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