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)

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)

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)

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.

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)

Background Professional autonomy, which directly affects the quality of professional nursing in patient care, and cognitive flexibility, which is an important factor for adaptation to change and developing nursing roles, are important concepts for nursing. Research objectives This research was carried out to determine the effect of cognitive flexibility on attitudes towards professional autonomy in nurses. Research design This was a descriptive study. Participants and research context The research was conducted with 415 nurses working in a city hospital of a (...) province, meeting the inclusion criteria and agreeing to participate in the study. A questionnaire form, The Cognitive Flexibility Inventory (CFI), and the Attitude Toward Professional Autonomy Scale for Nurses (APASN) were used to collect data. Ethical considerations Ethical approval was obtained from the university ethics committee before starting the study. Institutional permission was obtained from the city hospital where the study was conducted. Electronic informed consent was obtained from the nurses included in the study. Findings In the study, the mean CFI score was 80.62 ± 11.55 and the mean APASN score was 70.42 ± 18.79. There was a weak positive correlation (r = 0.270; p < 0.05) between CFI and APASN scores. Moreover, the effect of the CFI mean score on the APASN mean score was found to be statistically significant (β = 0.278; p < 0.001). Furthermore, CFI explains 7.7% of APASN. Conclusion In the study, nurses’ attitudes towards professional autonomy and cognitive flexibility scores were found to be at a good level. Cognitive flexibility has a positive effect on attitudes towards professional autonomy. Interventional studies that will increase the level of cognitive flexibility are recommended in the development of nurses' attitudes towards professional autonomy. (shrink)

In _Civilization and Its Discontents_, Freud made abundantly clear what he thought about the biblical injunction, first articulated in Leviticus 19:18 and then elaborated in Christian teachings, to love one's neighbor as oneself. “Let us adopt a naive attitude towards it,” he proposed, “as though we were hearing it for the first time; we shall be unable then to suppress a feeling of surprise and bewilderment.” After the horrors of World War II, the Holocaust, and Stalinism, Leviticus 19:18 seems even (...) less conceivable—but all the more urgent now—than Freud imagined. In _The Neighbor_, three of the most significant intellectuals working in psychoanalysis and critical theory collaborate to show how this problem of neighbor-love opens questions that are fundamental to ethical inquiry and that suggest a new theological configuration of political theory. Their three extended essays explore today's central historical problem: the persistence of the theological in the political. In “Toward a Political Theology of the Neighbor,” Kenneth Reinhard supplements Carl Schmitt’s political theology of the enemy and friend with a political theology of the neighbor based in psychoanalysis. In “Miracles Happen,” Eric L. Santner extends the book's exploration of neighbor-love through a bracing reassessment of Benjamin and Rosenzweig. And in an impassioned plea for ethical violence, Slavoj Žižek’s “Neighbors and Other Monsters” reconsiders the idea of excess to rehabilitate a positive sense of the inhuman and challenge the influence of Levinas on contemporary ethical thought. A rich and suggestive account of the interplay between love and hate, self and other, personal and political, _The Neighbor_ has proven to be a touchstone across the humanities and a crucial text for understanding the persistence of political theology in secular modernity. This new edition contains a new preface by the authors. (shrink)

This book is about the epistemological views and arguments of the early Stoics. It discusses such questions as: How is knowledge possible, and what is it? How do we perceive things and acquire notions of them? Should we rely on arguments? How do we come to make so many mistakes? The author tries to give a comprehensive and conservative account of Stoic epistemology as a whole as it was developed by Chrysippus. He emphasizes how the epistemological views of the Stoics (...) are interrelated among themselves and with views from Stoic physics and logic. There are a number of Stoic views and arguments that we will never know about. But there are passages on Stoic epistemology in Sextus Empiricus, Galen, Plutarch, Cicero, and a few others authors. The book is like a big jigsaw puzzle of these scattered pieces of evidence. (shrink)

Introspective crocodiles and exhibitionist writers, queered gender and temporality, critiques of capitalism and canon, experimental form and technique, speculative storylines traversing the citysca...

Contributed seminar papers on Jaina Philosophy and doctrines.

Новая книга известного философа, историка и индолога Л.В.Шапошниковой — новое слово в осмыслении фигуры И.В.Сталина. Кто он, откуда и какова была цель его жизни — нам предстоит разобраться в этой книге. Если мы не сделаем этого, утверждает автор, то останемся слепыми, верящими в несуществующие мифы и соблазнительные легенды. Личность и деятельность «вождя всех времен и народов» рассматриваются с позиций нового космического мышления, согласно которому исторический процесс является важнейшей составляющей космической эволюции и подчиняется законам Космоса. Центральная тема книги — борьба между (...) Светом и тьмой, которая в ХХ веке обрела острейший и тяжелейший характер и перешла в пространство планеты Земля. Издание адресовано широкому кругу читателей. (shrink)

De 1815 - avec le Congrès de Vienne qui inaugure une ère de Restauration - à mars 1848, avec les répercussions de la révolution de février en Europe, la période du Vormârz ("avant mars") se caractérise, au sein du monde germanique, par une vie intellectuelle d'une particulière effervescence. Les grandes philosophies qui se sont construites pour dépasser Kant, avec Fichte, Schelling et Hegel, autorisent bon nombre de penseurs allemands à considérer l'Allemagne comme étant philosophiquement en avance sur son temps, ou (...) tout au moins à la pointe de la modernité. Cette avance théorique tranche pourtant avec la réalité politique et sociale de l'époque, façonnée par Metternich. Une solution de cette contradiction dans laquelle se trouve l'Allemagne semble alors résider, aux yeux de certains auteurs, dans l'idée suivant laquelle il ne resterait plus à l'Allemagne qu'à réaliser sa philosophie. Le présent ouvrage entend contribuer à l'analyse de la façon dont le thème de la réalisation de la philosophie est élaboré par, ou à partir des réflexions de plusieurs auteurs de l'époque. Il s'agit des Jeunes Hégéliens, et principalement : Eduard Gans, Heinrich Heine, Arnold Ruge, Ludwig Feuerbach, Max Stirner, David Strauss, les frères Bruno et Edgar Bauer, Moses Hess, Michel Bakounine, August von Cieszkowski, Karl Marx et Friedrich Engels."--Page 4 of cover. (shrink)

1. Hŏryŏng, t'ŏng piŏ yŏnghwarhan maŭm -- 2. Ajik tŭrŏnaji anŭn maŭm esŏ chigak i kanŭng han'ga -- 3. Mibal kwa kijil ŭn ŏttŏn kwan'gye in'ga -- 4. Umjiginŭn maŭm kwa koyohan maŭm -- 5. Chigak ŭi sŏnggyŏk kwa kŭ yŏnwŏn e kwanhan munje.

I argue that environmental ignorance is a group-based form of substantive ignorance that is analogous to race-based ignorance, showing that they are structurally and functionally similar and sometimes overlap. While race theorists offer promising solutions toward eliminating race-based ignorance, I argue that something far more is needed in the environmental case. I turn to panpsychism as a possible solution. Though I conclude that it is too radical for most Americans to willingly embrace, I incorporate a notion of “encounter” to argue (...) that an expanded conception of home helps with the conceptual overhaul needed to overcome environmental ignorance. (shrink)

A brief and critical survey of wave-particle duality and nonlocality aspects of light is presented. A recent attempt to establish a reasonable framework for nonlocal realistic theories based on physically sound arguments and a proposed experiment to decide between such theories and the usual interpretation of quantum mechanical formalism are reviewed. It is shown that a nonlocal realistic approach may raise some new questions which could be answered by means of a program based on a sequence of experiments.