A Philosophical Companion To First-order Logic

A Philosophical Companion to First-Order Logic Edited, with an Overview, by R.I. G. Hughes Hackett Publishing Company, Inc. Indianapolis/Cambridge Copyright © 1993 by Hackett Publishing Company, Inc. All rights reserved Printed in the United States of America 99 98 97 96 95 94 234567 Cover and text design by Dan Kirklin For further information, please address Hackett Publishing Company, Inc. P.O. Box 44937 Indianapolis, Indiana 46244-0937 Library of Congress Cataloging-in-Publication Data A philosophical companion to first-order logic/[ compiled and edited by] R.I.G. Hughes. p. em. Includes bibliographical references, index. ISBN 0-87220-182-1 (alk. paper) ISBN 0-87220-181-3 (pbk.: alk. paper) I. First-order logic. I. Hughes, R.I. G. BC128.P55 1993 160--dc20 93-14456 CIP The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences-Permanence of Paper for Printed Library Materials, ANSI 239.48-1984. @ Contents Preface vii Introductions 1 Introduction W. V. Quine 2 Logical Appraisal P. F. Strawson 6 Propositional Logic: Semantics 3 Do Conditionals Have Truth Conditions? Dorothy Edgington 28 4 What Do 'ct and 'R' Stand for, Anyway? Richard E. Grandy 50 5 Theories of Truth Paul Horwich 62 Propositional Logic: ProofTheory 6 The Justification of Deduction Susan Haack 76 Metalogic 7 Meanings of Implication John Corcoran 8 Truth and Proof Alfred Tarski 85 101 Quantificational Logic: Semantics 9 Kant, Malcolm, and the Ontological Argument Jonathan Bennett 126 10 Quantifiers Michael Dummett 136 11 162 Existence and Quantification W. V. Quine Table of Contents Definite Descriptions 12 The Significance of"On Denoting" Peter Hylton 178 Quantificationa1 Logic: Proof Theory 13a Gentzen's Analysis of First-Order Proofs 13b On the Idea of a General Proof Theory Dag Prawitz 202 212 Overviews 14 What Is Logic? Ian Hacking 225 15 259 On First-Order Logic R.I.G. Hughes Bibliography 291 Index 303 Preface Although this collection of essays can be used in various ways, it was designed to accompany a one-term course in formal first-order logic. Two years ago, when I set out to compile it, I sent off a proposed table of contents, together with a letter explaining the project and a request for comments and suggestions, to about fifty philosophers in North America and elsewhere. The number who responded was very high, too high for me to list every one of them here. My thanks to them all; at my prompting they unearthed papers from bottom drawers, drew my attention to others that I had overlooked, and helped me to make up my mind about those I was already considering. (Nothing reinforces the feeling that a given direction is the way to go quite as effectively as the advice, "I wouldn't do that if I were you.") I apologize to individual correspondents whose favorite essays were left out; how much I owe to them collectively can be gauged by the fact that only five of the selections on my original list have survived. The resulting anthology includes two introductory pieces, eleven papers dealing with specific topics (twelve, if the two b