# Methods of Logic

Harvard University Press, 1982 - Philosophy - 333 pages

This widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate- functor logic and the affinities between higher set theory and the elementary logic of terms, Quine's new edition will serve admirably both for classroom and for independent use.

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### Contents

 Introduction 1 TRUTH FUNCTIONS 7 Negation Conjunction and Alternation 9 Truth Functions 16 The Conditional 21 Grouping 27 TruthValue Analysis 33 Consistency and Validity 40
 GENERAL THEORY OF QUANTIFICATION 165 Schemata Extended 167 Substitution Extended 174 Pure Existentials 182 The Main Method 190 Application 195 Completeness 203 Lowenheims Theorem 209

 Implication 45 Words into Symbols 53 Equivalence 60 Alternational Normal Schemata 68 Simplification 74 Duality 79 Axioms 85 GENERAL TERMS AND QUANTIFIERS 91 Categorical Statements 93 Venns Diagrams 98 Syllogisms 102 Limits of These Methods 109 Boolean Schemata 114 Tests of Validity 121 Some Boolean Incidentals 128 The Bound Variable 132 Quantification 136 Rules of Passage Monadic Schemata 142 Prenexity and Purity 148 Validity Again 154 Substitution 160
 Decisions and the Undecidable 213 Functional Normal Forms 219 Herbrands Method 224 Other Methods for Validity 232 Deduction 237 Soundness 245 Deductive Strategy 248 GLIMPSES BEYOND 257 Singular Terms 259 Identity 265 Descriptions 274 Elimination of Singular Terms 278 Elimination of Variables 283 Classes 288 Number 294 Axiomatic Set Theory 300 Partial Answers to Exercises 305 Bibliography 320 Index 327 Copyright