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LOGIC

Logic: The Basics is a hands-on introduction to the philosophically alive eld of logical inquiry. Covering both classical and non-classical theories, it presents some of the core notions of logic such as validity, basic connectives, identity, free logic and more. This book: introduces some basic ideas of logic from a semantic and philosophical perspective uses logical consequence as the focal concept throughout considers some of the controversies and rival logics that make for such a lively eld. This accessible guide includes chapter summaries and suggestions for further reading as well as exercises and sample answers throughout. It is an ideal introduction for those new to the study of logic as well as those seeking to gain the competence and skills needed to move to more advanced work in logic. Jc Beall is Professor of Philosophy at the University of Connecticut, USA, where he is Director of the UConn Logic Group. His books include Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic with Bas van Fraassen, Logical Pluralism with Greg Restall, and Spandrels of Truth.

THE BASICS

ACTING BELLA MERLIN ANTHROPOLOGY PETER METCALF ARCHAEOLOGY (SECOND EDITION) CLIVE GAMBLE ART HISTORY GRANT POOKE AND DIANA NEWALL THE BIBLE JOHN BARTON BLUES DICK WEISSMAN BUDDHISM CATHY CANTWELL CRIMINAL LAW JONATHAN HERRING CRIMINOLOGY SANDRA WALKLATE ECONOMICS TONY CLEAVER EUROPEAN UNION (SECOND EDITION) ALEX WARLEIGH-LACK FILM STUDIES AMY VILLAREJO FINANCE ERIK BANKS FOLK MUSIC RONALD COHEN INTERNATIONAL RELATIONS PETER SUTCH AND JUANITA ELIAS INTERNET JASON WHITTAKER ISLAM COLIN TURNER JAZZ CHRISTOPHER MEEDER

JUDAISM JACOB NEUSNER LANGUAGE (SECOND EDITION) R.L. TRASK LITERARY THEORY (SECOND EDITION) HANS BERTENS MANAGEMENT MORGEN WITZEL MARKETING (SECOND EDITION) KARL MOORE AND NIKETH PAREEK OPERA DENISE GALLO PHILOSOPHY (FOURTH EDITION) NIGEL WARBURTON POETRY JEFFREY WAINWRIGHT POLITICS (FOURTH EDITION) STEPHEN TANSEY AND NIGEL JACKSON THE QUR0 AN MASSIMO CAMPANINI RELIGION (SECOND EDITION) MALORY NYE ROMAN CATHOLICISM MICHAEL WALSH SEMIOTICS (SECOND EDITION) DANIEL CHANDLER SHAKESPEARE (SECOND EDITION) SEAN MCEVOY SOCIOLOGY MARTIN ALBROW TELEVISION STUDIES TOBY MILLER THEATRE STUDIES ROBERT LEACH WORLD MUSIC RICHARD NIDEL

LOGIC T H E BA S I C Sj c be a l l

First published 2010 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon. OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Avenue, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group, an informa businessThis edition published in the Taylor & Francis e-Library, 2010. To purchase your own copy of this or any of Taylor & Francis or Routledges collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.

2010 Jc Beall 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 and 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 Beall, J. C. Logic : the basics / J.C. Beall. p. cm. (The basics) Includes bibliographical references and index. 1. Logic. I. Title. BC108.B347 2010 160dc22 2009046227ISBN 0-203-85155-2 Master e-book ISBN

ISBN10: 0-415-77498-5 (hbk) ISBN 10: 0-415-77499-3 (pbk) ISBN 10: 0-203-85155-2 (ebk) ISBN 13: 978-0-415-77498-7 (hbk) ISBN 13: 978-0-415-77499-4 (pbk) ISBN 13: 978-0-203-85155-5 (ebk)

For Katrina Higgins for everything. And for Charles & Beverly Beall for everything else.

PREFACEA book should have either intelligibility or correctness; to combine the two is impossible. Bertrand Russell (1901) This book presents a few basic ideas in logical studies, particularly some ideas in philosophical logiclogic motivated largely by philosophical issues. The book aims not only to introduce you to various ideas and logical theories; it aims to give you a avor for logical theorizingtheorizing about logic in the face of apparently logic-relevant phenomena. If the book is successful, youll not only be in position to pursue logic at a deeper level; youll be motivated to do so. The book takes a wholly one-sided approach to logic: namely, the so-called semantic or model-theoretic side. You should be warned: there is much, much more to logic than is foundor even hinted atin this book. A particularly conspicuous omission is so-called proof theory: no deductive systems of any sort are discussed in this book. This omission is unfortunate in various ways butgiven space limitations on this bookit allows a more leisurely discussion of a wider array of ideas than would otherwise be possible. A handful of widely available further readings are suggested throughout, and a few themnamely, ones that are repeatedly mentionedprovide adequate proof systems for the canvassed logics (model-theoretically understood). Unsolicited advice to readers This book is intended to be read in order, with each chapter presupposing its predecessors. If youve already had some elementary logic training, some of the early chapters can be skipped; however, the book is intended chiey for those who have had very little, if any, logic training. While mastering them often requires patience and careful thinking, logical ideas are often fairly intuitive. Usually, when an idea

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initially seems hard or too abstract, a bit more thinking will eventually do the trick. My advice is that in times of initial diculty you give the matter a bit more thought. Moreover, dont just work to master the given matters. Try hard to think about dierent logical options from those explicitly canvassed in the book. For example (though this wont make much sense before you read a few chapters), if a theory claims that the right logic works this way, try to think about an alternative theory according to which the right logic works that way. The benet of such alternative thinking is two-fold: youll get the chance to do some logical theorizing on your own, and perhaps even come up with a new logical theory; and, more importantly, the exploration will probably be quite enjoyable, no matter how hard you have to think. Unsolicited advice to teachers This book has been used successfully in three dierent classroom settings. First course in logic. The text has been used as a fairly gentle introduction to logical studies for all manner of majors (science and humanities/arts), supplemented with handouts giving adequate proof systems (e.g., tableau or natural deduction). Many students often go on to do a regular classical rst-order logic course, and then proceed to do further studies, either as a major or minor, in philosophy or philosophical logic. Supplement to philosophy of logic. The text has been used as a required supplemental text in introductory and advanced philosophy of logic courses. In such courses, the focus is the philosophy of logic(s), with this book providing some of the logical ideas that feed the philosophy. Early (post-) graduate course. The text has been used as a sort of transition text for students entering analytic programs in philosophy. In this capacity, the text is used as a source of basic logical ideas, with a slant on philosophically motivated logical ideas, and is usually used as a predecessor to much more in-depth study of philosophical logic (i.e., formal logics motivated by philosophy). Despite such success, the book can undoubtedly be improved, and teachers are hereby encouraged to send suggestions for improve-

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ment. (Note that a supplemental manual of answersand other materialmay be made available to teachers.)

Brief history of the book I was invited to write a book on logic for the Routledge Basics series, which I think is a good and useful series, and I was happy to contribute. The troubleas logicians and logic teachers will knowis that the universe cannot possibly t another introductory logic textbook; it is already overly stued, indeed bursting to rid itself of elementary logic texts. As a result, this book was not to beand, given the state of the universe, could not beanother introductory logic textbook. And so it isnt. On the other hand, the book was not to be another logic for dummies or picturebook presentation of logical ideas. (Actually, the latter wouldve been good, but, alas, I didntand still dontknow how to do it.) Instead, the book was to give at least a bit of real logical content for those wanting to introduce themselves to aspects of logical theorizing; and the book was to do so with the goal of breadth over depth; but, again, there was to be real content, and so breadth had to suer a little bit while depth had to be deep enoughbut not too deep. What you have before you is my rst attempt to do what was to be done. Though it was not my aim when I set about writing the chapters, I found it dicult not to conform to earlier ideas expressed in some of my previous work. This is particularly the case with Logical Pluralism (2005), which I wrote with my friend and longstanding logical colleague Greg Restall. That booknamely, Logical Pluralismis suggested as further reading for those who wish to pursue the philosophy of logic, and in particular the philosophy of logical rivalry, in more depth. While philosophical issues motivate this books contents, the philosophy of logic is barely discussed. The tension between breadth, depth, and short-but-intelligible is a challenging constraint. My hope, in the end, is as above: that this book not only prepares you for deeper, more detailed logical study, but that it motivates you to do so.

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