Meaning and Argument: An Introduction to Logic Through Language

Meaning and Argument......Page 5
Contents......Page 7
Preface to Revised Second Edition......Page 15
Preface to Second Edition......Page 16
Preface to Revised Edition......Page 17
Acknowledgments......Page 18
Introduction to Teacher......Page 21
 1.1 Arguments......Page 25
  1.1.2 Premises and Conclusion......Page 26
 1.2 Putting Arguments into a Standard Format......Page 27
 1.3 Multiple Conclusions......Page 29
 1.4 Deductive Validity......Page 30
 1.6 Missing Premises and Conclusions......Page 33
 2.1 Formal Validity......Page 37
 2.2 Quotation Marks......Page 39
 2.3 Metalinguistic Variables......Page 41
 2.4 Non-formal Validity......Page 43
 2.5 The Need for Propositional Logic......Page 44
  2.5.1 Symbolic Notation......Page 45
 2.6 The Type/Token Distinction......Page 46
 3.1 Logical Conjunction......Page 51
 3.2 Distinguishing Deductive from Non-deductive Aspects of Conjunction......Page 53
 3.4 Series Decompounding......Page 54
 3.6 Symbolizing Logical Conjunctions......Page 55
 4.1 Logical Negation......Page 62
 4.2 Some Other Negative Expressions......Page 63
 4.5 Symbolizing Logical Negations......Page 65
 4.6 Ambiguity and the Need for Groupers......Page 66
 4.7 Review of Symbols......Page 67
 4.9 Argument Forms Continued......Page 68
 4.10 Symbolizing Logical Negations Continued......Page 71
 5.1 Well-formed Formulas......Page 76
 5.2 Scope......Page 77
 5.3 Main Connective......Page 78
 5.4 Truth Tables......Page 79
  5.4.1 Truth Table Analyses of Statements......Page 81
  5.4.2 Truth Table Analyses of Arguments......Page 84
 6.1 Logical Disjunction......Page 88
 6.2 Disjunction and Negation......Page 89
 6.3 Iterations and Groupers......Page 91
 6.4 Inclusive versus Exclusive ‘Or’......Page 93
 6.5 Symbolizing Logical Disjunctions Continued......Page 96
 7.1 Conditionals with Constituent Statements......Page 99
 7.3 Logical Conditionals......Page 100
 7.5 Necessary and Sufficient Conditions......Page 102
 7.6 Only If......Page 104
 7.7 Unless......Page 106
 7.8 Since, Because......Page 108
 7.9 Conditionals and Groupers......Page 109
 7.10 If and Only If......Page 110
 7.11 A Revised Grammar for Well-formedness in PL......Page 111
  7.12.1 Validity......Page 119
  7.12.2 Contradiction, Tautology, Contingency......Page 122
  7.12.3 Consistency......Page 124
  7.12.4 Logical Equivalence......Page 125
 8.1 Reviewing Validity......Page 129
 8.2 Tree Trunks and Compound and Atomic Statements......Page 130
  8.3.1 Non-branching Rules......Page 131
  8.3.2 Branching Rules......Page 132
 8.4 Strategies......Page 134
 8.5 Truth Trees and Invalidity......Page 137
 8.6 Propositional Logic and Counter-examples (Counter-models)......Page 141
  8.7.1 Consistency......Page 143
  8.7.2 Contradiction, Tautology, Contingency......Page 144
  8.7.3 Logical Equivalence......Page 146
 9.1 Limits of Propositional Logic......Page 149
 9.2 Singular Terms......Page 150
 9.3 Property Predicates......Page 152
 9.4 Quantifiers......Page 154
  9.4.2 Symbolizing Simple Existential Statements......Page 155
  9.4.3 Simple Universal Quantifier Statements......Page 157
  9.4.4 Negations of Existentials......Page 158
 9.5 Complex Predicates......Page 159
 9.6 Well-formedness in PPL......Page 162
  9.7.1 Existential Quantifiers and General Terms......Page 165
  9.7.2 Universal Quantifiers and General Terms......Page 167
10 Evaluating Arguments in Property Predicate Logic......Page 175
 10.1 Quantifiers and Scope......Page 176
  10.2.1 Quantifier Exchange Rule (QE)......Page 177
  10.2.2 Universal Quantifier Rule (UQ)......Page 178
  10.2.3 Existential Quantifier Rule (EQ)......Page 181
 10.3 Super Strategy......Page 184
 10.4 Property Predicate Logic and Counter-examples (Counter-models)......Page 186
 10.5 PPL Logical Equivalences and Non-equivalences......Page 188
  10.6.2 Logical Equivalence......Page 190
  10.6.3 Contradiction, Logical Truth, Contingency......Page 191
 11.1 Literal Meaning......Page 192
 11.2 ‘Any’ as an Existential......Page 193
 11.3 Restrictive Relative Clauses......Page 195
  11.4.1 Deixis and Anaphora......Page 196
  11.4.2 Quantification and Anaphora......Page 197
 11.5 Only......Page 200
 11.6 Restrictive Words in English......Page 202
 11.7 Evaluating Symbolizations of English in Logical Notation......Page 205
 12.1 Limits of Property Predicate Logic......Page 211
 12.2 Convention 1: Number......Page 213
 12.3 Convention 2: Order......Page 214
 12.4 Convention 3: Active/Passive Voice......Page 215
 12.5 Convention 4: Single Quantifiers......Page 217
 12.6 Variables......Page 219
  12.6.2 Convention 6: Variables and Property Predicates......Page 220
  12.6.3 General Comments about Variables......Page 221
13 Relational Predicate Logic with Nested Quantifiers......Page 227
 13.1 Multiply General Statements......Page 229
 13.2 Universal Quantifier Procedure......Page 232
 13.4 Double Binding Variables......Page 233
  13.4.1 Kicking Out......Page 236
 13.5 Systematic and Analytic Procedures......Page 237
 13.6 A Grammar for Well-formedness in RPL......Page 238
 13.7 Nested Quantifiers, Variables, and Scope......Page 240
 13.8 Order and Scope Refinements......Page 241
  13.8.1 The Order and Scope Procedure......Page 244
 13.9 Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL......Page 246
 14.1 RPL Arguments without Quantifiers......Page 249
 14.2 RPL Arguments without Nested Quantifiers......Page 250
 14.3 RPL Arguments with Nested Quantifiers......Page 252
 14.4 Choosing Singular Terms to Instantiate......Page 253
 14.5 Infinite Truth Trees for RPL Arguments......Page 254
 14.6 Summary of Truth Tree Strategies......Page 256
 14.7 Relational Predicate Logic and Counter-examples (Counter-models)......Page 259
 15.1 Negation......Page 264
 15.2 ‘Only’ as a Quantifier......Page 266
 15.3 Restrictive Relative Clauses......Page 269
  15.3.1 The Quantificational Restrictive Relative Clause Procedure......Page 270
 15.4 Quantifiers and Anaphora......Page 272
  15.4.1 Repair Algorithm......Page 274
 15.5 Anaphora and Restrictive Relative Clauses......Page 277
 15.6 Anaphora Across Sentences......Page 282
 15.7 Quantification in English......Page 285
 16.1 Limits of Relational Predicate Logic......Page 288
  16.2.1 Identity-out Rule......Page 290
  16.2.2 Identity-in Rule......Page 291
  16.3.1 ‘Only’ Again......Page 293
  16.3.2 Words of Distinction: Except, But, Other (than), Besides, Else......Page 294
  16.4.1 At Least n......Page 296
  16.4.2 At Most n (No More than n)......Page 299
  16.4.3 Exactly n......Page 301
  16.4.5 Combinatorics (optional)......Page 303
 16.5 Definite Descriptions......Page 304
  16.5.1 The Definite Description Quantifier Procedure......Page 308
  16.5.3 Plural Definite Descriptions......Page 309
 17.1 Prepositional Phrases......Page 314
 17.2 The Event Approach......Page 316
  17.3.1 Fixing Referents and Binding Anaphoric Pronouns......Page 318
  17.3.2 Quantification over Events......Page 319
  17.3.4 Methodological Reflections......Page 320
 17.4 Adverbial Modification......Page 321
 17.5 Problems with the Event Approach......Page 324
  A1.1 Prepositional Phrases......Page 328
  A1.2 Conversational Inferences and Deductive Validity......Page 329
  A1.3 Relative Clauses......Page 331
  A2.1 Modalities and Negation......Page 334
  A3.1 Explication of the Material Conditional Truth Table......Page 335
   A3.1.2 Conditionals and conversational inferences......Page 338
   A3.1.3 Paradoxes of implication revisited......Page 340
  A4.1 Only......Page 341
   A4.2.1 Existential import......Page 342
   A4.2.2 Scalar inferences......Page 343
  A4.3 More on Literal Meaning......Page 344
  A4.4 Adjectival Modification and Predication......Page 345
  A4.5 A Non-standard Quantifier – Most......Page 349
  A5.1 Passive Voice: Another Argument for Variables......Page 350
   A5.1.1 Passive voice for nested quantifier procedure......Page 352
   A5.2.1 Symmetry, asymmetry, non-symmetry......Page 353
   A5.2.2 Transitivity, intransitivity, non-transitivity......Page 354
   A5.2.3 Total reflexivity, reflexivity, irreflexivity, and non-reflexivity......Page 355
  A6.1 ‘Only’ and Existential Import......Page 357
  A6.2 Descriptions and Anaphora......Page 358
  A6.3 Plural Anaphora......Page 359
   A6.3.2 Singular indefinite antecedents of plural pronouns......Page 364
   A6.3.3 Partitives......Page 366
  A6.4 Existence......Page 367
  A6.6 Properties of the Identity Relationship......Page 368
  A6.7 The Superlative......Page 369
 A7 Verbs and their Modifiers......Page 370
  A7.1 Infinitives and Gerunds......Page 371
  A7.2 Reference to Events......Page 373
  A7.3 The Logic of Perceptual Verbs......Page 374
 Chapter 1......Page 376
 Chapter 2......Page 377
 Chapter 3......Page 378
 Chapter 4......Page 381
 Chapter 5......Page 383
 Chapter 6......Page 384
 Chapter 7......Page 386
 Chapter 8......Page 393
 Chapter 9......Page 398
 Chapter 10......Page 401
 Chapter 11......Page 412
 Chapter 12......Page 417
 Chapter 13......Page 418
 Chapter 14......Page 420
 Chapter 15......Page 433
 Chapter 16......Page 439
 Chapter 17......Page 446
 Appendix......Page 447
Logical Symbols......Page 449
Index......Page 450