The Power of Logic

Cover Page......Page 1
Title Page......Page 4
Copyright Page......Page 5
About the Authors......Page 6
Brief Contents......Page 8
Preface......Page 15
Contents......Page 9
CHAPTER 1: Basic Concepts......Page 22
1.1 Validity and Soundness......Page 25
Exercise 1.1......Page 31
Argument Forms......Page 35
Understanding Conditional Statement......Page 38
Famous Valid Forms......Page 40
■ Summary of Famous Valid Forms......Page 45
■ The Famous Forms Method......Page 47
■ Summary of Definitions......Page 48
Exercise 1.2......Page 49
Counterexamples......Page 54
The Counterexample Method......Page 57
Categorical Statements and Arguments......Page 60
■ The Counterexample Method......Page 67
Exercise 1.3......Page 68
1.4 Strength and Cogency......Page 71
■ Summary of Definitions......Page 77
Exercise 1.4......Page 78
Notes......Page 81
2.1 Arguments and Nonarguments......Page 84
Exercise 2.1......Page 88
2.2 Well-Crafted Arguments......Page 91
■ Principles for Rewriting Arguments as Well-Crafted Ones......Page 106
Exercise 2.2......Page 107
2.3 Argument Diagrams......Page 116
Exercise 2.3......Page 120
Notes......Page 128
3.1 Logic, Meaning, and Emotive Force......Page 130
Exercise 3.1......Page 136
3.2 Definitions......Page 138
Extensional and Intensional Definitions......Page 139
■ Types of Extensional and Intensional Definitions......Page 144
Definition by Genus and Difference......Page 145
■ Criteria for Evaluating Definitions by Genus and Difference......Page 150
Exercise 3.2......Page 151
3.3 Using Definitions to Evaluate Arguments......Page 155
Exercise 3.3......Page 160
Notes......Page 165
CHAPTER 4: Informal Fallacies......Page 168
1. Argument Against the Person (Ad Hominem Fallacy)......Page 170
2. Straw Man Fallacy......Page 172
3. Appeal to Force (Ad Baculum Fallacy)......Page 174
4. Appeal to the People (Ad Populum Fallacy)......Page 176
5. Appeal to Pity (Ad Misericordiam Fallacy)......Page 177
6. Appeal to Ignorance (Ad Ignorantiam Fallacy)......Page 178
7. Red Herring (Also Known as Missing the Point or Ignoratio Elenchi)......Page 180
■ Summary of Fallacies Involving Irrelevant Premises......Page 181
Exercise 4.1......Page 182
8. Equivocation......Page 187
9. Amphiboly......Page 189
10. Composition......Page 192
11. Division......Page 193
Exercise 4.2......Page 195
12. Begging the Question (Petitio Principii)......Page 198
13. False Dilemma......Page 201
14. Appeal to Unreliable Authority (Ad Verecundiam Fallacy)......Page 203
15. False Cause Fallacy......Page 204
16. Complex Question......Page 207
■ Summary of Fallacies Involving Unwarranted Assumptions......Page 209
Exercise 4.3......Page 210
Notes......Page 216
5.1 Standard Forms of Categorical Statements......Page 218
Quality and Quantity......Page 220
Putting Categorical Statements into Standard Form......Page 221
■ Summary of Stylistic Variants......Page 222
Exercise 5.1......Page 223
5.2 The Traditional Square of Opposition......Page 226
Exercise 5.2......Page 229
Conversion......Page 232
Obversion......Page 233
Contraposition......Page 234
Exercise 5.3......Page 237
6.1 Standard Form, Mood, and Figure......Page 244
Exercise 6.1......Page 247
6.2 Venn Diagrams and Categorical Statements......Page 250
Exercise 6.2......Page 259
6.3 Venn Diagrams and Categorical Syllogisms......Page 260
Exercise 6.3......Page 267
6.4 The Modern Square of Opposition......Page 269
Exercise 6.4......Page 276
6.5 Enthymemes......Page 278
Exercise 6.5......Page 281
Sorites......Page 282
Removing Term-Complements......Page 285
Exercise 6.6......Page 287
6.7 Rules for Evaluating Syllogisms......Page 290
■ Summary of Rules for Determining the Validity of Categorical Syllogisms......Page 293
Exercise 6.7......Page 294
Notes......Page 296
CHAPTER 7: Statement Logic: Truth Tables......Page 298
7.1 Symbolizing English Arguments......Page 299
Negations......Page 300
Conjunctions......Page 302
Disjunctions......Page 304
Conditionals......Page 306
Biconditionals......Page 308
Putting It All Together......Page 309
Symbol System for Statement Logic: A More Precise Formulation......Page 317
Exercise 7.1......Page 319
7.2 Truth Tables......Page 323
Conjunctions......Page 324
Material Conditionals......Page 325
Material Biconditionals......Page 327
■ Summary of Truth Tables for the Five Compounds......Page 329
Exercise 7.2......Page 330
7.3 Using Truth Tables to Evaluate Arguments......Page 331
■ Remembering Truth Conditions......Page 338
Exercise 7.3......Page 340
7.4 Abbreviated Truth Tables......Page 343
Exercise 7.4......Page 349
7.5 Logically Significant Categories and Relationships......Page 352
Tautology, Contradiction, and Contingency......Page 353
Equivalence, Contradictoriness, Consistency, and Inconsistency......Page 355
Interesting Facts About These Categories and Relationships......Page 357
Exercise 7.5......Page 361
Note......Page 364
8.1 Implicational Rules of Inference......Page 366
Exercise 8.1......Page 382
8.2 Five Equivalence Rules......Page 388
■ Summary of the First Set of Equivalence Rules......Page 396
Exercise 8.2......Page 398
8.3 Five More Equivalence Rules......Page 402
■ Summary of the Second Set of Equivalence Rules......Page 406
Exercise 8.3......Page 407
8.4 Conditional Proof......Page 413
Exercise 8.4......Page 419
8.5 Reductio ad Absurdum......Page 422
■ Summary of Tips for Constructing Proofs......Page 426
Exercise 8.5......Page 428
8.6 Proving Theorems......Page 432
■ Summary of Definitions......Page 435
Exercise 8.6......Page 436
Notes......Page 437
CHAPTER 9: Predicate Logic......Page 440
9.1 Predicates and Quantifiers......Page 441
Exercise 9.1......Page 451
9.2 Demonstrating Invalidity......Page 456
Exercise 9.2......Page 463
9.3 Constructing Proofs......Page 465
Universal Instantiation......Page 467
Existential Generalization......Page 469
■ Existential Generalization (EG)......Page 471
Existential Instantiation......Page 472
Universal Generalization......Page 475
■ Universal Generalization (UG)......Page 478
Exercise 9.3......Page 479
9.4 Quantifier Negation, RAA, and CP......Page 485
Exercise 9.4......Page 490
9.5 The Logic of Relations: Symbolizations......Page 493
Exercise 9.5......Page 498
9.6 The Logic of Relations: Proofs......Page 502
Exercise 9.6......Page 506
9.7 Identity: Symbolizations......Page 511
Exercise 9.7......Page 515
9.8 Identity: Proofs......Page 517
Exercise 9.8......Page 520
Notes......Page 521
10.1 Inductive and Deductive Logic: Contrasts and Clarifications......Page 524
Exercise 10.1......Page 530
Arguments from Authority......Page 532
Induction by Enumeration......Page 534
Exercise 10.2......Page 538
Mill’s Methods......Page 540
Scientific Reasoning......Page 544
Exercise 10.3......Page 549
10.4 Arguments from Analogy......Page 555
■ Summary of Arguments from Analogy......Page 558
Exercise 10.4......Page 559
Notes......Page 563
The Classical Theory......Page 566
The Relative Frequency Theory......Page 568
The Subjectivist Theory......Page 570
Exercise 11.1......Page 572
11.2 The Rules of Probability......Page 573
Exercise 11.2......Page 582
11.3 Bayes’ Theorem......Page 584
Exercise 11.3......Page 589
Notes......Page 594
Answer Key......Page 596
Photo Credits......Page 668
Glossary/Index......Page 670