The Logic Book

Merrie Bergmann received her Ph.D. in philosophy from the University of Toronto and is currently an Associate Professor in the Computer Science Department at Smith College. She has published articles in formal semantics and logic, philosophy of language, and computational linguistics. James Moor received his Ph.D. in history and philosophy of science from Indiana University and is currently a Professor of Philosophy at Dartmouth College. He has developed software for teaching logic and has published articles in philosophy of science, philosophy of mind, logic, philosophy of artificial intelligence, and computer ethics. Jack Nelson received his Ph.D. in philosophy from the University of Chicago and is currently Associate Dean of the College of Liberal Arts and Sciences and the Interim Chair of the Philosophy Department at Arizona State University. He has developed software for teaching logic and has published articles in personal identity, epistemology, and philosophy of science.

Chapter 1: INTRODUCTION TO DEDUCTIVE LOGIC1.1 Introduction1.2 Core Concepts of Deductive Logic1.3 Special Cases of Logical Concepts1.4 Deductive Validity and Soundness1.5 Inductive Arguments1.6 Logical Consistency, Truth, Falsity, and Equivalence1.7 Special Cases of ValidityChapter 2: SYNTAX AND SYMBOLIZATION2.1 The Syntax of SL2.2 Introduction to Symbolization2.3 More Complex Symbolizations2.4 Non-Truth-Functional Uses of ConnectivesChapter 3: Sentential Logic: Semantics3.1 Truth-Value Assignments and Truth-Tables for Sentences3.2 Truth-Functional Truth, Falsity, and Indeterminacy3.3 Truth-Functional Equivalence3.4 Truth-Functional Consistency3.5 Truth-Functional Entailment and Truth-Functional Validity3.6 Truth-Functional Properties and Truth-Functional ConsistencyChapter 4: Sentential Logic: Truth-Trees4.1 The Truth-Tree Method4.2 Truth-Tree Rules 4.3 Using Truth-Trees to test for other TruthsChapter 5: Sentential Logic: Derivations5.1 The Derivation System SD5.2 Basic Concepts of SD5.3 Strategies for Constructing Derivations in SD5.4 The Derivation System SD+ Chapter 6: Sentential Logic: Metatheory6.1 Mathematical Induction6.2 Truth-Functional Completeness6.3 The Soundness of SD and SD+6.4 The Completeness of SD and SD+Chapter 7: Predicate Logic: Syntax and Symbolization7.1 Predicates, Singular Terms, and Quantity Expressions of English7.2 The Formal Syntax of PL7.3 Introduction to Symbolization7.4 Symbolization Fine-Tuned7.5 The Language PLE (Predicte Logic Extended)Chapter 8: Predicate Logic: Semantics8.1 Interpretations8.2 Quantificational Truth, Falsehood, and Indeterminacy8.3 Quantificational Equivalence and Consistency8.4 Quantification Entailment and Validity8.5 Truth-Functional Expansions8.6 Semantics for Predicate Logic with Identity and FunctorsChapter 9: Predicate Logic: Truth-Trees9.1 Truth-Tree RUles for PL9.2 Truth-Trees and Quantificational Consistency9.3 Truth-Trees and Other Semantic Properties9.4 Fine-Tuning the Tree Method9.5 Trees for PLEChapter 10: Predicate Logic: Derivations10.1 The Derivation System PD10.2 Using Derivations to Establish Syntactic Properties of PD10.3 The Derivation System PD+10.4 The Derivation System PDEChapter 11: Predicate Logic: Metatheory11.1 Semantic Preliminaries for PD11.2 Semantic Preliminaries for PLE11.3 The Soundness of PD, PD+, and PDE11.4 The Completeness of PD, PD+, and PDE11.5 The Soundness of the Tree Method11.6 The Completeness of the Tree MethodSelected BibliographyIndexIndex of Symbols