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A Companion to Philosophical Logic Blackwell Companions to Philosophy A Companion to Philosophical Logic Edited by DALE JACQUETTE A Companion to Philosophical Logic Blackwell Companions to Philosophy This outstanding student reference series offers a comprehensive and authoritative survey of philosophy as a whole. Written by today’s leading philosophers, each volume provides lucid and engaging coverage of the key figures, terms, topics, and problems of the field. Taken together, the volumes provide the ideal basis for course use, represent- ing an unparalleled work of reference for students and specialists alike. Already published in the series 20. A Companion to Analytic Philosophy Edited by A. P. Martinich and David Sosa 1. The Blackwell Companion to Philosophy, 21. A Companion to Genethics Second Edition Edited by Justine Burley and John Harris Edited by Nicholas Bunnin and Eric Tsui-James 22. A Companion to Philosophical Logic Edited by Dale Jacquette 2. A Companion to Ethics 23. A Companion to Early Modern Edited by Peter Singer Philosophy 3. A Companion to Aesthetics Edited by Steven Nadler Edited by David Cooper 24. A Companion to Philosophy in the 4. A Companion to Epistemology Middle Ages Edited by Jonathan Dancy and Ernest Sosa Edited by Jorge J. E. Gracia and 5. A Companion to Contemporary Political Timothy B. Noone Philosophy 25. A Companion to African-American Edited by Robert E. Goodin and Philip Pettit Philosophy 6. A Companion to Philosophy of Mind Edited by Tommy L. Lott and Edited by Samuel Guttenplan John P. Pittman 7. A Companion to Metaphysics 26. A Companion to Applied Ethics Edited by Jaegwon Kim and Ernest Sosa Edited by R. G. Frey and Christopher Heath Wellman 8. A Companion to Philosophy of Law and Legal Theory 27. A Companion to the Philosophy of Edited by Dennis Patterson Education Edited by Randall Curren 9. A Companion to Philosophy of Religion Edited by Philip L. Quinn and Charles Taliaferro 28. A Companion to African Philosophy Edited by Kwasi Wiredu 10. A Companion to the Philosophy of Language Edited by Bob Hale and Crispin Wright 29. A Companion to Heidegger Edited by Hubert L. Dreyfus and 11. A Companion to World Philosophies Mark A. Wrathall Edited by Eliot Deutsch and Ron Bontekoe 30. A Companion to Rationalism 12. A Companion to Continental Philosophy Edited by Alan Nelson Edited by Simon Critchley and William Schroeder 31. A Companion to Ancient Philosophy Edited by Mary Louise Gill and 13. A Companion to Feminist Philosophy Pierre Pellegrin Edited by Alison M. Jaggar and Iris Marion Young 32. A Companion to Pragmatism Edited by John R. Shook and 14. A Companion to Cognitive Science Joseph Margolis Edited by William Bechtel and George Graham 33. A Companion to Nietzsche 15. A Companion to Bioethics Edited by Keith Ansell Pearson Edited by Helga Kuhse and Peter Singer 34. A Companion to Socrates 16. A Companion to the Philosophers Edited by Sara Ahbel-Rappe and Edited by Robert L. Arrington Rachanar Kamtekar 17. A Companion to Business Ethics 35. A Companion to Phenomenology and Edited by Robert E. Frederick Existentialism 18. A Companion to the Philosophy of Science Edited by Hubert L Dreyfus and Edited by W. H. Newton-Smith Mark A Wrathall 19. A Companion to Environmental Philosophy Edited by Dale Jamieson Blackwell Companions to Philosophy A Companion to Philosophical Logic Edited by DALE JACQUETTE © 2002, 2006 by Blackwell Publishing Ltd BLACKWELL PUBLISHING 350 Main Street, Malden, MA 02148-5020, USA 9600 Garsington Road, Oxford OX4 2DQ, UK 550 Swanston Street, Carlton, Victoria 3053, Australia The right of Dale Jacquette to be identified as the Author of the Editorial Material in this Work has been asserted in accordance with the UK Copyright, Designs, and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs, and Patents Act 1988, without the prior permission of the publisher. First published 2002 First published in paperback 2006 by Blackwell Publishing Ltd 1 2006 Library of Congress Cataloging-in-Publication Data A companion to philosophical logic/edited by Dale Jacquette. p. cm. (Blackwell companions to philosophy ; 22) Includes bibliographical references and index. ISBN 0-631-21671-5 (alk. paper) 1. Logic. I. Jacquette, Dale. II. Series. BC71.C65 2002 160—dc21 2001043236 ISBN-13: 978-0-631-21671-1 (hardback) ISBN-13: 978-1-4051-4575-6 (paperback) ISBN-10: 1-4051-4575-7 (paperback) A catalogue record for this title is available from the British Library. 1 Set in 10 on 12 /2 pt Photina by SNP Best-set Typesetter Ltd, Hong Kong Printed and bound in the United Kingdom by TJ International, Padstow, Cornwall The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp processed using acid-free and elementary chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. For further information on Blackwell Publishing, visit our website: www.blackwellpublishing.com Contents List of Contributors viii Preface xi Acknowledgments xiii Introduction: Logic, Philosophy, and Philosophical Logic – Dale Jacquette 1 Part I Historical Development of Logic 9 11 Ancient Greek Philosophical Logic – Robin Smith 11 12 History of Logic: Medieval – E. P. Bos and B. G. Sundholm 24 13 The Rise of Modern Logic – Rolf George and James Van Evra 35 Part II Symbolic Logic and Ordinary Language 49 14 Language, Logic, and Form – Kent Bach 51 15 Puzzles about Intensionality – Nathan Salmon 73 16 Symbolic Logic and Natural Language – Emma Borg and Ernest Lepore 86 Part III Philosophical Dimensions of Logical Paradoxes 103 17Logical Paradoxes – James Cargile 105 18 Semantical and Logical Paradox – Keith Simmons 115 19 Philosophical Implications of Logical Paradoxes – Roy A. Sorensen 131 Part IV Truth and Definite Description in Semantic Analysis 143 10 Truth, the Liar, and Tarski’s Semantics – Gila Sher 145 11 Truth, the Liar, and Tarskian Truth Definition – Greg Ray 164 12 Descriptions and Logical Form – Gary Ostertag 177 13 Russell’s Theory of Definite Descriptions as a Paradigm for Philosophy – Gregory Landini 194 Part V Concepts of Logical Consequence 225 14 Necessity, Meaning, and Rationality: The Notion of Logical Consequence – Stewart Shapiro 227 15 Varieties of Consequence – B. G. Sundholm 241 16 Modality of Deductively Valid Inference – Dale Jacquette 256 v CONTENTS Part VI Logic, Existence, and Ontology 263 17 Quantifiers, Being, and Canonical Notation – Paul Gochet 265 18 From Logic to Ontology: Some Problems of Predication, Negation, and Possibility – Herbert Hochberg 281 19 Putting Language First: The ‘Liberation’ of Logic from Ontology – Ermanno Bencivenga 293 Part VII Metatheory and the Scope and Limits of Logic 305 20 Metatheory – Alasdair Urquhart 307 21 Metatheory of Logics and the Characterization Problem – Jan Wole´nski 319 22 Logic in Finite Structures: Definability, Complexity, and Randomness – Scott Weinstein 332 Part VIII Logical Foundations of Set Theory and Mathematics 349 23 Logic and Ontology: Numbers and Sets – José A. Benardete 351 24 Logical Foundations of Set Theory and Mathematics – Mary Tiles 365 25 Property-Theoretic Foundations of Mathematics – Michael Jubien 377 Part IX Modal Logics and Semantics 389 26 Modal Logic – Johan van Benthem 391 27 First-Order Alethic Modal Logic – Melvin Fitting 410 28 Proofs and Expressiveness in Alethic Modal Logic – Maarten de Rijke and Heinrich Wansing 422 29 Alethic Modal Logics and Semantics – Gerhard Schurz 442 30 Epistemic Logic – Nicholas Rescher 478 31 Deontic, Epistemic, and Temporal Modal Logics – Risto Hilpinen 491 Part X Intuitionistic, Free, and Many-Valued Logics 511 32 Intuitionism – Dirk van Dalen and Mark van Atten 513 33 Many-Valued, Free, and Intuitionistic Logics – Richard Grandy 531 34 Many-Valued Logic – Grzegorz Malinowski 545 Part XI Inductive, Fuzzy, and Quantum Probability Logics 563 35 Inductive Logic – Stephen Glaister 565 36 Heterodox Probability Theory – Peter Forrest 582 37 Why Fuzzy Logic? – Petr Hájek 595 Part XII Relevance and Paraconsistent Logics 607 38 Relevance Logic – Edwin D. Mares 609 39 On Paraconsistency – Bryson Brown 628 40 Logicians Setting Together Contradictories: A Perspective on Relevance, Paraconsistency, and Dialetheism – Graham Priest 651 Part XIII Logic, Machine Theory, and Cognitive Science 665 41 The Logical and the Physical – Andrew Hodges 667 42 Modern Logic and its Role in the Study of Knowledge – Peter A. Flach 680 43 Actions and Normative Positions: A Modal-Logical Approach – Robert Demolombe and Andrew J. I. Jones 694 vi CONTENTS Part XIV Mechanization of Logical Inference and Proof Discovery 707 44 The Automation of Sound Reasoning and Successful Proof Finding – Larry Wos and Branden Fitelson 709 45 A Computational Logic for Applicative Common LISP – Matt Kaufmann and J. Strother Moore 724 46 Sampling Labeled Deductive Systems – D. M. Gabbay 742 Resources for Further Study 771 Index 776 vii Contributors Kent Bach, Professor of Philosophy, San Francisco State University, California. José A. Benardete, Professor of Philosophy, University of Syracuse, New York. Ermanno Bencivenga, Professor of Philosophy, University of California, Irvine, California. Emma Borg, Lecturer in Philosophy, University of Reading, UK. E. P. Bos, University
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