We are pleased to present this special issue of the journal History and Philosophy of Logic dedicated to the square of opposition.The square of opposition is a diagram and a theory of opposition re...

This special issue of Logica Universalis (Springer) deals with the relations between logic and religion, broadly conceived. It 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)

These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting (...) with Godel's paradox --so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination. Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction, all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way. (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.

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.

Go back to An-fang, the Peace Square at An-Fang, the Beginning Place at An-Fang, where all things start (… ) An-Fang was near a city, the only living city with a pre-atomic name (… ) The headquarters of the People Programmer was at An-Fang, and there the mistake happened: A ruby trembled. Two tourmaline nets failed to rectify the laser beam. A diamond noted the error. Both the error and the correction went into the general computer. Cordwainer SmithThe Dead Lady (...) of Clown Town, 1964. (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 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)

t.l. Introduction à une anthropologie philosophique.

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)

"Christian philosophy" is commonly regarded as an oxymoron, philosophy being thought incompatible with the assumptions and conclusions required by religious faith. According to this way of thinking, philosophy and theology must forever remain distinct. In From Theology to Theological Thinking, Jean-Yves Lacoste takes a different approach. Stepping back from contemporary philosophical concerns, Lacoste--a leading figure in the philosophy of religion--looks at the relationship between philosophy and theology from the standpoint of the history of ideas. He notes in particular (...) that theology and philosophy were not considered separate realms until the high Middle Ages, this distinction being a hallmark of the modern era that is coming to an end. Lacoste argues that the intellectual task before us now is to work in the frontier region between or beyond these domains, work he identifies as "the task of thinking." With this argument, Lacoste resets our understanding of Western Christian thought, contending that a new way of thinking that is at once philosophical and theological will be the lasting discourse of Christianity. (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)

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)

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of (...) opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts. (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.

Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente et ce qui est représenté, joue un rôle fondamental dans la plupart des activités humaines, qu’elles soient scientifiques, artistiques ou religieuses. C’est cette dimension symbolique, sa portée, son fonctionnement et sa signification dans des domaines aussi variés que la chimie, la théologie, (...) les mathématiques, le code de la route et bien d’autres qui est l’objet du livre La Pointure du symbole. -/- Jean-Yves Béziau, franco-suisse, est docteur en logique mathématique et docteur en philosophie. Il a poursuivi des recherches en France, au Brésil, en Suisse, aux États-Unis (UCLA et Stanford), en Pologne et développé la logique universelle. Éditeur-en-chef de la revue Logica Universalis et de la collection Studies in Universal Logic (Springer), il est actuellement professeur à l’Université Fédérale de Rio de Janeiro et membre de l’Académie brésilienne de Philosophie. SOMMAIRE -/- PRÉFACE L’arbitraire du signe face à la puissance du symbole Jean-Yves BÉZIAU La logique et la théorie de la notation (sémiotique) de Peirce (Traduit de l’anglais par Jean-Marie Chevalier) Irving H. ANELLIS Langage symbolique de Genèse 2-3 Lytta BASSET -/- Mécanique quantique : quelle réalité derrière les symboles ? Hans BECK -/- Quels langages et images pour représenter le corps humain ? Sarah CARVALLO Des jeux symboliques aux rituels collectifs. Quelques apports de la psychologie du développement à l’étude du symbolisme Fabrice CLÉMENT Les panneaux de signalisation (Traduit de l’anglais par Fabien Shang) Robert DEWAR Remarques sur l’émergence des activités symboliques Jean LASSÈGUE Les illustrations du "Songe de Poliphile" (1499). Notule sur les hiéroglyphes de Francesca Colonna Pierre-Alain MARIAUX Signes de vie Jeremy NARBY Visualising relations in society and economics. Otto Neuraths Isotype-method against the background of his economic thought Elisabeth NEMETH Algèbre et logique symboliques : arbitraire du signe et langage formel Marie-José DURAND – Amirouche MOKTEFI Les symboles mathématiques, signes du Ciel Jean-Claude PONT La mathématique : un langage mathématique ? Alain M. ROBERT. (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)

Cet ouvrage regroupe plusieurs textes centrés sur les questions cardinales de la philosophie de Merleau-Ponty, de ses premières à ses dernières oeuvres, en particulier : les questions de l'incarnation, de l'expression, de la peinture, de la vision et bien sûr du style. L'analyse est donc plutôt orientée du côté de l'esthétique et des rapports existant entre philosophie et non-philosophie. Merleau-Ponty a donné toute son importance au silence de la peinture pour tenter de comprendre la dimension du langage et de l'expression.

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.

La conversion de la France à une politique de « réduction des risques » , est généralement interprétée comme l’indice d’un changement de paradigme en matière de toxicomanie. Il est néanmoins possible de la voir comme une forme de réagencement politique du monde des consommations de drogues, visant à définir de nouveaux seuils, les plus bas possibles, pour l’entrée dans des dispositifs de soin et de service. L’examen des visions du monde sur lesquelles reposent ces équipements politiques, en France comme (...) dans le reste de l’Union européenne, montre d’ailleurs que la vision du monde autonomiste y compose avec d’autres, compensatoires et additives, plus anciennement implantées. C’est sans doute pourquoi on retrouve, à divers niveaux, un véritable décalage entre les mesures volontaristes liées à ces politiques publiques et les contextes dans lesquels elles sont mises en œuvre : qu’il s’agisse des promoteurs, professionnels ou amateurs, ou qu’il s’agisse des destinataires, tout le monde semble s’accommoder d’un fonctionnement minimal de ces dispositifs, vérifiant ainsi une fois de plus la force des liens faibles.The French turn to the so-called « risk reduction policy » , is generally interpreted as a shift of the paradigm of drug addiction policies. One can, nevertheless, see it as a kind of new political layout of the drug addiction field, intended to define new thresholds for one’s entering in the treatment and care devices. When we examine the worldviews which sustain these political equipments , we can see that the autonomist worldview has to come to terms with others, namely : the compensatory and additive ones. That is probably why we can see, at various levels, a real discrepancy between the strong willings supporting the actions promoted by the risk reduction policies, and the contexts in which they take place : would it be the main actors , or the beneficiaries, everyone seems to be satisfied with a minimal functioning of these devices, verifying once again the strength of the weak ties. (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.

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)

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.

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.

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)

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 commenting the logo of the World Logic Day. (shrink)

L'expérience de la connaissance nous enseigne qu'il n'y a pas de Réalité Dernière, que tout train en cache un autre. Une évidence qu'il n'est pas facile d'accepter, d'où l'idée de ce train ultime, celui qui ne cacherait plus rien. La transparentisme postule l'existence, au-delà de la perception immédiate, d'un monde, d'un niveau de lecture, complètement intelligible, i.e, explicite et immédiat. D'où cette croyance en de prétendus "rayons X du savoir" qui nous dévoileraient l'envers de l'Univers.

L'expérience de la connaissance nous enseigne qu'il n'y a pas de Réalité Dernière, que tout train en cache un autre. Une évidence qu'il n'est pas facile d'accepter, d'où l'idée de ce train ultime, celui qui ne cacherait plus rien. La transparentisme postule l'existence, au-delà de la perception immédiate, d'un monde, d'un niveau de lecture, complètement intelligible, i.e, explicite et immédiat. D'où cette croyance en de prétendus "rayons X du savoir" qui nous dévoileraient l'envers de l'Univers.

French ethics of technology has followed a most peculiar path. Generally speaking, French philosophers of technology have dismissed the methodology of Applied Ethics as widely practiced. As a result, the most notorious thinkers have been those who have expressed the most considerable reservations about the “technical phenomenon.” I here attempt to establish that the most promising attempts to overcome this situation do not rise from social philosophy, but from a long-standing French tradition in the field of philosophy of life, supported (...) by an overriding project of integration of technology into culture. (shrink)

Les animaux peuvent-ils avoir des droits? La souffrance animale a-t-elle une importance morale? Les animaux sont-ils dotes de conscience? Telles sont les questions abordees dans cet ouvrage, qui se propose d'approfondir quelques pistes de reflexion a travers la lecture commentee de deux textes, l'un de John Stuart Mill (extrait de L'utilitarisme), l'autre de Donald Davidson (sur la cognition animale).

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.

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.

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.

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)

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)