Description
Book SynopsisOffers a presentation of classical first-order logic. This book presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague.
Trade Review“
Deduction is the best logic textbook on the market. It is modern, clean, elegant, sharp and direct. It is a perfect accompaniment to the most recent developments in philosophy and logic; in every sense the logic textbook for the twenty-first century.”
Rick Benitez, University of SydneyTable of ContentsPreface 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 Stalnaker’s Semantics: System CS 418
12.5 Lewis’s 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
