Introduction 1

Part 1 Language and Reasoning

Chapter 1 Classification

1.1 Concepts and Referents 9

1.2 Rules of Classification 13

1.2A Consistent Principle 13

1.2B Essential Attributes 15

1.3 Levels of Organization 18

Summary 22

Additional Exercises 22

Chapter 2 Definitions

2.1 The Functions of a Definition 26

2.2 Rules for Definitions 28

2.3 Constructing Definitions 36

Summary 42

Additional Exercises 42

Chapter 3 Propositions

3.1 Propositions and Word Meaning 48

3.1A Connotations 49

3.1B Metaphors 50

3.2 Propositions and Grammar 52

3.2A Propositions and Sentence Structure 52

3.2B Connectives 55

3.2C Restrictive and Nonrestrictive Clauses 57

3.2D Noun Clauses 60

Summary 63

Additional Exercises 63

Chapter 4 Argument Analysis

4.1 Elements of Reasoning 68

4.1A Premise, Conclusion, and Argument 68

4.1B Recognizing Arguments 69

4.2 Diagramming Arguments 73

4.3 Evaluating Arguments 79

4.4 Induction and Deduction 82

4.5 Implicit Premises 88

4.6 Distilling Arguments 91

Summary 97

Additional Exercises 98

Chapter 5 Fallacies

5.1 Subjectivist Fallacies 104

5.1A Subjectivism 104

5.1B Appeal to Majority 106

5.1C Appeal to Emotion 106

5.1D Appeal to Force (Argumentum ad Baculum) 108

5.2 Fallacies Involving Credibility 111

5.2A Appeal to Authority (Argumentum ad Verecundiam) 111

5.2B Ad Hominem 113

5.3 Fallacies of Context 116

5.3A False Alternative 117

5.3B Post Hoc 118

5.3C Hasty Generalization 118

5.3D Accident 120

5.3E Slippery Slope 121

5.3F Composition and Division 123

5.4 Fallacies of Logical Structure 127

5.4A Begging the Question (Circular Argument) 127

5.4B Equivocation 128

5.4C Appeal to Ignorance (Argumentum ad Ignorantiam) 130

5.4D Diversion 131

Summary 135

Additional Exercises 136

Part 2 Deductive Logic

Chapter 6 Categorical Propositions

6.1 Standard Form 145

6.1A Components of Categorical Propositions 145

6.1B Translating into Standard Form 148

6.2 The Square of Opposition 151

6.2A Contraries 152

6.2B Contradictories 152

6.2C Subalternates 153

6.2D Subcontraries 154

6.3 Existential Import 155

6.4 Venn Diagrams 158

6.5 Immediate Inference 163

6.5A Conversion 163

6.5B Obversion 166

6.5C Contraposition 170

Summary 174

Additional Exercises 175

Chapter 7 Categorical Syllogisms

7.1 The Structure of a Syllogism 179

7.2 Validity 184

7.3 Enthymemes 186

7.4 Rules of Validity 187

7.4A Distribution 187

7.4B The Rules 190

7.4C Enthymemes and Rules 196

7.5 Venn Diagrams 198

7.5A Diagramming Syllogisms 198

7.5B Enthymemes and Venn Diagrams 203

7.5C Venn Diagrams and Existential Import 207

Summary 214

Additional Exercises 214

Chapter 8 Reasoning with Syllogisms

8.1 Disjunctive Syllogisms 220

8.2 Hypothetical Syllogisms 225

8.2A Hypothetical Propositions 225

8.2B Forms of Hypothetical Syllogism 228

8.3 Distilling Deductive Arguments 233

8.3A Identifying the Form of a Syllogism 233

8.3B Nonstandard Quantifiers 237

8.4 Extended Arguments 242

8.4A Categorical Syllogisms in Extended Arguments 243

8.4B Hypothetical Syllogisms in Extended Arguments 245

8.4C Extended Arguments with Elements of Different Types 246

8.4D Compound Components 248

8.4E Distilling an Extended Argument 250

Summary 253

Additional Exercises 254

Chapter 9 Propositional Logic-Propositions

9.1 Connectives 261

9.1A Conjunction, Negation, and Disjunction 262

9.1B Conditional and Biconditional 266

9.1C Truth Functions 271

9.2 Statement Forms 275

9.3 Computing Truth Values 282

9.4 Formal Properties and Relationships 287

9.4A Tautologies, Self-Contradictions, and Contingencies 287

9.4B Equivalence, Contradiction, and Consistency 289

Summary 297

Additional Exercises 298

Chapter 10 Propositional Logic-Arguments

10.1 Truth Table Test of Validity 301

10.2 Truth Table Test: Short Form 306

10.3 Proof 311

10.3A Rules of Inference 311

10.3B Rules of Inference (Continued) 316

10.3C Constructing a Proof 322

10.4 Equivalence 329

10.4A Rules of Equivalence 330

10.4B Rules of Equivalence (Continued) 335

10.5 Conditional Proof and Reductio ad Absurdum 341

10.5A Conditional Proof 341

10.5B Reductio ad Absurdum 344

Summary 351

Additional Exercises 352

Chapter 11 Predicate Logic

11.1 Singular and Quantified Statements 361

11.1A Singular Statements 361

11.1B Quantified Statements 364

11.2 Categorical Statements 366

11.3 Quantifier Scope and Statement Forms 371

11.3A Compound Statements Within the Scope of a Quantifier 371

11.3B Combining Quantified Statements 373

11.4 Proof 377

11.4A Using Propositional Rules 377

11.4B Equivalence Rule: Quantifier Negation 379

11.4C Inference Rules 382

11.4D Strategies for Proof 388

11.4E Conditional Proof and Reductio ad Absurdum 393

11.5 Relations and Multiple Quantification 397

11.5A Relations 397

11.5B Overlapping Quantifiers 399

11.5C Proof with Relational Statements 403

Summary 409

Additional Exercises 410

Part 3 Inductive Logic

Chapter 12 Inductive Generalizations

12.1 Generalizing 417

12.1A Three Rules for Generalizing 419

12.2 Causality 423

12.3 Agreement and Difference 425

12.4 Concomitant Variations and Residues 431

Summary 438

Additional Exercises 438

Chapter 13 Argument by Analogy

13.1 Analogy and Similarity 442

13.2 Analysis and Evaluation 445

13.2A Finding the Connecting Term 447

13.2B Evaluation 449

Summary 453

Additional Exercises 453

Chapter 14 Statistical Reasoning

14.1 Logic and Statistics 456

14.2 Using Statistics in Argument 459

14.2A Totals and Ratios 459

14.2B Frequency and Distribution 460

14.2C Average and Median 463

14.3 Statistical Generalization 465

14.4 Statistical Evidence of Causality 470

14.4A Correlation and Causality 470

14.4B Evaluating Correlations 471

14.4C Experiments Versus Observational Studies 475

14.4D External Validity 476

Summary 479

Additional Exercises 479

Chapter 15 Explanation

15.1 Explanation and Argument 483

15.1A Diagramming Explanations 484

15.1B Evaluating Explanations 486

15.2 Adequacy of Hypotheses 488

15.2A Strength 488

15.2B Completeness 490

15.2C Informativeness 491

15.2D Combining the Standards 493

15.3 The Truth of Hypotheses 495

15.3A Testing Hypotheses 496

15.3B Plausibility 498

Summary 504

Additional Exercises 504

Chapter 16 Probability

16.1 Probability Measures 510

16.2 The Probability Calculus 516

16.2A Conjunction 516

16.2B Disjunction 518

16.2C Negation 519

16.2D Extending the Rules 520

Summary 525

Additional Exercises 526

Glossary 529

Answers to Selected Exercises 535

Index 597

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