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ISBN:0486495558
Author: Bertrand Russell
ISBN13: 978-0486495552
Title: An Essay on the Foundations of Modern Geometry (Dover Phoenix Editions)
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Language: English
Category: Mathematics
Publisher: Dover Publications (December 15, 2003)
Pages: 224

An Essay on the Foundations of Modern Geometry (Dover Phoenix Editions) by Bertrand Russell



Dover Books Explaining Science and Mathematics. Dover Books on Science. The Foundations of Geometry was first published in 1897, and is based on Russell's Cambridge dissertation as well as lectures given during a journey through the USA. This is the first reprint, complete with a new introduction by John Slater. It provides both an insight into the foundations of Russell's philosophical thinking and an introduction to the philosophy of mathematics and logic. As such it will be an invaluable resource not only for students of philosophy, but also for those interested in Russell's philosophical development.

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by Russell, Bertrand, 1872-1970. Publication date 1897. Topics Geometry - Foundations. Call number 117723764.

The Foundations of Geometry was first published in 1897, and is based on Russell's Cambridge dissertation as well as lectures given during a journey through the USA. This is the first reprint, complete with a new introduction by Professor John Slater. Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, was a Welsh philosopher, historian, logician, mathematician, advocate for social reform, pacifist, and prominent rationalist. Although he was usually regarded as English, as he spent the majority of his life in England, he was born in Wales, where he also died.

Humanism and Terror: An Essay on the Communist Problem. Maurice Merleau-Ponty. The present book belongs to these latter regions in so far as it presupposes a certain elementary knowledge of geometry but avoids on the other hand that field of abstract geometry which hardly requires the aid of any figures for its treatment. To most readers the striking feature of this book will be the method used, as it is not the conventional Cartesian one, but is based on the possibility of representing a point with coordinates x and y by the complex quantity z x jy (j2 - 1) as is already generally done in electrotechnics.

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Bertrand Russell is probably the most important philosopher of mathematics in the 20th century. He brought together his formidable knowledge of the subject and skills as a gifted communicator to provide a classic introduction to the philosophy of mathematics. Over 14 million journal, magazine, and newspaper articles.

Written by a Nobel laureate and one of the 20th century's most important logicians, this classic of science asks and answers a variety of basic questions about the intersection of philosophy and higher mathematics. Although Russell's conclusions are not the generally accepted modern solutions, his work offers exceptionally clear statements of important scientific problems and presents a logically coherent system. It is also a rich mine of insights, expressed with all of the author's usual clarity, precision, and elegantly reasoned analysis. This study is especially valuable for its coverage of the contributions of such thinkers as Kant, Lotse, Vaihinger, Herbart, Helmholtz, Erdmann, and Riemann. 1897 edition. 200 footnotes, mostly bibliographic.
Reviews: 2
Jay
accurate and speedy
Gold Crown
Geometry has been at the heart of western intellectual thinking since the Ancient Greeks. Euclid’s style became the model for thinking, logic and proof. We have suffered from this ever since. This book was Bertrand Russell’s first philosophical book: it could have been his last. Few have read it because it is almost unreadable; it is turgid, dense, excessively academic and deservedly ignored.
This book began life as Russell’s undergraduate dissertation at Cambridge, polished on the US lecture circuit and published in 1897 by The Cambridge University Press. For a perspective on Russell’s life, see my review of “Bertrand Russell – A Life” by Caroline Moorehead. His private education at home involved studying history and mathematics. He was admitted to Trinity College, Cambridge in 1890, where he studied mathematics. This was quite appropriate because this was the subject that Trinity was world-famous for. He graduated seventh in his class but then got his First Class degree in the Moral Sciences – a subject he was later to become infamous for as a prolific author. He was encouraged to write a dissertation as this was the only way for post-graduate study and if successful might result in a paid Trinity Fellowship. One of his teachers (James Ward, a Kantian) suggested writing on the new, controversial subject of Non-Euclidean Geometry (then called ‘metageometry’). He produced his first draft (134 pages) in three months: a testimony to his prolific writing talent. The only manuscript was examined in 1895 by two of his teachers, Ward and Alfred North Whitehead. The book was quite well received in France, where the foundations of mathematics were a hot topic but were largely ignored elsewhere, as too specialized. In fact, even Russell eventually did not view it too highly for in his intellectual biography (“My Philosophical Development”– 1959) he himself considered it “severely negatively”, regarding it as: “somewhat foolish”. In retrospect, he admits that he was first inspired by Kant’s question, ‘how is geometry possible?’, later acknowledging that it had been obsoleted by Einstein’s Theory of General Relativity (1916) and in summary: “I do not think there is anything valid therein.” This later judgment reflected Russell’s eventual position that he was using the ‘scientific method’ that discarded work later shown to deficient in evidence or logic. Philosophically, this was reinforced by Russell’s abandonment of Idealism and his eventual return to his adolescent commitment to the tradition of British Empiricism.