Deduction 2e

Preface to the Second Edition viii

Acknowledgments x

1 Basic Concepts of Logic 1

1.1 Arguments 1

1.2 Validity 16

1.3 Implication and Equivalence 23

1.4 Logical Properties of Sentences 27

1.5 Satisfiability 31

2 Sentences 36

2.1 The Language of Sentential Logic 36

2.2 Truth Functions 40

2.3 A Sentential Language 46

2.4 Symbolization 49

2.5 Validity 56

2.6 Truth Tables 60

2.7 Truth Tables for Formulas 63

2.8 Truth Tables for Argument Forms 68

2.9 Implication, Equivalence, and Satisfiability 71

3 Truth Trees 76

3.1 Thinking Backwards 76

3.2 Constructing Truth Trees 80

3.3 Negation, Conjunction, and Disjunction 84

3.4 The Conditional and Biconditional 93

3.5 Other Applications 101

4 Natural Deduction 107

4.1 Natural Deduction Systems 107

4.2 Rules for Negation and Conjunction 110

4.3 Rules for the Conditional and Biconditional 118

4.4 Rules for Disjunction 122

4.5 Derivable Rules 125

5 Quantifiers 137

5.1 Constants and Quantifiers 138

5.2 Categorical Sentence Forms 144

5.3 Polyadic Predicates 148

5.4 The Language Q 153

5.5 Symbolization 156

6 Quantified Truth Trees 173

6.1 Rules for Quantifiers 174

6.2 Strategies 178

6.3 Interpretations 189

6.4 Constructing Interpretations from Trees 199

7 Quantified Natural Deduction 206

7.1 Deduction Rules for Quantifiers 206

7.2 Universal Proof 214

7.3 Derived Rules for Quantifiers 220

8 Identity and Function Symbols 225

8.1 Identity 225

8.2 Truth Tree Rules for Identity 231

8.3 Deduction Rules for Identity 235

8.4 Function Symbols 238

9 Necessity 249

9.1 If 249

9.2 Modal Connectives 251

9.3 Symbolization 256

9.4 Modal Truth Trees 261

9.5 Other Tree Rules 265

9.6 World Travelling 268

9.7 Modal Deduction 278

9.8 Other Modal Systems 289

10 Between Truth and Falsehood 295

10.1 Vagueness and Presupposition 295

10.2 Many-Valued Truth Tables 300

10.3 Many-Valued Trees 314

10.4 Many-Valued Deduction 325

10.5 Fuzzy Logic 332

10.6 Intuitionistic Logic 344

11 Obligation 361

11.1 Deontic Connectives 362

11.2 Deontic Truth Trees 370

11.3 Deontic Deduction 381

11.4 Moral and Practical Reasoning 387

12 Counterfactuals 395

12.1 The Meaning of Counterfactuals 399

12.2 Truth Tree Rules for Counterfactuals 402

12.3 Deduction Rules for Counterfactuals 409

12.4 Stalnakerâs Semantics: System CS 418

12.5 Lewisâs Semantics: System CL 423

13 Common-Sense Reasoning 434

13.1 When Good Arguments Go Bad 435

13.2 Truth Trees 439

13.3 Defeasible Deduction 454

13.4 Defeasible Deontic Logic 466

14 Quantifiers and Modality 475

14.1 Quantified S5 475

14.2 Free Logic 487

Bibliography 504

Index 507