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Mathematics and Religion: Our Languages of Sign and Symbol is the sixth title published in the Templeton Science and Religion Series, in which scientists from a wide range of fields distill their experience and knowledge into brief tours of their respective specialties. In this volume, Javier Leach, a mathematician and Jesuit priest, leads a fascinating study of the historical development of mathematical language and its influence on the evolution of metaphysical and theological languages. Leach traces three historical moments of change in this evolution: the introduction of the deductive method in Greece, the use of mathematics as a language of science in modern times, and the formalization of mathematical languages in the nineteenth and twentieth centuries. As he unfolds this fascinating history, Leach notes the striking differences and interrelations between the two languages of science and religion. Until now there has been little reflection on these similarities and differences, or about how both languages can complement and enrich each other.
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Mathematics and Religion
Templeton Science and Religion Series In our fast-paced and high-tech era, when visual information seems so dominant, the need for short and compelling books has increased. This conciseness and convenience is the goal of the Templeton Science and Religion Series. We have commissioned scientists in a range of fields to distill their experience and knowledge into a brief tour of their specialties. They are writing for a general audience, readers with interests in the sciences or the humanities, which includes religion and theology. The relationship between science and religion has been likened to four types of doorways. The first two enter a realm of “conflict” or “separation” between these two views of life and the world. The next two doorways, however, open to a world of “interaction” or “harmony” between science and religion. We have asked our authors to enter these latter doorways to judge the possibilities. They begin with their sciences and, in aiming to address religion, return with a wide variety of critical viewpoints. We hope these short books open intellectual doors of every kind to readers of all backgrounds. Series Editors: J. Wentzel van Huyssteen & Khalil Chamcham Project Editor: Larry Witham
Mathematics and Religion Our L a nguag e s of Sig n a nd S ym bol
Javier Leach
Templeton Press
Templeton Press 300 Conshohocken State Road, Suite 550 West Conshohocken, PA 19428 www.templetonpress.org © 2010 by Javier Leach All rights reserved. No part of this book may be used or reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the written permission of Templeton Press. Typeset and designed by Gopa & Ted2, Inc. Library of Congress Cataloging-in-Publication Data Leach, Javier, 1942– Mathematics and religion : our languages of sign and symbol / Javier Leach. p. cm. Includes bibliographical references and index. ISBN-13: 978-1-59947-149-5 (pbk. : alk. paper) ISBN-10: 1-59947-149-3 (pbk. : alk. paper) 1. Mathematics. 2. Religion and science. 3. Signs and symbols. I. Title. BL265.M3L43 2010 201'.6510—dc22 2010008268 Printed in the United States of America 10 11 12 13 14 15 10 9 8 7 6 5 4 3 2 1
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Contents
Preface Chapter 1: Mathematics and Natural Sciences
vii 3
Chapter 2: Metaphysical Language
16
Chapter 3: Origins of Mathematics
35
Chapter 4: Euclid and Beyond
44
Chapter 5: Dawn of Science
55
Chapter 6: Mathematics Formalized
67
Chapter 7: Propositional Logic
93
Chapter 8: Language and Meaning
106
Chapter 9: Science, Langu