Logic and Philosophy: A Modern Introduction / Edition 10

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Overview

Excelling In Logic class doesn't have to be difficult. Logic and Philosophy: A Modern Introduction walks you through tough concepts with clear and concise explanations that put the study of logic into terms you'll understand and enjoy discovering. Whether logic is your favorite class or just a requirement, this edition teaches the concepts you need to know to get the skills that you want. Throughout, philosophical issues are intertwined with the key concepts of logic, so-that the book presents an exciting opportunity for discussing controversies normally not introduced in logic texts.
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Editorial Reviews

From the Publisher
"The book develops formal logic rigorously, but with an approach that students will find clear and accessible, especially with respect to the explanations of key concepts and the featured "walk-throughs" of proof techniques, etc."

"I would describe the book as a 'real logic book that is about as accessible as it gets."

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Product Details

  • ISBN-13: 9780495128441
  • Publisher: Cengage Learning
  • Publication date: 6/5/2006
  • Edition description: Older Edition
  • Edition number: 10
  • Pages: 544
  • Product dimensions: 6.30 (w) x 9.20 (h) x 0.80 (d)

Meet the Author

Alan Hausman received a Ph.D. in philosophy from Iowa State University and now teaches philosophy at Hunter College. He has published extensively on history of early modern philosophy, especially on the work of Hume, and on the work of Nelson Goodman.

Howard Kahane (deceased) is considered one of the founders of the critical-thinking movement, an approach to logic that makes it less abstract and more practical as a tool for analyzing political and social issues.

Paul Tidman received his Ph.D. in philosophy from the University of Notre Dame. He teaches philosophy at Mount Union College in Ohio.

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Table of Contents

Preface to the Eleventh Edition ix

Preface to the Tenth Edition xi

Chapter 1 Introduction 1

1 The Elements of an Argument 1

2 Deduction and Induction 5

3 Deductive Argument Forms 7

4 Truth and Validity 8

5 Soundness 11

6 Consistency 12

7 Contexts of Discovery and Justification 14

8 The Plan of This Book 14

Key Terms 16

Part 1 Sentential Logic 17

Chapter 2 Symbolizing in Sentential Logic 19

1 Atomic and Compound Sentences 20

2 Truth-Functions 21

3 Conjunctions 21

4 Non-Truth-Functional Connectives 25

5 Variables and Constants 25

6 Negations 27

7 Parentheses and Brackets 28

8 Use and Mention 29

9 Disjunctions 30

10 "Not Both" and "Neither . . . Nor" 33

11 Material Conditionals 35

12 Material Biconditionals 38

13 "Only If" and "Unless" 40

14 Symbolizing Complex Sentences 41

15 Alternative Sentential Logic Symbols 48

Key Terms 50

Chapter 3 Truth Tables 53

1 Computing Truth-Values 53

2 Logical Form 58

3 Tautologies, Contradictions, and Contingent Sentences 63

4 Logical Equivalences 69

5 Truth Table Test of Validity 70

6 Truth Table Test of Consistency 73

7 Validity and Consistency 74

8 The Short Truth Table Test for Invalidity 76

9 The Short Truth Table Test for Consistency 80

10 A Method of Justification for the Truth Tables 81

Key Terms 85

Chapter 4 Proofs 86

1 Argument Forms 86

2 The Method of Proof: Modus Ponens and Modus Tollens 88

3 Disjunctive Syllogism and Hypothetical Syllogism 91

4 Simplification and Conjunction 93

5 Addition and Constructive Dilemma 94

6 Principles of Strategy 97

7 Double Negation and DeMorgan's Theorem 103

8 Commutation, Association, and Distribution 106

9Contraposition, Implication, and Exportation 107

10 Tautology and Equivalence 107

11 More Principles of Strategy 111

12 Common Errors in Problem Solving 115

Key Terms 122

Chapter 5 Conditional and Indirect Proofs 123

1 Conditional Proofs 123

2 Indirect Proofs 132

3 Strategy Hints for Using CP and IP 137

4 Zero-Premise Deductions 138

5 Proving Premises Inconsistent 139

6 Adding Valid Argument Forms 141

7 An Alternative to Conditional Proof? 142

8 The Completeness and Soundness of Sentential Logic 144

9 Introduction and Elimination Rules 146

Key Terms 149

Chapter 6 Sentential Logic Truth Trees 151

1 The Sentential Logic Truth Tree Method 151

2 The Truth Tree Rules 152

3 Details of Tree Construction 154

4 Normal Forms and Trees 160

5 Constructing Tree Rules for Any Function 161

Key Terms 163

Part 2 Predicate Logic 165

Chapter 7 Predicate Logic Symbolization 167

1 Individuals and Properties 167

2 Quantifiers and Free Variables 171

3 Universal Quantifiers 172

4 Existential Quantifiers 177

5 Basic Predicate Logic Symbolizations 178

6 The Square of Opposition 180

7 Common Pitfalls in Symbolizing with Quantifiers 180

8 Expansions 183

9 Symbolizing "Only," "None but," and "Unless" 186

Key Terms 190

Chapter 8 Predicate Logic Semantics 191

1 Interpretations in Predicate Logic 191

2 Proving Invalidity 193

3 Using Expansions to Prove Invalidity 196

4 Consistency in Predicate Logic 197

5 Validity and Inconsistency in Predicate Logic 198

Key Terms 199

Chapter 9 Predicate Logic Proofs 200

1 Proving Validity 200

2 The Four Quantifier Rules 202

3 The Five Main Restrictions 209

4 Precise Formulation of the Four Quantifier Rules 213

5 Mastering the Four Quantifier Rules 216

6 Quantifier Negation 220

Key Term 225

Chapter 10 Relational Predicate Logic 226

1 Relational Predicates 226

2 Symbolizations Containing Overlapping Quantifiers 229

3 Expansions and Overlapping Quantifiers 229

4 Places and Times 234

5 Symbolizing "Someone," "Somewhere," "Sometime," and So On 235

6 Invalidity and Consistency in Relational Predicate Logic 240

7 Relational Predicate Logic Proofs 241

8 Strategy for Relational Predicate Logic Proofs 248

9 Theorems and Inconsistency in Predicate Logic 250

10 Predicate Logic Metatheory 253

11 A Simpler Set of Quantifier Rules 254

Chapter 11 Rationale Behind the Precise Formulation of the Four Quantifier Rules 257

1 Cases Involving the Five Major Restrictions 257

2 One-to-One Correspondence Matters 260

3 Accidentally Bound Variables and Miscellaneous Cases 264

4 Predicate Logic Proofs with Flagged Constants 269

Chapter 12 Predicate Logic Truth Trees 272

1 Introductory Remarks 272

2 General Features of the Method 273

3 Specific Examples of the Method 273

4 Some Advantages of the Trees 278

5 Example of an Invalid Argument with at Least One Open Path 279

6 Metatheoretic Results 280

7 Strategy and Accounting 283

Key Terms 285

Chapter 13 Identity and Philosophical Problems of Symbolic Logic 286

1 Identity 286

2 Definite Descriptions 292

3 Properties of Relations 294

4 Higher-Order Logics 297

5 Limitations of Predicate Logic 299

6 Philosophical Problems 303

7 Logical Paradoxes 310

Key Terms 317

Chapter 14 Syllogistic Logic 319

1 Categorical Propositions 322

2 Existential Import 322

3 The Square of Opposition 323

4 Conversion, Obversion, Contraposition 326

5 Syllogistic Logic - Not Assuming Existential Import 329

6 Venn Diagrams 332

7 Syllogisms 334

8 Determining Syllogism Validity 336

9 Venn Diagram Proofs of Validity or Invalidity 337

10 Five Rules for Determining Validity or Invalidity 342

11 Syllogistics Extended 345

12 Enthymemes 348

13 Sorites 349

14 Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared 351

Key Terms 355

Answers to Even-Numbered Exercise Items 358

Bibliography 419

Special Symbols 421

Index 423

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