Author: R. Torretti
Publisher: Springer Science & Business Media
ISBN: 9400999097
Category : Science
Languages : en
Pages : 473
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.
Philosophy of Geometry from Riemann to Poincaré
Author: R. Torretti
Publisher: Springer Science & Business Media
ISBN: 9400999097
Category : Science
Languages : en
Pages : 473
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.
Publisher: Springer Science & Business Media
ISBN: 9400999097
Category : Science
Languages : en
Pages : 473
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.
Beyond Geometry
Author: Peter Pesic
Publisher: Courier Corporation
ISBN: 0486453502
Category : Mathematics
Languages : en
Pages : 226
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.
Publisher: Courier Corporation
ISBN: 0486453502
Category : Mathematics
Languages : en
Pages : 226
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.
Relativity and Geometry
Author: Roberto Torretti
Publisher: Courier Corporation
ISBN: 0486690466
Category : Science
Languages : en
Pages : 417
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.
Publisher: Courier Corporation
ISBN: 0486690466
Category : Science
Languages : en
Pages : 417
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.
Philosophy and Geometry
Author: L. Magnani
Publisher: Springer Science & Business Media
ISBN: 9401096228
Category : Science
Languages : en
Pages : 284
Book Description
Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.
Publisher: Springer Science & Business Media
ISBN: 9401096228
Category : Science
Languages : en
Pages : 284
Book Description
Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.
Poincaré's Philosophy
Author: Elie Zahar
Publisher: Open Court Publishing
ISBN: 9780812694352
Category : Biography & Autobiography
Languages : en
Pages : 276
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.
Publisher: Open Court Publishing
ISBN: 9780812694352
Category : Biography & Autobiography
Languages : en
Pages : 276
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.
Reader's Guide to the History of Science
Author: Arne Hessenbruch
Publisher: Taylor & Francis
ISBN: 9781884964299
Category : History
Languages : en
Pages : 986
Book Description
First Published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.
Publisher: Taylor & Francis
ISBN: 9781884964299
Category : History
Languages : en
Pages : 986
Book Description
First Published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.
Galileo Unbound
Author: David D. Nolte
Publisher: Oxford University Press
ISBN: 0192528505
Category : Science
Languages : en
Pages : 384
Book Description
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Publisher: Oxford University Press
ISBN: 0192528505
Category : Science
Languages : en
Pages : 384
Book Description
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Categories for the Working Philosopher
Author: Elaine M. Landry
Publisher: Oxford University Press
ISBN: 019874899X
Category : Mathematics
Languages : en
Pages : 486
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.
Publisher: Oxford University Press
ISBN: 019874899X
Category : Mathematics
Languages : en
Pages : 486
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.
Geometry in History
Author: S. G. Dani
Publisher: Springer Nature
ISBN: 3030136094
Category : Mathematics
Languages : en
Pages : 759
Book Description
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
Publisher: Springer Nature
ISBN: 3030136094
Category : Mathematics
Languages : en
Pages : 759
Book Description
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
The Heritage of Kazimierz Ajdukiewicz
Author:
Publisher: BRILL
ISBN: 9004457399
Category : Biography & Autobiography
Languages : en
Pages : 400
Book Description
This book presents Kazimierz Ajdukiewicz's philosophy. Ajdukiewicz was one of the most distinguished and important philosophers of the contemporary Poland. He produced important ideas in logic, epistemology, philosophy of language, and ontology. He influenced Polish analytic philosophy very much. The collection gives a general account of Ajdukiewicz philosophy and it is the only full presentation of his ideas available in Western languages. The volume is of interest for everybody working in analytic philosophy.
Publisher: BRILL
ISBN: 9004457399
Category : Biography & Autobiography
Languages : en
Pages : 400
Book Description
This book presents Kazimierz Ajdukiewicz's philosophy. Ajdukiewicz was one of the most distinguished and important philosophers of the contemporary Poland. He produced important ideas in logic, epistemology, philosophy of language, and ontology. He influenced Polish analytic philosophy very much. The collection gives a general account of Ajdukiewicz philosophy and it is the only full presentation of his ideas available in Western languages. The volume is of interest for everybody working in analytic philosophy.