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The Logic Book,9780072401899
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The Logic Book



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McGraw-Hill Humanities/Social Sciences/Languages
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Table of Contents

Chapter 1: Basic Notions of Logic

1.1 Background

1.2 Why Study Logic

1.3 Sentences, Truth-Values, and Arguments

1.4 Deductive Validity and Soundness

1.5 Inductive Arguments

1.6 Logical Consistency, Truth, Falsity, and Equivalence

1.7 Special Cases of Validity

Chapter 2: Sentential Logic: Symbolization and Syntax

2.1 Symbolization and Truth-Functional Connectives

2.2 Complex Symbolizations

2.3 Non-Truth-Functional Connectives

2.4 The Syntax of SL

Chapter 3: Sentential Logic: Semantic

3.1 Truth-Value Assignments and Truth-Tables for Sentences

3.2 Truth-Functional Truth, Falsity, and Indeterminacy

3.3 Truth-Functional Equivalence

3.4 Truth-Functional Consistency

3.5 Truth-Functional Entailment and Truth-Functional Validity

3.6 Truth-Functional Properties and Truth-Functional Consistency

Chapter 4: Sentential Logic: Truth-Tree

4.1 Introduction

4.2 Truth-Tree Rules for Sentences Containing ‘tilde’, ‘wedge’, and ‘ampersand'

4.3 Rules for Sentences Containing ‘tilde’, ‘horseshoe’, and ‘triple bar’

4.4 More Complex Truth-Trees

4.5 Using Truth-Trees to Test for Truth-Functional Truth, Falsity, and Indeterminacy

4.6 Truth-Functional Equivalence

4.7 Truth-Functional Entailment and Truth-Functional Validity

Chapter 5: Sentential Logic: Derivation

5.1 The Derivation System SD

5.2 Applying the Derivation Rules of SD

5.3 Basic Concepts of SD

5.4 Strategies for Constructing Derivations in SD

5.5 The Derivation System SD+

Chapter 6: Sentential Logic: Metatheory

6.1 Mathematical Induction

6.2 Truth-Functional Completeness

6.3 The Soundness of SD and SD+

6.4 The Completeness of SD and SD+

Chapter 7: Predicate Logic: Symbolization and Syntax

7.1 Introduction

7.2 Predicates, Individual Constants, and Quantity Terms of English

7.3 Introduction to PL

7.4 Quantifiers Introduced

7.5 The Formal Syntax of PL

7.6 A-, E-, I-, and O- Sentences

7.7 Symbolization Techniques

7.8 Multiple Quantifiers with Overlapping Scope

7.9 Identify, Definite Descriptions, and Properties of Relations

Chapter 8: Predicate Logic: Semantic

8.1 Informal Semantics for PL

8.2 Quantificational Truth, Falsehood, and Indeterminacy

8.3 Quantificational Equivalence and Consistency

8.4 Quantification Entailment and Validity

8.5 Truth-Functional Expansions

8.6 Semantics for Predicate Logic with Identity

8.7 Formal Semantics of PL and PLI

Chapter 9: Predicate Logic: Truth-Tree

9.1 Expanding the Rules for Truth-Trees

9.2 Truth-Trees and Quantificational Consistency

9.3 Truth-Trees and Other Semantic Properties

9.4 Trees for PLI

9.5 Fine-Tuning the Tree Method

Chapter 10: Predicate Logic: Derivation

10.1 The Derivation System PD

10.2 Applying the Derivation Rules of PD

10.3 Basic Concepts of PD

10.4 Strategies for Constructing Derivations in PD

10.5 The Derivation System PD+

10.6 PD with Identity

Chapter 11: Predicate Logic: Metatheory

11.1 Semantic Preliminaries for PL

11.2 Semantic Preliminaries for PLE

11.3 The Soundness of PD, PD+, and PDE

11.4 The Completeness of PD, PD+, and PDE

11.5 The Soundness of the Tree Method

11.6 The Completeness of the Tree Method

Selected Bibliography


Index of Symbols

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