Space, Number, and Geometry from Helmholtz to Cassirer

Author: Francesca Biagioli

Publisher: Springer

ISBN: 3319317792

Category: Philosophy

Page: 239

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This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

Multiplicity and Ontology in Deleuze and Badiou

Author: Becky Vartabedian

Publisher: Springer

ISBN: 3319768379

Category: Philosophy

Page: 189

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This book approaches work by Gilles Deleuze and Alain Badiou through their shared commitment to multiplicity, a novel approach to addressing one of the oldest philosophical questions: is being one or many? Becky Vartabedian examines major statements of multiplicity by Deleuze and Badiou to assess the structure of multiplicity as ontological ground or foundation, and the procedures these accounts prescribe for understanding one in relation to multiplicity. Written in a clear, engaging style, Vartabedian introduces readers to Deleuze and Badiou’s key ontological commitments to the mathematical resources underpinning their accounts of multiplicity and one, and situates these as a conversation unfolding amid political and intellectual transformations.

Hermann von Helmholtz’s Mechanism: The Loss of Certainty

A Study on the Transition from Classical to Modern Philosophy of Nature

Author: Gregor Schiemann

Publisher: Springer Science & Business Media

ISBN: 1402056303

Category: Philosophy

Page: 284

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Focusing on Hermann von Helmholtz, this study addresses one of the nineteenth century’s most important German natural scientists. Among his most well-known contributions to science are the invention of the ophthalmoscope and grou- breaking work towards formulating the law of the conservation of energy. The volume of his work, reaching from medicine to physiology to physics and epis- mology, his impact on the development of the sciences far beyond German borders, and the contribution he made to the organization and popularization of research, all established Helmholtz’s prominence both in the academic world and in public cultural life. Helmholtz was also one of the last representatives of a conception of nature that strove to reduce all phenomena to matter in motion. In reaction to the increasingly insurmountable difficulties that program had in fulfilling its own standards for s- entific explanation, he developed elements of a modern understanding of science that have remained of fundamental importance to this day.

Scientific Representation

Paradoxes of Perspective

Author: Bas C. van Fraassen

Publisher: OUP Oxford

ISBN: 0191613746

Category: Philosophy

Page: 422

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Bas C. van Fraassen presents an original exploration of how we represent the world. Science represents natural phenomena by means of theories, as well as in many concrete ways by such means as pictures, graphs, table-top models, and computer simulations. Scientific Representation begins with an inquiry into the nature of representation in general, drawing on such diverse sources as Plato's dialogues, the development of perspectival drawing in the Renaissance, and the geometric styles of modelling in modern physics. Starting with Mach's and Poincaré's analyses of measurement and the 'problem of coordination', van Fraassen then presents a view of measurement outcomes as representations. With respect to the theories of contemporary science he defends an empiricist structuralist version of the 'picture theory' of science, through an inquiry into the paradoxes that came to light in twentieth-century philosophies of science. Van Fraassen concludes with an analysis of the complex relationship between appearance and reality in the scientific world-picture.

The Problem of Knowledge

Philosophy, Science, and History Since Hegel

Author: Ernst Cassirer

Publisher: Yale University Press

ISBN: 9780300010985

Category: Philosophy

Page: 334

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"Cassirer employs his remarkable gift of lucidity to explain the major ideas and intellectual issues that emerged in the course of nineteenth century scientific and historical thinking. The translators have done an excellent job in reproducing his clarity in English. There is no better place for an intelligent reader to find out, with a minimum of technical language, what was really happening during the great intellectual movement between the age of Newton and our own."—New York Times.

Mind and Nature

Selected Writings on Philosophy, Mathematics, and Physics

Author: Hermann Weyl

Publisher: Princeton University Press

ISBN: 9781400833320

Category: Mathematics

Page: 272

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Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.

Sense of Space, The

Author: David Morris

Publisher: SUNY Press

ISBN: 0791484599

Category: Philosophy

Page: 220

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The Sense of Space brings together space and body to show that space is a plastic environment, charged with meaning, that reflects the distinctive character of human embodiment in the full range of its moving, perceptual, emotional, expressive, developmental, and social capacities. Drawing on the philosophies of Merleau-Ponty and Bergon, as well as contemporary psychology to develop a renewed account of the moving, perceiving body, the book suggests that our sense of space ultimately reflects our ethical relations to other people and to the place we inhabit. "I like the combination of sober scholarship with imaginative thought and writing. David Morris is fully at home in phenomenology, while being quite knowledgeable of existing and pertinent scientific literature. Having mastered both, he creates a dynamic tension between them, showing how each can fructify the other, albeit in very different ways. The result is truly impressive.

Conquest of Body

Biopower with Biotechnology

Author: Polona Tratnik

Publisher: Springer

ISBN: 3319573241

Category: Science

Page: 100

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This book reflects on the phenomenon of biotechnology and how it affects the body and discusses a number of related issues, including visualization, mediation, and epistemology. The author offers a compelling thesis, arguing that the exploration of the human body has one ultimate aim: to gain knowledge of it and to conquer it. Exploration of body has an intrinsic link to power, since knowledge is constitutive for the power over the body. Ultimately the conquest of body means the power to intervene into life processes. The book breaks new ground with its study of body visualizations, from the Renaissance drawings to the medical imaging. In particular, it investigates their complex mediality. It also considers the extension and the reach of biopower that is now possible thanks to a wide range of engineering applications. The author originally questions the research approach by rethinking the relationship between mental and sensual examination. She takes into consideration the epistemological problem of the two modes of exploration: obtaining knowledge from empirical exploration and projecting that knowledge to the object of exploration.

Order Out of Chaos

Author: Ilya Prigogine,Isabelle Stengers

Publisher: Verso Books

ISBN: 1786631024

Category: Science

Page: 384

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A pioneering book that shows how the two great themes of classic science, order and chaos, are being reconciled in a new and unexpected synthesis. Order Out of Chaos is a sweeping critique of the discordant landscape of modern scientific knowledge. In this landmark book, Nobel Laureate Ilya Prigogine and acclaimed philosopher Isabelle Stengers offer an exciting and accessible account of the philosophical implications of thermodynamics. Prigogine and Stengers bring contradictory philosophies of time and chance into a novel and ambitious synthesis. Since its first publication in France in 1978, this book has sparked debate among physicists, philosophers, literary critics and historians.

EPSA15 Selected Papers

The 5th conference of the European Philosophy of Science Association in Düsseldorf

Author: Michela Massimi,Jan-Willem Romeijn,Gerhard Schurz

Publisher: Springer

ISBN: 331953730X

Category: Science

Page: 358

View: 6998

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This edited collection showcases some of the best recent research in the philosophy of science. It comprises of thematically arranged papers presented at the 5th conference of the European Philosophy of Science Association (EPSA15), covering a broad variety of topics within general philosophy of science, and philosophical issues pertaining to specific sciences. The collection will appeal to researchers with an interest in the philosophical underpinnings of their own discipline, and to philosophers who wish to study the latest work on the themes discussed.

Concepts of Space

The History of Theories of Space in Physics: Third, Enlarged Edition

Author: Max Jammer

Publisher: Courier Corporation

ISBN: 0486166473

Category: History

Page: 288

View: 4808

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Historical surveys consider Judeo-Christian notions of space, Newtonian absolute space, perceptions from 18th century to the present, more. Numerous quotations and references. "Admirably compact and swiftly paced style." — Philosophy of Science.

Foucault’s Strata and Fields

An Investigation into Archaeological and Genealogical Science Studies

Author: Maren Kusch

Publisher: Springer Science & Business Media

ISBN: 9401135401

Category: History

Page: 272

View: 601

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Heinrich Hertz: Classical Physicist, Modern Philosopher

Author: D. Baird,R.I. Hughes,Alfred Nordmann

Publisher: Springer Science & Business Media

ISBN: 9401588554

Category: Science

Page: 324

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The sub-title of this symposium is accurate and, in a curious way, promises more than it states: Classical Physicist, Modem Philosopher. Heinrich Hertz, as the con summate experimentalist of 19th century technique and as brilliant clarifying critic of physical theory of his time, achieved one of the fulfilments but at the same time opened one of the transition points of classical physics. Thus, in his 'popular' lecture 'On the Relations Between Light and Electricity' at Heidelberg in the Fall of 1889, Hertz identified the ether as henceforth the most fundamental problem of physics, as the conceptual mystery but also the key to understanding mass, electric ity, and gravity. Of Hertz's demonstration of electric waves, Helmholtz told the Physical Society of Berlin: "Gentlemen! I have to communicate to you today the most important physical discovery of the century. " Hertz, philosophizing in his direct, lucid, pithy style, once wrote "We have to imagine". Perhaps this is metaphysics on the horizon? In the early pages of his Principles of Mechanics, we read A doubt which makes an impression on our mind cannot be removed by calling it metaphysical: every thoughtful mind as such has needs which scientific men are accustomed to denote as metaphysical. (PM23) And at another place, concerning the terms 'force' and 'electricity' and the alleged mystery of their natures, Hertz wrote: We have an obscure feeling of this and want to have things cleared up.

The Neo-Kantian Reader

Author: Dermot Moran

Publisher: Routledge

ISBN: 9780415452533

Category: Philosophy

Page: 538

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The latter half of the nineteenth and the early part of the twentieth century witnessed a remarkable resurgence of interest in Kant's philosophy in Continental Europe, the effects of which are still being felt today.The Neo-Kantian Reader is the first anthology to collect the most important primary sources in Neo-Kantian philosophy, with many being published here in English for the first time. It includes extracts on a rich and diverse number of subjects, including logic, epistemology, metaphysics, philosophy of science, and transcendental idealism. Sebastian Luft, together with other scholars, provides clear introductions to each of the following sections (to the authors as well as to each text), placing them in historical and philosophical context: the Beginnings of Neo-Kantianism: including the work of Hermann von Helmholtz, Otto Liebman, Friedrich Lange, and Hermann Lotze the Marburg School: including Hermann Cohen, Paul Natorp, and Ernst Cassirer the Southwest School: including Wilhelm Windelband, Heinrich Rickert, Emil Lask, and Hans Vaihinger responses and Critiques: including Moritz Schlick, Edmund Husserl; Rudolf Carnap, and the 'Davos dispute' between Martin Heidegger and Ernst Cassirer. The Neo-Kantian Reader is essential reading for all students of Kant, nineteenth and twentieth century philosophy, history and philosophy of science, and phenomenology, as well as to those studying important philosophical movements such as logical positivism and analytic philosophy and its history.

Symmetry and Complexity

The Spirit and Beauty of Nonlinear Science

Author: Klaus Mainzer

Publisher: World Scientific

ISBN: 9814480819

Category: Science

Page: 448

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' Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity. Contents:Symmetry and Complexity in Early Culture and PhilosophySymmetry and Complexity in MathematicsSymmetry and Complexity in Physical SciencesSymmetry and Complexity in Chemical SciencesSymmetry and Complexity in Life SciencesSymmetry and Complexity in Economic and Social SciencesSymmetry and Complexity in Computer ScienceSymmetry and Complexity in Philosophy and Arts Readership: Upper-level undergraduates, graduate students, researchers, academics, and professionals in interdisciplinary sciences. Keywords:Symmetry;Symmetry Breaking;Complexity;Nonlinear Science;Dynamical System;Chaos;Bifurcation;Fractal;Computational System;Information Dynamics;Philosophy of Science;ArtsKey Features:Valuable insights from natural, social and computer sciencesAttractive pictures and illustrations enhancing the spirit and beauty of nonlinear scienceReviews:“This outstanding book is a general overview of the notion of symmetry and its many connections to the ideas of complexity … The book will be especially useful to the intelligent general reader as well as advanced undergraduate students looking for challenging technical problems to solve, reconfigure, or redefine.”Zentralblatt MATH '

Thought Experiments

Author: Roy A. Sorensen

Publisher: Oxford University Press on Demand

ISBN: 019512913X

Category: Philosophy

Page: 318

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This text analyses a variety of thought experiments, and explores what they are, how they work, and what their positive and negative aspects are. It also sets the theory within an evolutionary framework of advances in experimental psychology.

Between Two Worlds

Memoirs of a Philosopher-Scientist

Author: Mario Bunge

Publisher: Springer

ISBN: 331929251X

Category: Science

Page: 496

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To go through the pages of the Autobiography of Mario Bunge is to accompany him through dozens of countries and examine the intellectual, political, philosophical and scientific spheres of the last hundred years. It is an experience that oscillates between two different worlds: the different and the similar, the professional and the personal. It is an established fact that one of his great loves was, and still is, science. He has always been dedicated to scientific work, teaching, research, and training men and women in multiple disciplines. Life lessons fall like ripe fruit from this book, bringing us closer to a concept, a philosophical idea, a scientific digression, which had since been uncovered in numerous notes, articles or books. Bunge writes about the life experiences in this book with passion, naturalness and with a colloquial frankness, whether they be persecutions, banishment, imprisonment, successes, would-be losses, emotions, relationships, debates, impressions or opinions about people or things. In his pages we pass by the people with whom he shared a fruitful century of achievements and incredible depths of thought. Everything is remembered with sincerity and humor. This autobiography is, in truth, Bunge on Bunge, sharing everything that passes through the sieve of his memory, as he would say. Mario’s many grandchildren are a testament to his proud standing as a family man, and at the age of 96 he gives us a book for everyone: for those who value the memories that hold the trauma of his life as well as for those who share his passion for science and culture. Also, perhaps, for some with whom he has had disagreements or controversy, for he still deserves recognition for being a staunch defender of his convictions.

On the Hypotheses Which Lie at the Bases of Geometry

Author: Bernhard Riemann

Publisher: Birkhäuser

ISBN: 3319260421

Category: Mathematics

Page: 172

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This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.

Abductive Cognition

The Epistemological and Eco-Cognitive Dimensions of Hypothetical Reasoning

Author: Lorenzo Magnani

Publisher: Springer Science & Business Media

ISBN: 3642036317

Category: Computers

Page: 535

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This volume explores abductive cognition, an important but, at least until the third quarter of the last century, neglected topic in cognition. It aims at increasing knowledge about creative and expert inferences.