‘The mathematisation of time has limits,’ writes Derrida in ‘Ousia and Gramme.’ Taking this quote in all possible senses, this paper considers Derrida’s definition of limit as gramme, trace, and ap...

The following questions arising in connection with the géométrisation of modern physics are discussed: is the physical theory a bicomponent one or everything can be reduced to space? Whether the hypothesis of the macroscopic nature of space and time deals with the theoretical or empirical structure of physical theory? Is there géométrisation of quanta or quantisation of geometry?

SummaryA discussion of the relations between mathematics and reality has a double aspect: it may concern the status of mathematical concepts and their right to be considered as part of “reality”. But the history of scientific concepts shows that attempts to single out a so‐called reality are arbitrary and futile, and the intrusion of ontological thinking in science apparently has never been fruitful.Another way to look at the problem is to investigate the use of mathematical methods to attain knowledge or (...) power about “reality”, by which is generally meant physics . Many examples from the history of sciences show that it is almost impossible to tell in advance whether a mathematical concept or theory will be useful or not.For the time being, it has not yet been possible to apply mathematics in a significant and pregnant way to various sciences. It is advocated that what is needed are not sophisticated mathematical developments, but some rather simple mathematical structures that still have to be described and applied. The present trends in mathematics, which emphasize the understanding of simple and basic mathematical concepts, allow us to hope that significant progress in these directions can be expected. (shrink)

In his Elementorum Myologiae Specimen, Steno geometrizes “the new fabric of muscles” and their movement of contraction, so as to refute the main contemporary hypothesis about the functioning of the muscles. This physiological refutation relies on an abstract representation of the muscular fibre as a parallelepiped of flesh transversally linked to the tendons. Those two features have been comprehensively studied. But the method used by Steno, as well as the way he has chosen to present his physiological results, have so (...) far been neglected. Yet, Steno’s work follows a true synthetic order, which he conceives as a tool to separate uncertain anatomical “elements” from the certain ones. We will show that the true understanding of this “more geometrico” order is the only way to avoid frequent misconceptions of the scientific aim pursued by Steno, which is neither to give a mathematical explanation of the functioning of the muscles, nor to reduce the muscles to some mathematical shapes. (shrink)

In his Elementorum Myologiae Specimen, Steno geometrizes "the new fabric of muscles" and their movement of contraction, so as to refute the main contemporary hypothesis about the functioning of the muscles. This physiological refutation relies on an abstract representation of the muscular fibre as a parallelepiped of flesh transversally linked to the tendons. Those two features have been comprehensively studied. But the method used by Steno, as well as the way he has chosen to present his physiological results, have so (...) far been neglected. Yet, Steno's work follows a true synthetic order, which he conceives as a tool to separate uncertain anatomical "elements" from the certain ones. We will show that the true understanding of this "more geometrico" order is the only way to avoid frequent misconceptions of the scientific aim pursued by Steno, which is neither to give a mathematical explanation of the functioning of the muscles, nor to reduce the muscles to some mathematical shapes. (shrink)

This edited collection discusses phenomenological critiques of formalism and their relevance to the problem of responsibility and the life-world. The authors deal with themes of formalisation of knowledge in connection to the life-world, the natural world, the history of science and our responsibility for both our epistemic claims and the world in which we live. Readers will discover critiques of formalisation, the life-world and responsibility, and a collation and comparison of Patočka's and Husserl's work on these themes. Considerable literature on (...) Husserl is presented here and the two themes of epistemic responsibility and the life-world are discussed together. This work specifically emphasises the interrelatedness of these existential aspects of his work - self-responsibility and the crisis - as not only epistemological, but also related to human life. This volume also introduces Jan Patočka to English-speaking readers as a phenomenologist in his own right. Patočka shows us, in particular, the significance of the modern abyss between our thinking and the world. Readers will discover that this abyss is of concern for our everyday experience because it leads to a rupture in our understanding of the world: between the world of our living and its scientific construct. We see that Patočka continually emphasised the relevance of Husserl's work to existential questions relating to human responsibility and the life-world, which he admits is left largely implicit in Husserl's work. This edited collection will spark discussion on the question of responsibility against the backdrop of formalised knowledge which is increasingly inaccessible to human understanding. Despite the complexity of some of the analysed ideas, the authors discuss these themes in a clear and readable way. This work is scholarly, exact in its discussion and authoritative in its reading, but at the same time accessible to anyone motivated to understand these debates. (shrink)

C'est un ouvrage remarquable à bien des égards que Claude Ménard, qui est né au Québec en 1944 et a étudié en France l'histoire des sciences et l'économie avant d'enseigner l'histoire aux Pays-Bas, a récemment publié chez Flammarion sous le titre La formation d'une rationalité économique: A. A. Cournot. L'épistémologue des sciences sociales y trouvera une analyse intelligente et documentée d'une contribution qui occupe, par rapport à la formation de l'économie moderne, une place qui n'a probablement d'équivalent dans aucune autre (...) discipline. L'historien de la philosophie, tout autant que celui de l'économie, y appréciera l'éclairage neuf jeté sur l'œuvre d'un penseur dont l'importance a toujours été méconnue malgré le fait – ou peut-être plutôt à cause du fait – qu'au milieu du XIXe siècle, il se consacrait à des questions théoriques qui souvent n'allaient devenir importantes que pour les hommes du XXe siècle. L'historien des idées saura gré à l'auteur d'avoir su situer son analyse de la contribution de Cournot dans le contexte plus large des institutions et des idées qui ont fait du XIXe siècle le moment décisif de la reformulation moderne des idéologies. L'analyste des idéologies y trouvera donc aussi matière à réflexion puisque le rapport des sciences sociales et des idéologies y est abondamment discuté encore que, comme je chercherai à le montrer, le traitement proposé risque davantage, sur ce point, de laisser le lecteur sur sa faim. (shrink)

Au XVIIème siècle, c’est la découverte du principe d’inertie, un concept purement physique, qui permit de débloquer la théorisation du mouvement, en panne depuis Aristote. La plupart des philosophes et historiens des sciences caractérisent le tournant de la « science moderne » par sa mathématisation, arguant, comme Koyré, que le principe d’inertie découlerait de cette dernière, ou bien, comme Duhem, qu’il était déjà contenu dans l’impetus médiéval, ou encore, comme, Husserl et Kojève, en s’abstenant d’en parler. Et pourtant, la mathématisation (...) de la physique était en marche depuis l’époque hellénistique. L’originalité de Galilée est d’avoir mathématisé non pas la nature, mais, via le principe d’inertie, le temps. (shrink)

L'essor de la perspective linéaire a suscité de nombreuses polémiques tout au long du Quattrocento et du Cinquecento, opposant les partisans d'une géométrisation artificialiste de la vision à ceux qui vantaient les qualités du dessin d'après nature ou invoquaient des arguments de nature physiologique. Ces débats peuvent être retracés à partir des quatre alternatives qui en constituent le noyau dur : champ de vision restreint vs. large ; immobilité vs. mobilité oculaire ; tableau plan vs. curviligne ; vision monoculaire vs. (...) binoculaire. En retenant les premiers termes de ces quatre alternatives, l'histoire de la perspective a rejeté de nombreux systèmes hétérodoxes. Du point de vue de la mathématisation, l'intérêt de ces débats tient à ce qu'ils ont succédé, et non précédé, l'adoption du dispositif perspectif comme intersection de la pyramide visuelle. L'histoire de la perspective linéaire offre ainsi un authentique cas de justification a posteriori des fondements ou, pour ainsi dire, de mathématisation à rebours. (shrink)

This paper focuses on the mathematisation of mechanics in the seventeenth century, specifically on how the representation of compounded rectilinear motions presented in the ancient Greek Mechanica found its way into Newton’s Principia almost two thousand years later. I aim to show that the path from the former to the latter was optical: the conceptualisation of geometrical lines as paths of reflection created a physical interpretation of dia­grammatic principles of geometrical point-motion, involving the kinematics and dynamics of light reflection. (...) Upon the atomistic conception of light, the optical interpretation of such geometrical principles entailed their mechanical generalisation to local motion; rectilinear motion via the physico-mathemat­ics of reflection and the Mechanica’s parallelogram rule; circular motion via the physico-mathematics of reflection, the Archimedean squaring of the circle and the Mechanica’s extension of the parallelogram rule to centripetal motion. This appeal to the physico-mathematics of reflection forged a realist founda­tion for the mathematisation of motion. Whereas Aristotle’s physics rested on motions which had their source in the nature of the elements, early modern thinkers such as Harriot, Descartes, and Newton based their new principles of mechanical motion upon selected elements of the mechanics of light motion, projected upon the geometry of the parallelogram rule for rectilinear and, ultimately, circular motion. (shrink)

An Antique Prototype of the Modern Mathematisation of Psychology Ryszard Stachowski. (1) matter or that which is not in itself a particular thing, (2) form or essence, which is that precisely in accordance with which a thing is called a this, and ...

What reasons can a physicist have to reject the principle of a mathematical method, which he nonetheless uses and which he used frequently in his unpublished works? We are concerned here with Galileo’s doubts and objections against Cavalieri’s “geometry of indivisibles.” One may be astonished by Galileo’s behaviour: Cavalieri’s principle is implied by the Galilean mathematization of naturally accelerated motion; some Galilean demonstrations in fact hinge on it. Yet, in the Discorsi Galileo seems to be opposed to this principle. e (...) fundamental reason of Galileo’s reluctance with respect to Cavalieri’s geometry is to be sought in Galileo’s ideal of intelligibility. It is true that Galilean physics, and more particularly Galileo’s theories of motion and matter, faces deep paradoxes, which Cavalieri’s geometry succeeds to avoid, thanks to a clear determination of the concept of “aggregatum.” But while avoiding these difficulties, Cavalieri does not furnish any solution for the problems raised by Galilean physics. (shrink)

In the Quattrocento and Cinquecento the rise of linear perspective caused many polemics which opposed the supporters of an artificial geometrisation of sight to those who were praising the qualities of the drawing according to nature, or were invoking some arguments on a physiological basis. These debates can be grouped according to the four alternatives that form their central concerns: restricted vs. broad field of vision; ocular immobility vs. mobility; curvilinear vs. planar picture; monocular vs. binocular vision. By retaining the (...) first terms of these four alternatives, the history of perspective eliminated many heterodox constructions. From the viewpoint of mathematisation the interest of these debates is that they succeeded, rather than preceded, the adoption of a perspective system defined by the intersection of the visual pyramid. Thus the history of linear perspective constitutes a genuine case of a posteriori justification, or, put differently, it gives us a case of upside down mathematisation. (shrink)

The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in terms (...) of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.Keywords: Epistemic Programme; Game theory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)

The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal apparatus of (...) recursive operations such as the set-theoretic operation merge has led to a mathematisation of the object of inquiry, producing a strong analogy with discrete mathematics and especially arithmetic. The main product of this error has been the assumption that natural, like some formal, languages are discretely infinite. I will offer an alternative means of capturing the insights and observations related to this posit in terms of scientific modelling. My chief aim will be to draw from the larger philosophy of science literature in order to offer a position of grammars as models compatible with various foundational interpretations of linguistics while being informed by contemporary ideas on scientific modelling for the natural and social sciences. (shrink)

Voir : https://philosophie.ens.fr/Dir-avec-D-Garber-The-Mechanisation-of-Natural-Philosophy.html.

In several accounts of what models are and how they function a specific view dominates. This view contains the following characteristics. First, there is a clear-cut distinction between theories, models and data and secondly, empirical assessment takes place after the model is built. This view in which discovery and justification are disconnected is not in accordance with several practices of mathematical business-cycle model building. What these practices show is that models have to meet implicit criteria of adequacy, such as satisfying (...) theoretical, mathematical and statistical requirements, and be useful for policy. In order to be adequate, models have to integrate enough items to satisfy such criteria. These items include besides theoretical notions, policy views, mathematisations of the cycle and metaphors also empirical data and facts. So, the main thesis of this chapter is that the context of discovery is the successful integration of those items that satisfy the criteria of adequacy. Because certain items are empirical data and facts, justification can be built-in. (shrink)

Within the philosophy of science, the realism debate has been revitalised by the development of forms of structural realism. These urge a shift in focus from the object oriented ontologies that come and go through the history of science to the structures that remain through theory change. Such views have typically been elaborated in the context of theories of physics and are motivated by, first of all, the presence within such theories of mathematical equations that allow straightforward representation of the (...) relevant structures; and secondly, the implications of such theories for the individuality and identity of putative objects. My aim in this talk is to explore the possibility of extending such views to biological theories. An obvious concern is that within the context of the latter it is typically insisted that we cannot find the kinds of highly mathematised structures that structural realism can point to in physics. I shall indicate how the model-theoretic approach to theories might help allay such concerns. Furthermore, issues of identity and individuality also arise within biology. Thus Dupre has recently noted that there exists a ‘General Problem of Biological Individuality’ which relates to the issue of how one divides ‘massively integrated and interconnected’ systems into discrete components. In response Dupre advocates a form of ‘Promiscuous Realism’ that holds, for example, that there is no unique way of dividing the phylogenetic tree into kinds. Instead I shall urge serious consideration of those aspects of the work of Dupre and others that lean towards a structuralist interpretation. By doing so I hope to suggest possible ways in which a structuralist stance might be extended to biology. (shrink)

Structural realism is arguably one of the most influential movements to have emerged in philosophy of science in the last decade or so. Advocates of this movement attempt to answer epistemological and/or ontological questions concerning science by arguing that the key to all such questions is the mathematical formalism of a theory. This is so, according to structural realists, because the mathematical formalism encodes all and only what is important about a theory’s target domain, namely its structure. Almost without exception, (...) discussions of structural realism centre on the natural sciences and in particular on modern physics. Given that a number of other sciences are less – indeed in some cases much less – mathematised than modern physics, does structural realism have anything informative to say about them? In this talk, I take up the task of articulating what structural realists ought to say about the social sciences if they are to consider themselves as offering a coherent philosophy for the whole of science. (shrink)

This study, presenting a history of the measurement of light intensity from its first hesitant emergence to its gradual definition as a scientific subject, explores two major themes. The first concerns the adoption by the evolving physics and engineering communities of quantitative measures of light intensity around the turn of the twentieth century. The mathematisation of light measurement was a contentious process that hinged on finding an acceptable relationship between the mutable response of the human eye and the more (...) easily stabilised, but less encompassing, techniques of physical measurement. -/- A second theme is the exploration of light measurement as an example of ‘peripheral science’. Among the characteristics of such a science, I identify the lack of a coherent research tradition and the persistent partitioning of the subject between disparate groups of practitioners. Light measurement straddled the conventional categories of ‘science’ and ‘technology’, and was influenced by such distinct factors as utilitarian requirements, technological innovation, human perception and bureaucratisation. Peripheral fields such as this, which may be typical of much of modern science and technology, have hitherto received little attention from historians. -/- These themes are pursued with reference to the social and technological factors which were combined inextricably in the development of the subject. The intensity of light gained only sporadic attention until the late nineteenth century. Measured for the utilitarian needs of the gas lighting industry from the second half of the century, light intensity was appropriated by members of the nascent electric lighting industry, too, in their search for a standard of illumination. By the turn of the century the ‘illuminating engineering movement’ was becoming an organised, if eclectic, community which promoted research into and standards for the measurement of light intensity. -/- The twentieth-century development of the subject was moulded by organisation and institutionalisation. Between 1900 and 1920, the new national and industrial laboratories in Britain, America and Germany were crucial in stabilising the subject. In the inter-war period, committees and international commissions sought to standardise light measurement and to promote research. Such government- and industry-supported delegations, rather than academic institutions, were primarily responsible for the ‘construction’ of the subject. Practitioners increasingly came to interpret the three topics of photometry (visible light measurement), colorimetry (the measurement of colour) and radiometry (the measurement of invisible radiations) as aspects of a broader study, and enthusiastically applied them to industrial and scientific problems. -/- From the 1920s, the long-established visual methods of observation were increasingly replaced by physical means of light measurement, a process initially contingent on scientific fashion more than demonstrated superiority. New photoelectric techniques for measuring light intensity engendered new commercial instruments, a trend which accelerated in the following decade when photometric measurement was applied with limited success to a range of industrial problems. Seeds sowed in the 1920s – namely commercialisation and industrial application, the transition from visual to ‘physical’ methods, and the search for fundamental limitations in light measurement – gave the subject substantially the form it was to retain over the next half-century. (shrink)

En 1814, Ampère publie une théorie de la combinaison chimique des corps qu'il fonde sur la science des cristaux de Hauy, sur « les résultats de belles expériences » de Gay-Lussac et sur une hypothèse « sur la proportionnalité entre les volumes des gaz et leur nombre de particules ». A la même époque, il met en évidence, en philosophie, les rôles de l'abstraction et des « rapports » dans les connaissances humaines ; ces concepts éclairent la mathématisation mise en (...) œuvre dans cette théorie chimique. Bien que conçue tardivement, la classification des sciences d'Ampère nous aide à situer, rétrospectivement, la théorie des combinaisons chimiques dans les sciences mathématiques et physiques. (shrink)

Ansgar Lyssy,Christian Leduc | : Le principe de moindre action fut découvert dans le domaine de l’optique et dans celui de la mathématisation du corps en mouvement à l’intérieur d’une structure de forces. Aussi bien Euler que Maupertuis prennent appui sur une compréhension métaphysique de la nature pour justifier l’extension de ce principe à un principe général de physique. Dans le présent article, je soutiens que les deux croient que la nature elle-même ne saurait employer de moyens inutiles pour ses (...) fins, et est donc économique. Le principe de moindre action peut être compris comme une tentative d’intégrer l’idée métaphysique d’une « économie de la nature » à l’intérieur du domaine de la science. | : The principle of least action was discovered in the realm of optics and in the mathematical properties of a body moving within a framework of forces. Both Euler and Maupertuis rely on a metaphysical understanding of nature to justify the expansion of this principle into a general principle of physics. In this paper, I argue that both believe that nature itself uses no unnecessary means for its ends, thus is economical. The principle of least action can be understood as the attempt to integrate this metaphysical idea of an “economy of nature” into the realm of science. (shrink)

In the late eighteenth century Newton's Principia was studied in the Scottish universities under the influence of the local school of ‘Common Sense’ philosophy. John Robison, holding the key chair of natural philosophy at Edinburgh from 1774 to 1805, provided a new conception of ‘mechanical philosophy’ which proved crucial to the emergence of physics in nineteenth century Britain. At Cambridge the emphasis on ‘mixed mathematics’ was taken to a new level of refinement and application by the introduction of analytical methods (...) in the 1820s. The fusion of these two schools, with emphasis on conceptual unity on the one hand, and mathematisation on the other, came about from the 1830s onwards, and reached full expression in the new framework of a unified mathematical physics based on the energy principle. (shrink)

There is a well-documented paradigm-shift in eighteenth century Jesuit philosophy and science, at the very least in Central Europe: traditional scholastic version(s) of Aristotelianism were replaced by early modern rationalism (Wolff's systematisation of Leibnizian philosophy) and early modern science and mathematics. In the field of probability, this meant that the traditional Jesuit engagement with probability, uncertainty, and truthlikeness (in particular, as applied to moral theology) could translate into mathematical language, and can be analysed against the background of the accounts of (...) probability, pre-mathematical Jesuit logic, Wolff's conceptual analysis, and Bernoullian mathematisation. The works of two Jesuit philosophers, Berthold Hauser and Sigismund Storchenau, can be related to this context. The core of their logic of (epistemic) probability is the account of negation (or ‘contradiction’) and implication (or ‘argument’), in particular, the algorithms for computing the reliability of one piece of evidence when compared to the respective counter-evidence and for computing the probability of a conclusion given the probability of its premises. (shrink)

Des deux Essais réunis dans ce volume, l'un, Introduction à la lecture de Platon, présente, dans une première partie, une analyse de la composition subtile et raffinée du dialogue socratique : œuvre dramatique qui présuppose la présence d'un personnage n'y figurant pas, celle du lecteur-auditeur, auquel est dévolu le rôle de comprendre le sens caché du débat et d'en tirer les conclusions. Conclusions que Socrate, délibérément, évite de formuler, mais qui y sont nécessairement impliquées. Ce que l'auteur démontre en prenant (...) comme exemples le Ménon, le Protagoras et le Théétète. La deuxième partie de l'Introduction offre une étude de La République en soulignant l'actualité paradoxale des problèmes fondamentaux qui y sont discutés par Platon. Faisant suite à l'Introduction, les Entretiens sur Descartes reproduisent les conférences données par l'auteur à l'Université du Caire lors du tricentenaire du Discours de la méthode. Ces Entretiens développent une conception de la philosophie de Descartes comme catharsis spirituelle et intellectuelle qui ouvre à l'homme la voie vers la vérité, et vers Dieu. Descartes échappe ainsi au scepticisme et au désarroi qui ont suivi le bouillonnement confus de la Renaissance. La science cartésienne, toute périmée qu'elle soit, est présentée comme un effort prodigieux pour réaliser l'idéal - ou le rêve - de la mathématisation totale de l'Univers, ressuscité, de nos jours par Einstein. (shrink)

La « figure vitruvienne », héritée du traité De architectura de Vitruve, et les variations auxquelles elle donne lieu dans les arts à la Renaissance révèlent une grande diversité de formes et un remaniement du canon antique. En s’appuyant sur une méthode historique et conceptuelle, l’article entend mettre à jour les enjeux esthétiques suscités par la représentation du corps humain dans les arts, en tenant compte de la diversité des voies empruntées par les artistes de la Renaissance, influencés qui plus (...) est par la tentation de la mathématisation, la physiognomonie et la recherche de l’expressivité. (shrink)

This analysis of Herbert Marcuse’s appropriation of the argument concerning the “mathematization of nature” in Edmund Husserl’s Crisis of the European Sciences and Transcendental Phenomenology shows that Marcuse and Husserl both assume that the perception of real, concrete individuals in the lifeworld underlies formal scientific abstractions and that the critique of the latter requires a return to such qualitative perception. In contrast, I argue that no such return is possible and that real, concrete individuals are constituted by the relation between (...) a given perception and its horizon. In this manner, Marcuse’s social critique can be combined with Husserl’s theoretical-perceptual one, making possible an ecological critique. L’analyse de l’appropriation que fait Herbert Marcuse de l’argument concernant la « mathématisation de la nature » dans la Crise des sciences europe ennes et la phénoménologie transcendantale de Husserl démontre que Marcuse et Husserl assument tous les deux que la perception des individus réels concrets dans le monde de la vie sous-tend les abstractions scientifiques formelles et que la critique de ces dernières nécessite un retour à la perception qualificative. J’avance au contraire qu’un tel retour n’est pas possible et que les individus réels concrets sont constitués par la relation entre une perception donnée et son horizon. Nous pouvons alors combiner la critique sociale de Marcuse avec la critique théorico-perceptuelle de Husserl pour en faire une critique égologique. (shrink)

Blasius of Parma deals with intensification and remission of accidental forms, and the related concept of « latitude » in at least three texts : the Questiones de latitudinibus formarum, the Questio disputata de intensione et remissione formarum and Question 10 on Book V of the Physics. The paper is focussed on the two last. Blasius discusses theses about the ontological status of qualities and their relation to their subject of inherence through the issue of their intensification or weakening, at (...) the borderline of physics and metaphysics. In the same time, he takes sides for the calculating procedures that were on debate since the beginning of the 14th century. In binding the quality and its subject closely together, Blasius does not go as far as the Oxford Calculators in the mathematisation of intensive magnitudes. Nonetheless, he does attempt to integrate the new tools into his physics and his ontology. (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)

La 4e de couverture indique : "Dans cet ouvrage de référence consacré à une analyse approfondie du thème du consentement aux soins dans la pratique médicale, M.-F. Civil porte son regard de médecin et de philosophe sur les comportements de bon nombre de praticiens à l'heure actuelle plus ou moins soumis à la « mathématisation » de la médecine. Loin de se contenter d'un état des lieux complet de la question, il nous conduit pas à pas sur les chemins d'une (...) « éthique existentielle » tout à fait singulière, renvoyant à des situations pratiques de soins où délibérer avant d'agir et réfléchir à l'action déjà prise permet aux patients d'exprimer le sens donné à leur vécu dans le cadre de leur projet de vie immédiate ou future. Son approche très phénoménologique, aux côtés notamment de Heidegger et Husserl, ouvre la porte à un vaste chantier de réflexion pour tous ceux qui envisagent de se pencher sur la manière concrète d'être-au-monde en médecine comme souci pour soi et pour les autres. Ainsi ce livre interpelle les étudiants, les chercheurs, les professionnels de santé, mais également tous ceux qui ont été, ou seront, tôt ou tard, confrontés au problème du consentement.". (shrink)