An Essay on the Foundations of Geometry (Classic Reprint) - Couverture souple

Bertrand A. W. Russell

Couverture souple

ISBN 10 : 1330166345 ISBN 13 : 9781330166345

Editeur : Forgotten Books, 2018

Synopsis

Delve into how geometry finds its foundations across logic, psychology, and mathematics. This rigorous study traces the growth of metageometry and its impact on how we understand space, distance, and shape.

Bertrand A. W. Russell’s work blends history, philosophy, and technical insight. It surveys early questions about the nature of space, explores non‑Euclidean ideas, and analyzes how projective and metrical geometry interrelate. The text draws on lectures and scholarly correspondence to map a complex debate about what geometry can claim to prove and what it must assume.

• How metageometry emerged in three creative periods and what each period sought to show about parallels and space


• Connections between geometry, logic, and psychology, including Kant’s and Lotze’s views


• Critical examinations of notable theories and the role of axioms in geometric reasoning


• Arguments about space as subjective, objective, or something in between, and their implications for geometry

Ideal for readers of philosophy of mathematics, logic, and the foundations of geometry who want a careful, historically grounded analysis.

A propos du livre

Présentation de l'éditeur

Excerpt from An Essay on the Foundations of Geometry

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."

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

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1330166345
• ISBN 13: 9781330166345
• Reliure: Broché
• Nombre de pages: 219
• Coordonnées du fabricant: Copytech (UK) Ltd, Trading as Printondemand-worldwide.com; gpsr@podww.com; ; 9 Culley Court; Orton Southgate; Peterborough; Cambridgeshire; PE2 6WA; Royaume-Uni
• Personne responsable: Easy Access System Europe Oü, 16879218; +358405003575; gpsr.requests@easproject.com; ; Mustamäe tee 50; Tallinn; 10621; Estonie