Philosophy And Geometry

Author : L. Magnani
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401096225

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Philosophy and Geometry by L. Magnani Pdf

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 : R. Torretti
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400999091

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Philosophy of Geometry from Riemann to Poincaré by R. Torretti Pdf

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 : Paul Carus
Publisher : Cosimo, Inc.
Page : 149 pages
File Size : 50,6 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 9781596050068

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The Foundations of Mathematics by Paul Carus Pdf

In this brief treatise, Carus traces the roots of his belief in the philosophical basis for mathematics and analyzes that basis after a historical overview of Euclid and his successors. He then examines his base argument and proceeds to a study of different geometrical systems, all pulled together in his epilogue, which examines matter, mathematics, and, ultimately, the nature of God.

Author : André VandenBroeck
Publisher : Inner Traditions
Page : 168 pages
File Size : 45,8 Mb
Release : 1987-06-01
Category : Body, Mind & Spirit
ISBN : 0892811161

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Philosophical Geometry by André VandenBroeck Pdf

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 : Vincenzo de Risi
Publisher : Springer Science & Business Media
Page : 658 pages
File Size : 44,6 Mb
Release : 2007-08-08
Category : Science
ISBN : 9783764379865

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Geometry and Monadology by Vincenzo de Risi Pdf

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 : Lorenzo Magnani
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 52,8 Mb
Release : 2001-05-31
Category : History
ISBN : 0792369335

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Philosophy and Geometry by Lorenzo Magnani Pdf

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 : Remo Bodei
Publisher : University of Toronto Press
Page : 516 pages
File Size : 55,6 Mb
Release : 2018-08-08
Category : Philosophy
ISBN : 9781487517793

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Geometry of the Passions by Remo Bodei Pdf

The passions have long been condemned as a creator of disturbance and purveyor of the temporary loss of reason, but as Remo Bodei argues in Geometry of the Passions, we must abandon the perception that order and disorder are in a constant state of collision. By means of a theoretical and historical analysis, Bodei interprets the relationship between passion and reason as a conflict between two complementary logics. Geometry of the Passions investigates the paradoxical conflict-collaboration between passions and reason, and between individual and political projects. Tracing the roles passion and reason have played throughout history, including in the political agendas of Descartes, Hobbes, and the French Jacobins, Geometry of the Passions reveals how passion and reason may be used as a vehicle for affirmation rather than self-enslavement.

Author : Paul Carus
Publisher : Unknown
Page : 0 pages
File Size : 50,9 Mb
Release : 1908
Category : Geometry
ISBN : LCCN:80031456

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The Foundations of Mathematics. A Contribution to the Philosophy of Geometry by Paul Carus Pdf

Author : Carus Paul
Publisher : Wentworth Press
Page : 146 pages
File Size : 41,6 Mb
Release : 2019-02-28
Category : History
ISBN : 0526375507

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The Foundations of Mathematics; A Contribution to the Philosophy of Geometry by Carus Paul Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Michel Serres
Publisher : Bloomsbury Publishing
Page : 280 pages
File Size : 55,5 Mb
Release : 2017-02-23
Category : Philosophy
ISBN : 9781474281416

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Geometry by Michel Serres Pdf

In this third installment of his classic 'Foundations' trilogy, Michel Serres takes on the history of geometry and mathematics. Even more broadly, Geometry is the beginnings of things and also how these beginnings have shaped how we continue to think philosophically and critically. Serres rejects a traditional history of mathematics which unfolds in a linear manner, and argues for the need to delve into the past of maths and identify a series of ruptures which can help shed light on how this discipline has developed and how, in turn, the way we think has been shaped and formed. This meticulous and lyrical translation marks the first ever English translation of this key text in the history of ideas.

Author : L. Magnani
Publisher : Unknown
Page : 276 pages
File Size : 53,8 Mb
Release : 2001-11-30
Category : Electronic
ISBN : 9401096236

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Philosophy and Geometry by L. Magnani Pdf

Author : Bertrand Russell
Publisher : DigiCat
Page : 211 pages
File Size : 47,9 Mb
Release : 2022-08-15
Category : Fiction
ISBN : EAN:8596547171324

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An essay on the foundations of geometry by Bertrand Russell Pdf

DigiCat Publishing presents to you this special edition of "An essay on the foundations of geometry" by Bertrand Russell. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.

Author : Francesca Biagioli
Publisher : Springer
Page : 239 pages
File Size : 53,7 Mb
Release : 2016-08-22
Category : Philosophy
ISBN : 9783319317793

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Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli Pdf

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.

Author : Paul Carus
Publisher : Forgotten Books
Page : 156 pages
File Size : 50,9 Mb
Release : 2015-06-02
Category : Philosophy
ISBN : 1440059608

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The Foundations of Mathematics by Paul Carus Pdf

Excerpt from The Foundations of Mathematics: A Contribution to the Philosophy of Geometry Finally, he adds what he calls Common Notions which embody some general principles of logic (of pure reason) specially needed in geometry, such as that things which are equal to the same thing are equal to one another; that if equals be added to equals, the wholes are equal, etc. I need not mention here perhaps, since it is a fact of no consequence, that the readings of the several manuscripts vary, and that some propositions (e. g., that all right angles are equal to one another) are now missing, now counted among the postulates, and now adduced as common notions. The commentators of Euclid who did not understand the difference between Postulates and Common Notions, spoke of both as axioms, and even to-day the term Common Notion is mostly so translated. In our modern editions of Euclid we find a statement concerning parallel lines added to either the Postulates or Common Notions. Originally it appeared in Proposition 29 where it is needed to prop up the argument that would prove the equality of alternate angles in case a third straight line falls upon parallel straight lines. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Josette Campbell,Chris Hayhurst
Publisher : The Rosen Publishing Group, Inc
Page : 114 pages
File Size : 44,7 Mb
Release : 2015-07-15
Category : Juvenile Nonfiction
ISBN : 9781499461282

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Euclid by Josette Campbell,Chris Hayhurst Pdf

Euclid, a Greek mathematician, flourished around 300 BCE. It was he who shaped geometry into what it is today. As a result, he became known as the father of geometry. Euclid founded his own school in Alexandria, Egypt, and gained a reputation as an exceptional geometry teacher. The Elements, his thirteen-volume treatise on mathematics and geometry, was considered to be one of the most influential mathematical works in history. Readers consider some of the definitions and postulates from this great work. They also learn about ancient Greek civilization and the renowned Greek mathematicians and philosophers who influenced Euclid's thinking.