First Order Logic: A Concise Introduction

Description

Front Cover Front Inside Cover Half Title Title Page Copyright Page Contents Preface to the First Edition Preface to the Second Edition Acknowledgments 1. Introduction 1.00 Logic: What’s Not to Like? 1.01 Practice Makes Less Imperfect 1.02 Ls and Lp 2. The Language Ls 2.00 A Formal Language 2.01 Sentential Constants and Variables 2.02 Truth-Functional Connectives 2.03 Negation: ¬ 2.04 Conjunction: ∧ 2.05 Sentential Punctuation 2.06 Disjunction: ∨ 2.07 The Conditional: ⊃ 2.08 Conditionals, Dependence, and Sentential Punctuation 2.09 The Biconditional: ≡ 2.10 Complex Truth Tables 2.11 The Sheffer Stroke: | 2.12 Translating English into Ls 2.13 Conjunction 2.14 Disjunction 2.15 Conditionals and Biconditionals 2.16 Troublesome English Constructions 2.17 Truth Table Analyses of Ls Sentences 2.18 Contradictions and Logical Truths 2.19 Describing Ls 2.20 The Syntax of Ls 2.21 The Semantics of Ls 3. Derivations in Ls 3.00 Sentential Sequences 3.01 Object Language and Metalanguage 3.02 Derivations in Ls 3.03 The Principle of Form 3.04 Inference Rules: MP, MT 3.05 Sentence Valence 3.06 Hypothetical Syllogism: HS 3.07 Rules for Conjunction: ∧I, ∧E 3.08 Rules for Disjunction: ∨I, ∨E 3.09 Conditional Proof: CP 3.10 Indirect Proof: IP 3.11 Transformation Rules: Com, Assoc, Taut 3.12 Transformation Rules: DeM 3.13 Transformation Rules: Dist, Exp 3.14 Rules for Conditionals: Contra, Cond 3.15 Biconditional Sentences: Bicond 3.16 Constructive Dilemma: CD 3.17 Acquiring a Feel for Derivations 3.18 Proving Invalidity 3.19 Theorems 3.20 Soundness and Completeness of Ls 4.The Language Lp 4.00 Frege’s Legacy 4.01 Terms 4.02 Terms in Lp 4.03 Quantifiers and Variables 4.04 Bound and Free Variables 4.05 Negation 4.06 Complex Terms 4.07 Mixed Quantification 4.08 Translational Odds and Ends 4.09 Identity 4.10 At Least, at Most, Exactly 4.11 Definite Descriptions 4.12 Comparatives, Superlatives, Exceptives 4.13 Times and Places 4.14 The Domain of Discourse 4.15 The Syntax of Lp 4.16 The Semantics of Lp 4.17 Logic and Ontology 5. Derivations in Lp 5.00 Preliminaries 5.01 Quantifier Transformation 5.02 Universal Instantiation: UI 5.03 Existential Generalization: EG 5.04 Existential Instantiation: EI 5.05 Universal Generalization: UG 5.06 Quantifier Rules Summary 5.07 Identity: ID 5.08 Theorems in Lp 5.09 Invalidity in Lp 5.10 Prenex Normal Form 5.11 Soundness and Completeness of Lp Solutions to Even-Numbered Exercises Index Back Inside Cover Back Cover