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)

Abstract: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)

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)

Ce livre retrace le cheminement du chercheur: le journal de ses intuitions, ses espoirs, ses doutes, ses certitudes, - jusqu'au silence d'avril 1908. Il replace la quete dans l'activite d'ensemble du savant: monographies, cours de linguistique generale, travaux de mythographie. Il la situe dans un paysage intellectuel scrupuleusement balise. Par dela des considerations d'une technicite souvent rebutante, et non exemptes de contradictions (parfois flagrantes), il s'attache a suivre le fil d'une quete autant mystique que linguistique. Par surcroit il donne a (...) lire le texte de Lucrece (accompagne de sa traduction), et la facon dont le transfigurent les Cahiers (dont une part importante est reproduite en fac simile). Il en soumet la lecture a certaines epreuves (dont un test informatique), qui demontrent que le phenomene echappe a la prison binaire qu'evoquait R. Barthes (son/graphie, demontre/indemontrable...), et reste d'une implacable actualite: qu'il pose dans toute son acuite la problematique d'une ecriture. Reste largement meconnu, Saussure le sera-t-il moins apres ce livre? Une chose est sure: on ne pourra, une fois ces pages refermees, conserver le meme regard sur celui qui fut en linguistique, selon le mot de Benveniste, une 'autre facon de commencer'. (shrink)

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.

Jean Nicod (1893–1924) is a French philosopher and logician who worked with Russell during the First World War. His PhD, with a preface from Russell, was published under the title La géométrie dans le monde sensible in 1924, the year of his untimely death. The book did not have the impact he deserved. In this paper, I discuss the methodological aspect of Nicod’s approach. My aim is twofold. I would first like to show that Nicod’s definition of various notions of (...) equivalence between theories anticipates, in many respects, the (syntactic and semantic) model-theoretic notion of interpretation of a theory into another. I would secondly like to present the philosophical agenda that led Nicod to elaborate his logical framework: the defense of rationalism against Bergson’s attacks. (shrink)

Jean Nicod (1893–1924) is a French philosopher and logician who worked with Russell during the First World War. His PhD, with a preface from Russell, was published under the titleLa géométrie dans le monde sensiblein 1924, the year of his untimely death. The book did not have the impact he deserved. In this paper, I discuss the methodological aspect of Nicod’s approach. My aim is twofold. I would first like to show that Nicod’s definition of various notions of equivalence between (...) theories anticipates, in many respects, the (syntactic and semantic) model-theoretic notion of interpretation of a theory into another. I would secondly like to present the philosophical agenda that led Nicod to elaborate his logical framework: the defense of rationalism against Bergson’s attacks. (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)

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)

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)

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)

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)

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)

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...

English summary: This volume offers French readers important texts of modern philosophical mathematics, addressing in particular ontological questions and others on mathematical objects, how to demonstrate the need for mathematical truths, and how to explain that mathematics apply to the real world. French description: Le compagnonnage entre la philosophie et les mathematiques ne date pas d'hier. Mais l'emergence des nouvelles logiques, au debut du XXe siecle, a profondement modifie la forme des interactions entre les deux disciplines, suscitant de nouvelles interrogations (...) et modifiant la formulation des problemes herites de la tradition. Ce premier volume vise a rendre accessible aux lecteurs francophones des textes importants de la philosophie contemporaine des mathematiques. Il est plus particulierement consacre aux questions ontologiques et a celles liees aux fondements: Qu'est-ce qu'un objet mathematique? Comment rendre compte de la necessite des verites mathematiques? Comment expliquer que les mathematiques s'appliquent au monde reel? (shrink)

This article has two purposes: first, to describe some archival discoveries about Nicod’s family background, academic development and political life; and second, to publish and comment on a newly discovered article by Nicod about Russell. This article acclaims not only Russell’s achievements in logic and philosophy—as one might expect from such a devoted protégé as Nicod—but also (albeit only in glimpses permitted by France’s wartime censorship) his anti-war politics and writings. As the reader will realize, the two objectives are connected: (...) what the archives reveal and what the article illustrates is a hitherto underappreciated level of political awareness and pacifist commitment in Nicod. (shrink)

RÉSUMÉ: Pasch est généralement considéré comme le premier à avoir proposé une axiomatisation de la géométrie. Mais ses Vorlesungen über neure Geometrie (1882) contiennent plusieurs éléments étrangers au paradigme hilbertien. Pasch soutient ainsi que la « géométrie élémentaire », dont il propose une axiomatisation complète, est une théorie empiriquement vraie. Les commentateurs considèrent généralement les différences entre la méthode de Pasch et celle qui deviendra standard après Hilbert comme autant de défauts affectant une pensée encore inaboutie. Notre but consiste au (...) contraire à reconstruire la cohérence et l’originalité de l’approche de Pasch. Nous donnerons d’abord un aperçu du contexte historique dans lequel les Vorlesungen s’inscrivent, pour tenter ensuite de réconcilier l’effort d’axiomatisation et l’empirisme de Pasch. Nous insisterons notamment sur les remarquables procédures logiques que Pasch met sur pied afin d’adapter sa pratique mathématique aux contraintes dictées par sa réflexion philosophique.ABSTRACT: Pasch is usually credited with having presented the first axiomatization of a geometrical theory, but the Vorlesungen über neuere Geometrie (1882) 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 the Vorlesungen. 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)

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)

In lieu of an abstract, here is a brief excerpt of the content:January 28, 2009 (12:22 pm) G:\WPData\TYPE2802\russell 28,2 051red.wpd russell: the Journal of Bertrand Russell Studies n.s. 28 (winter 2008–09): 171–90 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 eviews A RELATIONAL DISPUTE Sébastien Gandon iufz/zphier / U. Blaise Pascal 63000 Clermont-Ferrand, France [email protected] Stewart Candlish. The Russell/Bradley Dispute and Its SigniWcance for TwentiethCentury Philosophy. Basingstoke and New York: Palgrave Macmillan, 2007. Pp. xix, 235. isbn (...) 978-0-230-50685-5. £49.99; us$84.95 (hb). Candlish’s book aims at giving a “fair” description of the notorious Russell/ Bradley dispute, that is, a more balanced one than the version that is usually told. The standard account is the one given by Russell, and, as Russell was a party of the debate, it is no surprise that he seriously misconstrued Bradley’s arguments. Attempting to set the historical record straight, Candlish then opposes Russell’s description of the dispute. The author is quite clear, however, on the fact that he does not himself endorse the Idealistic point of view (p. xi). The two Wrst chapters of the book are introductory: the Wrst one is a presentation of the stereotypical picture that the author intends to demolish, while the second is an outline of Bradley’s metaphysics. Chapters 3 and 4 are devoted to a confrontation between Russell and Bradley’s theories of judgment and truth. Chapters 5 and 6 are dedicated to a rehabilitation of Bradley’s writings about relation. In these four chapters, Candlish attempts to show that Russell’s arguments against Bradley were not as devastating as they are supposed to be, and that Bradley’s insights were quite powerful—so much so that they have been rediscovered by some later philosophers, such as Wittgenstein, for instance. The concluding chapter is an attempt to explain the decline of monistic idealism after Bradley. Candlish does not only aim at oTering a “fair” account of the Russell/Bradley dispute. This goal is extended by a more general plea for the introduction of an historical perspective in analytic philosophy. According to Candlish, “our implicit acceptance of a distorted version of philosophy’s recent past has serious consequences ” (p. 19): one of them is that, by misunderstanding our own history, we “misunderstand ourselves and the nature of what we are about” (ibid.); another is that, by being deprived of any way to connect what we do in philosophy January 28, 2009 (12:22 pm) G:\WPData\TYPE2802\russell 28,2 051red.wpd 172 Reviews with what some of the philosophers of the past have done, “we may, as a result, fall under the impression that only we, and those obviously like us, are really doing philosophy, at least as it ought to be done” (ibid.). From this perspective, Russell’s confrontation with Bradley seems to represent a rather good topic: not only does it epitomize a turning-point in Russell’s intellectual evolution and in the emergence of the new tradition, but it also shows how easily the new and victorious analytic philosophy has misconstrued its own history. If I entirely share Candlish’s conviction about the necessity of introducing an historical perspective in analytical philosophy, I am not convinced by Candlish’s own reconstruction of the dispute. In a nutshell, what I Wnd very useful in the book is all that concerns Bradley, and some of the parts devoted to Russell (especially, the analysis of his theory of judgment). What I do not agree with is, Wrst, Candlish’s way of doing history of philosophy; second, his treatment of Russell’s works; and third, his general conception of the use of logic in philosophy. Candlish really succeeds in expounding to the modern eye both the coherence of Bradley’s thought, and the diUculty of grasping it. His analysis of the role Bradley gave to “intellectual satisfaction” (pp. 26–7, 33) and to the “principles of suUcient reason” (pp. 46–7) is very enlightening—it explains why Bradley, while endorsing a kind of methodological scepticism, denied that ultimate contingencies were given in experience (p. 48). Candlish also does a great job of presenting... (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...

In Die Zahlen (1888), Dedekind defines an infinite set as a set that is isomorphic with one of its proper parts. In The World and the Individual (1900), the American philosopher Josiah Royce relates Dedekind’s notion to Fichte’s and Hegel’s concept of Self defined as an entity that reflects itself into itself. The first aim of this article is to explain Royce’s analysis and to put it in its proper context, that of a critique of Bradley’s mystical idealism. The second (...) aim is to urge a shift in focus in Dedekind’s scholarship: instead of addressing the question of the relationship between mathematics and philosophy in Dedekind’s work through the supposed intentions of its author, it is more fruitful to analyze the reception that philosophers have made of his texts. (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.

Review of Russell’s Unknown Logicism by Sébastien Gandon.

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)

Richard Janko's acclaimed translation of Aristotle's _Poetics_ is accompanied by the most comprehensive commentary available in English that does not presume knowledge of the original Greek. Two other unique features are Janko's translations with notes of both the _Tractatus Coislinianus_, which is argued to be a summary of the lost second book of the Poetics, and fragments of Aristotle’s dialogue On Poets, including recently discovered texts about catharsis, which appear in English for the first time.

Ṣadr, Muḥammad Bāqir; Islamic philosophy; 20th century.

Classical Sanskrit commentary on Brahmasūtra; includes original Sanskrit text with English translation.

The article discusses two bioart projects that bring the symbolically core human substances of blood, sweat and tears into technologically mediated relationships with plants and fungi to explore human kinship with other species: Tarah Rhoda’s BS&T (short for ‘blood, sweat and tears’) and OurGlass, and Saša Spačal’s MycoMythologies: Patterning. The article analyses the art projects through the lens of the molecular gaze and different perspectives on kinning, bringing anthropological conceptualizations of kinship together with Haraway’s pathways to connect with other species. (...) How can bioart use technologies to explore interspecies kinship through a molecular gaze? And may such artworks contribute to the toning down of human exceptionality in the face of a precarious future? We find that artworks providing a molecular gaze on interspecies biological processes may risk a decontextualized approach to complex relational processes but may also create new visions of filiation even with biological organisms imagined to be genetically distant from humans, thus spurring awareness of the fragile interrelationships among species. (shrink)

Introduction:To meet and take care of people with dementia implicate professional and moral challenges for caregivers. Using force happens daily. However, staff also encounter challenges with the management in the units. Managing the caretaking function is also significant in how caretakers experience working in dementia care.Purpose:The purpose of this study is to explore the caregiver’s experiences with ethical challenges in dementia care settings and the significance of professional leadership in this context.Method:The design is qualitative, and data appear through narrative interviews. (...) A total of 23 caretakers participated in the study. The transcribed interviews were subjected to a phenomenological-hermeneutical interpretation.Ethical considerations:The respondents signed an informed consent for participation prior to the interviews. They were assured anonymity and confidentiality in the publication of the data. Ricoeur’s method for interpretation ensures anonymity as the researcher relates to the data as one collective text. The study is part of a larger research project in ethics, in its entirety approved in line with the Helsinki Convention.Results:The findings show that the caretakers experienced inadequacy. Some of them described a negative work atmosphere where they experienced that their leaders did not take them seriously. Because of this, informal negative sub-groups functioned as an exclusive debriefing arena. Some of the informants described the opposite experience where the leaders actively supported them.Discussion:The analyses of the findings are discussed in light of the concepts of trust and mistrust in leadership.Conclusion:There is a correlation between the leadership and the caregivers’ experience of being in difficult situations. (shrink)

The Principles of Biomedical Ethics by Beauchamp and Childress is a classic in the field of medical ethics. The first edition was published in 1979 and “unleashed” the four principles of respect for autonomy, non-maleficence, beneficence, and justice on the newly emerging field. These principles were argued to be mid-level principles mediating between high-level moral theory and low-level common morality, and they immediately became very popular in writings about medical ethics. Over the years Beauchamp and Childress have developed this approach (...) and vigorously defended it against the various criticisms that have been raised. The 5th edition of this book is, as all the …. (shrink)

Theologians are split into two groups: those who embrace prosperity theology and those who oppose it; both sides on scriptural grounds. Those criticising it embrace cessationism in its diversity, while its supporters are mainly found among Pentecostals and Charismatics, who are continuationists. Continuationists believe and teach that all gifts of the Spirit are still available to the church today, therefore should be practised by the church just as they were operative during the apostolic era. Therefore, it is clear that prosperity (...) preachers are continuationists. They believe and practice healing and miracle gifts today. A review of the literature, biblical texts, historical teachings, and Pentecostal and Neo-Pentecostal (also referred to as charismatic and neo-charismatic) form the basis of this article. It addresses the positive features of prosperity teachers’ beliefs and methods as well as how they exploit the dreams, fears, and aspirations of people living in poverty. The theology of sharing, as articulated by Nicholas B.H. Bhengu, is proposed as a solution to creating parity between the rich and the poor.Contribution: This article seeks to balance opposing theological approaches with the prosperity gospel. It does this by introducing a theology of sharing as taught by Nicholas Bhengu based on the philosophy of Ubuntu, a way of life among African people. The challenge for theologians on both sides of the argument is finding a way to accommodate the other side’s contributions. (shrink)

Analyzes the origin, structure and resolution of Kant's antinomies of reason from a systematic rather than a historical perspective, exploring the relationship between the theoretical antinomies and the practical antinomy in order to indicate their similarities and differences and to suggest the dependence of the latter on the former.

Without seeking to diminish its authority as the Word of God, this article acknowledges the Fourth Gospel as a brilliant piece of literary artistry by the implied author. The aim of this article is to substantiate this assertion by conducting a study on focalisation and illustrating how it invites the implied reader’s participation in the narrative. This contribution acknowledges the existence of insightful contributions on the topic, particularly in relation to the Fourth Gospel. However, it asserts that the study of (...) the performative nature of focalisation in this particular Gospel has not received the attention it deserves. The main contribution of this article is its analysis of a selected narrative of the Fourth Gospel using focalisation as an analytical tool, with the objective of demonstrating that the Fourth Gospel is performative in nature, crafted and formulated to consistently engage the implied reader in considering its purpose, as stated in 20:30–31.Contribution: The article showcases that focalisation, when used as an analytical tool, can unlock, and enable the interpreter of the Fourth Gospel to recognise its performative nature to the implied reader of the text. This is critical, given that the text is crafted to encourage the reader to participate in it by making decisions regarding their faith in Jesus Christ. (shrink)