This book offers insights relevant to modern history and epistemology of physics, mathematics and, indeed, to all the sciences and engineering disciplines emerging of 19th century. This research volume is the first of a set of three Springer books on Lazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines in General (Essai sur les machines en général [1783] 1786). The other two forthcoming volumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) and Géométrie de position (1803). Lazare (...) Carnot – l'organisateur de la victoire – in Essai sur le machine en général (1786) assumed that the generalization of machines was a necessity for society and its economic development. Subsequently, his new coming science applied to machines attracted considerable interest for technician, as well, already in the 1780’s. With no lack in rigour, Carnot used geometric and trigonometric rather than algebraic arguments, and usually went on to explain in words what the formulae contained. His main physical– mathematical concepts were the Geometric motion and Moment of activity–concept of Work . In particular, he found the invariants of the transmission of motion (by stating the principle of the moment of the quantity of motion) and theorized the condition of the maximum efficiency of mechanical machines (i.e., principle of continuity in the transmission of power). While the core theme remains the theories and historical studies of the text, the book contains an extensive Introduction and an accurate critical English Translation – including the parallel text edition and substantive critical/explicative notes – of Essai sur les machines en général (1786). The authors offer much-needed insight into the relation between mechanics, mathematics and engineering from a conceptual, empirical and methodological, and universalis point of view. As a cutting–edge writing by leading authorities on the history of physics and mathematics, and epistemological aspects, it appeals to historians, epistemologist–philosophers and scientists (physicists, mathematicians and applied sciences and technology). (shrink)

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of (...) Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal. (shrink)

I describe two approaches to modelling the universe, the one having its origin in topos theory and differential geometry, the other in set theory. The first is synthetic differential geometry. Traditionally, there have been two methods of deriving the theorems of geometry: the analytic and the synthetic. While the analytical method is based on the introduction of numerical coordinates, and so on the theory of real numbers, the idea behind the synthetic approach is to furnish the subject of geometry with (...) a purely geometric foundation in which the theorems are then deduced by purely logical means from an initial body of postulates. The most familiar examples of the synthetic geometry are classical Euclidean geometry and the synthetic projective geometry introduced by Desargues in the 17th century and revived and developed by Carnot, Poncelet, Steiner and others during the 19th century. The power of analytic geometry derives very largely from the fact that it permits the methods of the calculus, and, more generally, of mathematical analysis, to be introduced into geometry, leading in particular to differential geometry (a term, by the way, introduced in 1894 by the Italian geometer Luigi Bianchi). That being the case, the idea of a “synthetic” differential geometry seems elusive: how can differential geometry be placed on a “purely geometric” or “axiomatic” foundation when the apparatus of the calculus seems inextricably involved? To my knowledge there have been two attempts to develop a synthetic differential geometry. The first was initiated by Herbert Busemann in the 1940s, building on earlier work of Paul Finsler. Here the idea was to build a differential geometry that, in its author’s words, “requires no derivatives”: the basic objects in Busemann’s approach are not differentiable manifolds, but metric spaces of a certain type in which the notion of a geodesic can be defined in an intrinsic manner. I shall not have anything more to say about this approach. The second approach, that with which I shall be concerned here, was originally proposed in the 1960s by F.. (shrink)

Traditionally, there have been two methods of deriving the theorems of geometry: the analytic and the synthetic. While the analytical method is based on the introduction of numerical coordinates, and so on the theory of real numbers, the idea behind the synthetic approach is to furnish the subject of geometry with a purely geometric foundation in which the theorems are then deduced by purely logical means from an initial body of postulates. The most familiar examples of the synthetic geometry are (...) classical Euclidean geometry and the synthetic projective geometry introduced by Desargues in the 17th century and revived and developed by Carnot, Poncelet, Steiner and others during the 19th century. The power of analytic geometry derives very largely from the fact that it permits the methods of the calculus, and, more generally, of mathematical analysis, to be introduced into geometry, leading in particular to differential geometry (a term, by the way, introduced in 1894 by the Italian geometer Luigi Bianchi). That being the case, the idea of a “synthetic” differential geometry seems elusive: how can differential geometry be placed on a “purely geometric” or “axiomatic” foundation when the apparatus of the calculus seems inextricably involved? To my knowledge there have been two attempts to develop a synthetic differential geometry. The first was initiated by Herbert Busemann in the 1940s, building on earlier work of Paul Finsler. Here the idea was to build a differential geometry that, in its author’s words, “requires no derivatives”: the basic objects in Busemann’s approach are not differentiable manifolds, but metric spaces of a certain type in which the notion of a geodesic can be defined in an intrinsic manner. I shall not have anything more to say about this approach. The second approach, that with which I shall be concerned here, was originally proposed in the 1960s by F. W. Lawvere, who was in fact striving to fashion a decisive axiomatic framework for continuum mechanics.. (shrink)

Faut-il lire Les deux sources de la morale et de la religion comme la suite de L’évolution créatrice où sont suggérées des questions d’ordre moral et religieux mais laissées là comme « pierre d’attente » ? Ce n’est pas une théodicée qui s’élabore dans le dernier ouvrage de Bergson et sa continuité avec L’évolution créatrice est sans doute à rechercher ailleurs. Elle pourrait notamment être envisagée à partir de « l’application » à la théorie sociale des Deux sources du second (...) principe de la thermodynamique de Carnot, interprété par Bergson au troisième chapitre de L’évolution créatrice. Ce principe serait le lien implicite entre l’ouvrage de 1907 et celui de 1932.Can we read The Two Sources of Morality and Religion as a logical follow-up to Creative Evolution, since, in the latter work, there is place for glimpses on ethical and religious matters ? The present paper shows that The Two Sources – in no way a theodicy – depends on Creative Evolution for a methodological reason. The Two Sources « applies » to the social theory Bergson’s interpretation of Carnot’s second law of thermodynamics, such as it is presented in the third chapter of Creative evolution. This interpretation thus becomes the unseen link between the 1907 and 1932 books. (shrink)

I characterize Bishop's constructive mathematics as an alternative to classical mathematics, which makes use of the actual infinity. From the history an accurate investigation of past physical theories I obtianed some ones - mainly Lazare Carnot's mechanics and Sadi Carnot's thermodynamics - which are alternative to the dominant theories - e.g. Newtopn's mechanics. The way to link together mathematics to theoretical physics is generalized and some general considerations, in particualr on the geoemtry in theoretical physics, are obtained.that.

A la fin du XIXe siècle, beaucoup de physiciens pensaient être arrivés au bout de leur discipline. La gravitation de Newton, la thermodynamique de Carnot, les équations de Maxwell : on pensait avoir tout compris ou presque. Il restait bien quelques observations inexpliquées, que l'on pensait être des points de détail. Il n'en était rien. Au tout début du XXe siècle un phénomène anodin allait conduire les physiciens à la découverte des rayons cosmiques, ces particules extra-terrestres qui bombardent la (...) Terre. Leur étude va les accompagner pendant près d'un siècle et les aider à formuler, à comprendre et à mettre en lumière de nouvelles théories. Pas à pas, l'observation attentive de ces rayons et de leurs propriétés nous guide vers d'étonnantes découvertes comme celle de l'antimatière. Peu à peu, le monde de la physique quantique s'ouvre à nous, servant de base arrière à la physique fondamentale moderne, et repoussant sans cesse les limites de nos connaissances.. C'est cette aventure scientifique et humaine que nous raconte Antoine Letessier Selvon qui mêle avec talent la grande épopée historique au récit de son expérience personnelle et de son quotidien de chercheur. (shrink)

ABSTRACT Robert Owen’s ideas and achievements largely shaped French republicanism in the 1830s and 1840s, particularly through the action of former Saint-Simonian socialists. This article explores this process, focusing on two of its major actors: the philosophers Pierre Leroux and Jean Reynaud, who joined the Republican Party in 1833. The two friends formulated an ambitious and influential republican doctrine in their Encyclopédie Nouvelle, in which Owen’s philosophy was largely mobilised, most particularly when Leroux theorised his religion de la fraternité on (...) the model of the ‘Religion of Charity’. Furthermore, Reynaud implemented key elements of Owen’s educational principles in the Second Republic’s policies when he became a leading figure of Hippolyte Carnot’s Ministère de l’instruction publique et des cultes in 1848. Finally, as the two men had a great influence on George Sand, sometimes described as Leroux’s ‘prophetess’, they introduced her to Owen’s ideas, which she presented and discussed in her novels. Thus, even if they sometimes remained ambivalent towards the British reformer, Leroux and Reynaud introduced parts of his thought and ideals into French republicanism, be it in terms of ideology, policies, or literary mythologies. (shrink)

Se realiza una revisión bibliográfica con el objetivo de analizar los diferentes códigos éticos y deontológicos internacionales, regionales y nacionales de los que se nutre la especialidad de psiquiatría. Se concluye que el comportamiento ético se basa en el sentido de la responsabilidad individual de cada psiquiatra hacia cada paciente y en la capacidad de ambos para determinar cuál es la conducta correcta y más apropiada. Las normas externas y las directrices, tales como los códigos de conducta profesional, las aportaciones (...) de la ética y de las normas legales, no garantizan por sí solas la práctica ética de la medicina, pero constituyen un importante marco referencial. A literature review was performed with the objective of analyzing the various international, regional and national ethical and deontological codes that the psychiatry specialty feeds on. It is concluded that ethical behavior is based on the sense of individual responsibility of each psychiatrist to each patient and the ability of both to determine what the correct and appropriate behavior is. External standards and guidelines, such as professional codes of conduct, the study of ethics and legal standards alone do not guarantee the ethical practice of medicine but are an important framework. (shrink)

In 1824 Sadi Carnot published Réflexions sur la Puissance Motrice du Feu in which he founded almost the entire thermodynamics theory. Two years after his death, his friend Clapeyron introduced the famous diagram PV for analytically representing the famous Carnot’s cycle: one of the main and crucial ideas presented by Carnot in his booklet. Twenty-five years later, in order to achieve the modern version of the theory, Kelvin and Clausius had to reject the caloric hypothesis, which had (...) influenced a few of Carnot’s arguments. Relying on the possibility of studying the history of science by means of logical investigation, in this paper I shall propose an historical/epistemological research on Sadi Carnot’s original thermodynamics theory in which the French scientist presents more than two principles, all of which are expressed by double negated sentences (generally speaking) within non-classical logic. (shrink)

In this paper we discuss in some depth the main theorems pertaining to Carnot’s theory of transversals, their initial reception by Servois, and the applications that Brianchon made of them to the theory of conic sections. The contributions of these authors brought the long-forgotten theorems of Desargues and Pascal fully to light, renewed the interest in synthetic geometry in France, and prepared the ground from which projective geometry later developed.

Lazare Carnot was the unique example in the history of science of someone who inadvertently owed the scientific recognition he eventually achieved to earlier political prominence. He and his son Sadi produced work that derived from their training as engineers and went largely unnoticed by physicists for a generation or more, even though their respective work introduced concepts that proved fundamental when taken up later by other hands. There was, moreover, a filial as well as substantive relation between the (...) work of father and son. Sadi applied to the functioning of heat engines the analysis that his father had developed in his study of the operation of ordinary machines. Specifically, Sadi's idea of a reversible process originated in the use his father made of geometric motions in the analysis of machines in general. (shrink)

I explore some of the ways that assumptions about the nature of substance shape metaphysical debates about the structure of Reality. Assumptions about the priority of substance play a role in an argument for monism, are embedded in certain pluralist metaphysical treatments of laws of nature, and are central to discussions of substantivalism and relationalism. I will then argue that we should reject such assumptions and collapse the categorical distinction between substance and property.

We present historical and epistemological notes on the relationships between Chemistry–Physics as dating back to two scientific revolutions: Lavoisier’s Traité Élémentaire de Chimie (1789) and by Sadi Carnot’s Réflexions sur la Puissance Motrice du Feu (1824). Their scientific paradigms and mathematical interpretations of chemical and physical phenomena did not made use of infinitesimal analysis as, i.e., exposed within mechanics and, generally speaking, they were totally different from notable Newtonian paradigm survived until to 19th century. An anomaly was, and two (...) revolutions were produced. (shrink)

Our concern is in explaining how and why models give us useful knowledge. We argue that if we are to understand how models function in the actual scientific practice the representational approach to models proves either misleading or too minimal. We propose turning from the representational approach to the artefactual, which implies also a new unit of analysis: the activity of modelling. Modelling, we suggest, could be approached as a specific practice in which concrete artefacts, i.e., models, are constructed with (...) the help of specific representational means and used in various ways, for example, for the purposes of scientific reasoning, theory construction and design of experiments and other artefacts. Furthermore, in this activity of modelling the model construction is intertwined with the construction of new phenomena, theoretical principles and new scientific concepts. We will illustrate these claims by studying the construction of the ideal heat engine by Sadi Carnot. (shrink)

Comment fonctionne l’image sur le vase François ? Parmi les associations thématiques ou formelles que François Lissarague met en évidence sur ce cratère, on relèvera ici celles qui établissent un rapport entre l’épopée et l’histoire, notamment celle que vit Athènes depuis sa refondation par Solon.The Athens of Solon on the François Vase. How does the François Vase function? Among the thematic and formal associations, underlined by François Lissarague, this study emphasises those establishing a connection between the epic and history, notably (...) Athenian history since the Solonian “refoundation”. (shrink)

S'il est un point que les réflexions contemporaines sur le temps ont mis en relief et inscrit profondément dans notre conscience, c'est que l'avenir qu'on espère dépend directement du présent qu'on réalise. Telle est notre attitude en face du présent, telle elle sera inéluctablement en face de l'avenir; et donc l'avenir lui-même, puisque ce dernier n'est rien sinon un présent caché encore, au cœur d'un présent déjà actuel, et explicite. Il est en effet de l'essence même de notre condition humaine (...) d'avoir un présent structuré et comme stratifié. Certes on peut imaginer le présent comme un point sans épaisseur, comme la limite évanescente entre un segment de ligne qui marque le passé à jamais révolu, et l'avenir qui se meut vers nous pour basculer inexorablement vers le non-être en franchissant ce présent. Mais cette image, utile pour bien des tâches, ne correspond d'aucune manière à la réalité vivante de la conscience humaine et des activités qui lui sont propres. Nous sommes dans le présent ce que nous sommes et ce que, en un sens, nous croyons pouvoir dire que nous avons été. Une grande partie de ce que nous appelons le passé, notre passé personnel et sans doute notre passé spécifique, est présent, non seulement à titre de souvenir, pouvant être, ou non, évoqué, mais à titre de schéma dynamique modifiant notre être-au-monde, notre présente réaction au réel le plus réel, à la situation où nous avons à déployer notre activité. (shrink)

1. Falsafat al-rūḥ -- 2. Falsafat al-ʻaqūl -- 3. Raḥīq al-nafs -- 4. al-Qadāʼ wa-al-qadar.

Le philosophe Jean Baudrillard (1929-2007) a-t-il vraiment existé? Que reste-t-il de lui? "Une élégance certaine de la pensée", affirme l'un de ses meilleurs interprètes, François L'Yvonnet. Le philosophe de La Société de consommation, des Stratégies fatales et des Cool Memories s'attachait à l'idée du fragment comme mode de pensée : car dans le détail, tout est parfait, c'est dans sa reproduction que tout se complique. François L'Yvonnet explore cinq fragments de la philosophie de Jean Baudrillard et de sa biographie pour (...) mieux saisir l'éclat et la jubilation d'une pensée toujours vivante et contemporaine. (shrink)

RésuméLa notion de «rationalité de l'Univers » a varié au cours du temps, le long dialogue de l'esprit et de la nature ayant toujours abouti à ce que Le Roy appelait « l'évolution de l'évidence et la plasticité de la raison ».L'échec de l'explication mécanique de l'Univers a conduit James Jeans à déclarer que le monde ressemble plutôt « à une grande pensée » qu'à une grande machine », car on ne peut en donner qu'une description mathématique. En réalité, la (...) physique moderne n'est ni plus ni moins mathématique que l'ancienne; elle est seulement plus générale. James Jeans confond les mathématiques pures et les mathématiques appliquées.Eddington prétend déduire les lois générales et les constantes physiques de la nature de considérations épistémologiques a priori. C'est un retour à Kant. Malheureusement les postulate dont il part comme évidents n'ont point paru tels au XVIIe siècle et n'ont été admis que sous la contrainte de l'expérience. Sa théorie ne prévoit ni les neutrons ni les mésons. Elle est vouée à l'échec.La possibilité de trouver un formalisme mathématique applicable à un domaine expérimental ne préjuge en rien la rationalité de l'Univers, car un mathématicien habile sera toujours capable de faire rentrer même un monde « erratique » dans un vêtement mathématique approprié. (shrink)

L'article explore la notion wébérienne de «domination rationnelle» comme outil pour analyser les rapports entre les efforts de gestion des populations indigènes par l'État colonial, et le développement d'une forme spécifique de rationalité scientifique, prenant pour objet ces populations: les savoirs anthropologiques. En s'appuyant sur le cas de l'Afrique coloniale française, on s'efforce de montrer comment les dimensions d'instrumentation (avec la production d'instruments d'identification et de compréhension) et de légitimation sont essentielles dans l'émergence de savoirs sur les sociétés et les (...) cultures indigènes, d'abord au sein des appareils administratifs, mais aussi dans les institutions savantes métropolitaines. L'appui au développement de la science de l'homme se fait dans le cadre de projets de « rationalisation » de la colonisation qui rapprochent des savants et des réformateurs liés à l 'École coloniale, voulant redéfinir la profession d'administrateur colonial comme «spécialiste des indigènes». (shrink)

Le but de ce texte est de mettre en évidence les équi­valences entre la façon dont le concept de conatus résout, dans l'Éthique, le problème de l'unité modale complexe. en rendant consis­tant le concept de chose singulière en tant que celle-ci doit être consi­dérée comme un légitime sujet d'attribution d'états, et la façon dont ce même concept dessine le rapport cognitif de l'esprit avec lui-même, rapport par lequel l'esprit se saisit comme sujet de ses états et qui ca­ractérise la notion (...) moderne de subjectivité. Ainsi, en éclairant cet as­pect du concept spinoziste de chose singulière. on comprendra aussi, de façon indirecte, l'une des conditions par lesquelles les choses peuvent, dans la doctrine spinoziste, devenir des objets ou des signes pour la connaissance humaine. (shrink)

Suppose that the ultimate point of ethics is to make the world a better place. If it is, we must face the question: better in what respect? If the good is prior to the right — that is, if the rationale for all requirements of the right is that they serve to further the good in one way or another — then what is this good? Is there a single fundamental value capable of underlying and unifying all of our moral (...) categories? If so, how might it defeat the claims of rival candidates for this role? If not, is there instead a plurality of basic goods, each irreducible to any of the others? In that case, how do they fit together into a unified picture of the moral life? These are the questions I wish to address, in a necessarily limited way. To many the questions will seem hopelessly old-fashioned or misguided. Some deontologists will wish to reverse my ordering of the good and the right, holding that the right constrains acceptable conceptions of the good. For many contractarians, neither the good nor the right will seem normatively basic, since both are to be derived from a prior conception of rationality. Finally, some theorists will reject the classification of moral theories in terms of their basic normative categories, arguing that the whole foundationalist enterprise in ethics should be abandoned. In the face of these challenges to the priority of the good, and in light of the many current varieties of moral skepticism and relativism, I cannot provide a very convincing justification for raising the questions I intend to discuss. (shrink)