Le problème de la vérité a toujours préoccupé l'esprit humain; il hante pour ainsi dire l'homme d'aujourd'hui. Dans les brèves réflexions qui vont suivre, nous nous proposons de présenter une approximation tres limitée de ce problème tel qu'il se pose à la philosophic traditionnelle, à savoir: Le caractère historique et relatifde la connaissance humaine est-il conciliable avec I'affirmation de vérites immuables?

Inλ-calculus, the strategy of leftmost reduction (“call-by-name”) is known to have good mathematical properties; in particular, it always terminates when applied to a normalizable term. On the other hand, with this strategy, the argument of a function is re-evaluated at each time it is used.To avoid this drawback, we define the notion of “storage operator”, for each data type. IfT is a storage operator for integers, for example, let us replace the evaluation, by leftmost reduction, ofϕτ (whereτ is an integer, (...) andϕ anyλ-term) by the evaluation oftτϕ. Then, this computation is the same as the following: first computeτ up to some reduced formτ 0, and then applyϕ toτ 0. So, we have simulated “call-by-value” evaluation within the strategy of leftmost reduction.The main theorem of the paper (Corollary of Theorem 4.1) shows that, in a second orderλ-calculus, using Gödel's translation of classical intuitionistic logic, we can find a very simple type (or specification) for storage operators. Thus, it gives a way to get such operators, which is to prove this type in second order intuitionistic predicate calculus. (shrink)

The relation between morality and rationality (in the sense of rational choice and rational behaviour) is a prominent theme in (the tradition of) moral philosophy. D. Gauthier’s account of this relation is an extraordinarily impressive one. He attempts to demonstrate a general coincidence (at different levels) between rationality and morality. His approach is discussed in what follows, and it will be shown that most of his ‘coincidence claims’ are exaggerated.

, which uses the intuitionistic propositional calculus, with the only connective →. It is very important, because the well known Curry-Howard correspondence between proofs and programs was originally discovered with it, and because it enjoys the normalization property: every typed term is strongly normalizable. It was extended to second order intuitionistic logic, in 1970, by J.-Y. Girard [4], under the name of system F, still with the normalization property.More recently, in 1990, the Curry-Howard correspondence was extended to classical logic, following (...) Felleisen and Griffin [6] who discovered that the law of Peirce corresponds to control instructions in functional programming languages. It is interesting to notice that, as early as 1972, Clint and Hoare [1] had made an analogous remark for the law of excluded middle and controlled jump instructions in imperative languages.There are now many type systems which are based on classical logic; among the best known are the system LC of J.-Y. Girard [5] and the λμ-calculus of M. Parigot [11]. We shall use below a system closely related to the latter, called the λ c -calculus [8, 9]. Both systems use classical second order logic and have the normalization property.In the sequel, we shall extend the λ c -calculus to the Zermelo-Frænkel set theory. The main problem is due to the axiom of extensionality. To overcome this difficulty, we first give the axioms of ZF in a suitable (equivalent) form, which we call ZF ɛ. (shrink)

We describe here a simple method in order to obtain programs from proofs in second-order classical logic. Then we extend to classical logic the results about storage operators proved by Krivine for intuitionistic logic. This work generalizes previous results of Parigot.

Introduction. Il est bien connu que la correspondance de Curry-Howard permet d'associer un programme, sous la forme d'un λ-terme, à toute preuve intuitionniste, formalisée dans le calcul des prédicats du second ordre. Cette correspondance a été étendue, assez récemment, à la logique classique moyennant une extension convenable du λ-calcul. Chaque théorème formalisé en logique du second ordre correspond donc à une spécification de programme.Il se pose alors le problème, en général tout à fait non trivial, de trouver la spécification associée (...) à un théorème donné; autrement dit, de déterminer le comportement opérationnel commun aux λ-termes associés aux diverses démonstrations formelles du théorème considéré.Cette question est résolue ici pour le théorème de complétude de la logique classique.La première étape consiste à formaliser convenablement ce théorème en logique du second ordre. Ce travail est fait complètement dans la section 1. Il a comme sous-produit, peut-être inattendu, de montrer que ce théorème est prouvable en logique intuitionniste du second ordre. Ceci, toutefois, à condition d'introduire une légère variante de la notion de modèle, en admettant un modèle supplémentaire trivial, où toute formule est satisfaite.On notera, à ce sujet, que des preuves intuitionnistes du théorème de complétude de la logique intuitionniste, utilisant des variantes de la notion de modele de Kripke, ont été données par H. Friedman [7] et W. Veldman [8]. On remarquera également qu'un argument de G. Kreisel [2] montre que le théorème de complétude habituel de la logique intuitionniste n'a pas de preuve intuitionniste. (shrink)

In this article first appeared in 1997, Jean-Louis Chrétien examines the meaning of prayer in Kierkegaard’s writings and existence. By focusing on the difficulties of this task and with meticulous attention to the vast work of the Danish philosopher, Chrétien describes prayer as a tense and agonistic experience, akin to the evangelical struggle between Jacob and the angel. Just like in his well-known phenomenological analysis, “The Wounded Word: Phenomenology of Prayer”, the author identifies in prayer a paradoxical articulation (...) of struggle and peace, gift and endeavour, speaking and listening, through which the human being is profoundly transformed and finally learns to truly say “thank you”. (shrink)

Artificial intelligency can bring speed and reliability to drug discovery process. It represents an additional intelligence, which in any case can replace the strategic and logic creative insight of the medicinal chemist who remains the architect and molecule master designer. In terms of drug design, artificial intelligency, deep learning machines, and other revolutionary technologies will match with the medicinal chemist’s natural intelligency, but for sure never go beyond. This manuscript tries to assess the impact of the artificial intelligency on drug (...) discovery today. (shrink)

Christianism often mentions perfumes. Its liturgy based on Scripture uses incense and balm. A reading from the Bible and the lives of saints reveals many extraordinary perfumes (“odours of sanctity”). The Virgin Mary holds extreme importance among saints and it is quite common to see her spreading miraculous fragrances. These are subtle, discrete but pleasant signals from Heaven. They are sent to everyone in order to convert non‑believers or turn back believers to the faith in God. The divine origin of (...) perfumes is tied up with the memories and hopes from Paradise. It marks bodies escaping from death and entering into eternal life. (shrink)

Cet article étudie l’apparente convergence qui s’opère, depuis quelques années, entre l’ approche en termes de Systèmes Nationaux d’Innovation et la théorie évolutionniste du changement technologique. Ce processus s’appuie sur une conception spécifique du processus d’innovation lui-même. Dans ce contexte, l’innovation est un processus cognitif, qui s’exprime à plusieurs niveaux – local, national, sectoriel et international – et dans de nombreuses dimensions – technologique, organisationnelle et institutionnelle. Cette approche attribue un rôle central aux acteurs publics et aux institutions mais révèle, (...) dans le même temps, les difficultés intrinsèques à toute tentative de synthèse entre des théories souvent hétérogènes.This paper examines the apparent convergence between the National Systems of Innovation approach and evolutionary theories of technological change. This convergence is organized around a complex and specific conception of the innovation process itself In this context, innovation is a cognitive, a multilevel – i.e. local, national, sectorial and international –, a historical and multidimensional – i.e. technological, organizational and institutional – process. This conception gives a central place to public actors and institutions but shows the strong difficulty inherent to the elaboration of a coherent evolutionary theory of economic change. In effect, it seems difficult to articulates heterogeneous concepts within a global framework. (shrink)

Há anos ou décadas, vemos países que estavam em marcha em direção à democracia como a Rússia, a Turquia e mesmo reais democracias como o Brasil, se tornarem verdadeiras democraduras, ou se encaminharem para esse tipo de regime, a Hungria por exemplo, mas igualmente outros países. Os analistas políticos continuam lutando para entender a origem e a natureza desse direcionamento sobre o qual a leitura de Tocqueville ainda fornece um esclarecimento notável, cujas análises mantêm perfeita atualidade; é um grande pensador (...) para os dias atuais que estabelece como, para pensar o surgimento da democracia e os problemas que aparecem a ela, é apropriado partir do estado social democrático. (shrink)

Contrairement à l’apparence, Plotin est un philosophe du mouvement et de la genèse. Tout être, même éternel, est pensé à partir des actes qui l’engendrent. Même ce qui n’a pas de genèse est décrit génétiquement. L’article étudie quelques unes des figures de ce mouvement (la course, la danse, la trace), et leurs prolongements au-delà de Plotin. Il établit que cette mobilité donne à Plotin son style unique, qui anticipe à certains égards celui de l’idéalisme allemand. Loin d’être une caractéristique générale (...) du néoplatonisme ancien, cette écriture du mouvement forme une singularité significative de Plotin. (shrink)

Tenir la Bible pour inspirée, c’est croire qu’elle est à la fois divine et humaine, tout entière humaine et tout entière divine. Et que cette Ecriture soit inspirée signifie la coexistence en elle du vivant et du mort, du présent et du passé, de l’un et du multiple. L’affirmation de l’inspiration des Ecritures n’est donc pas seulement descriptive de leur nature et de leur objet, ni normative quant à la nature et à l’objet de la foi ; elle est aussi (...) prescriptive quant à la manière ou aux manières dont nous pouvons les lire et user d’elles. L’unique propos de ces pages est de tenter de répondre, au moins dans certains traits essentiels, à cette question : qu’est-ce que lire les Ecritures bibliques comme inspirées ? qu’est-il possible de dégager dans l’acte de lire mis en jeu qui lui serait propre et le caractériserait comme tel ? S’il ne s’agit en aucune façon d’esquisser une typologie des interprétations de la Bible ni de rappeler les étapes de l’histoire de l’exégèse, il s’agit de s’en tenir à ce qu’appelle du lecteur la présence d’un livre – d’un ensemble de livres – de divine provenanceTo accept the Bible as inspired is to believe that it is both divine and human, totally human and totally divine. That this Writing is inspired signifies coexistence within it of the living and dead, the present and past, and the one and the many. Affirmation of the Scripture¹s inspiration is, then, not only descriptive of its nature and object, nor merely normative as regards the nature and object of faith. It is also prescriptive as to the way or ways in which we can read them and use them. The unique aim of these pages is to attempt to answer, at least in certain essential features, this question: What does it mean to read these biblical Writings as inspired? Is it possible to separate in the act of reading a practice that is proper to it and to characterize it as such? This article is in no way about outlining a typology of interpretations of the Bible, nor a summary of the stages of the history of exegesis; it is only concerned with that which the presence of a book of divine origin –a group of books– demand of the reader. (shrink)

Aristotle’s Prior Analytics identifies deductions simpliciter with inferential necessity, so that a deduced conclusion is necessarily inferred from some premises. Modern logical reconstructions claim that inferential necessity in Aristotle corresponds to logical validity. However, this logical reconstruction fails on two accounts. First, logical validity does not highlight Aristotle’s distinction between inferential necessity and predicative necessity, meaning that the inferential necessity of a deduction is not of the same kind as the predicative necessity of a non‑deductive argument. Second, logical validity does (...) not explain the relevance of Aristotle’s distinction between complete and incomplete deductions. Logicians speak of complete deduction by adding the term “obvious” or “transparent” to logical validity, and then criticize Aristotle’s view for being unclear. However, Aristotle’s position is not confronted with this difficulty. There is nothing to add to inferential necessity, which already means complete deducibility, as opposed to incomplete deducibility, deemed to be potentially complete. Accordingly, the Prior Analytics reduces the incomplete deductions to the complete deductions in order to prove the potential, inferential necessity of the incomplete deductions. Logical validity would have been faithful to Aristotle’s text, if it had been possible to coin a notion of potential validity, distinct from both validity and invalidity. (shrink)

This paper shows that Aristotle's De Interpretatione does not separate syntax from semantics. Linguistic sentences are not syntactic entities, and non-linguistic meanings are not semantic propositions expressed by linguistic sentences. In fact, Aristotle resorts to a mental conception of meaning, distinguishing linguistic meanings in a given language from non-linguistic mental contents in relation to actual things: while the former are not the same for all, the latter are shared by everyone. Aristotle is not a modern logician, like Boole, Frege, or (...) Russell, in so far as a mental conception of meaning does not reveal an abstract semantics for a syntactic language. (shrink)

The immemorial and recollection -- The reserve of forgetting -- The unforgettable -- The sudden and the unhoped for -- Retrospection.

Research on teachers’ professional identity integrates many constructs that are treated independently in most cases. This study described the associations between components of teacher professional identity and their association with teachers’ general pedagogical beliefs. Secondary teachers completed a survey about several components of their identity and general pedagogical beliefs. Multidimensional scaling revealed that the components could be mapped on two dimensions: form of motivation and degree of subject specificity. The resulting map revealed four meaningful groups of components. Furthermore, whereas direct (...) transmission general pedagogical beliefs were found to be strongly tied to an identity grounded in the subject taught, constructivist beliefs were independent of identity components. This study provides new insight into the stru... (shrink)

L’une des conséquences indirectes de la rupture de l’unité confessionnelle aux temps modernes, fut une exploration accélérée du passé chrétien. Pour cela, une masse régulièrement accrue de documents venait nourrir deux représentations antagonistes de l’histoire de l’Eglise, lesquelles étaient défendues par des travaux d’érudition au service de deux conceptions de l’histoire, qui étaient aussi bien deux théologies de l’Eglise. Cependant, l’exigence de proximité des sources devait induire un mode particulier d’écriture de l’histoire qui transcenderait les frontières confessionnelles, tout en maintenant (...) des positions différentes. La prise en compte des documents allait notamment renforcer une certaine critique, pour laquelle surgissent notamment les noms de Mabillon et de Le Nain de Tillemont, même si les positions continueraient de se différencier tout au long du XVIIe siècle.One of the indirect consequences of the break up of confessional unity in modern times was an accelerated exploration of the Christian past. In the process, a constantly increasing mass of documents came to fuel two opposing representations of the history of the Church. These representations were supported by works of erudition in keeping with two different conceptions of history, which were also two theologies of the Church. The use of new sources became required, however, and led it to a particular way of writing history that would transcend confessional boundaries, while maintaining different positions. Taking these documents into account strengthened a critical current that gave rise to Mabillon and Le Nain de Tillemont, even though the positions continued to differ throughout 17th century. (shrink)