Contents Preface xv CHAPTER 1 Basic Concepts 1 1.1 Validity and Soundness 4 ■ Summary of Defi nitions 10 Exercise 1.1 10 1.2 Forms and Validity 14 Argument Forms 14 Understanding Conditional Statements 17 Famous Valid Forms 19 The Famous Forms Method 25 ■ Summary of Famous Valid Forms 25 ■ The Famous Forms Method 26 ■ Summary of Defi nitions 28 Exercise 1.2 28 1.3 Counterexamples and Invalidity 33 Counterexamples 33 The Counterexample Method 36 Categorical Statements and Arguments 36 ■ The Counterexample Method 46 ■ Summary of Defi nitions 47 Exercise 1.3 48 1.4 Strength and Cogency 50 ■ Summary of Defi nitions 56 Exercise 1.4 57 Notes 60 CHAPTER 2 Identifying Arguments 63 2.1 Arguments and Nonarguments 63 ■ Summary of Defi nitions 67 Exercise 2.1 68 viii how38197_fm_i-xx.indd Page viii 1/30/12 7:30 PM user-f502/Volume/201/MH01577/how38197_disk1of1/0078038197/how38197_pagefiles 2.2 Well-Crafted Arguments 70 ■ Summary of Principles for Constructing Well-Crafted Arguments 86 ■ Summary of Defi nitions 86 Exercise 2.2 86 2.3 Argument Diagrams 95 Exercise 2.3 99 Notes 104 CHAPTER 3 Logic and Language 107 3.1 Logic, Meaning, and Emotive Force 109 ■ Summary of Defi nitions 113 Exercise 3.1 114 3.2 Defi nitions 116 Extensional and Intensional Defi nitions 116 ■ Summary of Defi nitions 123 Defi nition by Genus and Difference 123 ■ Summary of Criteria for Evaluating Defi nitions by Genus and Difference 130 ■ Summary of Defi nitions 130 Exercise 3.2 131 3.3 Using Defi nitions to Evaluate Arguments 135 ■ Summary of Defi nitions 139 Exercise 3.3 140 Notes 145 CHAPTER 4 Informal Fallacies 147 4.1 Fallacies of Irrelevance 149 Argument Against the Person ( Ad Hominem Fallacy) 149 Straw Man Fallacy 152 Appeal to Force ( Ad Baculum Fallacy) 153 Appeal to the People ( Ad Populum Fallacy) 155 Appeal to Pity ( Ad Misericordiam Fallacy) 156 Appeal to Ignorance ( Ad Ignorantiam Fallacy) 157 Red Herring ( Ignoratio Elenchi Fallacy) 159 ■ Summary of Defi nitions 160 Exercise 4.1 161 4.2 Fallacies Involving Ambiguity 166 Equivocation 166 Amphiboly 168 Contents ix how38197_fm_i-xx.indd Page ix 1/30/12 7:30 PM user-f502/Volume/201/MH01577/how38197_disk1of1/0078038197/how38197_pagefiles Composition 171 Division 173 ■ Summary of Defi nitions 174 Exercise 4.2 174 4.3 Fallacies Involving Unwarranted Assumptions 177 Begging the Question ( Petitio Principii ) 177 False Dilemma 180 Appeal to Unreliable Authority ( Ad Verecundiam Fallacy) 182 False Cause Fallacy 183 Complex Question 186 ■ Summary of Defi nitions 188 Exercise 4.3 189 Notes 195 CHAPTER 5 Categorical Logic: Statements 197 5.1 Standard Forms of Categorical Statements 197 Quality and Quantity 199 ■ Summary of Standard Forms 199 Putting Categorical Statements into Standard Form 200 ■ Summary of Stylistic Variants 201 Exercise 5.1 202 5.2 The Traditional Square of Opposition 205 ■ Summary of Defi nitions 209 Exercise 5.2 209 5.3 Further Immediate Inferences 212 Conversion 212 Obversion 214 Contraposition 216 ■ Summary of Defi nitions 218 ■ Summary Table: Conversion, Obversion, and Contraposition 219 Exercise 5.3 219 CHAPTER 6 Categorical Logic: Syllogisms 225 6.1 Standard Form, Mood, and Figure 225 ■ Summary of Defi nitions 229 Exercise 6.1 229 6.2 Venn Diagrams and Categorical Statements 232 ■ Summary of Diagrams of Categorical Statements 241 Exercise 6.2 241 6.3 Venn Diagrams and Categorical Syllogisms 242 Exercise 6.3 248 x Contents how38197_fm_i-xx.indd Page x 1/30/12 7:30 PM user-f502/Volume/201/MH01577/how38197_disk1of1/0078038197/how38197_pagefiles 6.4 The Modern Square of Opposition 250 Exercise 6.4 257 6.5 Enthymemes 259 Exercise 6.5 262 6.6 Sorites and Removing Term-Complements 263 Sorites 263 Removing Term-Complements 266 Exercise 6.6 268 6.7 Rules for Evaluating Syllogisms 271 ■ Summary of Rules for Determining the Validity of Categorical Syllogisms 274 Exercise 6.7 275 Notes 277 CHAPTER 7 Statement Logic: Truth Tables 279 7.1 Symbolizing English Arguments 280 Negations 281 Conjunctions 284 Disjunctions 285 Conditionals 287 Biconditionals 289 Putting It All Together 290 Symbol System for Statement Logic: A More Precise Formulation 296 ■ Summary of Defi nitions 299 Exercise 7.1 299 7.2 Truth Tables 303 Negations 304 Conjunctions 304 Disjunctions 305 Conditionals 305 Biconditionals 307 ■ Summary of Truth Tables for the Five Compounds 309 ■ Summary of Defi nitions 310 Exercise 7.2 310 7.3 Using Truth Tables to Evaluate Arguments 311 ■ Remembering Truth Conditions 317 ■ Summary of Truth Table Method 320 Exercise 7.3 320 7.4 Abbreviated Truth Tables 322 ■ Summary of the Abbreviated Truth Table Method 329 Exercise 7.4 329 Contents xi how38197_fm_i-xx.indd Page xi 1/30/12 7:30 PM user-f502/Volume/201/MH01577/how38197_disk1of1/0078038197/how38197_pagefiles 7.5 Logically Signifi cant Categories and Relationships 333 Tautology, Contradiction, and Contingency 333 Equivalence, Contradictoriness, Consistency, and Inconsistency 336 Concluding Observations 338 ■ Summary of Defi nitions 341 Exercise 7.5 341 Note 343 CHAPTER 8 Statement Logic: Proofs 345 8.1 Implicational Rules of Inference 345 ■ Summary of Implicational Rules 359 Exercise 8.1 360 8.2 Five Equivalence Rules 365 ■ Summary of the First Set of Equivalence Rules 372 Exercise 8.2 374 8.3 Five More Equivalence Rules 378 ■ Summary of the Second Set of Equivalence Rules 382 Exercise 8.3 382 8.4 Conditional Proof 388 Exercise 8.4 394 8.5 Reductio ad Absurdum 397 ■ Summary of Tips for Constructing Proofs 400 Exercise 8.5 402 8.6 Proving Theorems 406 Exercise 8.6 409 Notes 411 CHAPTER 9 Predicate Logic 413 9.1 The Language of Predicate Logic 413 Predicates, Constants, and Variables 414 The Universal Quantifi er 415 The Existential Quantifi er 418 The Language of Predicate Logic: A More Precise Formulation 420 ■ Summary of Symbolizations 424 ■ Summary of Defi nitions 425 Exercise 9.1 426 9.2 Demonstrating Invalidity 430 ■ Summary of the Finite Universe Method 438 xii Contents how38197_fm_i-xx.indd Page xii 1/30/12 7:30 PM user-f502/Volume/201/MH01577/how38197_disk1of1/0078038197/how38197_pagefiles ■ Summary of Defi nitions 438 Exercise 9.2 438 9.3 Constructing Proofs 440 Universal Instantiation 442 ■ Summary of Universal Instantiation (UI) 444 Existential Generalization 445 ■ Summary of Existential Generalization (EG) 446 Existential Instantiation 447 ■ Summary of Existential Instantiation (EI) 450 Universal Generalization 450 ■ Summary of Universal Generalization (UG) 453 Exercise 9.3 453 9.4 Quantifi er Negation, RAA, and CP 460 ■ Summary of Tips for Predicate Logic 465 Exercise 9.4 465 9.5 The Logic of Relations: Symbolizations 468 ■ Summary of Symbolizations 471 ■ Summary of Defi nitions 473 Exercise 9.5 473 9.6 The Logic of Relations: Proofs 477 Exercise 9.6 481 9.7 Identity: Symbolizations 486 Exercise 9.7 490 9.8 Identity: Proofs 490 Exercise 9.8 492 Notes 496 CHAPTER 10 Inductive Logic 499 10.1 Inductive and Deductive Logic 499 ■ Summary of Defi nitions 505 Exercise 10.1 505 10.2 Ordinary Reasoning: Authority, Analogy, and Enumeration 507 Arguments from Authority 507 ■ Summary of Arguments from Authority 509 Arguments from Analogy 509 ■ Summary of Arguments from Analogy 513 Induction by Enumeration 513 Contents xiii how38197_fm_i-xx.indd Page xiii 1/30/12 7:30 PM user-f502/Volume/201/MH01577/how38197_disk1of1/0078038197/how38197_pagefiles xiv Contents ■ Summary of Induction by Enumeration 517 ■ Summary of Defi nitions 517 Exercise 10.2 518 10.3 Scientifi c Reasoning: Mill's Method 522 Mill's Methods 523 Scientifi c Reasoning 526 ■ Summary of Mill's Methods 531 Exercise 10.3 531 10.4 Probabilistic Reasoning: The Rules of Probability 536 The Rules of Probability 537 Bayes' Theorem 545 ■ Summary of the Rules of Probability 549 ■ Summary of Defi nitions 550 Exercise 10.4 550 Notes 556 Answer Key 559 Photo Credits 627 Glossary/Index 629 how38197_fm_i-xx.indd Page xiv 2/2/12 3:21 PM user-f502/Volume/201/MH01577/how38197_disk1of1/0078038197/how38197_pagefiles