"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)

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 define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is tudied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.

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)

Par-delà toute prise de position idéologique ou politicienne, la réflexion sur l'écologie est devenue de plus en plus présente dans notre société contemporaine, et les musiciens n'ont pas tardé à se sentir fortement concernés, ce qui a suscité, de leur part, des réponses de multiples natures. Certains compositeurs ont cherché à investir des lieux plus ouverts que la traditionnelle salle de concert, tandis que d'autres ont eu recours aux moyens technologiques et médiatiques les plus récents pour capter et diffuser les (...) sons qui nous entourent afin de les reprendre à leur compte ou de dialoguer avec eux, voire les révéler tels quels. La musique ayant de plus en plus tendance à envahir notre quotidien, d'autres encore ont entrepris de créer de nouveaux types d'environnement et de signalétique sonores. Et ces tentatives s'accompagnent fréquemment de confrontations avec différentes disciplines artistiques. L'initiateur d'une telle démarche n'était-il pas Erik Satie avec sa "musique d'ameublement"? Mais qu'aurait-il pensé du matraquage de la Muzak quelques décennies plus tard? (shrink)

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.

Pourquoi cet admirable eloge de la phronesis qu'est le Livre VI de l'Ethique a Nicomaque a-t-il donne lieu a tant d'interpretations differentes et meme contradictoires, tant de lectures passionnees et parfois militantes? Peut-etre parce que la maniere propre qu'a Aristote de penser la verite pratique, d'articuler l'intelligence aux circonstances, de l'enraciner dans une culture vivante, reussit une synthese dont nous ne cessons de chercher a percer le secret. Un commentaire continu du Livre VI est suivi ici d'une discussion de quelques (...) questions essentielles et se prolonge en ouvrant quelques perspectives. (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 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)

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.

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 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)

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)

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)

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.

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.

After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we discuss the emergence of universal logic as a general theory of logical systems, making comparison with universal algebra and the project of mathesis universalis. In a third part we critically present three lines of research connected to universal logic: logical pluralism, (...) non-classical logics and cognitive science. (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.

The abolition of slavery after the Revolution of 1789 has always been hailed by the French secular State as proof of the progressivist nature of the Republic. Nevertheless, there has never been any attempt to seriously confront the French involvement in the trade of slaves, which lasted for two centuries. France, a colonial power until the 1960s, which still retains several overseas possessions with an Afro-Caribbean population, has a large resident black population in the mainland which feels it has been (...) deprived of its memory and history and seeks official recognition of the role of the State in the trade of slaves. This article tries to show how a black collective identity and consciousness emerged around the fight for the recognition of slavery as a crime against humanity and the claim for financial compensation. This black collective identity competes with the Jewish community, which was granted financial compensation for the Shoah and which successfully lobbied the State to recognize that it was partly responsible for the genocide in World War II. While some radical black activists seek an alliance with part of the Islamic movement, they are also competing over the recognition of their collective identity by the State with the growing Muslim community whose memory is that of colonization and second-class citizenship. (shrink)

On cherche à démontrer que les logiques de fonctionnement de la formation professionnelle continue rendent difficile la réalisation d’objectifs contenus dans la législation de 1971. En effet, loin de contribuer à la promotion sociale du plus grand nombre des salariés, la formation professionnelle continue se caractérise surtout par des inégalités d’accès et des mécanismes discriminants qui participent au maintien de l’employabilité pour ceux qui sont déjà pourvus des qualifications les plus hautes et les plus compétitives.

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)

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)

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.

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)

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.

We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem.

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 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)