Introduction To Non-Classical Logic Graham Priest

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An Introduction to Non-Classical Logic

This revised and considerably expanded edition of An Introduction to Non-Classical Logic brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. Part I, on propositional logic, is the old Introduction, but contains much newmaterial. Part II is entirely novel, and covers quantification and identity for all the logics in Part I. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly and accessibly, using devices such as tableau proofs, and their relations to current philosophical issues and debates is discussed. Students with a basic understanding of classical logicwill find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area. graham p riest is Boyce Gibson Professor of Philosophy, University of Melbourne and Arché Professorial Fellow, Departments of Philosophy, University of St Andrews. His mostrecent publications include Towards Non-Being (2005) and Doubt Truth to be a Liar (2006).

An Introduction to Non-Classical Logic
From If to Is
Second Edition
GR A HAM PRIEST
University of Melbourne and University of St Andrews

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building,Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521854337 © Graham Priest 2001, 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the writtenpermission of Cambridge University Press. First published in print format 2008

ISBN-13 978-0-511-39361-7 ISBN-13 978-0-521-85433-7 ISBN-13 978-0-521-67026-5

eBook (EBL) hardback paperback

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To all those from whom I have learned

Contents

Preface to the First Edition Preface to the Second Edition Mathematical Prolegomenon 0.1 Set-theoretic Notation 0.2 Proof by Induction 0.3 Equivalence Relations and Equivalence Classes Part I Propositional Logic 1 Classical Logic and the Material Conditional 1.1 Introduction1.2 The Syntax of the Object Language 1.3 Semantic Validity 1.4 Tableaux 1.5 Counter-models 1.6 Conditionals 1.7 The Material Conditional 1.8 Subjunctive and Counterfactual Conditionals 1.9 More Counter-examples 1.10 Arguments for ⊃ 1.11 ∗ Proofs of Theorems 1.12 History 1.13 Further Reading 1.14 Problems 2 Basic Modal Logic 2.1 Introduction 2.2 Necessity and Possibility

page xvii xxi xxvii xxviixxix xxx 1 3 3 4 5 6 10 11 12 13 14 15 16 18 18 18 20 20 20
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Contents

2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12

Modal Semantics Modal Tableaux Possible Worlds: Representation Modal Realism Modal Actualism Meinongianism *Proofs of Theorems History Further Reading Problems

21 24 28 28 29 30 31 33 34 34 36 36 36 38 42 45 46 49 51 56 60 60 60 64 64 64 65 67 69 72 72 73 74 7677 79

3 Normal Modal Logics 3.1 Introduction 3.2 Semantics for Normal Modal Logics 3.3 Tableaux for Normal Modal Logics 3.4 Infinite Tableaux 3.5 S5 3.6 Which System Represents Necessity? 3.6a The Tense Logic K t 3.6b Extensions of K t 3.7 *Proofs of Theorems 3.8 History 3.9 Further Reading 3.10 Problems 4 Non-normal Modal Logics; Strict Conditionals 4.1 Introduction 4.2 Non-normal Worlds 4.3...