Proof Theory History and Philosophical Significance
hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of
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SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Managing Editor:
JAAKKO HINTIKKA, Boston University Editors: DIRK VAN DALEN, University of Utrecht, The Netherlands DONALD DAVIDSON, University of California, Berkeley THEO A.F. KUIPERS, University of Groningen, The Netherlands PATRICK SUPPES, Stanford University, California JAN WOLENSKI, iagiellonian University, Krakow, Poland
VOLUME 292
PROOF THEORY History and Philosophical Significance Edited by
VINCENT F. HENDRICKS University of Copenhagen. Denmark
STIG ANDUR PEDERSEN and KLAUS FROVIN J0RGENSEN University of Roskilde, Denmark
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A c.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-5553-8
ISBN 978-94-017-2796-9 (eBook)
DOI 10.1007/978-94-017-2796-9
Printed onacid-free paper
All Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2000 Softcover reprint of the hardcover 1st edition 2000 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.
CONTENTS Preface ................................................................. ix Contributing Authors ................................................. , xi HENDRICKS, PEDERSEN AND J0RGENSEN / Introduction .......... 1 PART 1. REVIEW OF PROOF THEORY SOLOMON FEFERMAN / Highlights in Proof Theory ................ , 11 1. Review of Hilbert's Program and Finitary Proof Theory ......... , 2. Results of Finitary Proof Theory via Gentzen's L-Calculi ......... 3. Shifting Paradigms .............................................. 4. Countably Infinitary Methods (Getting the Most Out of Logic) ... Notes .............................................................. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
11 14 21 25 29 29
PART 2. THE BACKGROUND OF HILBERT'S PROOF THEORY LEO CORRY / The Empiricist Roots of Hilbert's Axiomatic Approach 35 1. Introduction.............................................. . . . . . .. 2. Heinrich Hertz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. Carl Neumann. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4. Paul Volkman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5. Physics and Geometry in Hilbert's Early Courses ................. 6. Grundlagen der Geometrie and its Aftermath. . . . . . . . . . . . . . . . . . .. 7. Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Notes .............................................................. References. . . . . . . . . . . . . . . . . .
