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Handbook of Philosophical Logic. Volume I: Elements of Classical Logic PDF

503 Pages·1983·13.708 MB·English
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Preview Handbook of Philosophical Logic. Volume I: Elements of Classical Logic

HANDBOOK OF PHILOSOPHICAL LOGIC VOLUMEI SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE Managing Editor: J A A K K 0 HI N T I K K A, Florida State University, Tallahassee Editors: DON A L D D A V I D SON, University of California, BerkeZey GABRIEL NUCHELMANS, University of Leyden WE S LE Y C. SAL M 0 N, University of Pittsburgh VOLUME 164 HANDBOOK OF PHILOSOPHICAL LOGIC Volume I: Elements of Classical Logic Edited by D. GABBAY Department of Mathematics and Computer Science, Bar-Ilan University, Israel and F. GUENTHNER Neuphilologische Fakultaet, University of Tuebingen, West Germany D. REIDEL PUBLISHING COMPANY A MEMBER OF THE KLUWER ... ACADEMIC PUBLISHERS GROUP DORDRECHT/BOSTON/LANCASTER Library of Congress Cataloging in Publication Data Main entry under title: Elements of classical logic. (Handbook of philosophicallogicj v. 1) (Synthese libraryj v. 164) Bibliography: p. Includes indexes. 1. Logic-Addresses, essays, lectures. I. Gabbay, Dov M., 1945- . 11. Guenthner, Franz. Ill. Series. BC6.H36 1983 vol. 1 (BC71] 160s (160] 83-4276 Published by D. Reidel Publishing Company, P.O. Box 17,3300 AA Dordrecht, Holland. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 190 Old Derby Street, Hingham, MA 02043, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, Holland. ISBN-I 3:978-94-009-7068-7 eISBN-13:978-94-009-7066-3 DOl: 10.1007/978-94-009-7066-3 4-1290-300 ts All Rights Reserved © 1983 by D. Reidel Publishing Company 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 TO VOLUME I ACKNOWLEDGEMENTS ri PREFACE ~ A NOTE ON NOTATION xiii 1.1. W I L F RID HOD G E S / Elementary Predicate Logic 1 1.2. GO RAN S U ND HOLM / Systems of Deduction 133 1.3. HUG U E S LE B LA N C / Alternatives to Standard First-order Semantics 189 1.4. JO HA N VA N B ENT HEM and KEES DO ETS / Higher-order Logic 275 1.5. ALLEN HAZEN / Predicative Logics 331 1.6. DIRK V AN DALEN / Algorithms and Decision Problems: A Crash Course in Recursion Theory 409 NAMEINDEX ~9 SUB JE C TIN D EX 485 TABLE OF CONTENTS TO VOLUMES 11, Ill, AND IV 495 ACKNOWLEDGEMENTS The preparation of the Handbook of Philosophical Logic was generously supported by the Lady Davis Fund at Bar-Ilan University, Ramat-Gan, Israel and the Werner-Reimers-Stiftung, Bad Homburg, West Germany, which provided us· with the chance of discussing the chapters in the Handbook at various workshops with the contributors. It is a great pleasure to acknowl edge the assistance of these institutions during the preparation of this col lection. We benefitted further from the editorial and personal advice and help from the publisher. Most important of all, we would like to express our thanks to all the contributors to the Handbook for their unlimited goodwill, their professional counsel, as well as their friendly support. They have made the preparation of this collection a stimulating and gratifying enterprise. D. GAB BAY (Bar-Ilan University) F. G U ENT H N E R (University of Tuebingen) PREFACE The aim of the first volume of the present Handbook of Philosophical Logic is essentially two-fold: First of all, the chapters in this volume should provide a concise overview of the main parts of classical logic. Second, these chapters are intended to present all the relevant background material necessary for the understanding of the contributions which are to follow in the next three volumes. We have thought it to be of importance that the connections between classical logic and its 'extensions' (covered in Volume 11) as well as its most important 'alternatives' (covered in Volume Ill) be brought out clearly from the start. The first chapter presents a clear and detailed picture of the range of what is generally taken to be the standard logical framework, namely, predicate (or first-order quantificational) logic. On the one hand, this chapter surveys both propositionai logic and first-order predicate logic and, on the other hand, presents the main metalogical results obtained for them. Chapter 1.1 also contains a discussion of the limits of first-order logic, i.e. it presents an answer to the question: Why has predicate logic played such a formidable role in the formalization of mathematics and in the many areas of philo sophical and linguistic applications? Chapter 1.1 is prerequisite for just about all the other chapters in the entire Handbook, while the other chapters in Volume I provide more detailed discussions of material developed or hinted at in the first chapter. Chapters 1.2 centers on proof-theoretic questions and outlines several well-known frameworks for the development of a proof-theory for predicate logic. The semantic account for the logical systems presented in Chapter 1.1 is essentially model-theoretic; Chapter 1.3 surveys several alternatives to the standard model-theoretic semantics for predicate logic. Chapter 1.4 takes a big step beyond predicate logic by introducing languages where quantification is not only over individuals but also over higher-order entities, such as sets, functions, sets of sets, etc. Various results concerning second-order and higher-order logic as well as relevant material from abstract model theory are pulled together here. ix D. Gabbay and F. Guenthner (eds .), Handbook of Philosophical Logic, Vol. I, ix-xi. © 1983 by D. Reidel Publishing Company. x PREFACE Chapter 1.5 is essentially an introduction to ramified type theory and its philosophical and logical significance. The reason why it is included in the present volume is due to the fact that it covers material which over laps greatly with the contents of all of the volumes of the Handbook. Being most closely connected to the chapter on higher-order logic, it was decided to make it part of Volume I. Finally, Chapter 1.6 is a concise guide to a number of concepts from the theory of algorithms and decidability which will turn up in many later chapters in the discussion of the meta-mathematical properties of the logical systems presented here. In preparing the Handbook of Philosophical Logic, the editors have tried to follow a number of guidelines, the most important of which are the fol lowing. First, the field of philosophical logic being so vast and heterogeneous with roots in general philosophy, mathematical logic and theoretical linguistics to cite just a few, it was never our intention to aim for an exhaustive coverage of all the work done under the term philosophical logic. Most of the domains of investigation not covered in the present volumes were thus excluded on purpose as they seemed to belong more to such related disciplines like the philosophy of science or the philosophy of mathematics. Second, our pref erence has gone from the beginning towards the form of substantial self contained survey essays as opposed to a large number of short articles. The reason for this is twofold: there exist already many short expository surveys of practically all the topics covered in the Handbook, on the other hand, relatively detailed expositions of the main results and problems in the various fields simply cannot be accommodated in the space of a few pages. Third, the division of the Handbook into the present four volumes is not intended to imply a strict and theoretical division of work in philosophical logic into exactly these subareas. On the contrary, the four volumes should rather be regarded as a whole. Neither the place, order of appearance nor the relative length of the various contributions should be taken as indications of the general structure of the entire field of philosophical logic. The Handbook was conceived to be a guide to the many areas of philosophical logic without imposing a particular picture of either their relative merits or status within the field. Fourth and finally, the survey articles in the Handbook should be accessible and useful to researchers and students in a variety of fields. It is hoped that philosophers, logicians, mathematicians, linguists, psychol ogists, computer scientists and many others can fruitfully draw upon the material presented in these volumes and arrive perhaps at the conclusion that these fields are not quite as independent as they might previously have PREFACE xi thought. Although in some cases new results are included in the presentation, the emphasis in every essay is on providing a general survey of the subject in question. The level of sophistication and the required prerequisites are on the whole rather uniform. As pointed out above, it is in addition the essential function of Volume I to put the necessary background for later papers at the reader's disposition. D. M. GABBA Y F. GUENTHNER

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