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