Table of Contents

Preface to Revised Second Edition xiii Preface to Second Edition xiv Preface to Revised Edition xv Acknowledgments xvi Introduction to Teacher 1 1 A Brief Introduction to Key Terms 5 1.1 Arguments 5 1.1.1 What is a Statement? 6 1.1.2 Premises and Conclusion 6 1.2 Putting Arguments into a Standard Format 7 1.3 Multiple Conclusions 9 1.4 Deductive Validity 10 1.5 Soundness 13 1.6 Missing Premises and Conclusions 13 2 Argument Forms and Propositional Logic 17 2.1 Formal Validity 17 2.2 Quotation Marks 19 2.3 Metalinguistic Variables 21 2.4 Non-formal Validity 23 2.5 The Need for Propositional Logic 24 2.5.1 Symbolic Notation 25 2.6 The Type/Token Distinction 26 3 Conjunction 31 3.1 Logical Conjunction 31 3.2 Distinguishing Deductive from Non-deductive Aspects of Conjunction 33 3.3 Phrasal Logical Conjunctions 34 3.4 Series Decompounding 34 3.5 Using 'Respectively' 35 3.6 Symbolizing Logical Conjunctions 35 4 Negation 42 4.1 Logical Negation 42 4.2 Some Other Negative Expressions 43 4.3 A Point about Methodology 45 4.4 A Point on Ambiguity 45 4.5 Symbolizing Logical Negations 45 4.6 Ambiguity and the Need for Groupers 46 4.7 Review of Symbols 47 4.8 Using 'Without' 48 4.9 Argument Forms Continued 48 4.10 Symbolizing Logical Negations Continued 51 5 Truth Tables 56 5.1 Well-formed Formulas 56 5.2 Scope 57 5.3 Main Connective 58 5.4 Truth Tables 59 5.4.1 Truth Table Analyses of Statements 61 5.4.2 Truth Table Analyses of Arguments 64 6 Disjunction 68 6.1 Logical Disjunction 68 6.2 Disjunction and Negation 69 6.3 Iterations and Groupers 71 6.4 Inclusive versus Exclusive 'Or' 73 6.5 Symbolizing Logical Disjunctions Continued 76 7 Conditionals 79 7.1 Conditionals with Constituent Statements 79 7.2 Conditionals without Constituent Statements 80 7.3 Logical Conditionals 80 7.4 Symbolizing Conditionals in PL 82 7.5 Necessary and Sufficient Conditions 82 7.6 Only If 84 7.7 Unless 86 7.8 Since, Because 88 7.9 Conditionals and Groupers 89 7.10 If and Only If 90 7.11 A Revised Grammar for Well-formedness in PL 91 7.12 Summarizing Truth Tables 99 7.12.1 Validity 99 7.12.2 Contradiction, Tautology, Contingency 102 7.12.3 Consistency 104 7.12.4 Logical Equivalence 105 8 Truth Trees 109 8.1 Reviewing Validity 109 8.2 Tree Trunks and Compound and Atomic Statements 110 8.3 Truth Tree Rules 111 8.3.1 Non-branching Rules 111 8.3.2 Branching Rules 112 8.4 Strategies 114 8.5 Truth Trees and Invalidity 117 8.6 Propositional Logic and Counter-examples (Counter-models) 121 8.7 Logical Properties and Relations Revisited 123 8.7.1 Consistency 123 8.7.2 Contradiction, Tautology, Contingency 124 8.7.3 Logical Equivalence 126 9 Property Predicate Logic 129 9.1 Limits of Propositional Logic 129 9.2 Singular Terms 130 9.3 Property Predicates 132 9.4 Quantifiers 134 9.4.1 Simple Existential Quantifier Statements 135 9.4.2 Symbolizing Simple Existential Statements 135 9.4.3 Simple Universal Quantifier Statements 137 9.4.4 Negations of Existentials 138 9.5 Complex Predicates 139 9.6 Well-formedness in PPL 142 9.7 Quantifiers Modifying General Terms 145 9.7.1 Existential Quantifiers and General Terms 145 9.7.2 Universal Quantifiers and General Terms 147 10 Evaluating Arguments in Property Predicate Logic 155 10.1 Quantifiers and Scope 156 10.2 The Truth Tree Method Extended 157 10.2.1 Quantifier Exchange Rule (QE) 157 10.2.2 Universal Quantifier Rule (UQ) 158 10.2.3 Existential Quantifier Rule (EQ) 161 10.3 Super Strategy 164 10.4 Property Predicate Logic and Counter-examples (Counter-models) 166 10.5 PPL Logical Equivalences and Non-equivalences 168 10.6 Other Logical Properties and Relations 170 10.6.1 Consistency 170 10.6.2 Logical Equivalence 170 10.6.3 Contradiction, Logical Truth, Contingency 171 11 Property Predicate Logic Refinements 172 11.1 Literal Meaning 172 11.2 'Any' as an Existential 173 11.3 Restrictive Relative Clauses 175 11.4 Pronouns Revisited 176 11.4.1 Deixis and Anaphora 176 11.4.2 Quantification and Anaphora 177 11.5 Only 180 11.6 Restrictive Words in English 182 11.7 Evaluating Symbolizations of English in Logical Notation 185 12 Relational Predicate Logic 191 12.1 Limits of Property Predicate Logic 191 12.2 Convention 1: Number 193 12.3 Convention 2: Order 194 12.4 Convention 3: Active/Passive Voice 195 12.5 Convention 4: Single Quantifiers 197 12.6 Variables 199 12.6.1 Convention 5: Variables and Quantifiers 200 12.6.2 Convention 6: Variables and Property Predicates 200 12.6.3 General Comments about Variables 201 13 Relational Predicate Logic with Nested Quantifiers 207 13.1 Multiply General Statements 209 13.2 Universal Quantifier Procedure 212 13.3 Existential Quantifier Procedure 213 13.4 Double Binding Variables 213 13.4.1 Kicking Out 216 13.5 Systematic and Analytic Procedures 217 13.6 A Grammar for Well-formedness in RPL 218 13.7 Nested Quantifiers, Variables, and Scope 220 13.8 Order and Scope Refinements 221 13.8.1 The Order and Scope Procedure 224 13.9 Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL 226 14 Extending the Truth Tree Method to RPL 229 14.1 RPL Arguments without Quantifiers 229 14.2 RPL Arguments without Nested Quantifiers 230 14.3 RPL Arguments with Nested Quantifiers 232 14.4 Choosing Singular Terms to Instantiate 233 14.5 Infinite Truth Trees for RPL Arguments 234 14.6 Summary of Truth Tree Strategies 236 14.7 Relational Predicate Logic and Counter-examples (Counter-models) 239 15 Negation, Only, and Restrictive Relative Clauses 244 15.1 Negation 244 15.2 'Only' as a Quantifier 246 15.3 Restrictive Relative Clauses 249 15.3.1 The Quantificational Restrictive Relative Clause Procedure 250 15.4 Quantifiers and Anaphora 252 15.4.1 Repair Algorithm 254 15.5 Anaphora and Restrictive Relative Clauses 257 15.6 Anaphora Across Sentences 262 15.7 Quantification in English 265 16 Relational Predicate Logic with Identity 268 16.1 Limits of Relational Predicate Logic 268 16.2 Extending the Truth Tree Method to RPL= 270 16.2.1 Identity-out Rule 270 16.2.2 Identity-in Rule 271 16.3 Sameness and Distinctness in English 273 16.3.1 'Only' Again 273 16.3.2 Words of Distinction: Except, But, Other (than), Besides, Else 274 16.4 Numerical Adjectives 276 16.4.1 At Least n 276 16.4.2 At Most n (No More than n) 279 16.4.3 Exactly n 281 16.4.4 Counting Pairs 283 16.4.5 Combinatorics (optional) 283 16.5 Definite Descriptions 284 16.5.1 The Definite Description Quantifier Procedure 288 16.5.2 Definite Descriptions as Anaphors 289 16.5.3 Plural Definite Descriptions 289 17 Verbs and their Modifiers 294 17.1 Prepositional Phrases 294 17.2 The Event Approach 296 17.3 Indirect Support of the Event Approach 298 17.3.1 Fixing Referents and Binding Anaphoric Pronouns 298 17.3.2 Quantification over Events 299 17.3.3 Conversational Inferences and Events 300 17.3.4 Methodological Reflections 300 17.4 Adverbial Modification 301 17.5 Problems with the Event Approach 304 Appendix 308 A1 Conjunction 308 A1.1 Prepositional Phrases 308 A1.2 Conversational Inferences and Deductive Validity 309 A1.3 Relative Clauses 311 A2 Negation and Disjunction 314 A2.1 Modalities and Negation 314 A2.2 Disjunction and Conversational Inferences 315 A3 Conditionals 315 A3.1 Explication of the Material Conditional Truth Table 315 A3.1.1 Paradoxes of implication 318 A3.1.2 Conditionals and conversational inferences 318 A3.1.3 Paradoxes of implication revisited 320 A3.2 'If 's and 'Then's without Conditionality 321 A4 Property Predicate Logic 321 A4.1 Only 321 A4.2 Conversational Inferences 322 A4.2.1 Existential import 322 A4.2.2 Scalar inferences 323 A4.3 More on Literal Meaning 324 A4.4 Adjectival Modification and Predication 325 A4.5 A Non-standard Quantifier - Most 329 A5 Relational Predicate Logic 330 A5.1 Passive Voice: Another Argument for Variables 330 A5.1.1 Passive voice for nested quantifier procedure 332 A5.2 Properties of Relations 333 A5.2.1 Symmetry, asymmetry, non-symmetry 333 A5.2.2 Transitivity, intransitivity, non-transitivity 334 A5.2.3 Total reflexivity, reflexivity, irreflexivity, and non-reflexivity 335 A6 Relational Predicate Logic with Identity 337 A6.1 'Only' and Existential Import 337 A6.2 Descriptions and Anaphora 338 A6.3 Plural Anaphora 339 A6.3.1 Plural definite descriptions as anaphors 344 A6.3.2 Singular indefinite antecedents of plural pronouns 344 A6.3.3 Partitives 346 A6.4 Existence 347 A6.5 Intensionality 348 A6.6 Properties of the Identity Relationship 348 A6.7 The Superlative 349 A6.8 Identity and Predicative Adjectives 350 A7 Verbs and their Modifiers 350 A7.1 Infinitives and Gerunds 351 A7.2 Reference to Events 353 A7.3 The Logic of Perceptual Verbs 354 Answers for Selected Exercises 356 Chapter 1 356 Chapter 2 357 Chapter 3 358 Chapter 4 361 Chapter 5 363 Chapter 6 364 Chapter 7 366 Chapter 8 373 Chapter 9 378 Chapter 10 381 Chapter 11 392 Chapter 12 397 Chapter 13 398 Chapter 14 400 Chapter 15 413 Chapter 16 419 Chapter 17 426 Appendix 427 Logical Symbols 429 Index 430

About the Author

Ernest Lepore is Director of the Center for Cognitive Science at Rutgers University. He is the author of numerous articles in philosophy of mind and is co-author (with Herman Cappelen) of Insensitive Semantics (Blackwell, 2004), co-author (with Jerry Fodor) of Holism (Blackwell, 1991). He is editor of Truth and Interpretation (Blackwell, 1989). He is co-editor (with Zenon Pylyshyn) of What is Cognitive Science? (Blackwell, 1999), and co-editor (with Robert Van Gulick) of John Searle and His Critics (Blackwell, 1992), as well as general editor of the series Philosophers and Their Critics, also published by Wiley-Blackwell. Sam Cumming is Assistant Professor of Philosophy at the University of California, Los Angeles.