The Power of Logic

Cover Page......Page 1
Half Title Page......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
About the Authors......Page 7
Brief Contents......Page 8
Contents......Page 9
Preface......Page 16
CHAPTER 1 Basic Concepts......Page 23
1.1 Validity and Soundness......Page 26
Exercise 1.1......Page 32
Argument Forms......Page 36
Understanding Conditional Statements......Page 39
Famous Valid Forms......Page 41
■ Summary of Famous Valid Forms......Page 47
■ The Famous Forms Method......Page 48
Exercise 1.2......Page 50
Counterexamples......Page 55
The Counterexample Method......Page 58
■ The Counterexample Method......Page 68
■ Summary of Defi nitions......Page 69
Exercise 1.3......Page 70
1.4 Strength and Cogency......Page 72
■ Summary of Defi nitions......Page 78
Exercise 1.4......Page 79
Notes......Page 82
2.1 Arguments and Nonarguments......Page 85
■ Summary of Definitions......Page 89
Exercise 2.1......Page 90
2.2 Well-Crafted Arguments......Page 92
Exercise 2.2......Page 108
2.3 Argument Diagrams......Page 117
Exercise 2.3......Page 121
Notes......Page 126
3.1 Logic, Meaning, and Emotive Force......Page 129
■ Summary of Definitions......Page 135
Exercise 3.1......Page 136
Extensional and Intensional Definitions......Page 138
Definition by Genus and Difference......Page 145
■ Summary of Definitions......Page 152
Exercise 3.2......Page 153
3.3 Using Definitions to Evaluate Arguments......Page 157
■ Summary of Definitions......Page 161
Exercise 3.3......Page 162
Notes......Page 167
CHAPTER 4 Informal Fallacies......Page 169
Argument Against the Person ( Ad Hominem Fallacy)......Page 171
Straw Man Fallacy......Page 174
Appeal to Force ( Ad Baculum Fallacy)......Page 175
Appeal to the People ( Ad Populum Fallacy)......Page 177
Appeal to Pity ( Ad Misericordiam Fallacy)......Page 178
Appeal to Ignorance ( Ad Ignorantiam Fallacy)......Page 179
Red Herring ( Ignoratio Elenchi Fallacy)......Page 181
■ Summary of Definitions......Page 182
Exercise 4.1......Page 183
Equivocation......Page 188
Amphiboly......Page 190
Composition......Page 193
Division......Page 195
Exercise 4.2......Page 196
Begging the Question ( Petitio Principii )......Page 199
False Dilemma......Page 202
Appeal to Unreliable Authority ( Ad Verecundiam Fallacy)......Page 204
False Cause Fallacy......Page 205
Complex Question......Page 208
■ Summary of Definitions......Page 210
Exercise 4.3......Page 211
Notes......Page 217
5.1 Standard Forms of Categorical Statements......Page 219
■ Summary of Standard Forms......Page 221
Putting Categorical Statements into Standard Form......Page 222
■ Summary of Stylistic Variants......Page 223
Exercise 5.1......Page 224
5.2 The Traditional Square of Opposition......Page 227
Exercise 5.2......Page 231
Conversion......Page 234
Obversion......Page 236
Contraposition......Page 238
■ Summary of Definitions......Page 240
Exercise 5.3......Page 241
6.1 Standard Form, Mood, and Figure......Page 247
Exercise 6.1......Page 251
6.2 Venn Diagrams and Categorical Statements......Page 254
Exercise 6.2......Page 263
6.3 Venn Diagrams and Categorical Syllogisms......Page 264
Exercise 6.3......Page 270
6.4 The Modern Square of Opposition......Page 272
Exercise 6.4......Page 279
6.5 Enthymemes......Page 281
Exercise 6.5......Page 284
Sorites......Page 285
Removing Term-Complements......Page 288
Exercise 6.6......Page 290
6.7 Rules for Evaluating Syllogisms......Page 293
■ Summary of Rules for Determining the Validity of Categorical Syllogisms......Page 296
Exercise 6.7......Page 297
Notes......Page 299
CHAPTER 7 Statement Logic: Truth Tables......Page 301
7.1 Symbolizing English Arguments......Page 302
Negations......Page 303
Conjunctions......Page 306
Disjunctions......Page 307
Conditionals......Page 309
Biconditionals......Page 311
Putting It All Together......Page 312
Symbol System for Statement Logic: A More Precise Formulation......Page 318
Exercise 7.1......Page 321
7.2 Truth Tables......Page 325
Conjunctions......Page 326
Conditionals......Page 327
Biconditionals......Page 329
■ Summary of Truth Tables for the Five Compounds......Page 331
Exercise 7.2......Page 332
7.3 Using Truth Tables to Evaluate Arguments......Page 333
■ Remembering Truth Conditions......Page 339
Exercise 7.3......Page 342
7.4 Abbreviated Truth Tables......Page 344
Exercise 7.4......Page 351
Tautology, Contradiction, and Contingency......Page 355
Equivalence, Contradictoriness, Consistency, and Inconsistency......Page 358
Concluding Observations......Page 360
Exercise 7.5......Page 363
Note......Page 365
8.1 Implicational Rules of Inference......Page 367
■ Summary of Implicational Rules......Page 381
Exercise 8.1......Page 382
8.2 Five Equivalence Rules......Page 387
■ Summary of the First Set of Equivalence Rules......Page 394
Exercise 8.2......Page 396
8.3 Five More Equivalence Rules......Page 400
Exercise 8.3......Page 404
8.4 Conditional Proof......Page 410
Exercise 8.4......Page 416
8.5 Reductio ad Absurdum......Page 419
■ Summary of Tips for Constructing Proofs......Page 422
Exercise 8.5......Page 424
8.6 Proving Theorems......Page 428
Exercise 8.6......Page 431
Notes......Page 433
9.1 The Language of Predicate Logic......Page 435
Predicates, Constants, and Variables......Page 436
The Universal Quantifier......Page 437
The Existential Quantifier......Page 440
The Language of Predicate Logic: A More Precise Formulation......Page 442
■ Summary of Symbolizations......Page 446
■ Summary of Definitions......Page 447
Exercise 9.1......Page 448
9.2 Demonstrating Invalidity......Page 452
Exercise 9.2......Page 460
9.3 Constructing Proofs......Page 462
Universal Instantiation......Page 464
■ Summary of Universal Instantiation (UI)......Page 466
Existential Generalization......Page 467
■ Summary of Existential Generalization (EG)......Page 468
Existential Instantiation......Page 469
Universal Generalization......Page 472
Exercise 9.3......Page 475
9.4 Quantifier Negation, RAA, and CP......Page 482
Exercise 9.4......Page 487
9.5 The Logic of Relations: Symbolizations......Page 490
■ Summary of Symbolizations......Page 493
Exercise 9.5......Page 495
9.6 The Logic of Relations: Proofs......Page 499
Exercise 9.6......Page 503
9.7 Identity: Symbolizations......Page 508
Exercise 9.7......Page 512
9.8 Identity: Proofs......Page 514
Exercise 9.8......Page 517
Notes......Page 518
10.1 Inductive and Deductive Logic......Page 521
Exercise 10.1......Page 527
Arguments from Authority......Page 529
Arguments from Analogy......Page 531
Induction by Enumeration......Page 535
■ Summary of Definitions......Page 539
Exercise 10.2......Page 540
10.3 Scientific Reasoning: Mill’s Method......Page 544
Mill’s Methods......Page 545
Scientific Reasoning......Page 548
Exercise 10.3......Page 553
10.4 Probabilistic Reasoning: The Rules of Probability......Page 558
The Rules of Probability......Page 559
Bayes’ Theorem......Page 567
■ Summary of the Rules of Probability......Page 571
Exercise 10.4......Page 572
Notes......Page 578
Answer Key......Page 581
Photo Credits......Page 649
Glossary/Index......Page 651