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| To the Instructor | |
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| To the Student | |
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| Acknowledgements | |
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| Fundamentals | |
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| Recognizing Arguments | |
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| Some Typical Conclusion Indicators | |
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| Some Typical Premise Indicators | |
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| Distinguishing Sentences and Statements | |
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| Two General Categories of Argument: Deductive and Inductive Arguments | |
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| Deductive and Inductive Indicator Words | |
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| Evaluating Inductive Arguments: The Strong, the Weak, and the Inductively Sound | |
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| Evaluating Deductive Arguments: The Valid, the Invalid, and the Dedictively Sound | |
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| Deciding Whether an Argument is Valid or Invalid | |
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| Consistency and Inconsistency Implication | |
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| Logical Equivalence | |
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| Necessity | |
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| Ideals | |
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| Appendix: Some Logical Puzzles | |
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| Glossary | |
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| Truth-Functional Logic | |
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| Introductory Truth-Functional Logic | |
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| Simple and Compound Sentences, Sentence Operators, and the Conjunction | |
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| Negation | |
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| Disjunction | |
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| Truth-Functions and Truth-Functional Compound Sentences | |
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| Conditional Sentences | |
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| Biconditional Sentences | |
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| Glossary | |
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| Translating English into Logical Symbols | |
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| Symbolizing Sentences Containing More than One Operator | |
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| Throwing the Tilde into the Mix | |
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| From And to Or and Back Again--With a Few Nots Thrown In | |
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| Some General Hints on Symbolizing | |
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| Translating Conditionals and Biconditionals | |
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| Symbolizing Necessary and Sufficient Conditions | |
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| Glossary | |
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| Our New Language Gets a Name and a Formal Syntax | |
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| The Language TL | |
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| How to Calculate the Truth-Value of the Whole from the Values of the Parts | |
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| Glossary | |
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| Truth-Table Analysis | |
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| Constructing a Truth-Table for a Formula | |
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| Eight-Row Tables | |
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| How to Make Your Own Tautology Detector Using Just Paper and Pencil | |
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| How to Make an Inexpensive Contradiction Detector for Home or Office | |
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| The Contingency Detector: Don't Leave Home without It | |
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| Testing an Argument for Validity | |
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| Showing an Argument Invalid with a Partial Truth-Table | |
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| Testing a Pair of Sentences for Equivalences | |
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| Glossary | |
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| The Concept of Logical Form | |
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| Sentence Forms | |
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| Argument Forms | |
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| The Disjunctive Syllogism Form | |
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| The Modus Ponens Form | |
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| The Modus Tollens Form | |
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| The Hypothetical Syllogism Form | |
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| Valid Argument Forms | |
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| Invalid Argument Forms | |
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| Concluding Comments | |
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| Appendix: Contradictory and Tautological Sentence Forms | |
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| Glossary | |
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| Truth-Functional Natural Deduction | |
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| The Disjunctive Syllogism Rule | |
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| The Modus Ponens Rule | |
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| The Modus Tollens Rule | |
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| The Hypothetical Syllogism Rule | |
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| Proving that a Conclusion Validly Follows | |
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| The System TD | |
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| Proofs | |
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| Glossary | |
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| Four More Inference Rules | |
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| The Simplification Rule | |
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| The Conjunction Rule | |
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| The Addition Rule | |
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| The Constructive Dilemma Rule | |
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| Some Unsolicited Advice on Learning to Construct Proofs | |
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| Proof Strategies | |
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| Some Additional Suggestions Concerning Strategy | |
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| Appendix: Some Common Deduction Errors | |
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| Indirect Proofs and Conditional Proofs | |
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| The Indirect Proof Rule | |
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| The Conditional Proof Rule | |
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| Nested Proofs | |
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| Proving Sentences Tautological | |
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| The Law of Noncontradiction | |
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| Glossary | |
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| Replacement Rules | |
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| The Commutative Rule | |
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| The Associative Rule | |
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| The Double Negation Rule | |
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| DeMorgan's Rule | |
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| The Distribution Rule | |
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| Five More Replacement Rules | |
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| The Transposition Rule | |
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| The Implication Rule | |
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| The Exportation Rule | |
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| The Tautology Rule | |
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| The Equivalence Rule | |
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| Are Replacement Rules Worth the Bother? | |
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| Glossary | |
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| Indirect and Conditional Proofs with Replacement Rules | |
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| Indirect Proofs with Replacement Rules | |
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| Conditional Proof with Replacement Rules | |
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| Proving Tautologies | |
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| Glossary | |
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| Two Informal Topics | |
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| Definition | |
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| The Purposes of Definition | |
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| Five Types of Definition | |
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| Two Types of Meaning | |
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| Constructing a Definition: Techniques | |
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| Rules for Intensional Definitions | |
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| Glossary | |
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| Informal Fallacies | |
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| Fallacies of No Evidence | |
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| Fallacies of Little Evidence | |
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| Fallacies of Language | |
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| Glossary | |
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| A Summary of the Fallacies | |
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| Aristotelian Categorical Logic | |
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| The Logic of Categorical Statements | |
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| Categorical Sentences | |
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| Quality and Quantity | |
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| The Traditional Square of Opposition | |
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| Translating English Sentences into Standard Categorical Forms | |
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| Equivalence Rules for Aristotelian Logic | |
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| Dropping the Assumption of Existential Import | |
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| The Modern Square of Opposition | |
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| Glossary | |
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| Categorical Syllogisms | |
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| Logical Form | |
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| Venn Diagrams | |
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| Testing a Categorical Syllogism for Validity with Venn Diagrams | |
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| Diagramming Aristotelian Categorical Syllogisms | |
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| Diagramming from the Boolean Standpoint | |
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| The Sorites | |
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| Testing a Sorites with Venn Diagrams | |
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| Enthememes | |
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| Refutation by Logical Analogy | |
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| Appendix: Rules for Evaluating Categorical Syllogisms | |
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| Modern Quantificational Logic | |
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| Quantificational Logic I: The Language QL | |
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| Two Types of Sentences | |
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| General Sentences | |
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| A Syntax for our New Language | |
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| The Vocabulary of QL | |
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| Symbolizing General Sentences | |
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| Categorical Sentences | |
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| The Old ""Quantifier Switch"" Trick | |
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| Switching Quantifiers on Categoricals | |
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| Symbolizing Complicated General Sentences | |
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| Denying Existence | |
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| The Only Way to Go | |
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| What is a Cat-Dog? | |
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| Glossary | |
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| The Language of Quantificational Logic II: Relations | |
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| Sentences with a Quantifier-Dyadic Predicate Combo | |
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| Any and Every | |
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| Reflexive Sentences | |
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| Sentences with Overlapping Quantifiers | |
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| ""What Are You Talking About?"" The Universe of Discourse | |
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| Dean Martin, Universal Love, and a Summary of Logic Relations | |
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| To Be or Not To Be: The Logic of Identity | |
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| The Identity Sign | |
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| Appendix: Properties of Relations | |
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| Glossary | |
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| Proofs with Monadic Predicates | |
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| The Universal Instantiation Rule | |
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| Existential Generalization | |
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| Existential Instantiation | |
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| Memories of Geometry Class: Universal Generalization | |
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| One New Replacement Rule: Quantifier Exchange | |
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| Naming Our System | |
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| Glossary | |
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| Interpretations, Invalidity, and Semantics | |
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| Interpretations of Multiply Quantified Sentences | |
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| Using Interpretations to Show Invalidity | |
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| Semantics | |
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| The Monadic Predicate Test | |
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| Glossary | |
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| Conditional and Indirect Quantifier Proofs | |
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| Adding Truth-Functional Replacement Rules to the Mix | |
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| Putting QD on a Diet: A Reduced Set of Quantifier Rules | |
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| Proving Logical Truths | |
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| Proofs with Overlapping Quantifiers | |
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| Properties of Relations | |
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| Proofs with Identity | |
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| Properties of the Identity Relation | |
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| Glossary | |
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| Modal Logic | |
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| Introductory Modal Logic | |
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| To Shave or Not to Shave: That Is the Question | |
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| Five Modal Properties | |
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| Possible Truths, Possible Falsehoods, Contingencies | |
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| Necessary Truths | |
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| Necessary Falsehoods | |
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| Putting Statements into Symbols | |
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| Translating English Sentences into Modal Symbols | |
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| A Name and Syntax for our Modal Language | |
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| The Vocabulary for ML | |
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| The Grammar for ML | |
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| Linking Modal Operators | |
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| ""It Ain't Necessarily So,"" Or, Trading a Diamond for a Box and a Box for a Diamond | |
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| Modal Operators Need Scope, Too | |
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| Modal Relations | |
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| Scopes of the Dyadic Modal Operators | |
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| Symbolizing with Dyadic Operators | |
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| Modal Operators Are Not Truth-Functional | |
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| Appendix: There's Nothing New under the Sun | |
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| Glossary | |
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| Modal Logic: Methods of Proof | |
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| Five Modal Principles | |
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| Six Inference Rules | |
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| The Possibility to Necessity Rule | |
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| The Necessitation Rule | |
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| Four Modal Replacement Rules | |
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| Validity in S5 | |
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| Proving Theorems of S5 | |
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| Another Inference Rule: The Tautology Necessitation Rule | |
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| Putting an S5 Formula on a Diet: S5 Reduction | |
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| The Modal Fallacy | |
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| Glossary | |
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| Induction | |
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| Inductive Reasoning | |
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| Analogical Reasoning | |
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| Evaluating Analogical Arguments | |
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| Analogies as Models | |
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| Enumerative Induction | |
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| Statistical Inductive Generalization | |
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| Inference to the Best Explanation | |
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| What Makes One Explanation Better than Another? | |
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| Glossary | |
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| Scientific Reasoning | |
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| Scientific Reasoning | |
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| Comments on the Steps | |
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| Confirming and Disconfirming Scientific Hypotheses | |
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| The Confirmation of a Scientific Hypothesis | |
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| The Disconfirmation of a Scientific Hypothesis | |
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| The Fact of the Cross | |
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| What Makes One Hypothesis Better than Another? | |
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| Case Studies | |
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| Cause and Effect and Mill's Method | |
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| Cause and Effect | |
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| Mill's Method of Agreement | |
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| Mill's Method of Difference | |
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| The Joint Method of Agreement and Difference | |
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| Mill's Method of Residues | |
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| Mill's Method of Concomitant Variation | |
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| Glossary | |
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| Appendices | |
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| Truth-Trees | |
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| Truth | |
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| Answers to Selected Exercises | |
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| Index | |