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