The Art of Reasoning: An Introduction to Logic and Critical Thinking (Fourth Edition)

A clear and accessible introduction to the elements of logic, with a wealth of problems and exercises. Students learn logic by practicing it—by working through problems, analyzing existing arguments, and constructing their own arguments in plain language and symbolic notation. The Art of Reasoning not only introduces the principles of critical thinking and logic in a clear, accessible, and logical manner—thus practicing what it preaches—but it also provides ample opportunity for students to hone their skills and master course content. The Art of Reasoning: An Introduction to Logic and Critical Thinking -1 About the Author 5 Contents in Brief 7 Contents 9 Preface 13 Introduction 19 Part One: Language & Reasoning 25 Chapter 1: Classification 27 1.1 Concepts and Referents 27 1.2 Rules of Classification 31 1.3 Levels of Organization 36 Summary 40 Key Terms 40 Additional Exercises 40 Chapter 2: Definitions 44 2.1 The Functions of a Definition 44 2.2 Rules for Definitions 46 2.3 Constructing Definitions 54 Summary 60 Key Terms 60 Additional Exercises 60 Chapter 3: Propositions 65 3.1 Propositions and Word Meaning 66 3.2 Propositions and Grammar 70 Summary 81 Key Terms 81 Additional Exercises 81 Chapter 4: Argument Analysis 85 4.1 Elements of Reasoning 86 4.2 Diagramming Arguments 91 4.3 Evaluating Arguments 97 4.4 Induction and Deduction 100 4.5 Implicit Premises 106 4.6 Distilling Arguments 109 Summary 115 Key Terms 115 Additional Exercises 116 Chapter 5: Fallacies 121 5.1 Subjectivist Fallacies 122 5.2 Fallacies Involving Credibility 129 5.3 Fallacies of Context 134 5.4 Fallacies of Logical Structure 145 Summary 153 Key Terms 153 Additional Exercises 154 Part Two: Deductive Logic 161 Chapter 6: Categorical Propositions 163 6.1 Standard Form 163 6.2 The Square of Opposition 169 6.3 Existential Import 173 6.4 Venn Diagrams 176 6.5 Immediate Inference 181 Summary 192 Key Terms 192 Additional Exercises 193 Chapter 7: Categorical Syllogisms 197 7.1 The Structure of a Syllogism 197 7.2 Validity 202 7.3 Enthymemes 204 7.4 Rules of Validity 205 7.5 Venn Diagrams 216 Summary 232 Key Terms 232 Additonal Exercises 232 Chapter 8: Reasoning with Syllogisms 237 8.1 Disjunctive Syllogisms 238 8.2 Hypothetical Syllogisms 243 8.3 Distilling Deductive Arguments 251 8.4 Extended Arguments 260 Summary 271 Key Terms 271 Additional Exercises 272 Chapter 9: Propositional Logic—Propositions 278 9.1 Connectives 279 9.2 Statement Forms 293 9.3 Computing Truth Values 300 9.4 Formal Properties and Relationships 305 Summary 315 Key Terms 315 Additional Exercises 316 Chapter 10: Propositional Logic—Arguments 318 10.1 Truth Table Test of Validity 319 10.2 Truth Table Test: Short Form 324 10.3 Proof 329 10.4 Equivalence 347 10.5 Conditional Proof and Reductio ad Absurdum 359 Summary 369 Key Terms 369 Additional Exercises 370 Chapter 11: Predicate Logic 378 11.1 Singular and Quantified Statements 379 11.2 Categorical Statements 384 11.3 Quantifier Scope and Statement Forms 389 11.4 Proof 395 11.5 Relations and Multiple Quantification 415 Summary 427 Key Terms 427 Additional Exercises 428 Part Three: Inductive Logic 433 Chapter 12: Inductive Generalizations 435 12.1 Generalizing 435 12.2 Causality 441 12.3 Agreement and Difference 443 12.4 Concomitant Variations and Residues 449 Summary 456 Key Terms 456 Additional Exercises 456 Chapter 13: Argument by Analogy 460 13.1 Analogy and Similarity 460 132. Analysis and Evaluation 463 Summary 471 Additional Exercises 471 Chapter 14: Statistical Reasoning 474 14.1 Logic and Statistics 474 14.2 Using Statistics in Argument 477 14.3 Statistical Generalization 483 14.4 Statistical Evidence of Causality 488 Summary 497 Key Terms 497 Additional Exercises 497 Chapter 15: Explanation 501 15.1 Explanation and Argument 501 15.2 Adequacy of Hypotheses 506 15.3 The Truth of Hypotheses 513 Summary 522 Key Terms 522 Additional Exercises 522 Chapter 16: Probability 527 16.1 Probability Measures 528 16.2 The Probability Calculus 534 Summary 543 Key Terms 543 Additional Exercises 544 Glossary 547 Answers to Selected Exercises 553 Index 615 Categorical Propositions 625 Propositional Logic 627 **A clear and accessible introduction to the elements of logic, with a wealth of problems and exercises.** __The Art of Reasoning__