Elementary Logic

Harvard University Press, 1980 - Philosophy - 129 pages
Now much revised since its first appearance in 1941, this book, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truth-function logic along with a complete proof procedure for the logic of quantifiers. Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters.

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Contents

 Introduction 1 STATEMENT COMPOSITION 5 Conjunction 8 Denial 11 Or 13 But although unless 15 If 17 General and Subjunctive Conditionals 20
 Implication between Schemata 65 TruthFunctional Implication 66 QUANTIFICATION 71 Quantifiers 73 Variables and Open Sentences 75 Variants of Some 78 Some Restricted 79 No 82

 Because hence that 22 Reduction to Conjunction and Denial 24 Grouping 26 Verbal Cues to Grouping 28 Paraphrasing Inward 30 TRUTHFUNCTIONAL TRANSFORMATIONS 35 Instances 39 Equivalent Schemata 40 TruthFunctional Equivalence 43 Replacement 44 Transformation 47 Proofs of Equivalence 50 Alternation and Duality 52 Normal Schemata 55 Validity 59 TruthFunctional Truth 60 Inconsistency and TruthFunctional Falsity 63
 Every 84 Variants of Every 86 Persons 89 Times and Places 90 Quantification in Context 93 QUANTIFICATIONAL INFERENCE 97 Predicates 99 Restraints on Introducing 101 Substitution Extended 104 Validity Extended 107 Equivalence Extended 109 Inconsistency Proofs 112 Logical Arguments 116 Identity and Singular Terms 119 Membership 122 Index 127 Copyright