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Logic Logic is a comprehensive introduction to the major concepts and techniques involved in the study of logic. It explores both formal and philosophical logic and examines the ways in which we can achieve good reasoning. The methods of logic are essential to an understanding of philosophy and are also crucial in the study of mathematics, computing, linguistics and in many other domains. Individual chapters include: • Propositions and arguments • Truth tables • Trees • Conditionality • Natural deduction • Predicate, names and quantifiers • Definite descriptions Logic is an exceptionally clear introduction to the subject and is ideally suited to students taking an introductory course in logic. Greg Restall is Associate Professor in Philosophy at Melbourne University, Australia. Fundamentals of Philosophy Series editor: John Shand This series presents an up-to-date set of engrossing, accurate and lively introductions to all the core areas of philosophy. Each volume is written by an enthusiastic and knowledgeable teacher of the area in question. Care has been taken to produce works that while even-handed are not mere bland expositions, and as such are original pieces of philosophy in their own right. The reader should not only be well informed by the series, but also experience the intellectual excitement of being engaged in philosophical debate itself. The volumes serve as an essential basis for the under-graduate courses to which they relate, as well as being accessible and absorbing for the general reader. Together they comprise an indispensable library of living philosophy. Published: Greg Restall Logic Richard Francks Modern Philosophy Dudley Knowles Political Philosophy Piers Benn Ethics Alexander Bird Philosophy of Science Stephen Burwood, Paul Gilbert and Kathleen Lennon Philosophy of Mind Colin Lyas Aesthetics Alexander Miller Philosophy of Language Forthcoming: Suzanne Stern-Gillet Ancient Philosophy Logic An introduction Greg Restall LONDON AND NEW YORK First published 2006 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN 270 Madison Ave, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2006. “To purchase your own copy of this or any of Taylor & Francis or Routledge's collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2006 Greg Restall All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Restall, Greg, 1969– Logic: an introduction/Greg Restall. p. cm.—(Fundamentals of philosophy) Includes bibliographical references and index. 1. Logic. I. Title. II. Series. BC108.R47 2005 160–dc22 2005015389 ISBN 0-203-64537-5 Master e-book ISBN ISBN 0-203-69367-1 (Adobe e-Reader Format) ISBN 10:0-415-40067-8 (hbk) ISBN 10:0-415-40068-6 (pbk) ISBN 13:9-78-0-415-40067-1 (hbk) ISBN 13:9-78-0-415-40068-8 (pbk) ISBN 0-203-64537-5 Master e-book ISBN ISBN 0-203-69367-1 (Adobe e–Reader Format) ISBN 0-415-40067-8 (Print Edition) To my teachers, and to my students. Contents Acknowledgements ix Introduction 1 5 PART 1 Propositional logic 1 Propositions and arguments 6 2 Connectives and argument forms 14 3 Truth tables 26 4 Trees 40 5 Vagueness and bivalence 57 6 Conditionality 65 7 Natural deduction 75 82 PART 2 Predicate logic 8 Predicates, names and quantifiers 83 9 Models for predicate logic 94 10 Trees for predicate logic 110 11 Identity and functions 125 12 Definite descriptions 137 13 Some things do not exist 144 14 What is a predicate? 155 15 What is logic? 160 Bibliography 164 Index 167 Acknowledgements Many people have contributed to this book. I thank my students, who never fail to come up with new insights each time I teach this material. Two students from my 1998 class, Alicia Moss and David Wilson, went above and beyond the call of duty in collating embarrassingly long lists of errors in the early drafts of this manuscript. I owe special thanks to James Chase, who used a draft of this text in an introductory logic course and who provided many of the exercises and examples. My research assistant Robert Anderson helped find some errors and infelicities of expression in the final draft. I thank my own teachers, especially Rod Girle, Graham Priest and John Slaney. They will each find some of their ideas and attitudes reflected in this text. I will be pleased if I am as able to inspire and enthuse others as my teachers have been able to inspire and enthuse me. Finally, thanks to my family: First, to Christine Parker, whose love and companionship has taught me more than I can express in words. Second, to Zachary Luke Parker Restall, who has been learning to reason just as I have been finishing writing this book. Greg Restall The University of Melbourne [email protected] March 2003