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)

The Limits of Free Will presents influential articles by Paul Russell concerning free will and moral responsibility. The problems arising in this field of philosophy, which are deeply rooted in the history of the subject, are also intimately related to a wide range of other fields, such as law and criminology, moral psychology, theology, and, more recently, neuroscience. These articles were written and published over a period of three decades, although most have appeared in the past decade. Among the (...) topics covered: the challenge of skepticism; moral sentiment and moral capacity; necessity and the metaphysics of causation; practical reason; free will and art; fatalism and the limits of agency; moral luck, and our metaphysical attitudes of optimism and pessimism. (shrink)

Recent interest in non-well-founded set theories has been concentrated on Aczel's anti-foundation axiom AFA. I compare this axiom with some others considered by Aczel, and argue that another axiom, FAFA, is superior in that it gives the richest possible universe of sets consistent with respecting the spirit of extensionality. I illustrate how using FAFA instead of AFA might result in an improvement to Barwise and Etchemendy's treatment of the liar paradox.

After Confucius is a collection of eight studies of Chinese philosophy from the time of Confucius to the formation of the empire in the second and third centuries B.C.E. As detailed in a masterful introduction, each essay serves as a concrete example of thick description - an approach invented by philosopher Gilbert Ryle - which aims to reveal the logic that informs an observable exchange among members of a community or society. To grasp the significance of such exchanges, it is (...) necessary to investigate the networks of meaning on which they rely. Paul R. Goldin argues that the character of ancient Chinese philosophy can be appreciated only if we recognize the cultural codes underlying the circulation of ideas in that world. Thick description is the best preliminary method to determine how Chinese thinkers conceived of their own enterprise. Who were the ancient Chinese philosophers? What was their intended audience? What were they arguing about? How did they respond to earlier thinkers, and to each other? Why did those in power wish to hear from them, and what did they claim to offer in return for patronage? Goldin addresses these questions as he looks at several topics, including. (shrink)

Wittgenstein’s philosophical achievement lies in the development of a new philosophical method rather than in the elaboration of a particular philosophical system. Dr Paul Johnston applies this innovative method to the central problems of moral philosophy: whether there can be ‘truth’ in ethics, or what the meaning of objectivity might mean in the context of moral deliberation. Wittgenstein and Moral Philosophy, first published in 1989, represents the first serious and rigorous attempt to apply Wittgenstein’s method to ethics. The conclusions (...) arrived at differ radically from those dominating contemporary ethical discussion, revealing an immense discrepancy between the ethical concepts employed in everyday moral decision-making and the way in which these are discussed by philosophers. Dr Johnston examines ways of eliminating this discrepancy in order to gain a clearer picture of the proper nature of moral claims, and at the same time provides new insights into Wittgenstein’s conception of philosophy. (shrink)

In this wide-ranging interdisciplinary work, Paul W. Kahn argues that political order is founded not on contract but on sacrifice. Because liberalism is blind to sacrifice, it is unable to explain how the modern state has brought us to both the rule of law and the edge of nuclear annihilation. We can understand this modern condition only by recognizing that any political community, even a liberal one, is bound together by faith, love, and identity.Putting Liberalism in Its Place draws (...) on philosophy, cultural theory, American constitutional law, religious and literary studies, and political psychology to advance political theory. It makes original contributions in all these fields. Not since Charles Taylor's The Sources of the Self has there been such an ambitious and sweeping examination of the deep structure of the modern conception of the self.Kahn shows that only when we move beyond liberalism's categories of reason and interest to a Judeo-Christian concept of love can we comprehend the modern self. Love is the foundation of a world of objective meaning, one form of which is the political community. Arguing from these insights, Kahn offers a new reading of the liberalism/communitarian debate, a genealogy of American liberalism, an exploration of the romantic and the pornographic, a new theory of the will, and a refoundation of political theory on the possibility of sacrifice.Approaching politics from the perspective of sacrifice allows us to understand the character of twentieth-century politics, which combined progress in the rule of law with massive slaughter for the state. Equally important, this work speaks to the most important political conflicts in the world today. It explains why American response to September 11 has taken the form of war, and why, for the most part, Europeans have been reluctant to follow the Americans in their pursuit of a violent, sacrificial politics. Kahn shows us that the United States has maintained a vibrant politics of modernity, while Europe is moving into a postmodern form of the political that has turned away from the idea of sacrifice. Together with its companion volume, Out of Eden, Putting Liberalism in Its Place finally answers Clifford Geertz's call for a political theology of modernity. (shrink)

For a standard Finsler F on a manifold M, the domain is the whole tangent bundle T M and the fundamental tensor g is positive-definite. However, in many cases, these two conditions hold in a relaxed form only, namely one has either a psuedo-Finsler metric or a conic Finsler metric. Our aim is twofold. First, we want to give an account of quite a few subtleties that appear under such generalizations, say, for conic pseudo-finsler metrics. Second, we aim to provide (...) some criteria that determine when a pseudo-Finsler metric F obtained as a general homogeneous combination of Finsler metrics and one-forms is again a Finsler-metric -- or, more precisely, that the conic domain on which g remains positive-definite. Such a combination generalizes the known -metrics in different directions. Remarkably, classical examples of Finsler metrics are reobtained and extended, with explicit computations of their fundamental tensors. (shrink)

La 4e de couverture indique : "" La majorité des Français pensait comme Bossuet ; tout d'un coup, les Français pensent comme Voltaire c'est une révolution ", écrit Paul Hazard dans ce livre devenu un classique. De 1680 à 1715 s'affrontent, en effet, les idées les plus contradictoires et les plus puissantes. L'ordre classique, qui avait repris force après la Renaissance, paraissait éternel. Or, vers 1680, tout se met à bouger. Un air extérieur semble souffler dans le solennel édifice (...) ; des esprits ont l'audace de prétendre que les Modernes valent bien les Anciens, que le progrès doit l'emporter sur la tradition, la science sur la foi. " Il s'agissait de savoir si l'humanité continuerait sa route en se fiant aux mêmes guides ou si des chefs nouveaux lui feraient faire volte-face pour la conduire vers d'autres terres promises. " Une époque charnière donc, où l'esprit de doute surgit partout. Le goût des récits de voyage élargit les horizons et ébranle les certitudes acquises ; on discute de la Bible, de l'authenticité des textes sacrés, des mystères ; les libres penseurs font la guerre à la tradition ; on parle de religion naturelle, de mort naturelle, de droit naturel ; on rêve d'une ère de bonheur terrestre fondée sur la raison et sur la science, les philosophes prônent la tolérance. C'est ce formidable bouillonnement d'idées et d'hommes que décrit Paul Hazard, en retraçant en quelque sorte l'histoire des origines de l'Europe contemporaine.". (shrink)

_William Empson: Prophet Against Sacrifice_ provides the most coherent account of Empson's diverse career to date. While exploring the richness of Empson's comic genius, Paul H. Fry serves to discredit the appropriation of his name in recent polemic by the conflicting parties of deconstruction and politicized cultural criticism. He argues that Empson is a larger, more important figure than the orthodox in either camp can acknowledge, deserving to be considered alongside such versatile critics as Walter Benjamin, Kenneth Burke and (...) Roland Barthes. (shrink)

With articles by Maarit Jänterä-Jareborg, Petar Sarcevic, Hans Ulrich Jessurun d'Oliveira, Paul Volken, national reports from Venezuela, Switzerland, China, Hungaria and Germany and news from The Hague as well as texts, materials and recent developments.

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.

It has recently been shown by Vargas, (4) that the passive coordinate transformations that enter the Robertson test theory of special relativity have to be considered as coordinate transformations in a seven-dimensional space with degenerate metric. It has also been shown by Vargas that the corresponding active coordinate transformations are not equal in general to the passive ones and that the composite active-passive transformations act on a space whose number of dimensions is ten (one-particle case) or larger (more than one (...) particle).In this paper, two different (families of) electrodynamics are constructed in ten-dimensional space upon the coordinate free form of the Maxwell and Lorentz equations. The two possibilities arise from the two different assumptions that one can naturally make with respect to the acceleration fields of charges, when these fields are related to their relativistic counterparts. Both theories present unattractive features, which indicates that the Maxwell-Lorentz framework is unsuitable for the construction of an electrodynamics for the Robertson test theory of the Lorentz transformations. It is argued that this construction would first require the formulation of Maxwell-Lorentz electrodynamics in the form of a connection in Finsler space. If such formulation is possible, the sought generalization would consist in simply changing bases in the tangent spaces of the manifold that supports the connection. In addition, the number of dimensions of the space of the Robertson transformations would be ten, but not greater than ten. (shrink)

This paper is part of a symposium on Paul Moser, _Philosophy After Objectivity (Oxford University Press, 1993). The paper identifies and clarifies the main themes of _Philosophy After Objectivity.

The self-portrait of an intellectual reveals his childhood in Vienna, wounds at the Russian front in the German army, encounters with the famous, innumerable love affairs, four marriages, and refusal to accept a "petrified and tyrannical ...

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.

"In this wonderfully engaging and informative collection we hear the voice of a different Paul Bowles. Writing on a wide range of subjects--jazz, film music, classical music, popular music, ethnic music--he is direct, opinionated, incisive, analytical, humorous, and passionate."—Millicent Dillon, author of You Are Not I: A Portrait of Paul Bowles.

Paul Helm is a distinguished philosopher, with particular interests in the philosophy of religion. His work covers some of the most important aspects of the field as it has developed in the last thirty years with particular contributions to metaphysics, religious epistemology and philosophical theology. In celebration of Helm's life's work, Reason in the Service of Faith brings together a range of his essays which reflect these central concerns of his thought. Over thirty of Helm's selected essays and four (...) unpublished articles are gathered into five parts: Metaphilosophical issues, Action, Change and Personal Identity, Epistemology, God and Creation, Providence and Prayer. The volume is prefaced with a short editorial introduction and ends with an extensive bibliography of Helm's published works. Demonstrating the important connection between Helm's theological and philosophical interests across his body of work, this collection is a remarkable resource for scholars of religion, philosophy and theology. (shrink)

Paul and Religion demonstrates the continuing and contemporary relevance of the most important, and most controversial, figure of early Christianity. Paul Gooch interrogates the Pauline writings for their meaning as well as implications for religion as an entire form of life, a stance on the world expressed in distinctive practices. Bringing a philosophical approach to this topic, he connects Paul's ideas to lived experience. In a conversational style, Gooch explores Paul's experience of grace and his dismissal (...) of distinctive markers of religious identity in favour of love as binding together a community. Contrary to common expectations, he finds within Paul's letters material for conversations about issues in our day, such as gender and sexuality. From his close reading of the Letters, Gooch argues that the Pauline religious form of life is not identical with institutional Christianity. Indeed, his conclusions may be welcome to those who belong to other faiths. (shrink)

When Swiss artist Paul Klee died in 1940, he left behind not only paintings that are a testament to his prodigious skill and vision but also a trove of writings and lectures that highlight his impressive intellectual prowess. Paul Klee: Philosophical Vision: From Nature to Art is the fully illustrated catalog accompanying an eponymous exhibition opening in 2012 at the McMullen Museum of Art that focuses on the philosophical depth of Klee's art. Demonstrating how ideas developed in Klee's (...) written work are realized in his paintings, Paul Kleeputs a keen emphasis on the artist as philosopher, both in his theoretical writings and in his artistic works. Klee's philosophy of nature and of the genesis of natural things is explored, as are the ways in which Klee translated these ideas into form, line, and color. His paintings are also decoded to reveal Klee as an astute critic of modern society, taking up topics as various as the impact of technology on art and the political failures of Germany that led to the rise of Hitler and Nazism. The exhibition and catalog will also look at twentieth- and twenty-first-century philosophers who have discussed Klee's work, including Benjamin, Heidegger, Foucault, and Merleau-Ponty, and will articulate the broad impact that Klee's art has had on recent philosophical thought. This book brings together contributions by an international group of scholars and also includes a new translation of Klee's "On Modern Art." A beautiful and rigorous treatment of one of the twentiethcentury's most famous painters, Paul Klee not only reveals the man himself as a thinker and artist, but also creates a larger paradigm for how philosophical ideas shape art, and vice versa. (shrink)

This collection of essays by philosophers and educationalists of international reputation, all published here for the first time, celebrates Paul Hirst's professional career. The introductory essay by Robin Barrow and Patricia White outlines Paul Hirst's career and maps the shifts in his thought about education, showing how his views on teacher education, the curriculum and educational aims are interrelated. Contributions from leading names in British and American philosophy of education cover themes ranging from the nature of good teaching (...) to Wittgensteinian aesthetics. The collection concludes with a paper in which Paul Hirst sets out his latest views on the nature of education and its aims. The book also includes a complete bibliography of works by Hirst and a substantial set of references to his writing. (shrink)

Paul Horwich gives the definitive exposition of a prominent philosophical theory about truth, `minimalism'. His theory has attracted much attention since the first edition of Truth in 1990; he has now developed, refined, and updated his treatment of the subject, while preserving the distinctive format of the book. This revised edition appears simultaneously with a new companion volume, Meaning; the two books demystify central philosophical issues, and will be essential reading for all who work on the philosophy of language.

Paul E. Griffiths argues that most research on the emotions has been as misguided as Aristotelian efforts to study "superlunary objects" - objects...

This is a translation and critical edition of two documents on the Kapp Putsch and the origins of the united-front policy in the German Communist Party. The documents were written by the kpd leader Paul Levi and their titles and dates are, respectively: ‘Letter to the Central Committee of the Communist Party of Germany’ and ‘Open Letter of the Zentrale of the United Communist Party of Germany’. They are a documentary appendix to our essay ‘Paul Levi and the (...) Origins of the United-Front Policy in the Communist International’, published in this issue of Historical Materialism. (shrink)

The format of this Library of Living Philosophers volume differs from that of its fifteen predecessors. Because of Sartre's failing eyesight, it was not possible for him either to read the critical essays or to respond in the usual way to his critics. Nor did he feel able to prepare an autobiography. Thus, in order to collect the material needed for the volume, it was necessary to conduct personal taped interviews with Sartre and then to have those interviews translated, edited, (...) and arranged in an order that would approximate as closely as possible the customary format of the volumes in the Library of Living Philosophers series. Skillfully and conscientiously conducted, the interviews themselves resulted in a unique and valuable document. At the time they occurred, Sartre was in good health except for his near-blindness, and he answered questions in a lively and easy manner. Although he seemed most comfortable when talking autobiographically, he nevertheless responded to many of the philosophical questions raised by the contributors to this volume. (shrink)

This text examines the philosophy of Paul Weiss. Much of Dr Weiss's impact has come through his example, discussions, and such activities as founding and editing the Review of Metaphysics and founding and leading the Metaphysical Society of America.

Paul Ricoeur has been hailed as one of the most important thinkers of the century. Oneself as Another, the clearest account of his "philosophical ethics," substantiates this position and lays the groundwork for a metaphysics of morals.

What was René Girard’s attitude towards philosophy? What philosophers influenced him? What stance did he take in the philosophical debates of his time? What are the philosophical questions raised by René Girard’s anthropology? In this interview, Paul Dumouchel sheds light on these issues.

Paul Thagard describes how his current work in neurophilosophy grew out of a long series of engagements with philosophy, philosophy of science, cognitive science, neural networks, and theoretical neuroscience. Each of these engagements had cumulative advantages over its predecessors. Neurophilosophy is prospering by applying insights about the workings of the brain to central problems in epistemology, metaphysics, and ethics.

Paul Feyerabend's globally acclaimed work, which sparked and continues to stimulate fierce debate, examines the deficiencies of many widespread ideas about scientific progress and the nature of knowledge. Feyerabend argues that scientific advances can only be understood in a historical context. He looks at the way the philosophy of science has consistently overemphasized practice over method, and considers the possibility that anarchism could replace rationalism in the theory of knowledge. -- Amazon.com.