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Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general `malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.
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PART I
LOGIC, MATHEMATICS AND INFORMATION
BRIDGING THE GAP: PHILOSOPHY, MATHEMATICS, AND PHYSICS
BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE
Editor ROBERT S. COHEN, Boston University
Editorial Advisory Board THOMAS F. GLICK, Boston University ADOLF GRUNBAUM, University of Pittsburgh SAHOTRA SARKAR, Boston University SYLVAN S. SCHWEBER, Brandeis University JOHN J. STACHEL, Boston University MARX W. WARTOFSKY, Baruch College of
the City University of New York
VOLUME 140
BRIDGING THE GAP PHILOSOPHY, MATHEMATICS, AND PHYSICS
Lectures on the Foundations of Science
Edited by GIOVANNA CORSI Department of Philosophy. University of Florence. Italy MARIA LUISA DALLA CHIARA Department of Philosophy. University of Florence. Italy and
GIAN CARLO GHIRARDI Department of Theoretical Physics. University of Trieste. Italy
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
Library of Congress Cataloging-in-Publication Data Bridging the gap: pn1losophy. mathematics. and physics: lectures on the foundations of sCience! edited by Giovanna Corsi. Maria LUisa Dalla Chiara. Gian Carlo Ghirardi. p. cm. -- (Boston studies in the philosophy of SClence ; v. 140) Includes bibliographical references. ISBN 0-7923-1761-0 (HB : aCid-free paper) 1. Science--Phi losophy. I. Corsi. Giovanna. II. Dalla Chiara. Marla Luisa. III. Ghirardl. G. C. IV. Series. 0175.87854 1992 501--oc2G
92-12617
ISBN 0-7923-1761-0
Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
All Rights Reserved
© 1993 Kluwer Academic Publishers
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, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
TABLE OF CONTENTS vii
PREFACE
xi
ACKNOWLEDGEMENTS
PART I: LOGIC, MATHEMATICS AND INFORMATION
CARLO CELLUCCI I Theory of Deduction FABIO BELLISSIMA I An Introduction to Modal Semantics EGON BORGER I Complexity of Logical Decision Problems: An Introduction DAG PRAWITZ I Remarks on Hilbert's Program for the Foundation of Mathematics SOLOMON FEFERMAN I Working Foundations - '91 K. TAlllR SHAH I Minds and Brains, Algorithms and Machines GIUSEPPE LONGO I Remarks on Information and Mind
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