Moritz Pasch is usually seen today as a precursor of Hilbert. The Vorlesungen über neuere Geometrie is indeed one of the few works Hilbert referred to in the Grundlagen. Unfortunately, Hilbert's epoch-making book has eclipsed Pasch's achievement; so much so that Pasch's Vorlesungen has not been yet translated into English. But as Pollard emphasizes, it would be a mistake to reduce Pasch's research to his work on the foundations of geometry. Pasch published another book on the foundations of real analysis (...) and arithmetic in 1882, and two other works, respectively, in 1909 and in 1914 . Pasch thus aimed not only to analyze the foundations of geometry but also to elaborate a complete theory of mathematical knowledge. This ambition brought him close to the logicists . But, unlike them, Pasch was a resolute empiricist: he considered that ‘geometry and number theory are branches of empirical science’ 1 and that all mathematical concepts must be derived from a set of notions abstracted from our experience.Pasch made his whole career in Giessen — that is, outside of the major German research centers. Heavily burdened with administrative duties, Professor Pasch seems to have found time for his research only in 1917, when he retired at the age of 67. As Pollard notes, nearly half of Pasch's published output appeared after his sixty-eighth birthday! This volume is a translation of fourteen articles dating from the later period of Pasch's life, ordered by the time of their publication. The papers are preceded by a substantial introduction by Stephen Pollard, the editor and translator of all the papers. Aside from his correspondence with Frege, this volume is thus the first translation of Pasch's work …. (shrink)

This article analyzes the operations of the French group Lafarge in Syria during the civil war between 2011 and 2014, to understand the conflict-sensitive practices of a multinational company (MNC) in an area of limited statehood (ALS). We examine how and why the company decided to continue operating its plant in Syria during this intrastate conflict, resulting in financing terrorist groups like ISIS. We highlight the key operational and managerial decisions made by headquarters and local operations and relate them to (...) the conflict situation in the ALS in question. We contribute, with the idea of the firm’s “organization of short-sightedness,” to the understanding of how strategic decisions may lead to a structural inability to fully comprehend the local dangers and the implications for the employees, and how this may lead to a redefinition of legitimate and illegitimate stakeholders in conflict zones. A drawn-out process, stemming from a willingness to stay at all cost in an ALS environment, leads to misinterpretation of the danger and an acute dependency on local stakeholders. (shrink)

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics, meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

The goal of this paper is to connect Rota's discussion of the Husserlian notion of Fundierung with Rota's project of giving combinatorics a foundation in his 1964 paper ‘On the foundations of combinatorial theory I’. Section 2 gives the basic tenets of this seminal paper. Sections 3 and 4 spell out the connections made there between Rota's philosophical writings and his mathematical achievements. Section 5 shows how these two developments fit into Rota's analysis of the place of combinatorics in mathematics.

From 1905–1908 onward, Russell thought that his new ‘substitutional theory’ provided him with the right framework to resolve the set-theoretic paradoxes. Even if he did not finally retain this resolution, the substitutional strategy was instrumental in the development of his thought. The aim of this paper is not historical, however. It is to show that Russell's substitutional insight can shed new light on current issues in philosophy of mathematics. After having briefly expounded Russell's key notion of a ‘structured variable’, I (...) connect it to two ongoing discussions: the Caesar problem, and absolute generality. (shrink)

James Levine has recently argued that there is a tension between Russell’s Moorean semantical framework and Russell’s Peano-inspired analytical practice. According to Levine, this discrepancy runs deep in Russell’s thought from 1900 to 1918, and underlies many of the doctrinal changes occurring during this period. In this paper, I suggest that, contrary to what Levine claims, there is no incompatibility between Moore’s theory of meaning and the idea of informative conceptual analysis. I show this by relating Moore’s view of meaning (...) to his Sidgwick-inspired criticism of the so-called naturalistic fallacy. I maintain that Moore’s semantical framework has a methodological intent: following Sidgwick, Moore wants to block any attempt to justify ethical principles through setting ad hoc conditions on the meaning of the terms involved. Thus, far from grounding philosophical knowledge on subjective intuitions, as Levine suggests, Moore’s framework would provide us with the means to make room for a discursive and dialectic conception of philosophical inquiry. (shrink)

The paper aims at comparing Wittgenstein’s discussion of color exclusion in his to Johnson’s doctrine of determinable and determinate expounded in his. I first summarize Wittgenstein’s developments about the incompatibility of elementary propositions and about the logic of color statements. In the second part, I present and discuss Johnson’s doctrine in relation to Wittgenstein’s development. In a third conclusive moment, drawing on a early work of Prior, I argue that the distinction made by Wittgenstein and Johnson between predication and determination (...) should be looked at from a long term historical perspective. (shrink)

This article aims first at showing that Russell's general doctrine according to which all mathematics is deducible 'by logical principles from logical principles' does not require a preliminary reduction of all mathematics to arithmetic. In the Principles, mechanics (part VII), geometry (part VI), analysis (part IV-V) and magnitude theory (part III) are to be all directly derived from the theory of relations, without being first reduced to arithmetic (part II). The epistemological importance of this point cannot be overestimated: Russell's logicism (...) does not only contain the claim that mathematics is no more than logic, it also contains the claim that the differences between the various mathematical sciences can be logically justified?and thus, that, contrary to the arithmetization stance, analysis, geometry and mechanics are not merely outgrowths of arithmetic. The second aim of this article is to set out the neglected Russellian theory of quantity. The topic is obviously linked with the first, since the mere existence of a doctrine of magnitude, in a work dated from 1903, is a sign of a distrust vis-à-vis the arithmetization programme. After having shown that, despite the works of Cantor, Dedekind and Weierstrass, many mathematicians at the end of the 19th Century elaborated various axiomatic theories of the magnitude, I will try to define the peculiarity of the Russellian approach. I will lay stress on the continuity of the logicist's thought on this point: Whitehead, in the Principia, deepens and generalizes the first Russellian 1903 theory. (shrink)

Russell's philosophy is rightly described as a programme of reduction of mathematics to logic. Now the theory of geometry developed in 1903 does not fit this picture well, since it is deeply rooted in the purely synthetic projective approach, which conflicts with all the endeavours to reduce geometry to analytical geometry. The first goal of this paper is to present an overview of this conception. The second aim is more far-reaching. The fact that such a theory of geometry was sustained (...) by Russell compels us to question the meaning of logicism: how is it possible to reconcile Russell's global reductionist standpoint with his local defence of the specificities of geometry? * This paper was first presented at the conference ‘Qu'est ce que la géométrie aux époques modernes et contemporaines?’, organized by the Universität Köln and the Archives Poincaré. I would like to thank Philippe Nabonnand for having enlightened me about the issues relative to projective geometry. I would like also to thank Nicholas Griffin, Brice Halimi, Bernard Linsky, Marco Panza, Ivahn Smadja for their helpful discussions. Many thanks also to the two anonymous referees for their useful suggestions. CiteULike Connotea Del.icio.us What's this? (shrink)

Dans l'Appendice au livre I de The World and the Individual (1898), le philosophe américain Josiah Royce développe, en se fondant sur Was sind und was sollen die Zahlen ? de Dedekind, une critique détaillée du livre de Bradley Appearance and Reality. Se concentrant sur le fameux § 66, Royce maintient que la théorie de Dedekind peut être vue comme l'accomplissement du mouvement de pensée inauguré par Fichte et Hegel : le 'Soi idéal ' est infini et l'arithmétique est la (...) théorie de sa structure formelle. Cet article analyse le contenu de ce texte, en le mettant en relation avec la pensée de Russell et de Lotze. (shrink)

Présentation de cinq grands intellectuels catholiques. Réflexion sur la foi et la raison. Essai engagé et sujet à débat.

To illustrate the view that a speaker can have a partial understanding of a concept, Burge uses the example of Leibniz’s and Newton’s understanding of the concept of derivative. In a recent article, Sheldon Smith criticizes this example and maintains that Newton’s and Leibniz’s use of their derivative symbols does not univocally determine their references. The present article aims at challenging Smith’s analysis. It first shows that Smith misconstrues Burge’s position. It second suggests that the philosophical lessons one should draw (...) from the practice of the historians of philosophy are more ambivalent than what Smith thinks. (shrink)

Plutarque nous raconte [VP I.1, 12.4.4–5] que le grand Varron s’adressa un jour à un certain Tarutius, connu pour ses talents de mathématicien et d’astrologue, pour déterminer le jour et l’heure de la naissance de Romulus « de la même manière que l’on tire l’analyse des problèmes géométriques» [ὥσπερ αἱ τῶν γεωμετρικῶν ὑφηγοῦνται προβλημάτων ἀναλύσεις]. Or, puisque dans la science astrologique ancienne on pouvait prédire, en prenant le jour et l’heure de la naissance d’un homme, ce que lui ré...

ABSTRACTPasch is usually credited with having presented the first axiomatization of a geometrical theory, but theVorlesungen über neuere Geometrie contains many features which do not fit the Hilbertian paradigm. Thus Pasch, while axiomatizing his“elementary geometry,”claims that it is an empirically true theory. Scholars usually regard the discrepancies between Pasch and the post-Hilbertian standard method as mere inconsistencies of Pasch's theory. On the contrary, this article aims at reconstructing the coherence and originality of theVorlesungen.We will first display the historical background of (...) this work and then try to reconcile Pasch's logical axiomatic claim with his empiricist stance. More importantly, we will insist on the remarkable logical procedures worked out by Pasch in order to adapt his mathematical development to the strictures of his broad philosophical position. (shrink)

« Tout être humain désire une vie de qualité, c’est même là un souci ultime et constant. Peu importe qu’on la dise “bonne”, “réussie” ou “authentique”, c’est toujours à partir d’une certaine perception de la qualité que nous entreprenons nos projets, organisons nos discours sur le monde et accomplissons nos moindres gestes. Mais quelles sont les conditions d’une telle vie? Existe-t-il des critères permettant de l’évaluer? C’est en réponse à de telles interrogations qu’ont émergé les grandes réflexions de l’humanité sur (...) le beau, le bien et le vrai, tout comme l’intuition d’une continuité subtile entre ces idéaux, de même que les préoccupations pratiques sur la façon de conduire sa vie. Et c’est à l’horizon de ces idéaux que nous formulons encore les débats et nos conceptions sur la nature de l’expérience esthétique et de l’art, de l’éthique et de la morale, de la science et de la connaissance en général. Ainsi comprise, l’idée selon laquelle il existe un lien profond entre expérience esthétique, requêtes de l’éthique et objectifs de la connaissance est à la fois la plus ancienne et la plus actuelle des intuitions, comme l’attestent ces contrées de l’expérience quotidienne où qualités esthétiques et éthiques interagissent et s’alimentent mutuellement, tantôt en concordance harmonieuse, tantôt en discordance créatrice, et où la connaissance retrouve ses plus nobles alliés dans l’art ou la poésie. »C’est cette intuition que l’auteur s’attache à redéployer en en suivant la permanence et la profondeur chez des témoins et des commentateurs aussi illustres que Paul Ricoeur, John Dewey, R. W. Emerson, Jean-Marie Guyau, Friedrich Nietzsche, Henri Bergson, Nishida Kitaro, Mikel Dufrenne et Martha C. (shrink)

This book explores how far some leading philosophers, from Montaigne to Hume, used Academic Scepticism to build their own brand of scepticism or took it as its main sceptical target. The book offers a detailed view of the main modern key figures, including Sanches, Charron, La Mothe Le Vayer, Bacon, Gassendi, Descartes, Malebranche, Pascal, Foucher, Huet, and Bayle. In addition, it provides a comprehensive assessment of the role of Academic Scepticism in Early Modern philosophy and a complete survey of the (...) period. As a whole, the book offers a basis for a new, balanced assessment of the role played by scepticism in both its forms. Since Richard Popkin's works, there has been considerable interest in the role played by Pyrrhonian Scepticism in Early Modern Philosophy. Comparatively, Academic Scepticism was much neglected by scholars, despite some scattered important contributions. Furthermore, a general assessment of the presence of Academic Scepticism in Early Modern Philosophy is lacking. This book fills the void. (shrink)

Often portrayed as a period bound by the dogma of slavish obedience to the diktats of reason and progress, the Age of Enlightenment is revealed by this profound analysis to have been riddled with skeptical attitudes and characters, even in the Enlightenment's most codified locations, such as Germany. Most philosophers of the period are still widely regarded today as having been dominated by a core triple nexus of optimism, dogmatism and rationalism, and despite a growing body of literature exploring the (...) features of their work that could be regarded as informed by skepticism, this unrivaled survey points up the deficiencies of the former. This volume, then, offers an exploration of the impact of skepticism in both its historic and geographic dimensions, providing readers with a reevaluation of the role played by skepticism itself. The detailed narrative covers every identifiable instance of skepticism in the Eighteenth Century, tracing its influence of thought on major British, French and German philosophers, and including lesser-known figures whose contemporary influence requires their inclusion in a comprehensive study such as this. This volume, then, offers an exploration of the impact of skepticism in both its historic and geographic dimensions, providing readers with a reevaluation of the role played by skepticism itself. The detailed narrative covers every identifiable instance of skepticism in the Eighteenth Century, tracing its influen ce of thought on major British, French and German philosophers, and including lesser-known figures whose contemporary influence requires their inclusion in a comprehensive study such as this. (shrink)

This volume gathers the proceedings of the Paris conference in Philonic studies (2017), consisting of 23 papers by contributors from 8 countries. Fifty years after the Lyon conference, it aimed at taking a retrospective look at the intellectual contexts and the academic fields in which Philonic studies have penetrated, as well as the ways in which they evolved. The work of the Alexandrian became of major importance in the history of philosophy. It has been studied as a source of cultured (...) Christianity, in connection with Second Temple Judaism and the Alexandrian Jewish community, but also in the context of research on rabbinic Judaism, New Testament and philosophy of the imperial era. Ce volume rassemble les actes du colloque de Paris (2017), qui réunit 23 intervenants de 8 nationalités. Cinquante ans après le colloque de Lyon, il s'agissait de réfléchir aux milieux intellectuels et aux disciplines universitaires dans lesquels les études philoniennes avaient pénétré le monde de la recherche, les bases sur lesquelles elles avaient évolué. L'œuvre de l'Alexandrin a pris une importance majeure dans l'histoire de la philosophie ; elle a été explorée comme source du christianisme lettré, en lien avec le judaïsme de l'Époque du Second Temple et la communauté juive d'Alexandrie, mais aussi dans le cadre des études sur le judaïsme rabbinique, dans le développement des études sur le Nouveau Testament et sur la philosophie de l'époque impériale. (shrink)

In Philosophical Investigations 193–94, Wittgenstein draws a notorious analogy between the working of a machine and the application of a rule. According to the view of rule-following that Wittgenstein is criticizing, the future applications of a rule are completely determined by the rule itself, as the movements of the machine components are completely determined by the machine configuration. On what conception of the machine is such an analogy based? In this paper, I intend to show that Wittgenstein relied on quite (...) a specific scientific tradition very active at the beginning of the twentieth century: the kinematic or the general science of machines. To explain the fundamental tenets of this line of research and its links with Wittgenstein, I focus on Franz Reuleaux, whose works were known to Wittgenstein. The first payoff of this investigation is to help distance the functionalist framework from which this passage is often read: Wittgenstein’s machines are not computers. The second payoff is to explain why Wittgenstein talks about machines at this place in his discussion on rule-following: it is not the machine model in itself that is criticized in PI 193–94, but the “philosophical” temptation to generalize from it. (shrink)

Russellian incomplete symbols are usually conceived as an analytical residue—as what remains of the would-be entities when properly analyzed. This article aims to reverse the approach in raising another question: what, if any, does the incomplete symbol contribute to the completely analyzed language? I will first show that, from a technical point of view, there is no difference between the way Russell defines his denoting phrases in “On Denoting” and the way Frege defines his second-order concepts. But I will secondly (...) support that the two notions have two widely different conceptual meanings: the same logical procedures which are used by Frege to increase the deductive power of his system allow Russell to logically relate quantificational notation to ordinary language. Focusing on Russell’s treatment of OD’s puzzles, I will thirdly argue that this shift constitutes the source of a deep transformation in the way logic and language are related. (shrink)

Jean Nicod, born in 1893, died far too young in 1924. He is remembered today as one of the foreign disciples (among them Ludwig Wittgenstein and Norbert Wiener) attracted to Cambridge by Russell after the publication of the Principia. We publish here a translation of “Les tendances philosophiques de M. Bertrand Russell”, which appeared in the Revue de Métaphysique et de Morale in 1922. The article is testimony not only to Nicod’s philosophical talents, but also of how Russell’s philosophy could (...) be received in France at the beginning of the twentieth century. (shrink)

At the beginning of the 1890s, Schwarz and Peano (independently of each other) showed that Serret’s definition of the area of a surface was flawed. This paper first aims at describing the various methods that the mathematicians have used for correcting Serret’s reasoning; its second goal is to compare and to present more in detail two solutions: Lebesgue’s notorious construction and Peano’s definition.

Penelope Maddy's latest book, devoted to Wittgenstein's early and late philosophy of logic, can be seen as an extension of Maddy 2007, in which the thoughts of Descartes, Kant (and Car...

Le compagnonnage entre la philosophie et les mathématiques ne date pas d’hier. Mais l’émergence des nouvelles logiques, au début du XXe siècle, a profondément modifié la forme des interactions entre les deux disciplines, suscitant de nouvelles interrogations et modifiant la formulation des problèmes hérités de la tradition. Ce premier volume vise à rendre accessible aux lecteurs francophones des textes importants de la philosophie contemporaine des mathématiques. Il est plus particulièrement consacré aux questions ontologiques et à celles liées aux fondements : (...) Qu’est-ce qu’un objet mathématique? Comment rendre compte de la nécessité des vérités mathématiques? Comment expliquer que les mathématiques s’appliquent au monde réel? (shrink)

Ce texte discute certaines conclusions d’un article récent de F. Mülhölzer et vise à montrer que le logicisme russellien a les moyens de résister à la critique que Wittgenstein lui adresse dans la partie III des Remarques sur les fondements desmathématiques.This paper discusses some conclusions of a recent article from F.Mülhölzer. It aims at showing that Russell’s logicism has the means to overcome the criticisms Wittgenstein expounded in Remarks on the Foundations of Mathematics, part III.

This article aims at setting up a link between Russell’s work on the foundations of geometry and his notorious articles on perception, matter and sense-data published between 1910 and 1914. We firstly stress the fact that a russellian sense-datum is not a mental event: in The Problems of Philosophy, sense-data are as external to the mind as any physical thing. We next analyze the 1912 unpublished paper On Matter in which Russell, for the first time, attributes two positions, instead of (...) one, to a sense-datum: a place from which it is seen and a place where it is seen. This theoretical change allows Russell to regard the sense-datum as a neutral point of intersection of two differents classes: a series of physical events and a series of mental perspectives. The very idea that a same thing can be sorted according to different categories, and thus that the aristotelian mode of classification in genus and species is not the only possible one, is both the keystone of the 1914 theory of the relations between sense-data and physical things and the kernel of the subsequent rallying to « neutral monism ». We claim, in a third section, that this idea is itself an echo of the way Russell defines the projective geometry as a general theory of incidence relations in The Principes of Mathematics .RésuméL’article vise à établir un lien entre les travaux de Russell sur les fondements de la géométrie et ses célèbres textes des années 1911-1914 sur la perception, la matière et les sense-data. Nous insistons d’abord sur le fait que la notion russellienne de donnée sensorielle n’est pas phénoménaliste : les sense-data des Problèmes de Philosophie sont des objets extérieurs aussi peu mentaux que les corps matériels. L’accent est ensuite mis sur l’article On Matter : Russell y introduit pour la première fois l’idée que les sense-data n’ont pas une, mais deux positions — une position où ils sont vus et une position d’où ils sont vus. Cette manœuvre permet à Russell de considérer la donnée sensorielle comme le point d’intersection neutre de deux ensembles fondamentalement différents : une série « physique », matérielle, et une série de « perspectives », mentales. L’idée qu’une même chose peut être classée sous différentes catégories, donc que le mode de classification aristotélicien en espèce et en genre n’est pas le seul concevable, est à la fois la clé de voûte de la théorie des relations entre « sense-data » et « physical things » de 1914 et le nerf du ralliement ultérieur au « monisme neutre ». Nous défendons, dans une troisième partie, que ce canevas n’est lui-même qu’un lointain écho de la conception de la géométrie projective définie comme théorie générale des relations d’incidence développée par Russell dans The Principles of Mathematics. (shrink)

Résumé : L’article propose une démarche méthodologique permettant d’identifier la réflexion professionnelle chez des stagiaires en formation à l’enseignement. En effet, la capacité d’analyser sa pratique de façon réflexive est une composante d’une compétence professionnelle à développer selon le Ministère de l’Éducation du Québec. Une certaine forme de réflexion chez les étudiants est donc à acquérir et, du point de vue des tuteurs de stage, à faire acquérir. Quels sont les critères implicites que les enseignants associés des écoles ou les (...) superviseurs universitaires identifient afin d’évaluer la présence ainsi que la qualité de la compétence réflexive chez le stagiaire ? L’étude identifie une dizaine de points de repère afin de favoriser chez les tuteurs de stage l’évaluation de la compétence réflexive de leurs stagiaires. L’article valide ces critères à partir d’un extrait de discours de stagiaire, puis confronte cet extrait à une autre approche, consistant à détecter des reconceptualisations chez les stagiaires pour dépister de la réflexion. Une certaine cohérence s’établit avec les critères empiriques d’identification de la réflexion identifiés par induction chez les tuteurs de stage. S’ensuit une discussion sur ces critères en lien avec les approches méthodologiques adoptées. La recherche utilise un devis qualitatif et s’appuie sur des entretiens semi-structurés. Abstract : This article proposes a methodological process aimed at identifying professional reflection among student teachers in teacher education. The ability to analyze one’s practice reflectively is a component of one of the professional competencies that must be developed according to Quebec’s Ministry of Education. A certain form of reflection must therefore be acquired by students, and, from the standpoint of practicum supervisors, it must be developed in students. What are the implicit criteria that mentor teachers in schools or university-based supervisors identify in order to assess the presence and quality of student teachers' reflective competence? This study identifies a dozen guideposts to assist supervisors in this direction. The article first validates these criteria based on an excerpt of a student teachers’ statements, then submits the same excerpt to another approach aimed at detecting the student teacher’s reconceptualizations with a view to pinpointing reflection. A certain degree of coherence is established with the empirical criteria for identifying reflection as identified inductively by practicum supervisors. A discussion follows on these same criteria in line with the methodological approaches adopted. This research is based on a qualitative study and draws on semi-structured interviews. (shrink)

Despite an abundance of research on inter-organizational trust, researchers are only beginning to understand the process of trust deterioration as an inter-organizational phenomenon. This paper presents a case study examining the deteriorating relationship between two international high-tech firms. We surveyed respondents from the supplier firm to identify major elements that reduced the supplier's trust in its customer, using the dimensions of trust identified by Mayer et al. (1995). While violations of ability, integrity, and benevolence all contributed to trust reduction, early (...) violations of trustee benevolence contributed importantly to trust deterioration. Over time, the relationship became "sensitive," and respondents reported many incidents of trust violation. Managers reported primarily integrity- and benevolence-related incidents, while no pattern emerged among operations personnel. We examine the results in light of Hosmer's (1995) ethically-based trust principles. The supplier and customer would likely differ in their opinion of whether the customer was acting "ethically." This suggests that scholars need to examine how many principles can be violated before trust is eliminated, and whether any of the principles are particularly salient in business relationships. (shrink)

La musique occupe une place singulière au sein de la philosophie de G.W. Leibniz (1646-1716). Si les développements que ce dernier y consacre sont peu nombreux et dispersés à travers son œuvre, ils n'en dessinent pas moins les contours d'une philosophie de la musique aussi pénétrante que méconnue. Celle-ci apparait tout à la fois comme l'expression et le modèle privilégié de sa métaphysique générale, dont la portée esthétique reste largement à explorer. Une œuvre en particulier, cependant, semble avoir déjà donné (...) corps à cette esthétique musicale. Cette œuvre est celle de Jean-Sébastien Bach (1685-1750), dont l'écriture contrapuntique manifeste plus que toute autre une parenté structurelle avec la philosophie de Leibniz. À scruter l'architecture complexe de ses compositions, on peut y déceler comme un miroir de l'univers leibnizien, une expression sensible des principes mêmes de l'harmonie universelle. Au vu du contexte intellectuel dans lequel évoluait J.-S. Bach, cette parenté n'est du reste pas sans fondement historique. Il n'est ici que de mentionner l'implication du Cantor dans la société philosophique dirigée par Lorenz Mizler (1711-1778), élève de Wolff et héritier de Leibniz, à laquelle il dédia plusieurs de ses œuvres les plus hautement formelles, dont la dernière, inachevée, devait être 'L'Art de la fugue'. À travers l'étude de la conception leibnizienne de la musique, envisagée dans son rapport à la pensée musicale de J.-S. Bach, cet ouvrage explore les relations entre métaphysique et musique à la lumière du concept d'harmonie comme "unité dans la diversité. (shrink)

This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a worskhop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical (...) conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio Leòn-Sànchez and Ana Leòn-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro. (shrink)

The project of this Précis de philosophie de la logique et des mathématiques (vol. 1 under the direction of F. Poggiolesi and P. Wagner, vol. 2 under the direction of A. Arana and M. Panza) aims to offer a rich, systematic and clear introduction to the main contemporary debates in the philosophy of mathematics and logic. The two volumes bring together the contributions of thirty researchers (twelve for the philosophy of logic and eighteen for the philosophy of mathematics), specialists in (...) the history or philosophy of logic or mathematics. Each volume consists of ten chapters; each chapter is about forty pages, is independent from the others and deals with a particular philosophical question about logic or mathematics. The objective is to offer to the French-speaking reader a reference book. On many of the issues addressed, this Précis offers the first clear and thorough synthesis that is available in French. -/- This book is intended for third year / master's students, but also for teachers of philosophy in secondary or higher education, for logicians and mathematicians willing to take a philosophical look at the fundamental concepts of their discipline, and for any reader interested in the basic issues discussed in the philosophy of logic and mathematics. Each chapter is self-contained, although some basic training in logic (or in mathematics, as the case may be) is required. The book should be looked at as a comprehensive framework for contemporary discussions in the philosophy of logic and mathematics, while also giving some guidance on the disciplinary content required by these discussions. -/- The first three chapters of the present volume (on the philosophy of mathematics) are devoted to the history of the philosophy of mathematics: from antiquity to the modern era, and from this period to the foundational crisis of the nineteenth century, to the twentieth century. Next, four chapters deal with the crucial questions for the philosophy of mathematics of the twentieth century: the opposition and/or comparison of set theory and category theory as foundational frameworks for mathematics; mathematical constructivism; the analysis of calculability; and Benaceraff's problem. The two following chapters are focused on the philosophy of mathematical practice, by treating the notion of ideals of proof, in particular explanation and purity, and the notion of informal proof and the use of visual artifacts in mathematical argumentation. Finally the last chapter deals with the applicability of mathematics, including the role of probability. -/- In Chapter 1, Sébastien Maronne and David Rabouin present the history of the philosophy of mathematics from antiquity to the modern era. The goal is to show that the philosophy of mathematics has a history as ancient as mathematics and philosophy itself, a history largely continuous with the latter, often by staying out of sync with respect to the former. In Chapter 2, Sébastien Gandon discusses the question of the foundations of mathematics from Kant to the end of the nineteenth century. By tying this question to Kant, he is able to show that the discussion of the foundations of mathematics that occupied a large part of these two centuries has much older roots. Accent is placed on the differences between the framework proposed by Kant for making sense of classical mathematics and the use made by Frege and then Russell of logical tools for giving a different reading of arithmetic and real analysis. The link between between these different conceptions and the evolution of mathematics itself is also underlined. -/- Chapter 3, written by Hourya Benis-Sinaceur and Mirna Džamonja, deals with the evolution of mathematics in the twentieth century, notably the structuralist turn of Dedekind, E. Noether, and Bourbaki, and certain more recent developments. They devote themselves, among other things, to explaining how these developments can be understood as responses to and extensions of questions posed during the foundational debate of the immediately preceding era. -/- In Chapter 4, Jean-Pierre Marquis and Jean-Jacques Szczeciniarz discuss the different foundational options coming from set theory and category theory. They discuss, among other things, Lawvere's program to replace ZF with an axiomatization of the category of sets, the latter judged better adapted to the needs of contemporary mathematics. Different reactions, as much philosophical as technical, raised by this program are also taken into account. -/- Constructive mathematics are the object of Chapter 5, in which Gerhard Heinzmann and Mark van Atten examine in a critical and comparative manner a variety of constructivisms, including intuitionism, constructive type theory, predicativism, and finitism. -/- In Chapter 6, Guido Gherardi and Maël Pegny present computability theory, stressing its philosophical consequences. They discuss the basic concepts of this theory, for the computability of both the natural numbers and the real numbers. They then tackle the theory of computational complexity. -/- In Chapter 7, Andrea Sereni and Fabrice Pataut present Benacerraf's problem, opposing every possible account of mathematical knowledge to the availability of a theory of truth founded on an abstract ontology of mathematical objects. They give an overview of the original problem and its reformulation by Hartry Field, and reconstruct the debate that this problem has raised, by meeting at once the major opposing positions today of the analytic affiliation of the philosophy of mathematics, as much those on the platonist side as on that of nominalism. -/- In Chapter 8, Valeria Giardino and Yacin Hamami treat certain crucial aspects of the philosophy of mathematical practice. They deal in particular with the notion of an informal proof and on the role of artifacts in mathematical reasoning. They consider how such proofs, making use of these means, can contribute to the understanding of theorems and mathematical theories, thanks also to the role of visualisation and the aid of computer tools. -/- Why do mathematics often give several proofs of the same theorem? This is the question that Andrew Arana raises in Chapter 9, introducing the notion of an epistemic ideal and discuss two such ideals, the explanatoriness and purity of proof. -/- Chapter 10 is devoted to the applicability of mathematics in the study of empirical phenomena. After summarizing the history of this question, going back to Plato and Aristotle and passing by Mill and Kant, Daniele Molinini and Marco Panza reconstruct the contemporary debate, in relation, among other things, to questions raised in the philosophy of science. -/- Two appendices complete the volume. In the first Frédéric Patras treats the French tradition in philosophy of mathematics of the 20th century. In the second, Maria Carla Galavotti discusses the notion of probability and its use in science. (shrink)

This article investigates how the meanvariance efficient frontier defined by sovereign bonds of 20 developed countries is affected by the consideration of socially responsible indicators for countries in investment decision-making. For a global rating of socially responsible performances, we show that it is possible to build portfolios with an increased average rating without significantly harming the risk/return relationship. This result differs when considering sub-ratings related to the environment, social concerns and public governance. The results are good news for responsible investors (...) and suggest that socially responsible portfolios of sovereign bonds can be built without a significant loss of mean-variance efficiency. (shrink)

Human freedom is the central theme of modern political philosophy, and G. W. F. Hegel offers perhaps the most profound and systematic modern attempt to understand the state as the realization of human freedom. In this comprehensive examination of Hegel’s philosophy of freedom, Paul Franco traces the development of Hegel’s ideas of freedom, situates them within his general philosophical system, and relates them to the larger tradition of modern political philosophy. Franco then applies Hegel’s understanding of liberty to certain problems (...) in contemporary political theory. He argues that Hegel offers a powerful reformulation of liberalism that escapes many of the problematic assumptions of traditional liberal doctrine and yet avoids falling into the romantic and relativistic excesses of a substantial communitarianism. Devoting the major portion of his attention to Hegel’s masterpiece the _Philosophy of Right_, published in 1821, Franco provides a clear and nontechnical guide to the challenging arguments Hegel presents. Franco establishes the necessary context within which to understand the work and draws on Hegel’s other writings, including the unpublished lecture notes, to illuminate it. For the Hegel specialist as well as the reader with a more general interest in political philosophy and modern intellectual history, this book offers significant insights into Hegel’s ideas on the theme of human liberty. (shrink)