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Mathematical Undecidability, Quantum Nonlocality And MATHEMATICAL UNDECIDABILITY, QUANTUM NONLOCALITY AND THE QUESTION OF THE EXISTENCE OF GOD MATHEMATICAL UNDECIDABILITY, QUANTUM NONLOCALITY AND THE QUESTION OF THE EXISTENCE OF GOD Edited by ALFRED DRIESSEN Department ofApplied Physics, University ofTwente, Enschede, the Netherlands and ANTOINE SUAREZ The Institute for Interdisciplinary Studies, Geneva and Zurich, Switzerland SPRINGER SCIENCE+BUSINESS MEDIA, B.V. Library ofCongress Cataloging-in-Publication Data MatheMatlcal undecldabl1lty, quantuN nonlocallty and the quest Ion of the exlstence of God I Alfred Drlessen, Antolne Suarez, editors. p. cm. Includes blbliographlcal references and Index. ISBN 978-94-010-6283-1 ISBN 978-94-011-5428-4 (eBook) DOI 10.1007/978-94-011-5428-4 1. PhYS1CS--Phl1osophy. 2. Mathe.atlcs--Phl1osophy. 3. Ouantu. theory. 4. Gud--PfQ~f, Ontologieai. I. Drlessen, Alfred. II. Suarez, Antolne. OC6.M357 1997 530' .01--dc20 96-36621 ISBN 978-94-010-6283-1 Printed on acid-free paper All rights reserved © 1997 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1997 Softcover reprint of the hardcover 1st edition 1997 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. TABLE OF CONTENTS A. DRIESSEN and A. SUAREZ / Preface vii A. DRIESSEN and A. SUAREZ / Introduction Xl PART I: MATHEMATICS AND UNDECIDABILITY 1. H.-C. REICHEL / How can or should the recent developments in mathematics influence the philosophy of mathematics? 3 2. G.J. CHAITIN / Number and randomness: algorithmic information theory - new results on the foundations of mathematics 15 3. E CACACE / Meaning, reality and algorithms: implications of the Turing theorem 27 4. A. SUAREZ / The limits of mathematical reasoning: in arithmetic there will always be unsolved solvable problems 41 5. J.M. SCHINS / Mathematics: a pointer to an independent reality. Penrose's interpretation a/the Godel and Turing theorems 49 PART II: PHYSICS AND NONLOCALITY 6. ET. ARECCHI / A critical approach to complexity and self organization 59 7. J.S. BELL / Indeterminism and nonlocality 83 8. P. PLISKA / Nonlocality and the principle of free experimentation 101 9. A.M. FOX / Optical tests of Bell's theorem 121 v vi TABLE OF CONTENTS 10. A. SUAREZ / Nonlocal phenomena: physical explanation and philosophical implications 143 11. J .M. SCHINS / Quantum theory: a pointer to an independent reality. A discussion ofBernard d' Espagnat' s "veiled reality" 173 PART III: SCIENCE, META-SCIENCE AND THE EXISTENCE OF GOD 12. J. LAEUFFER / Scientism and scientific knowledge of things and God 185 13. P. DAVIES / Physics and the mind of God 193 14. A. DRIESSEN / The question of the existence of God in the book of Stephen Hawking: A brief history of time 203 15. A. DRIESSEN and A. SUAREZ / Final remarks: becoming aware of our fundamental limits in knowing and doing, implications for the question of the existence of God 215 NOTES ON CONTRIBUTORS 219 INDEX 223 PREFACE On January 22, 1990, the late John Bell held at CERN (European Laboratory for Particle Physics), Geneva a seminar organized by the Center of Quantum Philosophy, that at this time was an association of scientists interested in the interpretation of quantum mechanics. In this seminar Bell presented once again his famous theorem. Thereafter a discussion took place in which not only physical but also highly speculative epistemological and philosophical questions were vividly debated. The list of topics included: assumption of free will in Bell's theorem, the understanding of mind, the relationship between the mathematical and the physical world, the existence of unobservable causes and the limits of human knowledge in mathematics and physics. Encouraged by this stimulating discussion some of the participants decided to found an Institute for Interdisciplinary Studies (lIS) to promote philosoph­ ical and interdisciplinary reflection on the advances of science. Meanwhile the lIS has associated its activities with the Swiss foundation, Fondation du Leman, and the Dutch foundation, Stichting Instudo, registered in Geneva and Amsterdam, respectively. With its activities the lIS intends to strengthen the unity between the professional activities in science and the reflection on fun­ damental philosophical questions. In addition the interdisciplinary approach is expected to give a contribution to the progress of science and the socio­ economic development. At present three working groups are active within the lIS, i.e.: - the Center for Quantum Philosophy, - the Wealth Creation and Sustainable Development Group, - the Neural Science Group. Since the talk by John Bell, and encouraged by him in those months before his unexpected death, the Center for Quantum Philosophy of the lIS has organized a number of seminars at CERN and promoted several symposiums and seminars in collaboration with different European University Institutes and Foundations. I ,2 During the holidays around the New Year of 1993 a group of scientists and University students met in the Italian Alps for a symposium on Mathematical Undecidability, Quantum Nonlocality and the Question of I H. Thomas (ed.), NaturherrschaJt, Busse Seewald, Herford, Germany, 1991. 2 H.-Ch. Reichel and E. Pratde la Riba (eds.), NaturwissenschaJt und Weltbild, H61der-Pichler­ Tempsky, Vienna, 1992. A. Driessen and A. Suarez (eds.), Mathematical Undecidability, Quantwn Nonlocality and the Question of the Existence of God, vii-x. © 1997 Kluwer Academic Publishers. viii PREFACE the Existence of God. Each day of this meeting had its introductory lectures, followed by an infonnal discussion. Being present at all presentations and discussions the editors could observe a more than usual interest in the issues dealt with. Especially the manifold of disciplines represented by the attendees, like philosophy, physics, chemistry, mathematics and infonnation science gave rise to unusual observations and remarks. The unceasing interest in the discussion on the relationship between Unde­ cidability, Nonlocality and the Existence of God led the editors to the idea to prepare the present publication based mainly on the contributions of the above mentioned symposium. They are aware that the book cannot claim for any completeness. The experience, however, of the vivid exchange of thoughts in the different meetings justifies a preliminary summary of ideas. It is hoped that with this edition further debates and discussions will be strongly stimulated. The title chosen is intentionally quite provoking. How can mathematics and quantum physics be brought in connection with God? The introductory chapter intends to show the connection. The body of the book is distributed in three parts. The first discusses the nature of mathematical knowledge, complexity and undecidability. Thereafter physics and nonlocality plays a central role. At the end general aspects of science and meta-science are dealt with and brought in relation with the existence of God. The block about mathematics starts with the contribution of Hans-Christian Reichel, from the Institute of Mathematics of the University of Vienna, about the recent developments in mathematics and the relation with the philoso­ phy of mathematics. He discusses several concepts, like meaning, exactness, chaos, incompleteness, experimental mathematics, which ask for a deeper philosophical reflection. Gregory J. Chaitin from IBM Research Division, New York, one of the leading researchers on incompleteness and undecid­ ability, explains why there are fundamental limits to what we will ever be able to understand. Moreover he establishes the somewhat astonishing paral­ lelism between mathematics and statistical mechanics, and associates Godel 's incompleteness theorem with quantum mechanics. The next contribution is written by Filippo Cacace, an infonnation scientist from the University of Napoli, who examines the relation between undecidability and the generali­ ty of a given mathematical problem. His analysis of the implications of the Turing theorem corroborates the existence of limits in man's knowledge of physical reality. Antoine Suarez, physicist and philosopher of the Institute for Interdisciplinary Studies in Zurich, proves in a simple way that in arith­ metic there always will be solvable unsolved problems and raises the question whether such problems refer not to the existence of a superior intelligence outside human mind. In any case, the Kantian view that mathematics is an a priori mode of man's thinking has to be given up. Juleon M. Schins, physicist PREFACE ix from the University of Twente, finishes the first part with a discussion of Roger Penrose's interpretation of the GOdel and Turing theorems.3 The second part on physics and non locality starts with a contribution of F. Tito Arecchi, Director of the National Optics Laboratory at the University of Florence. He discusses the role of the three Cs - catastrophe, chaos and com­ plexity - for science and includes philosophical considerations. Thereafter the transcript is given of the above mentioned lecture by John Bell at CERN on indeterminism and nonlocality. It includes also a selection of the informal one-hour discussion. In the following three contributions, written by physi­ cists, the arguments leading to the Bell inequalities are further explained and an overview of experimental work is presented.
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