Bridging the Gap: Philosophy, Mathematics, and Physics Lectures on t

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 `mal

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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

3 39

71 87 99

125 141

PART II: PHYSICS AND PROBABILITY

PAOLO BUDINICH I Axioms and Paradoxes in Special Relativity

GIAN CARLO GHIRARDI / The Quantum Worldview: Its Difficulties and An Attempt To Overcome Them

TULLIO WEBER I Indeterminism, Nonseparability and the Einstein-Podolsky-Rosen Paradox GIANNI CASSINELLI and PEKKA J. LAHTI I Sigma-Convex Structures of the Sets of States and Probability Measures in Quantum Mechanics GIANPIERO CATIANEO I T

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