‘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...

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)

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)

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?

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)

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 ...

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

La notion de lieu occupe dans le système cartésien une place stratégique : elle en manifeste la singularité tant dans le domaine de la physique que dans celui de la métaphysique. En physique, les difficultés sont nombreuses : comment Descartes parvient-il à édifier une philosophie naturelle qui produit, notamment, les lois du choc et celle de la chute des graves, dans un cadre conceptuel qui nie l'existence du vide ainsi que celle de lieux différents? Jusqu'à quel point peut-on parler d'une (...) mathématisation du réel pour un corps de doctrine aussi peu algébrique que possible? Le spectre du roman cartésien doit être chassé afin de saisir la science cartésienne dans sa nouveauté radicale. Mais dès lors que l'on s'interroge sur les motifs conceptuels qui empêchent Descartes d'élaborer une mathématisation du réel, dont la Géométrie semble lui donner les moyens et les Regulae la méthode, on est conduit à préciser la nature des procédures résolutoires de la pensée, leur portée et leurs limites et, ainsi, à entrer de plain-pied dans le champ de la mathématique, tout d'abord, puis dans celui de la métaphysique. Dire ce qu'est et ce que peut un corps s'énonce à partir du savoir de ce qu'est et de ce que peut l'esprit. En effet, Descartes attribue à l'esprit la force et la puissance, non seulement d'inventer et de produire du nouveau, mais également celle, très concrète, d'imprimer une nouvelle détermination aux mouvements des esprits animaux. On peut considérer que la force chez Descartes est indexée au spirituel plutôt qu'au corporel et qu'en dehors de la question singulière de l'Eucharistie, elle n'est efficace qu'à la condition de ne pas être localisée stricto sensu en termes de lieu : Dieu agit dans le monde pour autant qu'il n'en fait pas partie et la glande pinéale est le siège principal de l'âme, sedes et non pas locus. Cette lecture de l'œuvre cartésienne trouve ainsi dans la notion de lieu un thème d'étude particulièrement fécond, dans la mesure où elle est mobilisée à la fois dans la physique et les mathématiques cartésiennes, mais également dans la question de la localisation de Dieu dans le monde, dans celle du Christ sous les espèces consacrées, et dans celle de l'âme dans le corps. Ainsi d'un lieu à un autre, nous sommes conduits au cœur du système cartésien, par un mouvement d'approfondissement réciproque des perspectives. (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)

L'épistémologie s'intéresse à la connaissance scientifique aux points de vue logique et méthodologique. Soit elle cherche les fondements du savoir qui précèdent la science elle-même, soit elle pose ses problèmes à l'intérieur de la science. Or, depuis que la science mathématique de la nature tend à une forme de mathématique pure, cette distinction classique n'est plus vraiment pertinente. Au-delà des questions épistémologiques habituelles, cet ouvrage propose une lecture critique de la science moderne, où la notion de "fondement" est élargie aux (...) "premiers gestes". Lorsque Galilée a formulé la loi de la chute des corps sous une forme mathématique, il a considéré que les corps du monde physique réel se déplacent dans un espace vide, qui est un milieu idéal. Il a ainsi violé l'interdit posé par Aristote sur le mouvement dans le vide, et depuis lors la question du rapport de la pensée à l'intuition a été soulevée dans le cadre d'une interrogation inédite sur la Nature. La science de la nature a poursuivi son chemin vers sa mathématisation à outrance, et les grandes étapes de ce chemin que sont les théories de la relativité et de la mécanique quantique ont fini par faire resurgir les fantômes de l'intuition qui sont comme des piqûres de rappel du sens de ce qui a été ouvert pour commencer. Il fallait donc poser la question qui fut celle de Husserl : avant de tomber dans le vide, les corps ne sont-ils pas tombés énigmatiquement du vide pour susciter les premiers gestes du savoir? La loi de Galilée ainsi questionnée devient l'emblème d'une interrogation philosophique inédite. Le vide d'où surgissent les phénomènes naturels renvoie en amont de la nature, vers le monde de la vie sur lequel la science n'a pas de prise bien qu'elle en émane. Qu'est-ce qui s'effectue dans ce monde? En essayant d'approfondir cette question, la phénoménologie retrouve dans la science cette dimension intuitive de l'expérience que la science met en question. Dans une métaphysique de la nature tirée de la philosophie transcendantale, Kant l'avait déjà esquissée sous la forme d'une équivoque de l'intuition. Equivoque aussi riche de sens que porteuse d'une énigme à l'horizon de ces premiers gestes du savoir qu'aucun savoir constitué ne peut épuiser. (shrink)

In this chapter I contend that Husserl’s investigations of reduction and givenness culminate in a hubris and a humility that are not precisely where Marion might look for them. In the first section of this essay I set out the main points in Marion’s reading of Husserl. I begin by outlining the broadening and breakthrough achieved in the early work, and then consider the shift that Marion sees presaged in the principle of all principles and announced in the reduction. On (...) the latter’s interpretation, appearing things are reduced to objects within the intentional immanence of consciousness. This process culminates in poor and flat phenomena that are modelled on the mathematising horizons of the subject. I go on to give a short outline of Marion’s alternative notions of the interloqué and the saturated phenomenon. I commence the second section by looking briefly at what I call Husserl’s philosophical hubris, brought out in some of his remarks concerning the subjective a priori. Hubris lies in the interpretation of everything as a meaning for me, from God through to the world. It does not lie in the taking of beings as objects within fixed horizons, for Husserl shows a notable humility towards the things themselves in their respective appearances. Such humility is not a rarity, but is threaded through the explications that follow on the procedures of epoché and reduction. In the rest of this section, my concern is to show that, as Husserl’s thought develops, he pays ever more attention to the original modes of givenness of transcendent things. In the third and final section, I suggest that he also does justice to the character of the world as non-objective ground and horizon. Philosophical hubris will in no way preclude empirical humility. (shrink)

De l'élimination des causes finales par la mathématisation de la physique à l'hypothèse de Kant-Laplace sur la formation du système solaire, puis au développement des sciences de la vie qui déterminent un nouveau champ de rationalité, le thème de la création au 18ème siècle est particulièrement apte à manifester l'évolution des rapports entre sciences, philosophie et métaphysique, jusqu'à son progressif effacement dans des philosophies aussi différentes que celles de Diderot, Hume et Kant.

RésuméDe l'delimination des causes finales par la mathématisation de la physique à l'hypothèse de Kant‐Laplace sur la formation du système solaire, puis au développement des sciences de la vie qui déterminent un nouveau champ de rationalité, le théme de la création au 18ème siècle est parti‐culièrement apte a manifester l'évolution des rapports entre sciences, philosophie et métaphysique, jusqu'à son progressif effacement dans des philosophies aussi differentes que celles de Diderot, Hume et Kant.

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)

In this paper I present and discuss the main objections of France Veber (1890- 1975) against mathematical logic in general and the work of Mihael Marki (1864-1939), the first modern logician in Slovenia, in particular. Marki tried to develop an algebra of logic in the spirit of Boole and Schröder, and thereby to provide an axiomatic system of syllogistics with the least number of axioms. Veber's general objection to this project was that it tries to represent the essential qualitative properties (...) of judgements and inferences in quantitative (extensional) terms. Veber also criticized the subject-predicate analysis of judgements and eventually rejected the whole idea of logic as being a calculus, with judgements being treated like equations and inferences like operations in a calculus. Although much in this criticism - which is in certain respects similar to Husserl's reservations about a complete "mathematisation" of logic - is unfounded and misguided, the attack on the idea of logic being essentially a calculus is still interesting and relevant today. This idea is a symptom of a philosophical "desease" resulting from a one-sided "diet", as Wittgenstein put it. Thus one can agree with Veber to the extent that logic has to take into account the meaning of sentences, not just their symbolic form, and that it is therefore an "art" which can never be fully formalized, requiring much more "understanding" than usually thought. (shrink)

In Descartes, the concept of a ‘universal science’ differs from that of a ‘mathesis universalis’, in that the latter is simply a general theory of quantities and proportions. Mathesis universalis is closely linked with mathematical analysis; the theorem to be proved is taken as given, and the analyst seeks to discover that from which the theorem follows. Though the analytic method is followed in the Meditations, Descartes is not concerned with a mathematisation of method; mathematics merely provides him with (...) examples. Leibniz, on the other hand, stressed the importance of a calculus as a way of representing and adding to what is known, and tried to construct a ‘universal calculus’ as part of his proposed universal symbolism, his ‘characteristica universalis’. The characteristica universalis was never completed—it proved impossible, for example, to list its basic terms, the ‘alphabet of human thoughts’—but parts of it did come to fruition, in the shape of Leibniz's infinitesimal calculus and his various logical calculi. By his construction of these calculi, Leibniz proved that it is possible to operate with concepts in a purely formal way. (shrink)

Le § 9 de la Krisis expose les étapes : idéalisation géométrique, mathématisation indirecte des qualités, induction savante, opérations aveugles du calcul. Une enquête historique confirme-t-elle le récit de Husserl ?

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)

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)