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The author, a Nobel Laureate and one of the 20th century's most important logicians, asks and answers basic questions about the intersection of philosophy and higher mathematics. 1897 edition.
An Essay on the Foundations of Geometry was first published in 1897 when Bertrand Russell was 25 years old. It marks his first major foray into analytic philosophy, a movement in which Russell is one of the founding members and figurehead. It provides a brilliant insight into Russell's early philosophical thought and an engaging and authoritative introduction to the philosophical and logical foundations of geometry - a version of which was fundamental to Einstein's theory of relativity. Russell explores and introduces the concepts of geometry and their philosophical implications, including a historical overview of geometrical theory, making it an invaluable resource not only for students of philosophy but anyone interested in the origins of the thought of one of the twentieth century's most important and widely-read philosophers. This Routledge Classics edition includes a new Foreword by Michael Potter.
Excerpt from An Essay on the Foundations of Geometry My thanks are due to Mr G. F. Stout and Mr A. N. Whitehead for kindly reading my proofs, and helping me by many useful criticisms. To Mr Whitehead I owe, also, the inestimable assistance of constant criticism and suggestion throughout the course of construction, especially as regards the philosophical importance of projective Geometry. 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.
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.
An Essay on the Foundations of Geometry by Bertrand Russell: Dive into the world of mathematical philosophy with Bertrand Russell's "An Essay on the Foundations of Geometry." In this thought-provoking work, Russell explores the philosophical underpinnings of geometry, challenging conventional notions and stimulating intellectual inquiry. Key Aspects of the Book "An Essay on the Foundations of Geometry": Philosophy of Mathematics: Bertrand Russell delves into the philosophical questions surrounding the nature of geometry, axioms, and mathematical truth. Educational Inquiry: The book invites readers to engage in critical thinking about the foundations of geometry and the implications for mathematical education. Intellectual Exploration: "An Essay on the Foundations of Geometry" encourages intellectual curiosity and a deeper understanding of the relationship between mathematics and philosophy. Bertrand Russell was a renowned philosopher, logician, and social critic known for his contributions to various fields of philosophy and mathematics. This essay reflects his dedication to the pursuit of knowledge and the exploration of fundamental questions.
An Essay on 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. Bertrand Russell's Preface from the book: The present work is based on a dissertation submitted at the Fellowship Examination of Trinity College, Cambridge, in the year 1895. Section B of the third chapter is in the main a reprint, with some serious alterations, of an article in Mind (New Series, No. 17). The substance of the book has been given in the form of lectures at the Johns Hopkins University, Baltimore, and at Bryn Mawr College, Pennsylvania. My chief obligation is to Professor Klein. Throughout the first chapter, I have found his "Lectures on non-Euclidean Geometry" an invaluable guide; I have accepted from him the division of Metageometry into three periods, and have found my historical work much lightened by his references to previous writers. In Logic, I have learnt most from Mr Bradley, and next to him, from Sigwart and Dr Bosanquet. On several important points, I have derived useful suggestions from Professor James's "Principles of Psychology."
This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.