Sophie Roux

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

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.

Mes réflexions sur Meyerson et les mathématiques ont pour origine trois questions : 1) Une idée reçue est que, des trois synthèses de Meyerson -- Identité et réalité, De l'explication dans les sciences et Du cheminement de la pensée -- , seule la dernière analyse les mathématiques, en elles-mêmes aussi bien que dans leurs rapports avec la pensée. La première question est donc de déterminer si cette idée reçue est correcte ou bien si l'on peut trouver dans les deux autres ouvrages des indications significatives sur le statut des mathématiques et sur leur fonction dans une théorie de la connaissance. 2) La deuxième question consiste à examiner une autre idée reçue, cautionnée cette fois par Meyerson. À plusieurs reprises, ce dernier a déclaré qu'il avait répété la même chose dans tous ses ouvrages : les outils conceptuels seraient restés identiques, mais appliqués à des objets ou dans des domaines divers, de la physique quantique à la pensée primitive. Il s'agit dans ce cas de savoir si cette déclaration est fondée, ou bien plutôt si l'on doit, par-delà l'identité des termes, souligner l'existence de différences de signification ou d'application telles que l'identité des outils conceptuels en devient problématique. 3) Meyerson s'est trouvé confronté à un ensemble d'épistémologues que, reprenant une expression de Léon Brunschvicg, il qualifie d'idéalistes mathématiques, d'un côté l'école de Marbourg avec Ernst Cassirer, Paul Natorp et Hermann Cohen, de l'autre, Gaston Milhaud, mais surtout Brunschvicg lui-même . S'il s'avère qu'il y a des thèses sur les mathématiques ailleurs que dans Du cheminement de la pensée, et qu'il y a certains infléchissements d'un lieu à l'autre de son œuvre, on peut se demander dans quelle mesure les critiques adressées à l'idéalisme mathématique ont évolué. Dans cet article, j'analyse les trois synthèses de Meyerson avec ces trois questions en arrière-plan : je ne les examine pas explicitement l'une après l'autre, ni a fortiori dans un ordre prédéterminé, mais plutôt de biais et au fur et à mesure qu'elles interviennent

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. This grand narrative began with the exhibition of quantitative laws that these heroes, Galileo and Newton for example, had disclosed: the law of falling bodies, according to which the speed of a falling body is proportional to the square of the time that has elapsed since the beginning of its fall; the law of gravitation, according to which two bodies are attracted to one another in proportion to the sum of their masses and in inverse proportion to the square of the distance separating them -- according to his own preferences, each narrator added one or two quantitative laws of this kind. The essential feature was not so much the examples that were chosen, but, rather, the more or less explicit theses that accompanied them. First, mathematization would be taken as the criterion for distinguishing between a qualitative Aristotelian philosophy and the new quantitative physics. Secondly, mathematization was founded on the metaphysical conviction that the world was created pondere, numero et mensura, or that the ultimate components of natural things are triangles, circles, and other geometrical objects. This metaphysical conviction had two immediate consequences: that all the phenomena of nature can be in principle submitted to mathematics and that mathematical language is transparent; it is the language of nature itself and has simply to be picked up at the surface of phenomena. Finally, it goes without saying that, from a social point of view, the evolution of the sciences was apprehended through what has been aptly called the "relay runner model," according to which science progresses as a result of individual discoveries. Grand narratives such as this are perhaps simply fictions doomed to ruin as soon as they are clearly expressed. In any case, the very assumption on which this grand narrative relies can be brought into question: even in the canonical domain of mechanics, the relevant epistemological units crucial to understanding the dynamics of the Scientific Revolution are perhaps not a few laws of motion, but a complex set of problems embodied in mundane objects. Moreover, each of the theses just mentioned was actually challenged during the long period of historiographical reappraisal, out of which we have probably not yet stepped. Against the sharp distinction between a qualitative Aristotelian philosophy and the new quantitative physics, numerous studies insist that Rome wasn't built in a day, so to speak. Since Antiquity, there have always been mixed sciences; the emergence of pre-classical mechanics depends on both medieval treatises and the practical challenges met by Renaissance engineers. It is indeed true that, for Aristotle, mathematics merely captures the superficial properties of things, but the Aristotelianisms were many during the Renaissance and the Early Modern period, with some of them being compatible with the introduction of mathematics in natural philosophy. In addition, the gap between the alleged program of mathematizing nature and its effective realization was underlined as most natural phenomena actually escaped mathematization; at best they were enrolled in what Thomas Kuhn began to rehabilitate under the appellation of the "Baconian sciences," i.e., empirical investigations aiming at establishing isolated facts, without relating them to any overarching theory. Hence, mathematization of nature cannot pretend to capture a historical fact: at most, it expresses an indeterminate task for generations to come. On top of these first two considerations, and against the thesis of the neutrality of the mathematical language, it was urged that mathematics is not "only a language" and that, exactly as other symbolic means or cognitive tools, it has its own constraints. For example, it has been thoroughly explained that the Euclidean theory of proportions both guides and frustrates the Galilean analysis of motion; its shortages were particularly clear with respect to the expression of continuity, which is crucial in the case of motion. Consequently, when calculus was invented and applied to the analysis of motion, it was not a transposition that left things as they stood. Even more clearly than in the case of a translation from one natural language to another, the shift from one symbolic language to another entails that certain possibilities are opened while others are closed. The cognitive constraints imposed by established mathematical theories, as seen in the theory of proportions or calculus, were not the only ones to be studied in relation to mathematization. Certain schemes dependent on the grammar of natural languages, e.g., the scheme of contrariety, or certain symbolic means of representation, e.g. geometrical diagrams and numerical tables, were also subject to such scrutiny. Lastly, it was insisted that, even if we concede the existence of scientific geniuses, mathematics is largely produced by intellectual communities and embedded within social practices. More attention was consequently paid to the forms of communication in given mathematical networks, or to the teaching of the discipline in, for example, Jesuit colleges and universities. The set of mathematical practices specific to specialized craftsmen, highly-qualified experts and engineers began to be studied in its own right. All these reflections may have helped us change our perspectives on the question of mathematization. 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. Consequently, before presenting the essays of this fascicle, I would like to say a few words in favor of a renewed study of the forms of mathematization in the history of the early sciences.

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.

On appelle « Affaire Sokal » l’ensemble de controverses que suscitèrent la publication en 1996 d’une parodie écrite par un physicien américain, Alan Sokal, puis, en 1997, de l’ouvrage Impostures intellectuelles, qu’il co-signa avec un physicien belge, Jean Bricmont. Dans Retours sur l’Affaire Sokal¸ des historiens des sciences reviennent sur cette affaire. Ils montrent qu’elle recouvre différentes controverses et qu’il faut distinguer ces dernières non seulement selon la nature des écrits qui les ont occasionnées, mais aussi en fonction des questions abordées, et peut-être surtout des manières de concevoir et pratiquer les échanges intellectuels. Les auteurs analysent en particulier ces controverses en France, aux États-Unis et au Royaume-Uni ; ils examinent aussi la façon dont ont été traités la relation entre le domaine scientifique et le domaine littéraire ou l’usage des métaphores en sciences.

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

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 ?

Goffi and Roux are interested in what makes some thought experiments work, while others do not work. They do not attempt to draw an a priori line between two types of thought experiments, but rather ask the following question: inasmuch as thought experiments are arguments, and notwithstanding the fact that some of them might involve the contemplation of an imaginary scenario, how is it that some of them work, while others do not? Taking inspiration from a counterfactual thought experiment presented by Nicholas Rescher, they treat thought experiments as argumentative procedures resembling tests of consistency, which invite the experimenter to seek the weakest link in her body of beliefs. Equipped with this method, they examine two well-known successful thought experiments (Galileo’s two bodies strapped together, and Thomson’s violinist) and discuss Mach’s notion of thought experiments. Thus they reach the hypothesis that successful thought experiments respect the three following conditions: they do not deal with things, but with beliefs; they mobilise a set of beliefs shared by the interlocutors; and this set of beliefs has a hierarchical structure. Using once again examples written at different periods and taken from various disciplines (Descartes’ receding bodies, Aristotle’s weaving shuttles), Goffi and Roux argue that each of those conditions is individually necessary for a thought experiment to work. They finally conclude on the limits and consequences of their approach.

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.