Merrie Bergmann,
Smith College James Moor,
Dartmouth College Jack Nelson,
Arizona State University
ISBN: 007353563x Copyright year: 2009
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: Semantics
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-Trees
4.1 The Truth-Tree Method
4.2 Truth-Tree Rules for Sentences Containing 'tilde', 'wedge', and 'ampersand'
4.3 Rules for Sentences Containing '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: Derivations
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 The Limitations of SL
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 Identity, Definite Descriptions, and Properties of Relations, and Functions
Chapter 8: Predicate Logic: Semantics
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 and Functors
8.7 Formal Semantics of PL and PLE
Chapter 9: Predicate Logic: Truth-Trees
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 PLE
9.5 Fine-Tuning the Tree Method
Chapter 10: Predicate Logic: Derivations
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 The Derivation System PDE
Chapter 11: Predicate Logic: Metatheory
11.1 Semantic Preliminaries for PD
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
2009