Table Of ContentAn Essay on the Foundations
of Geometry
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 philos-
ophy, 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 philo-
sophical implications, including a historical overview of geometrical theory,
making it an invaluable resource not only for students of philosophy but any-
one 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.
Bertrand Russell (1872–1970). A celebrated mathematician and
logician, Russell was and remains one of the most genuinely
widely read and popular philosophers of modern times.
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Bertrand
Russell
An Essay on the Foundations
of Geometry
With a new Foreword by Michael Potter
London and New York
Cover image: billnoll / Getty Images
First published in Routledge Classics 2023
by Routledge
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and by Routledge
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Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2008, 2023 Bertrand Russell Peace Foundation Ltd
Foreword © 2023 Michael Potter
The right of the Bertrand Russell Peace Foundation Ltd to be identified
as author of this work has been asserted by them in accordance with
sections 77 and 78 of the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or reproduced
or utilised in any form or by any electronic, mechanical, or other
means, now known or hereafter invented, including photocopying and
recording, or in any information storage or retrieval system, without
permission in writing from the publishers.
Trademark notice: Product or corporate names may be trademarks
or registered trademarks, and are used only for identification and
explanation without intent to infringe.
First published 1897 by Cambridge University Press
British Library C ataloguing-i n-P ublication Data
A catalogue record for this book is available from the British Library
Library of Congress C ataloging-i n-P ublication Data
A catalog record has been requested for this book
ISBN: 9 78-1 -0 32-3 1264-4 (h bk)
ISBN: 9 78- 1- 032- 31226-2 (p bk)
ISBN: 9 78-1 -0 03-3 0887-4 (e bk)
DOI: 10.4324/9 781003308874
Typeset in Joanna
by codeMantra
Contents
FOREWORD TO THE ROUTLEDGE CLASSICS EDITION ix
PREFACE xvii
Introduction: Our Problem Defined by its Relations to Logic,
Psychology and Mathematics 1
1 A Short History of Metageometry 8
2 Critical Account of Some Previous Philosophical
Theories of Geometry 55
3 Section A: The Axioms of Projective Geometry 117
Section B: The Axioms of Metrical Geometry 144
4 Philosophical Consequences 177
INDEX 201
Foreword to the
Routledge Classics Edition
As a student at Cambridge, Bertrand Russell read mathematics for
three years and moral sciences (philosophy) for one, sitting his fi-
nal exams in 1894. As was usual for anyone wishing to pursue an
academic career (there being at that time no PhD degree), he then
worked on a Fellowship dissertation without formal supervision, re-
ceiving only brief initial guidance from two of his undergraduate su-
pervisors, the philosopher James Ward and the mathematician A. N.
Whitehead. The subject he chose, the philosophical foundations of
geometry, was a development of one of the essays he had written for
Ward as an undergraduate. He submitted the dissertation at Trinity
College in August 1895 and was elected to a Fellowship on that ba-
sis shortly thereafter. He revised the dissertation over the next year
(partly, it seems, in response to criticisms Whitehead had made of its
focus on metrical rather than descriptive geometry) and the Essay on
the Foundations of Geometry was published in May 1897. The book
received some attention, especially in France, where it was the subject
