The Logic Book

The Logic Book......Page 2
Contents......Page 4
Preface......Page 6
Software......Page 7
Acknowledgments......Page 8
1.1 Background......Page 10
1.2 Why Study Logic?......Page 15
1.3 Sentences, Truth-Values, and Arguments......Page 16
1.3E Exercises......Page 19
1.4 Deductive Validity and Soundness......Page 21
1.4E Exercises......Page 25
1.5 Inductive arguments......Page 26
1.5E Exercises......Page 27
1.6 Logical Consistency, Truth, Falsity, and Equivalence......Page 28
1.6E Exercises......Page 31
1.7 Special Cases of Validity......Page 33
1.7E Exercises......Page 35
Glossary......Page 36
2.1 Symbolization and Truth-Functional Connectives......Page 37
Conjunction......Page 39
Disjunction......Page 42
Negation......Page 44
Combinations of Sentential Connectives......Page 47
Material Conditional......Page 50
Material Biconditional......Page 54
Summary of Some Common Connectives......Page 56
2.1E Exercises......Page 57
2.2 Complex Symbolizations......Page 59
Guidelines for Paraphrasing......Page 60
2.2E Exercises......Page 67
2.3 Non-Truth-Functional Connectives......Page 69
2.3E Exercises......Page 75
Object Language and Metalanguage, Use and Mention......Page 76
The Language SL......Page 78
2.4E Exercises......Page 82
Glossary......Page 83
3.1 Truth-Value Assignments and Truth-Tables for Sentences......Page 84
3.1E Exercises......Page 91
3.2 Truth-Functional Truth, Falsity and Indeterminacy......Page 92
3.2E Exercises......Page 101
3.3 Truth-Functional Equivalence......Page 102
3.3E Exercises......Page 105
3.4 Truth-Functional Consistency......Page 107
3.4E Exercises......Page 109
3.5 Truth-Functional Entailment and Truth-Functional Validity......Page 110
3.5E Exercises......Page 116
3.6 Truth-Functional Properties and Truth-Functional Consistency......Page 119
3.6E Exercises......Page 122
Glossary......Page 123
4.1 The Truth-Tree Method......Page 124
4.2 Truth-Tree Rules for Sentences Containing '-', 'v', and '&'......Page 125
4.2E Exercises......Page 138
4.3 Rules for Sentences Containing Material Conditional and Material Biconditional......Page 139
4.3E Exercises......Page 145
4.4 More Complex Truth-Trees......Page 146
4.4E Exercises......Page 152
4.5 Using Truth-Trees to Test for Truth-Functional Truth, Falsity, and Indeterminacy......Page 153
4.5E Exercises......Page 158
4.6 Truth-Functional Equivalence......Page 159
4.7 Truth-Functional Entailment and Truth-Functional Validity......Page 162
4.7E Exercises......Page 166
Summary......Page 168
5.1 The Derivation System SD......Page 169
Introduction and Elimination Rules for '&'......Page 171
Introduction and Elimination Rules for Material Conditional......Page 172
5.1.1E Exercises......Page 177
5.1.2 Introduction and Elimination Rules for '-'......Page 179
5.1.3 Introduction and Elimination Rules for 'v'......Page 184
5.1.3E Exercises......Page 186
5.1.4 Introduction and Elimination Rules for Material Biconditional......Page 187
5.1.4E Exercises......Page 188
5.1.5 Rule Summary......Page 189
5.1.5E Exercises......Page 196
5.2 Basic Concepts of SD......Page 198
5.3 Strategies for Constructing Derivations in SD......Page 202
Arguments......Page 206
Theorems......Page 210
Equivalence......Page 217
Inconsistency......Page 226
5.3E Exercises......Page 232
5.4 The Derivation System SD+......Page 237
Modus Tollens (MT)......Page 238
Rules of Replacement......Page 239
Double Negation (DN)......Page 240
Equivalence (Equiv)......Page 241
5.4E Exercises......Page 245
Glossary......Page 248
6.1 Mathematical Induction
......Page 249
6.1E Exercises......Page 256
6.2 Truth-Functional Completeness......Page 257
6.2E Exercises......Page 265
6.3 The Soudness of SD and SD+......Page 267
6.3E Exercises......Page 273
6.4 The Completeness of SD and SD+......Page 275
6.4E Exercises......Page 284
7.1 The Limitations of SL......Page 285
7.2 Predicates, Individual Constants, and Quantity Terms of English......Page 288
7.3 Introduction to PL......Page 293
7.3E Exercises......Page 296
7.4 Quantifiers Introduced......Page 299
7.4E Exercises......Page 305
7.5 The Formal Syntax of PL......Page 306
7.5E Exercises......Page 315
7.6 A-, E-, I-, AND O-SENTENCES......Page 317
7.6E Exercises......Page 330
7.7 Symbolization Techniques......Page 331
7.7E Exercises
......Page 348
7.8 Multiple Quantifiers with Overlapping Scope......Page 351
7.8E Exercises......Page 364
7.9 Identity, Definite Descriptions, Properties of Relations, and Functions......Page 368
The Identity Predicate......Page 369
Definite Descriptions......Page 374
Properties of Relations......Page 375
Functions......Page 377
The Syntax of PLE......Page 383
7.9E Exercises......Page 384
8.1 Informal Semantics for PL......Page 387
8.1E Exercises
......Page 397
8.2 Quantificational Truth, Falsehood, and Indeterminacy
......Page 400
8.2E Exercises
......Page 406
8.3 Quantificational Equivalence and Consistency
......Page 407
8.3E Exercises
......Page 411
8.4 Quantificational Entailment and Validity......Page 412
8.4E Exercises
......Page 415
8.5 Truth-Functional Expansions......Page 418
8.5E Exercises......Page 431
8.6 Semantics for Predicate Logic with Identity and Functors......Page 433
8.6E Exercises
......Page 449
8.7 Formal Semantics of PL and PLE......Page 452
8.7E Exercises
......Page 464
Glossary......Page 466
9.1 Expanding the Rules for Truth-Trees for PL......Page 467
9.2 Truth-Trees and Quantificational Consistency
......Page 476
9.2E Exercises
......Page 482
9.3 Truth-Trees and Other Semantic Properties
......Page 483
9.3E Exercises
......Page 489
9.4 Fine-Tuning the Tree Method for PL......Page 491
9.4E Exercises
......Page 505
9.5 Trees for PLE
......Page 507
9.5E Exercises
......Page 521
9.6 Fine-Tuning the Tree Method for PLE......Page 523
9.6E Exercises......Page 537
Summary......Page 538
10.1 The Derivation System PD......Page 541
10.1E Exercises......Page 558
10.2 Using Derivations to Establish Syntactic Properties of PD......Page 560
Arguments......Page 561
Theorems......Page 571
Equivalence......Page 576
Inconsistency......Page 585
10.2E Exercises......Page 589
10.3 The Derivation System PD+......Page 592
10.3E Exercises......Page 595
10.4 The Derivation System PDE......Page 597
Arguments......Page 608
Theorems......Page 610
Inconsistency......Page 611
10.4E Exercises......Page 613
Glossary
......Page 616
11.1 Semantic Preliminaries for PL......Page 617
11.2 Semantic Preliminaries for PLE......Page 632
11.3 The Soundness of PD, PD+, and PDE......Page 636
11.3E Exercises......Page 641
11.4 The Completeness of PD, PD+, and PDE......Page 642
11.4E Exercises......Page 657
11.5 The Soundness of the Tree Method......Page 659
11.5E Exercises......Page 668
11.6 The Completeness of the Tree Method......Page 669
11.6E Exercises......Page 682
Inductive Logic......Page 684
Philosophy of Logic......Page 685
Index......Page 686
Index of Symbols......Page 692
Derivation Rules of SD......Page 693
Derivation Rules of SD+......Page 694
Derivation Rules of PD......Page 695
Derivation Rules of PDE......Page 696
Truth-Tree Rules for SL......Page 697
Truth-Tree Rules for PLE......Page 698