# Symbolic Logic

## Edition: 2001

### Authors: Dale Jacquette

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This comprehensive intro text covers central topics of elementary and symbolic logic. It contains many problems and exercises and provides a solid foundation for continued study of advanced topics in logic.
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### Book details

List price: \$223.95
Publication date: 8/22/2000
Binding: Hardcover
Pages: 384
Size: 7.25" wide x 9.25" long x 0.75" tall
Weight: 2.134
Language: English

 Preface Introduction What Is Logic? Why Study Logic? How Shall We Study Logic? Concepts of Logic Propositions and Arguments Propositions Propositional Symbols Arguments Deductively Valid Arguments Inference Indicators Imagination Test for Deductive Validity Limiting Cases of Deductive Validity Conditional Arguments Reductio ad Absurdum Deductive Validity in Complex Arguments Soundness Summary: Propositions and Arguments Exercises Propositional Logic Propositional Syntax and Semantics Propositional Logic Syntax of Propositional Logic Propositional Connectives Truth Table Semantics Negation Conjunction Disjunction Conditional Biconditional Translating Propositions Colloquial Propositional Equivalents Disambiguating Propositional Relations Translating Arguments Summary: Propositional Syntax and Semantics Exercises Truth Tables Decision Methods Truth Tables Main Connectives Truth Table Setup Propositional Semantic Concepts Tautology, Inconsistency, and Contingency Classifying Wffs by Truth Tables Applications to Complex Wffs Truth Table Shortcuts Truth Tables for Consistency Truth Tables for Equivalence Truth Tables for Sequents Turbo Truth Tables Reduction of Propositional Connectives Summary: Truth Tables Exercises Truth Trees Truth Trees Stacking and Branching Truth Tree Rules Truth Tree Criteria Classifying Wffs by Truth Trees Truth Trees for Consistency Truth Trees for Equivalence Truth Trees for Sequents Summary: Truth Trees Exercises Propositional Natural Deduction Proofs Natural Deduction Anatomy of a Natural Deduction Proof Natural Deduction Rules Assumption (A) Reiteration (R) Double Negation (DN) Conjunction Introduction (andI) Conjunction Elimination (andE) Disjunction Introduction ([logical or]I) Disjunction Elimination ([logical or]E) Subproof Entrance and Exit Conditional Introduction ([superset or implies]I) Conditional Elimination ([superset or implies]E) Negation Introduction/Elimination ( IE) Biconditional Introduction ([identical with]I) Biconditional Elimination ([identical with]E) Derived Rule Reductions Proving Tautologies Proof Strategy Hints Valid Sequent and Tautology Proofs Summary: Propositional Natural Deduction Proofs Exercises Predicate Logic Predicate Syntax and Semantics Predicate Syntax Predicating Properties of Objects Quantifying Over Sets of Objects Predicate Wffs Quantifier Duality Propositional Connectives in Predicate Logic Translating Monadic Quantifications 'Only' Quantifications and Exceptions Translating Polyadic and Mixed Multiple Quantifications Internal Propositional Complexities Overlapping Quantifier Scopes Prenex Normal Form Ambiguous Quantifiers Translating Predicate Arguments Predicate Semantics Predicate Semantic Concepts Alternative Semantic Principles Circle Diagrams Summary: Predicate Syntax and Semantics Exercises Predicate Truth Trees Predicate Trees Identifying Main Operators Predicate Truth Tree Rules Classifying Wffs by Predicate Trees Predicate Trees for Consistency, Equivalence, and Validity Truth Tree Protocol for Predicate Logic Applications to Complex Wffs and Sequents Truth Tree Evaluation of Prenex Equivalents Square of Opposition Limitations of Predicate Trees Summary: Predicate Truth Trees Exercises Predicate Natural Deduction Proofs Natural Deduction Rules for Predicate Logic Universal Elimination ([for all]E) Existential Introduction ([exist]I) Universal Introduction ([for all]I) Existential Elimination ([exist]E) Strategy Hints Proving Valid Sequents in Predicate Logic Predicate Proofs of Prenex Equivalents Proving Tautologies in Predicate Logic The Barber Paradox Word Problems Logic of Relations Identity Specific Numbers of Objects Definite Description Deductive Incompleteness Summary: Predicate Natural Deduction Proofs Exercises Advanced Topics in Symbolic Logic Where Do We Go from Here? Metatheory Foundations of Mathematics Computers, Artificial Intelligence, and Machine Theory Modal Logic Nonstandard Logics Philosophical Applications History of Logic Reference List of Demonstration Problems Sources and Selected Readings Glossary-Index