According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. When this grand narrative was brought into question, our perspectives on the question of mathematization should have changed. It seems, however, that they were instead set aside, both because of a general distrust towards sweeping narratives that are always subject to the suspicion that they overlook the unyielding complexity of real history, (...) and because of a shift in our interests. The more obscure and idiosyncratic they are, an alchemist, a patron of the sciences or a lunatic collector is nowadays honored in journals of the history of sciences. As for the general issues involved in the question of mathematization, they are rejected as obsolete, or reserved for specialized journals in the history of mathematics. The article « Forms of mathematization » examines in general the notion of mathematization, distinguishes different forms of mathematization and defends a renewed study of the forms of mathematization in the history of the early sciences. (shrink)

Thought experiments being central to contemporary philosophy and science, the following questions were asked in recent literature. What is their definition? Are they heuristic devices, arguments, paradoxes? Are they comparable to real experiments? Do intuition and conceivability intervene? Equally imaginative thought experiments are found in ancient, medieval, and Renaissance texts. Paying attention to prime historical examples of thought experiments, we show that historical perspectives help answer these general questions.

This volume explores the relationship between physics and metaphysics in Descartes' philosophy. According to the standard account, Descartes modified the objects of metaphysics and physics and inverted the order in which these two disciplines were traditionally studied. This book challenges the standard account in which Descartes prioritizes metaphysics over physics. It does so by taking into consideration the historical reception of Descartes and the ways in which Descartes himself reacted to these receptions in his own lifetime. The book stresses the (...) diversity of these receptions by taking into account not only Cartesianisms but also anti-Cartesianisms, and by showing how they retroactively highlighted different aspects of Descartes' works and theoretical choices. The historical aspect of the volume is unique in that it not only analyzes different constructions of Descartes that emerged in the 18th, 19th and 20th centuries, but also reflects on how his work was first read by philosophers across Europe. Taken together, the essays in this volume offer a fresh and up-to-date contribution to this important debate in early modern philosophy. (shrink)

The History of scepticism from Erasmus to Spinoza is often called upon to support three theses: first, that Descartes had a dogmatic notion of systematic knowledge, and therefore of physics; second, that the hypothetical epistemology of physics which spread during the xviith century was the result of a general sceptical crisis; third, that this epistemology was more successful in England than in France. I reject these three theses: I point first to the tension in Descartes’ works between the ideal of (...) a completely certain science and a physics replete with hypotheses; further, I argue that the use of hypotheses by mechanical philosophers cannot be separated from their conception of physics; finally I show that, at the end of the xviith century, physicists in France as well as in England spoke through hypotheses and I examine different ways of explaining this shared practice. Richard H. Popkin’s book serves therefore as a starting point for insights into the general problem: to what extent and for what reasons some propositions in physics have been presented as hypotheses in the xviith century? (shrink)

The mechanical philosophy that emerged during the Scientific Revolution can be characterised as a reductionism according to which all physical phenomena are to be explained in terms of corpuscles of different sizes, shapes, and motions. It provided early modern natural philosophers with a unified view of nature that contrasted primarily with the Aristotelian view of nature, but also with other naturalist, hermetic, mystic, occultist, Paracelsian, and chymical accounts. Indeed, early modern natural philosophers devised mechanical explanations of almost every kind of (...) phenomena; even supranatural phenomena, such as transubstantiation, or phenomena today described as paranormal, like the action of sympathetic powder on a wound, the influence of the stars on terrestrial events, or the identification of thieves with a divining rod, were given mechanical explanations. Confronting this explanatory deluge, historians adopted two opposing narratives. The first narrative amounted to view the mechanical philosophy as a well-identified category that captured something about early modern natural philosophy. The critical narratives of the last thirty years, however, have deconstructed both the belief that it is an adequate historical category and the conviction that it made a positive contribution to the sciences. First, in an era that privileged microscopic case studies over sweeping panoramas, and emic over etic categories, ‘mechanical philosophy’ came to be thought of as lacking any real descriptive significance. Second, from an evaluative point of view, it has been claimed that the mechanical philosophy had no impact on the development of the new sciences. Considering these descriptive and evaluative challenges, taking the mechanical philosophy at face value is historically inadequate and philosophically naïve. Hence the questions addressed in this chapter: What to do with the mechanical philosophy? Does it have to be dropped completely as a category? And, if not, how is it to be used? My view is that it captures something of the transformations that we put under the umbrella of the Scientific Revolution, but that it is not possible to treat it as a naturally given category. Rather, to be employed usefully, it needs conceptual clarification and historical specification. (shrink)

The Mechanisation of Natural Philosophy is devoted to various aspects of the transformation of natural philosophy during the 16th and 17th centuries that is usually described as mechanical philosophy. Drawing the border between the old Aristotelianism and the « new » mechanical philosophy faces historians with a delicate task, if not an impossible mission. There were many natural philosophers who actually crossed the border between the two worlds, and, inside each of these worlds, there was a vast spectrum of doctrines, (...) arguments and intellectual practices. The expression mechanical philosophy is burdened with ambiguities. It may refer to at least three different enterprises: a description of nature in mathematical terms; the comparison of natural phenomena to existing or imaginary machines; the use in natural philosophy of mechanical analogies, i.e. analogies conceived in terms of matter and motion alone.However mechanical philosophy is defined, its ambition was greater than its real successes. There were few mathematisations of phenomena. The machines of mechanical philosophers were not only imaginary, but had little to do with the machines of mecanicians. In most of the natural sciences, analogies in terms of matter and motion alone failed to provide satisfactory accounts of phenomena.By the same authors: Mechanics and Natural Philosophy before the Scientific Revolution (Boston Studies in the Philosophy of Science 254). (shrink)

A biological function is supposed to be performed adequately, and hence may fail to do so: this is dysfunction. This raises two questions. One is how to make explicit the way in which function can be discriminated from dysfunction without confusing dysfunction with non-function. The second question is how what is “right” and “wrong” can be legitimated by natural regulatory norms. A function can be viewed as a quality to which at least one variable with a definite set of values (...) is associated. Accordingly, function and dysfunction are the same quality of the same trait, but differ in the values associated to this variable. Dysfunction occurs when the associated set of values does not match this normal state. Biological systems have the epistemic singularity that their existence is the consequence of two distinct causal regimes, the so-called “proximate” and “ultimate” causes, whose convergence defines a system’s prescriptive normality. Each cause imposes restrictive rules that limit the possible ways these systems can putatively exist. When a system is insensitive to ultimate cause, it is determined by proximate causation alone, and hence escapes its own prescriptive norms. In conclusion: The normality of a biological system is defined by the convergence of proximate and ultimate causes. A function is a variable-associated quality whose values are defined relative to the norms of the system. Dysfunction occurs when the set of values of the same variable does not match the normality of the system, which can occur when the system is insensitive to ultimate causation. (shrink)

During the seventeenth century there were different ways of opposing the new mechanical philosophy and the old Aristotelian philosophy. Remarkably enough, one of this way succeeded in becoming stable beyond the moment of its formulation, one according to which Descartes would be the benchmark by which the works of other natural philosophers of the seventeenth century fall either on the side of the old or the new. I consequently examine the French debate where this representation emerges, a debate that took (...) place along with the development of a Cartesian propaganda in the 1660s and the ensuing official condemnations of the philosophy of Descartes, which was said to constitute a danger for the mystery of Eucharist. But these condemnations pronounced in the name of theology, as numerous and radical as they were, were not considered to be sufficient. They were assisted by numerous polemical works, the audience of which were learned companies of courteous honnêtes gens, and the object of which was to defend a certain way of proceeding in natural philosophy. I consequently concentrate on two correlated questions, the question of what kind of ontological entities are necessary for the establishment of a good physics, and the correlated question of what norms should be adopted in natural philosophy. I show quite systematically that the criticisms of Cartesian philosophers by the Oratorian Jean-Baptiste de La Grange, the bishop Pierre-Daniel Huet, and various Jesuits, Ignace Pardies, Antoine Rochon, Louis Le Valois, Gabriel Daniel, René Rapin, and Honoré Fabri respond to the mockeries of Gérauld de Cordemoy, Jacques Rohault, Louis de La Forge, Bernard Lamy, Nicolas Malebranche or Antoine Arnauld concerning the scholastic entities. Not only do I contrast their philosophical arguments concerning ontological entities and the norms to be respected in physics, but also their ways of defining the philosophical enterprise and its public. (shrink)

On sait peu de choses d’Edme Mariotte, membre de l’Académie royale des sciences de 1668 à 1684. Une analyse de son Essai de logique montre cependant que, pour défendre ses pratiques expérimentales, il s’appropria des bribes venues de différentes traditions intellectuelles. Ainsi, ce livre examine ce qu’on entendait par « méthode » à la fin du XVIIe siècle, les épistémologies de la physique qui s’affrontaient alors, quelques débats ouverts par la gestion de l’héritage cartésien. Mais l’essentiel sera peut-être la question (...) suivante : comment reconstituer les idées d’un savant ordinaire, qui n’a ni bouleversé l’ordre des sciences, ni montré une perspicacité épistémologique exceptionnelle ? (shrink)

Early modern natural philosophers put forward the ontological program that was called "mechanical philosophy" and they gave mechanical explanations for all kinds of phenomena, such as gravity, magnetism, the colors of the rainbow, the circulation of the blood, the motion of the heart and the development of animals. For a generation of historians, the mechanical philosophy was regarded as the main alternative to Aristotelian orthodoxy during the so-called Scientific Revolution and mechanical explanations were presented as paving the way for the (...) use of experiments and mathematics in the understanding of natural phenomena. However, the historical category of mechanical philosophy was later criticized as being too broad, while early modern mechanical explanations were condemned by more epistemologically oriented minds for being incompatible with, or at least not necessarily connected to, the use of experiments and mathematics. In the last ten years, just as the new mechanistic literature emerged in philosophy of science, there has been a reevaluation of early modern mechanical explanations in a domain that had been until then considered as peripheral to the so-called Scientific Revolution, namely the domain of biology, anatomy, physiology and medicine. Although they were neither confirmed nor predictive, some early modern explanations in these domains appear to have a cognitive value similar to the value of contemporary mechanistic explanations. (shrink)

Four propositions relative to the laws of nature in the classical period must be noted. 1. Certain regularities in phenomena had been discovered. 2. A concept of law had emerged. 3. Classical science is characterized by the introduction of the notion of the legality of nature. 4. New uses of the word «law» had appeared in scientific texts. This article is devoted to the analysis of only this last proposition, that is to say to a terminological problem. First we will (...) describe the semantic uses of the word «law» that may have contributed to the constitution of its classical meaning: its specific usage, disciplinary usage, usage in physics, in mathematics, in metaphysics. Second we will analyze the various moments of the diffusion of the word in the sciences in the xviith century. The general thesis defended in the end is that if the term «law» had indeed been used in science with no reference to a law-giving God prior to the xviith century, only this reference, that is, the coming together of its physical and its metaphysical usage, allowed its generalization in the period between the xviith and xviiith centuries. (shrink)

Roux begins by exploring the texts in which the origins of the scientific notion of thought experiments are usually said to be found. Her general claim is simple: the emergence of the notion of thought experiments relies on a succession of misunderstandings and omissions. She then examines, in a more systematic perspective, the three characteristics of the broad category of thought experiments nowadays in circulation: thought experiments are counterfactual, they involve a concrete scenario and they have a well-delimited cognitive intention. (...) Her aim in exploring these characteristics is twofold. Firstly, it is to show that each of these characteristics, considered individually, may be taken in a more or less strict sense, and consequently to explain the proliferation of thought experiments. Secondly, it is to suggest that the recent debates on thought experiments might have arisen because these three characteristics are not easily conciliated when they are considered together. Finally, in a third and last section, the nine essays of the introduced book are presented. (shrink)

This volume deals with a variety of moments in the history of mechanics when conflicts arose within one textual tradition, between different traditions, or ...

We conceptualise a framework that incorporates psychological and non-psychological factors influencing pro-environmental behaviour. We conducted qualitative investigations in five sectors in South Africa, where individuals and groups are dealing with significant environmental issues, including climate change, biodiversity loss and land-use change. We found three fundamental elements necessary for behavioural change to be realised: awareness (A) is defined as an understanding that society and earth systems are connected; motivation (M) involves the personal and operational drivers that encourage an individual or organisation (...) to respond to new levels of awareness; and pathways (P) recognise the practical solutions and opportunities that facilitate actual change. AMP was built up from thirty-eight variables that cut across between three and five of the case studies, which were further grouped into fourteen categories. The inter-connectedness of AMP suggests that for pro-environmental behaviour to occur, attention cannot be focused on satisfying one of the elements in isolation. This is the first attempt to integrate theory from social psychology, sociology, organisational theory and management in a conceptual framework for pro-environmental behaviour. The AMP framework is useful for supporting practitioners or change-agents designing environmental sustainability initiatives. (shrink)

Levinas’ relationship to Platonism is ambiguous. In Totality and Infinity, indeed, references to Plato’s writings are multiple and Levinas depicts Plato as following two diverging paths. On the one hand, Levinas considers Plato’s writings to be works that consecrate the primacy of identity over difference, of the Same over the Other. On the other hand, Platonism is presented as a philosophy of absolute transcendence due to its refusal to make the Good a simple ontological principle and to its attempt to (...) free the Good from all forms of totality. The present study aims to show that, although Levinas criticizes the first path taken by Plato, he conceives of himself as partially in line with Plato’s philosophy of absolute transcendence, albeit in a paradoxical form. In this way, Levinas understands the meaning of the Platonic approach in an original way. (shrink)

During the seventeenth century there were different ways of opposing the new mechanical philosophy and the old Aristotelian philosophy. Remarkably enough, one of this way succeeded in becoming stable beyond the moment of its formulation, one according to which Descartes would be the benchmark by which the works of other natural philosophers of the seventeenth century fall either on the side of the old or the new. I consequently examine the French debate where this representation emerges, a debate that took (...) place along with the development of a Cartesian propaganda in the 1660s and the ensuing official condemnations of the philosophy of Descartes, which was said to constitute a danger for the mystery of Eucharist. But these condemnations pronounced in the name of theology, as numerous and radical as they were, were not considered to be sufficient. They were assisted by numerous polemical works, the audience of which were learned companies of courteous honnêtes gens, and the object of which was to defend a certain way of proceeding in natural philosophy. I consequently concentrate on two correlated questions, the question of what kind of ontological entities are necessary for the establishment of a good physics, and the correlated question of what norms should be adopted in natural philosophy. I show quite systematically that the criticisms of Cartesian philosophers by the Oratorian Jean-Baptiste de La Grange, the bishop Pierre-Daniel Huet, and various Jesuits, Ignace Pardies, Antoine Rochon, Louis Le Valois, Gabriel Daniel, René Rapin, and Honoré Fabri respond to the mockeries of Gérauld de Cordemoy, Jacques Rohault, Louis de La Forge, Bernard Lamy, Nicolas Malebranche or Antoine Arnauld concerning the scholastic entities. Not only do I contrast their philosophical arguments concerning ontological entities and the norms to be respected in physics, but also their ways of defining the philosophical enterprise and its public. (shrink)

In the history of the scientific revolution, Descartes is often considered as the mechanical philosopher par excellence, and opposed as such to the founder of mechanical science, that is to say, Galileo: this cliché is not without foundation, but it must not make us forget that Descartes was himself a practitioner of mechanical science. In the article "Cartesian Mechanics" I detail the meaning and reach of "mechanics" in the Cartesian corpus, and do so in three steps. 1. I begin by (...) explaining the genesis of the thesis which states that there is no difference between the physical and the mechanical; this thesis is so famous that it is often imagined that it is constituted in Descartes's first writings. But we can in fact show that the first works of Descartes and Beeckman arise from a "physico-mathematical" practice which does not necessarily imply a complete reworking of traditional physics, even if it might have favored the Cartesian ambition for a physics as certain as geometry; it was only in the late 1630s that Descartes began to systematically affirm the identity of physics and mechanics, or of "rules of motion", of "laws of Nature" and of "laws of mechanics". I then analyze the consequences of this affirmation. 2. In the second part of this article I provide a step-by-step commentary of the response proposed by Descartes in a letter to Mersenne in July 1638 to the question raised by Beaugrand's Geostatice (...) dissertatio mathematica (1636), that is to say the question of whether a body weighs more when it is farther from the center of Earth than when it is close. Compared with other texts of the Cartesian corpus, this sample of mechanics has been little analyzed (to my knowledge, the only analyses are those of P. Duhem, P. Costabel, A. Gabbey and D. Garber). This text is nonetheless extremely interesting: Descartes responds to the geostatic question in turn in terms of physics, then mathematics; even more interesting, the examination of the details of his procedures allows us to confront Cartesian statics to other writings, whether those of Guidobaldo del Monte, Galileo, Stevin, Mersenne or Roberval. 3. In the third and final section, I analyze the reasons that lead Descartes to exclude velocity from his statics, I examine the difficulties that his explanation of gravity created for statics, and conclude with the confrontation between mechanical philosophy and mechanical science in the case of Descartes. (shrink)

Sophie Roux confronte la critique du « sokalisme » qu’on trouve dans La Querelle des imposteurs d’Yves Jeanneret et la manière dont Impostures intellectuelles dessine le partage entre « littéraires » et « scientifiques ».

L’article « D’une Affaire aux autres » de Josquin Debaz et Sophie Roux, montre combien il est difficile de délimiter ce qu’on appelle « l’Affaire Sokal » et analyse, par un recensement aussi systématique que possible des articles de presse, la différence entre l’affaire américaine et l’affaire française.

Divided into eight sections, each with introductory essays, the selections offer rich and detailed insights into a diverse multinational philosophical landscape. Revealed in this pathbreaking work is the way in which traditional philosophical issues related to ethics, metaphysics, and epistemology, for instance, take on specific forms in Africa's postcolonial struggles. Much of its moral, political, and social philosophy is concerned with the turbulent processes of embracing modern identities while protecting ancient cultures.

Les progrès de la physique et l’essor des sciences cognitives dans la seconde moitié du XXe siècle ont remis au centre de la réflexion philosophique la question de la nature du mental et de sa relation avec le physique : et si Descartes s’était trompé en distinguant radicalement l’esprit et le corps? Si nos croyances, nos désirs, nos douleurs, nos craintes, nos espoirs, et plus généralement l’ensemble de notre vie mentale, n’étaient rien de plus que des processus physiques-cérébraux? Cela n’aurait-il (...) pas en outre l’avantage de résoudre le problème des rapports entre corps et esprit, en levant définitivement les difficultés associées au « dualisme » cartésien? L’abandon du dualisme des substances n’a pourtant pas suffi à supprimer le problème corps-esprit, qui continue d’alimenter aujourd’hui les plus vigoureux débats. Bien que le contexte des réflexions actuelles soit différent de celui de l’âge classique, la référence à Descartes est constante et sert une formulation plus précise des défis que la philosophie de l’esprit et les sciences cognitives contemporaines se doivent de surmonter. Comment l’expliquer et quel rôle l’histoire de la philosophie a-t-elle ici à jouer? (shrink)

In November 1664, a comet appeared in the European skies; by early March 1665, it had disappeared, but, at this very moment, another comet appeared, which stayed among the stars until mid-April. Observations of these two comets were made all over Europe, and even beyond. Although most secondary literature dedicated to these two comets has been focused on England and Italy, France was not to be outdone in terms of observations, small talk and publications. In this paper, I would like (...) to use the books that were published on these comets in France as a dispersive prism to understand the ongoing controversies about which principles should be accepted in natural philosophy in the mid-sixties. There were indeed several intellectual and institutional circumstances that gave a specific twist to the French debate: the sixties marked the beginning of the war between Jesuits and Cartesians that was to enflame learned France until the late nineties at least, they were also the period of gestation for the future Académie des sciences, and, finally, it is also during these years that French elites began to discredit systematically the practice of astrology as a popular superstition. My working hypothesis in this paper is that, in such circumstances, the two comets of 1664–1665 were an occasion for each camp to advocate publicly its positions about the proper principles for natural philosophy. By natural philosophical principles, I mean both ontological and epistemological principles. (shrink)

The ontological status of forces and their causal role in Descartes’ physical world is debated among Descartes scholars. The question of forces is embedded in another more general question, namely to determine which causal activity should be attributed to God, and which causal activity should be attributed to physical bodies. Three distinct positions were attributed to Descartes: 1. he was an occasionalist and he attributed no causal power to forces, 2. he was a pure conservationist and he conceived forces as (...) entities distinct from matter and motion, 3. he was a concurrentist who attributed causal activity both to God and to second causes, especially to forces and laws. These three interpretations seem to exhaust the possibilities. In this chapter however, I defend another interpretation of Descartes’ position, according to which God intervenes in this world only to conserve it by his ordinary concurrence (in this I agree with the conservationist interpretation), without, for all that, forces or laws being specific entities (in this I agree with the occasionalist interpretation). My interpretation leads to downplaying the strong relationship which is assumed to exist between Descartes’ physics and his metaphysics. (shrink)

Leaving aside here the question of the author of the Essai de logique, I show that, if Mariotte insisted on the specificity of physics, he also sought a certain inspiration in mathematics as to the way in which to lay out the propositions in a proof. To do so, I start off from the ontological distinction made in the Essai among three types of possibles; next we will show that the three types of propositions correspond to three types of knowledge, (...) and, correlatively, that the main problem of physics is that it is impossible to establish in a certain fashion universal sensory propositions; I next characterize the notion of principles of experience; finally, I examine a bit systematically the relationship between mathematics and physics. (shrink)

Résumé Cet article esquisse une généalogie du privilège que le terme concept a acquis en français par rapport à notion et à idée en se fondant non seulement sur les ouvrages des philosophes, mais sur des dictionnaires de langue philosophique. Il comprend quatre parties chronologiques. Après avoir étudié l’introduction des termes concept, notion, idée dans la langue philosophique, la première partie répertorie leurs usages dans les dictionnaires scolastiques du SVIIe siècle. La deuxième montre que Descartes a imposé idée en donnant (...) de ce terme une acception large et que les dictionnaires post-cartésiens la reprenne. La troisième établit que Kant a, contre cette acception large, introduit une distinction entre Begriff et Idee, mais que, initialement, les dictionnaires français refusèrent cette distinction. La quatrième et dernière partie est consacrée à un XXe siècle marqué par l’idéalisme allemand et l’analyse logique : aussi différentes qu’aient été ces deux traditions, elles ont été d’accord pour consacrer la prééminence du terme concept. (shrink)

Food Problems and Economic Problems in America, Africa, the Middle East and Asia : Struggles and Resignation What are the various dynamics of crisis, revolt, and resignation currently operating on the American and African continents, in the Middle East and in Asia. What effects do they have on the policies adopted to “get out of the crisis”? These are the issues which Greg Albo, Kako Nubukpo, Rhina Roux, Marie Noëlle Abiyaghi and Son Youg Woo address in this article. They examine (...) the consequences of neo-liberal capitalism and the succession of crises in food, oil, finance, and in the economy, before going on to explain how they emerge in their regional contexts where they take on their specific guises. (shrink)

We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with respect to a particular language or class of formulas, our method establishes claims that require heterogeneous forms of reasoning, relying on a Nelson-Oppen-style architecture in which special-purpose modules collaborate and share information. The framework is thus modular and extensible. A prototype implementation shows that the method is promising, (...) complementing techniques that are used by contemporary interactive provers. (shrink)

This book adds impetus to the nexus between human rights, human rights education and material reality. The dissonance between these aspects is of growing concern for most human rights educators in various social contexts. The first part of the book opens up new discourses and presents new ontologies and epistemologies from scholars in human rights, human rights education and human rights literacies to critique and/or justify the understandings of human rights' complex applications. Today's rapidly changing social contexts and new languages (...) attempting to understand ongoing dehumanization and violations, put enormous pressure on higher education, educators, individuals working in social sciences, policy makers and scholars engaged in curricula making. The second part demonstrates how global interactions between citizens from different countries with diverse understandings of human rights (from developed and developing democracies) question the link between human rights and it's in(ex)clusive Western philosophies. Continuing inhumane actions around the globe reflect the failure of human rights law and human rights education in schools, higher education and society at large. The book shows that human rights education is no longer a blueprint for understanding human rights and its universal or contextual values presented for multicomplexial societies. The final chapters argue for new ontologies and epistemologies of human rights, human rights education and human rights literacies to open-up difficult conversations and to give space to dissonant and disruptive discourses. The many opportunities for human rights education and literacies lies in these conversations. (shrink)

L'histoire des sciences suffit à réfuter la thèse de la mathématisation impossible, selon laquelle la mathématisation procéderait d'un formalisme abstrait manquant les choses mêmes ou la spécificité d'un domaine d'objets. Cette histoire montre en effet qu'on n'a pas cessé de mathématiser des choses dont il avait été longtemps dit qu'elles devaient, étant donné leur nature, éternellement résister à la mathématisation. À la thèse de la mathématisation impossible, il est dès lors tentant d'opposer la thèse de la mathématisation inéluctable, selon laquelle (...) une science bien formulée est une science mathématiquement constituée. Cette dernière thèse est cependant souvent associée à l'idée que l'introduction des mathématiques dans une discipline constituerait un processus qui ne présenterait aucune difficulté et qui ne serait suivie d'aucune perte. Contre cette idée, les articles rassemblés dans ce volume ont voulu, comme le titre de ce dernier l'indique, restituer à la mathématisation son caractère problématique. La méthode adoptée dans ce volume est résolument empirique : il s'appuie non pas sur des réflexions a priori sur ce que seraient les objets mathématiques, mais sur des études de cas empruntées à différentes périodes de l'histoire et à différentes sciences. Le pari a été fait que ces différentes rubriques pourraient être articulées les uns aux autres dans trois parties qui ont respectivement pour titres "Les exigences de la mesure : la quantification", "La formalisation : la puissance des formes symboliques", et "La modélisation, une nouvelle forme de mathématisation?" Assurément, une tendance historiographique générale de ces trente dernières années a consisté à privilégier les études de cas locales et singulières, ce qui nous a permis de prendre congé du style épique, qui néglige les détails de l'histoire. Cependant, l'espèce de nominalisme qui en résulte tourne rapidement court, si l'on en reste à ces études de cas singulières. Ce volume repose donc sur un pari : essayer d'articuler différentes études de cas de manière à dégager certaines formes de la mathématisation. Que ce pari ait été gagné ou perdu, ce sera au lecteur d'en juger. (shrink)

From early sage philosophers to Leopold Senghor of Senegal and Steve Biko of South Africa, African thinking has challenged the way we think. As we enter a new millenium, the perspectives provided in this volume offer wise and refreshing alternatives to problems of self and society, culture, aesthetics, metaphysics and religion. Out of Africa always something new, and in these pages contemporary problems of cross-cultural cognition and post-coloniality are not only addressed, but also enacted. The reader witnesses the collision and (...) the coalescence of cultures in the writings of philosophers from Africa. (shrink)

Purified nuclei are being used as a test system to study the regulation of nuclear enzymes in plants. Regulatory agents such as light, hormones and polyamines can stimulate kinases or phosphatases that control nuclear protein phosphorylation and they can modulate the activity of as yet unidentified enzymes required for transcript synthesis and/or stabilization. This essay summarizes current findings and discusses the advantages and pitfalls of using isolated nuclei to investigate how nuclear functions are controlled.

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean’s (...) elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved. (shrink)