Author: R. Torretti
Publisher: Springer Science & Business Media
ISBN: 9400999097
Category : Science
Languages : en
Pages : 473
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Book Description
Geometry has fascinated philosophers since the days of Thales and Pythagoras. In the 17th and 18th centuries it provided a paradigm of knowledge after which some thinkers tried to pattern their own metaphysical systems. But after the discovery of non-Euclidean geometries in the 19th century, the nature and scope of geometry became a bone of contention. Philosophical concern with geometry increased in the 1920's after Einstein used Riemannian geometry in his theory of gravitation. During the last fifteen or twenty years, renewed interest in the latter theory -prompted by advances in cosmology -has brought geometry once again to the forefront of philosophical discussion. The issues at stake in the current epistemological debate about geometry can only be understood in the light of history, and, in fact, most recent works on the subject include historical material. In this book, I try to give a selective critical survey of modern philosophy of geometry during its seminal period, which can be said to have begun shortly after 1850 with Riemann's generalized conception of space and to achieve some sort of completion at the turn of the century with Hilbert's axiomatics and Poincare's conventionalism. The philosophy of geometry of Einstein and his contemporaries will be the subject of another book. The book is divided into four chapters. Chapter 1 provides back ground information about the history of science and philosophy.
Author: Peter Pesic
Publisher: Courier Corporation
ISBN: 0486453502
Category : Mathematics
Languages : en
Pages : 226
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Book Description
Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincaré, and Cartan.
Author: Roberto Torretti
Publisher: Courier Corporation
ISBN: 0486690466
Category : Science
Languages : en
Pages : 417
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Book Description
Early in this century, it was shown that the new non-Newtonian physics -- known as Einstein's Special Theory of Relativity -- rested on a new, non-Euclidean geometry, which incorporated time and space into a unified "chronogeometric" structure. This high-level study elucidates the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phase of Relativity. After a discussion of Newtonian principles and 19th-century views on electrodynamics and the aether, the author offers illuminating expositions of Einstein's electrodynamics of moving bodies, Minkowski spacetime, Einstein's quest for a theory of gravity, gravitational geometry, the concept of simultaneity, time and causality and other topics. An important Appendix -- designed to define spacetime curvature -- considers differentiable manifolds, fiber bundles, linear connections and useful formulae. Relativity continues to be a major focus of interest for physicists, mathematicians and philosophers of science. This highly regarded work offers them a rich, "historico-critical" exposition -- emphasizing geometrical ideas -- of the elements of the Special and General Theory of Relativity.
Author: Elie Zahar
Publisher: Open Court Publishing
ISBN: 9780812694352
Category : Biography & Autobiography
Languages : en
Pages : 276
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Book Description
Henri Poincare (1854–1912) was one of the greatest mathematicians and philosophers of all time. He founded topology and made important contributions to theoretical physics. Yet despite his numerous achievements Poincare never constructed a systematic philosophy. In this book, Elie Zahar presents Poincare’s work for the first time as a unified system of thought.
Author: Claudio Canaparo
Publisher: Peter Lang
ISBN: 9783039115730
Category : Literary Collections
Languages : en
Pages : 294
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Book Description
This book is about the formation and development of Latin America as name, idea and concept, as well as the wider concepts of location, knowledge and the relationship between them. Latin America is not only a subject or an academic construct, it is also a perspective from which subjectivities are established, knowledge is developed and narratives are produced. This study argues that epistemology cannot exist in abstract terms, despite traditional academic arguments to the contrary. Therefore the author uses 'Latin America' to anchor his more general arguments in a particular location and calls this approach 'geo-epistemology'. The author discusses how the specificity of a particular location can contribute to the establishment of both a method of formulating human knowledge and the boundaries of what can be known. The text explores the relationship between philosophy, geography and geometry, and analyses the notions of science, empire and colonialism. In response to the contemporary debate on 'space of thinking', the author proposes a new concept of 'reversal thinking', which leads to an examination of the roles of language and writing from an epistemic point of view.
Author: Julian Lowell Coolidge
Publisher: Courier Corporation
ISBN: 0486158535
Category : Mathematics
Languages : en
Pages : 484
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Book Description
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
Author: María de Paz
Publisher: Springer Science & Business Media
ISBN: 9401787808
Category : Science
Languages : en
Pages : 195
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Book Description
This volume presents a selection of papers from the Poincaré Project of the Center for the Philosophy of Science, University of Lisbon, bringing together an international group of scholars with new assessments of Henri Poincaré's philosophy of science—both its historical impact on the foundations of science and mathematics, and its relevance to contemporary philosophical inquiry. The work of Poincaré (1854-1912) extends over many fields within mathematics and mathematical physics. But his scientific work was inseparable from his groundbreaking philosophical reflections, and the scientific ferment in which he participated was inseparable from the philosophical controversies in which he played a pre-eminent part. The subsequent history of the mathematical sciences was profoundly influenced by Poincaré’s philosophical analyses of the relations between and among mathematics, logic, and physics, and, more generally, the relations between formal structures and the world of experience. The papers in this collection illuminate Poincaré’s place within his own historical context as well as the implications of his work for ours.
Author: Michael Heidelberger
Publisher: Walter de Gruyter
ISBN: 3110206943
Category : Philosophy
Languages : en
Pages : 385
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Book Description
Naturwissenschaftler und Philosophen haben im Lauf der Wissenschaftsgeschichte unterschiedliche Auffassungen vom Hypothesencharakter empirischer Theorien entwickelt. Der Band widmet sich drei verschiedenen Epochen, in denen der Erkenntnisoptimismus erfolgreicher Wissenschaftspraxis auf ein wachsendes Bewusstsein der Grenzen naturwissenschaftlicher Einsicht trifft: der Frühen Neuzeit (Kopernikus, Kepler, Bacon, Galilei, Descartes, Boyle, Newton, Locke, mit einem Rückblick auf die mittelalterlichen Autoren Maimonides und Gersonides), dem mechanistischen Weltbild des 19. Jahrhunderts (Herschel, Whewell, Mill, C. G. J. Jacobi, Carl Neumann, Boutroux, Ch. S. Peirce, mit einem Rückblick auf Lagrange und d'Alembert) und dem 20. Jahrhundert mit dem Aufkommen der modernen Physik (Hertz, Poincaré, Vaihinger, Duhem, Heisenberg, Popper). Abgerundet wird der Band durch Studien zur Gegenwartsdiskussion des wissenschaftlichen Realismus und den Chancen einer hypothetischen Metaphysik der Natur.
Author: Elaine M. Landry
Publisher: Oxford University Press
ISBN: 019874899X
Category : Mathematics
Languages : en
Pages : 486
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Book Description
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.
Author: Éric Charpentier
Publisher: American Mathematical Soc.
ISBN: 082184718X
Category : Biography & Autobiography
Languages : en
Pages : 410
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Book Description
Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. In this book, twenty world experts present one part of Poincare's extraordinary work. Each chapter treats one theme, presenting Poincare's approach, and achievements.
