Logic

Preface Part I Setting the Stage Chapter 1 What Logic Studies A. Statements and Arguments B. Recognizing Arguments Exercises 1B C. Arguments and Explanations Exercises 1C D. Truth and Logic E. Deductive and Inductive Arguments Exercises 1E F. Deductive Arguments: Validity and Soundness Argument Form Counterexamples Part II Informal Logic Chapter 2 Language Matters A. Intension and Extension Terms, Use, and Mention Two Kinds of Meaning Proper Names Exercises 2A B. Using Intensional Definitions Synonymous Definitions Word Origin Definitions Operational Definitions Definition by Genus and Difference C. Using Extensional Definitions Ostensive Definitions Enumerative Definitions Definition by Subclass Exercises 2C D. Applying Definitions Stipulative Definitions Lexical Definitions Functional Definitions Precising Definitions Theoretical Definitions Persuasive Definitions Exercises 2D E. Guidelines for Informative Definitions Exercises 2E F. Cognitive and Emotive Meaning Exercises 2F G. Factual and Verbal Disputes Exercises 2G SUMMARY KEY TERMS LOGIC CHALLENGE: THE PATH Chapter 3 Diagramming Arguments A. The Basics of Diagramming Arguments B. Diagramming Extended Arguments Exercises 3B SUMMARY KEY TERMS LOGIC CHALLENGE: THE TRAIN TO VEGAS Chapter 4 Informal Fallacies A. Why Study Fallacies? B. Fallacies Based on Personal Attacks or Emotional Appeals Fallacies Based on Personal Attacks 1. Ad Hominem Abusive 2. Ad Hominem Circumstantial 3. Poisoning the Well 4. Tu Quoque Fallacies Based on Emotional Appeals 5. Appeal to the People 6. Appeal to Pity 7. Appeal to Fear or Force Summary of Fallacies Based on Personal Attacks Summary of Fallacies Based on Emotional Appeals Exercises 4B C. Weak Inductive Argument Fallacies Generalization Fallacies 8. Rigid Application of a Generalization 9. Hasty Generalization 10. Composition 11. Division 12. Biased Sample False Cause Fallacies 13. Post Hoc 14. Slippery Slope Summary of Weak Inductive Argument Fallacies Exercises 4C D. Fallacies of Unwarranted Assumption or Diversion Unwarranted Assumption 15. Begging the Question 16. Complex Question 17. Appeal to Ignorance 18. Appeal to an Unqualified Authority 19. False Dichotomy Fallacies of Diversion 20. Equivocation 21. Straw Man 22. Red Herring 23. Misleading Precision 24. Missing the Point Summary of Fallacies of Unwarranted Assumption and Diversion Exercises 4D E. Recognizing Fallacies in Ordinary Language Exercises 4E SUMMARY KEY TERMS LOGIC CHALLENGE: A CLEVER PROBLEM Part III Formal Logic Chapter 5 Categorical Propositions A. Categorical Propositions Exercises 5A B. Quantity, Quality, and Distribution Exercises 5B C. Existential Import D. The Modern Square of Opposition and Venn Diagrams Venn Diagrams Exercises 5D E. Conversion, Obversion, and Contraposition in the Modern Square Conversion Obversion Contraposition Diagrams Summary of Conversion, Obversion, and Contraposition Exercises 5E F. The Traditional Square of Opposition and Venn Diagrams Exercises 5F.1 Venn Diagrams and the Traditional Square Exercises 5F.2 G. Conversion, Obversion, and Contraposition in the Traditional Square Summary of Conversion, Obversion, and Contraposition Conversion Obversion Contraposition Exercises 5G H. Translating Ordinary Language into Categorical Propositions Missing Plural Nouns Nonstandard Verbs Singular Propositions Adverbs and Pronouns ""It Is False That..."" Implied Quantifiers Nonstandard Quantifiers Conditional Statements Exclusive Propositions ""The Only"" Propositions Requiring Two Translations Exercises 5H SUMMARY KEY TERMS LOGIC CHALLENGE: GROUP RELATIONSHIP Chapter 6 Categorical Syllogisms A. Standard-Form Categorical Syllogisms B. Mood and Figure Exercises 6B C. Diagramming in the Modern Interpretation Diagramming A-Propositions Diagramming E-Propositions Diagramming I-Propositions Diagramming O-Propositions Wrapping Up the X Is the Syllogism Valid? Exercises 6C D. Rules and Fallacies Under the Modern Interpretation Rule 1: The middle term must be distributed in at least one premise. Associated Fallacy: Undistributed Middle Rule 2: If a term is distributed in the conclusion, then it must be distributed in a premise. Associated Fallacies: Illicit Major/Illicit Minor Rule 3: A categorical syllogism cannot have two negative premises. Associated Fallacy: Exclusive Premises Rule 4: A negative premise must have a negative conclusion. Associated Fallacy: Affirmative Conclusion/Negative Premise Rule 5: A negative conclusion must have a negative premise. Associated Fallacy: Negative Conclusion/Affirmative Premises Rule 6: Two universal premises cannot have a particular conclusion. Associated Fallacy: Existential Fallacy Summary of Rules Exercises 6D E. Diagramming in the Traditional Interpretation A-Propositions E-Propositions Exercises 6E F. Rules and Fallacies Under the Traditional Interpretation Exercises 6F G. Ordinary Language Arguments Reducing the Number of Terms in an Argument Exercises 6G.1 Paraphrasing Ordinary Language Arguments Categorical Propositions and Multiple Arguments Exercises 6G.2 H. Enthymemes Exercises 6H I. Sorites Exercises 6I SUMMARY KEY TERMS LOGIC CHALLENGE: RELATIONSHIPS REVISITED Chapter 7 Propositional Logic A. Logical Operators and Translations Simple and Compound Statements Negation Conjunction Disjunction Conditional Distinguishing ""If"" from ""Only If"" Sufficient and Necessary Conditions Biconditional Summary of Operators and Ordinary Language Exercises 7A B. Compound Statements Well-Formed Formulas Exercises 7B.1 Main Operator Exercises 7B.2 Translations and the Main Operator Exercises 7B.3 C. Truth Functions Defining the Five Logical Operators Negation Conjunction Disjunction Conditional Biconditional Exercises 7C.1 Operator Truth Tables and Ordinary Language Propositions with Assigned Truth Values Exercises 7C.2 D. Truth Tables for Propositions Arranging the Truth Values The Order of Operations Exercises 7D E. Contingent and Noncontingent Statements Tautology Self-Contradiction Exercises 7E F. Logical Equivalence and Contradictory, Consistent, and Inconsistent Statements Logical Equivalence Exercises 7F.1 Contradictory, Consistent, and Inconsistent Statements Exercises 7F.2 G. Truth Tables for Arguments Validity Analyzing Sufficient and Necessary Conditions in Arguments Technical Validity Exercises 7G.1 Argument Forms Exercises 7G.2 H. Indirect Truth Tables Thinking Through an Argument A Shorter Truth Table Exercises 7H.1 Using Indirect Truth Tables to Examine Statements for Consistency Exercises 7H.2 SUMMARY KEY TERMS LOGIC CHALLENGE: A CARD PROBLEM Chapter 8 Natural Deduction A. Natural Deduction B. Implication Rules I Modus Ponens (MP) Modus Tollens (MT) Hypothetical Syllogism (HS) Disjunctive Syllogism (DS) Justification: Applying the Rules of Inference Exercises 8B C. Tactics and Strategy Applying the First Four Implication Rules Exercises 8C D. Implication Rules II Simplification (Simp) Conjunction (Conj) Addition (Add) Constructive Dilemma (CD) Applying the Second Four Implication Rules Exercises 8D E. Replacement Rules I De Morgan (DM) Double Negation (DN) Commutation (Com) Association (Assoc) Distribution (Dist) Applying the First Five Replacement Rules Exercises 8E F. Replacement Rules II Transposition (Trans) Material Implication (Impl) Material Equivalence (Equiv) Exportation (Exp) Tautology (Taut) Applying the Second Five Replacement Rules Exercises 8F G. Conditional Proof Exercises 8G H. Indirect Proof Exercises 8H I. Proving Logical Truths Exercises 8I SUMMARY KEY TERMS LOGIC CHALLENGE: THE TRUTH Chapter 9 Predicate Logic A. Translating Ordinary Language Singular Statements Universal Statements Particular Statements Paying Attention to Meaning Exercises 9A B. Four New Rules of Inference Universal Instantiation (UI) Universal Generalization (UG) Existential Generalization (EG) Existential Instantiation (EI) Summary of the Four Rules Tactics and Strategy Exercises 9B C. Change of Quantifier (CQ) Exercises 9C D. Conditional and Indirect Proof Conditional Proof (CP) Indirect Proof (IP) Exercises 9D E. Demonstrating Invalidity Counterexample Method Finite Universe Method Indirect Truth Tables Exercises 9E F. Relational Predicates Translations Exercises 9F.1 Proofs A New Restriction Change of Quantifier Conditional Proof and Indirect Proof Exercises 9F.2 G. Identity Simple Identity Statements ""Only"" ""The Only"" ""No... Except"" ""All Except"" Superlatives ""At Most"" ""At Least"" ""Exactly"" Definite Descriptions Summary of Identity Translations Exercises 9G.1 Proofs Exercises 9G.2 SUMMARY KEY TERMS LOGIC CHALLENGE: YOUR NAME AND AGE, PLEASE Part IV Inductive Logic? Chapter 10 Analogical Arguments A. The Framework of Analogical Arguments Exercises 10A B. Analyzing Analogical Arguments Criteria for Analyzing Analogical Arguments Exercises 10B C. Strategies of Evaluation Disanalogies Counteranalogy Unintended Consequences Combining Strategies Exercises 10C SUMMARY KEY TERMS LOGIC CHALLENGE: BEAT THE CHEAT Chapter 11 Legal Arguments A. Deductive and Inductive Reasoning B. Conditional Statements C. Sufficient and Necessary Conditions D. Disjunction and Conjunction E. Analyzing a Complex Rule Exercises 11E F. Analogies G. The Role of Precedent Exercises 11G SUMMARY KEY TERMS LOGIC CHALLENGE: A GUILTY PROBLEM Chapter 12 Moral Arguments A. Value Judgments Justifying ""Should"" Types of Value Judgments Taste and Value Exercises 12A B. Moral Theories Emotivism Consequentialism Egoism Utilitarianism Deontology Relativism Contrasting Moral Theories Exercises 12B C. The Naturalistic Fallacy D. The Structure of Moral Arguments E. Analogies and Moral Arguments Exercises 12E SUMMARY KEY TERMS LOGIC CHALLENGE: DANGEROUS CARGO Chapter 13 Statistical Arguments and Probability A. Samples and Populations Exercises 13A B. Statistical Averages Exercises 13B C. Standard Deviation Dividing the Curve The Size of the Standard Deviation How to Calculate the Standard Deviation Exercises 13C 625 D. What If the Results Are Skewed? E. The Misuse of Statistics Exercises 13E F. Probability Theories A Priori Theory Relative Frequency Theory Subjectivist Theory G. Probability Calculus Conjunction Methods Disjunction Methods Negation Method Exercises 13G H. True Odds in Games of Chance I. Bayesian Theory Exercises 13I SUMMARY KEY TERMS LOGIC CHALLENGE: THE SECOND CHILD Chapter 14 Causality and Scientific Arguments A. Sufficient and Necessary Conditions Exercises 14A B. Causality C. Mill's Methods Method of Agreement Method of Difference Joint Method of Agreement and Difference Method of Residues Method of Concomitant Variations Exercises 14C D. Limitations of Mill's Methods E. Theoretical and Experimental Science F. Inference to the Best Explanation G. Hypothesis Testing, Experiments, and Predictions Controlled Experiments Determining Causality H. Science and Superstition The Need for a Fair Test Verifiable Predictions Nontrivial Predictions Connecting the Hypothesis and Prediction Putting It All Together Science and Superstition The Allure of Superstition Exercises 14H SUMMARY KEY TERMS LOGIC CHALLENGE: THE SCALE AND THE COINS Online Chapter 15 Analyzing a Long Essay A. Childbed Fever B. Vienna Exercises 15B C. Miasm and Contagion Exercises 15C D. Semmelweis's Account of the Discovery Exercises 15D E. Initial Questions Exercises 15E F. A New Interpretation Exercises 15F SUMMARY BIBLIOGRAPHY Appendix A Cognitive Bias Heuristics Heuristics and Algorithms The Link Between Heuristics and Cognitive Biases Theories of Judgment Cognitive Biases 1. Belief Bias 2. Confirmation Bias 3. Status Quo Bias 4. Availability Bias 5. Halo Bias 6. Functional Fixedness Bias 7. Anchoring Bias 8. Gambling Biases 9. Frequency Bias 10. Ingroup Bias 11. Fundamental Attribution Bias Can We Overcome Cognitive Biases? Appendix B The LSAT and Logical Reasoning Introduction 1. Logical Reasoning 2. Deductive and Inductive Arguments 3. Identifying Conclusions and Premises A. Identifying the Conclusion B. Choosing the Best Missing Conclusion C. Assumptions: Choosing the Best Missing Premise 4. Additional Information that Strengthens or Weakens an Argument 5. Arguments that Use Either Analogical, Statistical, or Causal Reasoning A. Analogical Reasoning B. Statistical Reasoning C. Causal Reasoning 6. Explaining or Resolving Given Information 7. Argument Flaws A. Fallacies Based on Personal Attacks or Emotional Appeals B. Weak Inductive Argument Fallacies C. Fallacies of Unwarranted Assumption or Diversion 8.Recognizing Reasoning Patterns A. Class Terms B. Conditional Statements C. Translating Conditional Statements D. Distinguishing ""If"" from ""Only If"" E. Conditionals and Arguments F. Sufficient and Necessary Conditions 9. Continuing the Process Glossary Answers to Selected Exercises Index