion and ethics. Pope Pius XI forbade the participation of Catholics in that movement in 1926, which (...) was quite a blow and provoked quite an uproar since the majority of Catholic intellectuals were from Action française.The great Thomists of the time in particular and the bishops were reluctant in following the Pope's condemnation. Already the following year however, Jacques Maritain, who had sided with Action française for a long time, rallied to Rome. He contributed to a famous book Rome has spoken . Many followed him. He subsequently changed his basic views, fought for an integration of politics with morality as well as for a certain integration of politics and the Christian message, under the name Humanisme intégral, the title of one of his books. Jacques Maritain was born in 1882, died in 1975. The decisive years of his work are clearly the '30s and early '40s. (shrink)

Contre une interprétation déconstructiviste de la question de l'animalité, on s'attache à montrer, par une présentation précise des objections adressées à P. Singer par G. Francione, que l'éthique animale « classique » comporte en elle-même les ressources d'une pensée critique extrêmement audacieuse.

L'idée du cinéma comme " septième art ", Art total, synthèse des autres Arts, trouve son origine et ne se comprend vraiment que par rapport à la philosophie kantienne de l'Art. Cela peut sembler étonnant, mais c'est ce que fait apparaître de façon frappante, sur plusieurs points importants, l'étude du cinéma et de la manière dont les grands cinéastes et théoriciens se le sont eux-mêmes souvent représenté. La dimension philosophique, voire proprement métaphysique du cinéma, même du cinéma le plus simple (...) et le plus modeste, est en même temps liée à ce qui fait que le cinéma est un Art qui plaît tant populairement. Il y a là de quoi soupçonner ou entrevoir l'importance culturelle, sociale, morale et politique, peut-être, du cinéma le plus artistique. Il n'est pas nécessaire d'être spécialiste de philosophie pour lire l'ouvrage : tout ce qui est proprement philosophique y est expliqué simplement. Jean-Yves Chateau y montre à quelles conditions le cinéma peut être un Art, où se révèle avec une singulière clarté l'essence même de l'Art. En lui, sous des formes diverses, il y va toujours du monde lui-même et de la possibilité d'en faire un monde commun. (shrink)

We discuss the history of the revival of the theory of opposition, with its emerging paradigms of research, and the related events that are organized in this perspective, including the latest one in Leuven in 2022.

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 Kognitionswissenschaften, in der Linguistik, in KI-Bereichen wie der (Logik-basierten) Wissensrepräsentation eingesetzt, und auch in (...) der Philosophie verwendet (Kapitel 2). Mehrere Studien haben in den letzten Jahren gezeigt, dass Kant in weiten Teilen seines Systems Oppositionsverhältnisse verwendet, die der Struktur des logischen Quadrats entsprechen. Das logische Quadrat ist heute Gegenstand intensiver Forschung, da es neben der klassischen, auch die paravollständige und parakonsistente Negation abbildet (Kap. 3). Jüngst wurde zudem die Implementierbarkeit der kantischen Logik in ein formalisiertes deduktives System bewiesen. Die Bedeutung dieses Ergebnisses wird insbesondere im Hinblick auf die formalisierte Umsetzung der Sätze vom Widerspruch, vom zureichenden Grund und der Ausschließung des Mittleren erläutert (Kap. 4). Abschließend möchten wir ein paar Perspektiven für die Forschung zur formalen Logik bei Kant nennen (Kap. 5). -- -/- Note: No financial support acknowledged by the second autor (S. Kovač). (shrink)

Rarely is the problem of the diversity of languages taken into account whenever population groups are formed into States. When the problem does come up, it is later, in a primarily political context which tries to find political solutions, such as we may presently see them in Canada or in Belgium for instance. These solutions are few and they deal with situations that may contain a host of nuances.Certain countries have chosen a vehicular language while keeping their local languages: the (...) common language in the USSR is the language of one of its republics. In Senegal it is French, which is of a totally foreign origin but has the advantage of avoiding the rivalry existing among the native languages, and it also has a place within the international community. Other countries have accepted as official languages the different languages spoken within its borders. Thus Switzerland is officially tri-lingual (French, German, Italian), giving legal status to what somewhere else may simply be an accepted fact. Many Alsatians speak three languages (Alsatian, French, German). As far as it concerns countries with a strong linguistic heterogeneity, whether it be their history or their size making for a centralizing policy, they have adopted, with the resulting neglect of all others, the language or the idiom of the region which was politically or culturally the dominant one at the time of their unification. Pekinese has been extended to all of China, Florentine to Italy, Hindi to India. Some original combinations can be found: in Israel Jewish immigrants who came from more than seventy different countries, have again taken up the nation's old cultural and religious language, which had been out of use for two thousand years, and have placed it on equal footing with Arabic spoken by the local population, while English is being used for international relations. (shrink)

Despite its wealth and economic performances, Western Europe is anxious about its future and unable to solve its main problem: unemployment. Its great project is the building or Europe. But many questions have no real answers: how can we avoid social fractures? is globalisation and internationalisation a risk or chance? how should we fight corruption? Europe should be the best answer to those questions. But it depends on the answers to new questions: what are the social values on which we (...) want to build the European society of the next century. Eastern Europe is still poor. But the questions are the same and people are confronted with the same problems. Our common challenge is to build a society for the future. And for the first time of our long history, we have no model. We have to invent it. Firms and managers from Hungary and Eastern Europe have to bring their contribution and promote values and virtues as a major factor of the building of our common Europe. (shrink)

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)

In this article, Jean-Yves Lacoste lays out the central moments of Heidegger’s complicated relationship to Christian thinking, from his earliest studies under Carl Braig up to his death in 1976. With careful attention to personal letters, scholarly reviews, conferences, as well as major texts, Lacoste shows that this influence was mostly in one direction: despite the eagerness of theology to engage with Heidegger, Heidegger continually demonstrated reticence to approach theology except strictly on his own terms. The article closes (...) with a retrospective evaluation of the central themes of the original Heidegger et la Question de Dieu volume, which took up this investigation in France in 1979. Despite the fact that its publication predated many of Heidegger’s essential texts on this theme, these essays, in Lacoste’s estimation, remain a “perfectly timeless” resource for those seeking to understand the place of God within phenomenology. (shrink)

This paper aims to shed new light on Hegel’s rather problematic statements about Asian thinking and Chinese philosophy by disclosing the Orientalist antecedents found in Kant’s anthropological works. First, the notion of Orientalism will be defined with reference to Orientalism and “Orientalism Reconsidered” by Edward Said. Second, an exploration of Kant’s anthropological research will show that this constituted the turning point in the Western Orientalist perception of China which had a strong influence on Hegel Finally, it will be claimed that (...) Hegel’s Orientalist perception of China rests on a definition of culture as the expression of the “spirit of a people” that has recently been revised by contemporary post-colonial anthropologists. (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.

Jean-Yves Leloup nous propose ici deux lectures magistrales de deux géants de la culture occidentale : Nietzsche, l'athée et Maître Eckhart, le théologien-mystique. Il tente de remettre "à l'endroit" un texte de Nietzsche, Ecce Homo, souvent cité pour justifier tous les athéismes. Leloup montre que le Dieu en lequel Nietzsche voyait une "antithèse de la vie" n'a rien à voir avec le Dieu des Evangiles qui est au contraire une puissance de vie et de libération, une claire lumière (...) par laquelle le monde est vu. L'auteur, avec Maître Eckhart, nous entraîne ensuite au-delà des contraires, au-delà même de Dieu et de tous les Absolus que nous imaginons, vers notre essentielle et silencieuse liberté... Ce livre délicieux et audacieux nous montre, comme le disait Pascal, que "l'athéisme est une marque de force d'esprit, mais jusqu'à un certain degré seulement". (shrink)

Un mot d'usage quotidien, "danger", est devenu concept chez Heidegger. L'usage heideggerien de "danger" n'est pourtant pas celui de ce livre, qui refuse de s'engager de front dans la "question de l'être" au profit des manières ou modes d'être, dont il explore un échantillon sans prétention exhaustive mais utilisé comme trame heuristique. Mode d'être de l'oeuvre d'art, mode d'être de la "chose" ou du sacrement, mode d'être comme "existence" et comme "vie", un danger est toujours présent : l'existence, telle que (...) décrite chez Heidegger, est déconstituée par des phénomènes auxquels elle ne peut rendre justice ; la vie abrite l'existence mais court le risque perpétuel de n'être que dans les frontières de l'existence, etc. Et si l'étant nous est toujours donné dans un comment - comment de son apparaître, donc comment de son être -, rien ne garantit la pérennité de cette donation : presque tout étant, et d'abord l'étant que nous sommes, est en danger d'apparaître autre qu'il ne nous apparaît maintenant. Aussi convenait-il, après avoir ajointé le concept de vie à celui d'esprit, après avoir dit que la vie est "spirituelle", de justifier le titre du livre en liant "être" et "danger" ; et il restait au final le temps de proposer, dans l'élément du possible, l'hypothèse d'une eschatologie de l'être, avant tout de notre être, sur laquelle le danger n'aurait plus de prise. (shrink)

We present a single sequent calculus common to classical, intuitionistic and linear logics. The main novelty is that classical, intuitionistic and linear logics appear as fragments, i.e. as particular classes of formulas and sequents. For instance, a proof of an intuitionistic formula A may use classical or linear lemmas without any restriction: but after cut-elimination the proof of A is wholly intuitionistic, what is superficially achieved by the subformula property and more deeply by a very careful treatment of structural rules. (...) This approach is radically different from the one that consists in “changing the rule of the game” when we want to change logic, e.g. pass from one style of sequent to another: here, there is only one logic, which—depending on its use—may appear classical, intuitionistic or linear. (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)

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 detailed discussion about this phenomenon, as well as some possible solutions for it, are given. (shrink)

The article concerns the life paths and the complex situations of autism in Île-de-France (France). It is based on a participative research with professionals and beneficiaries of the Complex Situations of Autism Device (SCATED). The method is organized in 3 phases: 1°- analysis of the context of autism in Île-de-France through the exploitation of the national survey called “ES 2014”; 2°- co-construction between the research team and the professionals of the device of an updated database specific to the device, based (...) on the 2 100 complex autism situations monitored from 2010 to 2018, and the exploitation by the researchers of 452 situations extracted from this database; 3°- analysis of 11 diversified situations (32 interviews). The research offers a critical reading of behavioral disorders and analyzes the seven dimensions that participate in a process of reinforcing vulnerabilities in complex situations of autism. It makes a certain number of recommendations which are taken up by the Île-de-France Regional Agency as part of its strategic health plan. (shrink)

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)

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.