The Logic Book

This leading text for symbolic or formal logic courses presents all techniques and concepts with clear, comprehensive explanations, and includes a wealth of carefully constructed examples. Its flexible organization (with all chapters complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose. Title 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 ‘∼’, ‘∨’, and ‘&’ 4.3 Rules for Sentences Containing ‘⊃’ and ‘ ’ 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 Basic Concepts of SD 5.3 Strategies for Constructing Derivations in SD 5.4 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, 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 Quantificational 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 Fine-Tuning the Tree Method 9.5 Trees for PLE 9.6 Fine-Tuning the Tree Method for PLE CHAPTER 10 PREDICATE LOGIC: DERIVATIONS 10.1 The Derivation System PD 10.2 Using Derivations to Establish Syntactic Properties of PD 10.3 The Derivation System PD� 10.4 The Derivation System PDE 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 Index of Symbols Basic notions of logic Background Why study logic? Sentences, truth-values, and arguments Deductive validity and soundness Inductive arguments Logical consistency, truth, falsity, and equivalence Special cases of validity Sentential logic : symbolization and syntax Symbolization and truth-functional connectives Syntax complex symbolizations Non-truth-functional connectives The syntax of SL Sentential logic : semantics Truth-value assignments and truth-tables for sentences Truth-functional truth, falsity, and indeterminacy Truth-functional equivalence Truth-functional consistency Truth-functional entailment and truth-functional validity Truth-functional properties and truth-functional consistency Sentential logic : truth-trees The truth-tree method Truth-tree rules for sentences containing Rules for sentences containing and more complex truth-trees Using truth-trees to test for truth-functional truth, falsity, and indeterminacy Truth-functional equivalence Truth-functional entailment and truth-functional validity Sentential logic : derivations The derivation system SD Basic concepts of SD Strategies for constructing derivations in SD The derivation system SD1 Sentential logic : metatheory Mathematical induction Truth-functional completeness The soundness of SD and SD1 The completeness of SD and SD1 Predicate logic : symbolization and syntax The limitations of SL Predicates, individual constants, and quantity terms of English Introduction to PL Quantifiers introduced The formal syntax of PL A, E, I, O, U and O sentences Symbolization techniques Multiple quantifiers with overlapping scope Identity, definite descriptions, properties of relations, and functions Predicate logic : semantics Informal semantics for PL Quantificational truth, falsehood, and indeterminacy Quantificational equivalence and consistency Quantificational entailment and validity Truth-functional expansions Semantics for predicate logic with identity and functors Formal semantics of PL and PLE Predicate logic : truth-trees Expanding the rules for truth-trees Truth-trees and quantificational consistency Truth-trees and other semantic properties Fine-tuning the tree method Trees for PLE Fine-tuning the tree method for PLE Predicate logic : derivations The derivation system PD Using derivations to establish syntactic properties of pd The derivation system PD1 The derivation system PDE Predicate logic : metatheory Semantic preliminaries for PL Semantic preliminaries for PLE The soundness of PD and PDE The completeness of PD, PD1, and PDE The soundness of the tree method The completeness of the tree metho.