Table of Contents
Preface ix
Chapter 1 Introduction 1
1.1 Logic 1
1.2 Valid arguments 1
1.3 Sound arguments 3
1.4 The plan of this book 5
Part 1 Syllogistic, Informal, and Inductive Logic
Chapter 2 Syllogistic Logic 6
2.1 Easier translations 6
2.2 The star test 8
2.4 English arguments 11
2.4 Harder translations 15
2.5 Deriving conclusions 18
2.6 Venn diagrams 22
2.7 Idiomatic arguments 26
2.8 The Aristotelian view 29
Chapter 3 Meaning and Definitatinos 31
3.1 Uses of language 31
3.2 Lexical definitions 33
3.3 Stipulative definitions 38
3.4 Explaining meaning 40
3.5 Making distinctions 44
3.6 Analytic and synthetic 45
3.7 A priori and a posteriori 47
Chapter 4 Fallacies and Argumentation 51
4.1 Good arguments 51
4.2 Informal fallacies 55
4.3 Inconsistency 65
4.4 Constructing arguments 69
4.5 Analyzing arguments 72
Chapter 5 Inductive Reasoning 75
5.1 The statistical syllogism 75
5.2 Probability calculations 77
5.3 Philosophical questions 82
5.4 Reasoning from a sample 87
5.5 Analogical reasoning 90
5.6 Analogy and other minds 92
5.7 Mill's methods 94
5.8 Scientific laws 98
5.9 Best-explanation reasoning 105
5.10 Problems with induction 106
Part 2 Classical Symbolic Logic
Chapter 6 Basic Proppositional Logic 112
6.1 Easier translations 112
6.2 Basic truth tables 115
6.3 Truth evaluations 118
6.4 Unknown evaluations 119
6.5 Complex truth tables 120
6.6 The truth-table test 122
6.7 The truth-assignment test 126
6.8 Harder translations 132
6.9 Idiomatic arguments 134
6.10 S-rules 136
6.11 I-rules 139
6.12 Mixing S- and I-rules 143
6.13 Extended inferences 144
6.14 Logic and computers 145
Chapter 7 Propositional Proofs 146
7.1 Easier proofs 146
7.2 Easier refutations 154
7.3 Harder proofs 161
7.4 Harder refutations 170
7.5 Copi proofs 174
7.6 Truth trees 178
Chapter 8 Basic Quantificational Logic 182
8.1 Easier translations 182
8.2 Easier proofs 186
8.3 Easier refutations 191
8.4 Harder translations 196
8.5 Harder proofs 198
8.6 Copi proofs 203
Chapter 9 Relations and Identity 207
9.1 Identity translations 207
9.2 Identity proofs 209
9.3 Easier relations 214
9.4 Harder relations 216
9.5 Relational proofs 220
9.6 Definite descriptions 227
9.7 Copi proofs 229
Part 3 Advanced Symbolic Systems
Chapter 10 Basic Modal Logic 230
10.1 Translations 230
10.2 Proofs 234
10.3 Refutations 241
Chapter 11 Further Modal Systems 249
11.1 Galactic travel 249
11.2 Quantified translations 254
11.3 Quantified proofs 257
11.4 A sophisticated system 261
Chapter 12 Deontic and Imperative Logic 267
12.1 Imperative translations 267
12.2 Imperative proofs 269
12.3 Deontic translations 276
12.4 Deontic proofs 279
Chapter 13 Belief Logic 290
13.1 Belief translations 290
13.2 Belief proofs 291
13.3 Believing and willing 298
13.4 Willing proofs 301
13.5 Rationality translations 303
13.6 Rationality proofs 305
13.7 A sophisticated system 309
Chapter 14 A Formalized Ethical Theory 312
14.1 Practical reason 312
14.2 Consistency 313
14.3 The golden rule 315
14.4 Starting the GR proof 320
14.5 GR logical machinery 324
14.6 The symbolic GR proof 331
Part 4 Further Vistas
Chapter 15 Metalogic 334
15.1 Metalogical questions 334
15.2 Symbols 334
15.3 Soundness 336
15.4 Completeness 338
15.5 An axiomatic system 341
15.6 Gödel's theorem 342
Chapter 16 History of Logic 348
16.1 Ancient logic 348
16.2 Medieval logic 351
16.3 Enlightenment logic 353
16.4 Frege and Russell 354
16.5 After Principia 356
Chapter 17 Deviant Logics 359
17.1 Many-valued logic 359
17.2 Paraconsistent logic 361
17.3 Intuitionist logic 364
17.4 Relevance logic 365
Chapter 18 Philosophy of Logic 368
15.1 Abstract entities 368
18.1 Metaphysical structures 369
18.2 The basis for logical laws 371
18.4 Truth and paradoxes 374
18.5 Logic's scope 376
For Further Reading 377
Answers to Selected Problems 378
Chapter 2 378
Chapter 3 379
Chapter 4 382
Chapter 5 383
Chapter 6 385
Chapter 7 387
Chapter 8 391
Chapter 9 394
Chapter 10 397
Chapter 11 400
Chapter 12 402
Chapter 13 404
Chapter 14 408
Index 409
