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Author: André VandenBroeck
Publisher: Inner Traditions
ISBN: 9780892811168
Category : Body, Mind & Spirit
Languages : en
Pages : 168
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Book Description
Ancient Egyptians and Greeks (up to Euclid) saw in plane geometry much more than land-surveying. For the Greeks, Gaia or Ge (from which our word “geometry” derives) was a universe rather than a planet. Man was the measure of the cosmos and geometry was the expression of this faculty, the discipline through which one studied the unity of cosmic necessity and human thought. For this reason tradition has it that Plato inscribed on the gates of his Academy: “Only geometers enter here.” This aspect of the discipline was lost in modern times until studies such as those of Matila Ghyka rekindled an interest that culminated in R. A. Schwaller de Lubicz’s Pythagorean synthesis. Since it was essentially a rediscovery of unselfconscious modes of thinking, this synthesis did not pose the problem of foundations. Philosophical Geometry originated in the author’s perception of this problem while working with de Lubicz in Grasse, France, in 1960-61. Written in 1972, Philosophical Geometry was conceived as a textbook and took shape in a teaching situation, individual elaboration of theory being the declared aim. Defined as “the activity of establishing a necessary conduct for mind through a set of signs denoting a necessary conduct of facts,” Philosophical Geometry approaches a universal theme to which the existence of every human being contributes a chapter. Philosophical Geometry is, and has been, an avenue toward inscription of such fundamental experience.
Author: André VandenBroeck
Publisher: Inner Traditions
ISBN: 9780892811168
Category : Body, Mind & Spirit
Languages : en
Pages : 168
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Book Description
Ancient Egyptians and Greeks (up to Euclid) saw in plane geometry much more than land-surveying. For the Greeks, Gaia or Ge (from which our word “geometry” derives) was a universe rather than a planet. Man was the measure of the cosmos and geometry was the expression of this faculty, the discipline through which one studied the unity of cosmic necessity and human thought. For this reason tradition has it that Plato inscribed on the gates of his Academy: “Only geometers enter here.” This aspect of the discipline was lost in modern times until studies such as those of Matila Ghyka rekindled an interest that culminated in R. A. Schwaller de Lubicz’s Pythagorean synthesis. Since it was essentially a rediscovery of unselfconscious modes of thinking, this synthesis did not pose the problem of foundations. Philosophical Geometry originated in the author’s perception of this problem while working with de Lubicz in Grasse, France, in 1960-61. Written in 1972, Philosophical Geometry was conceived as a textbook and took shape in a teaching situation, individual elaboration of theory being the declared aim. Defined as “the activity of establishing a necessary conduct for mind through a set of signs denoting a necessary conduct of facts,” Philosophical Geometry approaches a universal theme to which the existence of every human being contributes a chapter. Philosophical Geometry is, and has been, an avenue toward inscription of such fundamental experience.
Author: André VandenBroeck
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 178
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Book Description
Author: Lorenzo Magnani
Publisher: Springer Science & Business Media
ISBN: 9780792369332
Category : History
Languages : en
Pages : 284
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Book Description
The book also ties together the concerns of philosophers of science and cognitive science researchers, 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 covered from a novel combination of both historical and contemporary perspectives."--Jacket.
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: Tim Maudlin
Publisher:
ISBN: 0198701306
Category : Mathematics
Languages : en
Pages : 374
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Book Description
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author: Paul Carus
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 162
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Book Description
Author: Adolf Grunbaum
Publisher: U of Minnesota Press
ISBN: 0816604908
Category : Science
Languages : en
Pages : 394
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Book Description
Geometry and Chronometry in Philosophical Perspective was first published in 1968. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. In this volume Professor Grünbaum substantially extends and comments upon his essay "Geometry, Chronometry, and Empiricism," which was first published in Volume III of the Minnesota Studies in the Philosophy of Science. Commenting on the essay when it first appeared J. J. C. Smart wrote in Mind (England): "In my opinion Adolf Grünbaum's paper ... supersedes nearly all that has been written on the logical status of physical geometry and chronometry." The full text of the essay is given here with the author's extension of it and his discussion of some of the critical comment it has evoked, particularly, a critique published by Hilary Putnam. Adolph Grünbaum is Andrew Mellon Professor of Philosophy at the University of Pittsburgh and the current president of the Philosophy of Science Association.
Author: Vincenzo de Risi
Publisher: Springer Science & Business Media
ISBN: 3764379863
Category : Science
Languages : en
Pages : 658
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Book Description
This book reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in his final years. The work’s main purpose is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics. This is the first ever, comprehensive historical reconstruction of Leibniz’s geometry.
Author: L. Magnani
Publisher: Springer Science & Business Media
ISBN: 9401096228
Category : Science
Languages : en
Pages : 284
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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.
Author: Bertrand Russell
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 221
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Book Description