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.

• Preface to Revised Second Edition xiii Preface to Second Edition xivPreface to Revised Edition xvAcknowledgments xviIntroduction to Teacher 11 A Brief Introduction to Key Terms 51.1 Arguments 51.1.1 What is a Statement? 61.1.2 Premises and Conclusion 61.2 Putting Arguments into a Standard Format 71.3 Multiple Conclusions 91.4 Deductive Validity 101.5 Soundness 131.6 Missing Premises and Conclusions 132 Argument Forms and Propositional Logic 172.1 Formal Validity 172.2 Quotation Marks 192.3 Metalinguistic Variables 212.4 Non-formal Validity 232.5 The Need for Propositional Logic 242.5.1 Symbolic Notation 252.6 The Type/Token Distinction 263 Conjunction 313.1 Logical Conjunction 313.2 Distinguishing Deductive from Non-deductive Aspects of Conjunction 333.3 Phrasal Logical Conjunctions 343.4 Series Decompounding 343.5 Using ‘Respectively’ 353.6 Symbolizing Logical Conjunctions 354 Negation 424.1 Logical Negation 424.2 Some Other Negative Expressions 434.3 A Point about Methodology 454.4 A Point on Ambiguity 454.5 Symbolizing Logical Negations 454.6 Ambiguity and the Need for Groupers 464.7 Review of Symbols 474.8 Using ‘Without’ 484.9 Argument Forms Continued 484.10 Symbolizing Logical Negations Continued 515 Truth Tables 565.1 Well-formed Formulas 565.2 Scope 575.3 Main Connective 585.4 Truth Tables 595.4.1 Truth Table Analyses of Statements 615.4.2 Truth Table Analyses of Arguments 646 Disjunction 686.1 Logical Disjunction 686.2 Disjunction and Negation 696.3 Iterations and Groupers 716.4 Inclusive versus Exclusive ‘Or’ 736.5 Symbolizing Logical Disjunctions Continued 767 Conditionals 797.1 Conditionals with Constituent Statements 797.2 Conditionals without Constituent Statements 807.3 Logical Conditionals 807.4 Symbolizing Conditionals in PL 827.5 Necessary and Sufficient Conditions 827.6 Only If 847.7 Unless 867.8 Since, Because 887.9 Conditionals and Groupers 897.10 If and Only If 907.11 A Revised Grammar for Well-formedness in PL 917.12 Summarizing Truth Tables 997.12.1 Validity 997.12.2 Contradiction, Tautology, Contingency 1027.12.3 Consistency 1047.12.4 Logical Equivalence 1058 Truth Trees 1098.1 Reviewing Validity 1098.2 Tree Trunks and Compound and Atomic Statements 1108.3 Truth Tree Rules 1118.3.1 Non-branching Rules 1118.3.2 Branching Rules 1128.4 Strategies 1148.5 Truth Trees and Invalidity 1178.6 Propositional Logic and Counter-examples (Counter-models) 1218.7 Logical Properties and Relations Revisited 1238.7.1 Consistency 1238.7.2 Contradiction, Tautology, Contingency 1248.7.3 Logical Equivalence 1269 Property Predicate Logic 1299.1 Limits of Propositional Logic 1299.2 Singular Terms 1309.3 Property Predicates 1329.4 Quantifiers 1349.4.1 Simple Existential Quantifier Statements 1359.4.2 Symbolizing Simple Existential Statements 1359.4.3 Simple Universal Quantifier Statements 1379.4.4 Negations of Existentials 1389.5 Complex Predicates 1399.6 Well-formedness in PPL 1429.7 Quantifiers Modifying General Terms 1459.7.1 Existential Quantifiers and General Terms 1459.7.2 Universal Quantifiers and General Terms 14710 Evaluating Arguments in Property Predicate Logic 15510.1 Quantifiers and Scope 15610.2 The Truth Tree Method Extended 15710.2.1 Quantifier Exchange Rule (QE) 15710.2.2 Universal Quantifier Rule (UQ) 15810.2.3 Existential Quantifier Rule (EQ) 16110.3 Super Strategy 16410.4 Property Predicate Logic and Counter-examples (Counter-models) 16610.5 PPL Logical Equivalences and Non-equivalences 16810.6 Other Logical Properties and Relations 17010.6.1 Consistency 17010.6.2 Logical Equivalence 17010.6.3 Contradiction, Logical Truth, Contingency 17111 Property Predicate Logic Refinements 17211.1 Literal Meaning 17211.2 ‘Any’ as an Existential 17311.3 Restrictive Relative Clauses 17511.4 Pronouns Revisited 17611.4.1 Deixis and Anaphora 17611.4.2 Quantification and Anaphora 17711.5 Only 18011.6 Restrictive Words in English 18211.7 Evaluating Symbolizations of English in Logical Notation 18512 Relational Predicate Logic 19112.1 Limits of Property Predicate Logic 19112.2 Convention 1: Number 19312.3 Convention 2: Order 19412.4 Convention 3: Active/Passive Voice 19512.5 Convention 4: Single Quantifiers 19712.6 Variables 19912.6.1 Convention 5: Variables and Quantifiers 20012.6.2 Convention 6: Variables and Property Predicates 20012.6.3 General Comments about Variables 20113 Relational Predicate Logic with Nested Quantifiers 20713.1 Multiply General Statements 20913.2 Universal Quantifier Procedure 21213.3 Existential Quantifier Procedure 21313.4 Double Binding Variables 21313.4.1 Kicking Out 21613.5 Systematic and Analytic Procedures 21713.6 A Grammar for Well-formedness in RPL 21813.7 Nested Quantifiers, Variables, and Scope 22013.8 Order and Scope Refinements 22113.8.1 The Order and Scope Procedure 22413.9 Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL 22614 Extending the Truth Tree Method to RPL 22914.1 RPL Arguments without Quantifiers 22914.2 RPL Arguments without Nested Quantifiers 23014.3 RPL Arguments with Nested Quantifiers 23214.4 Choosing Singular Terms to Instantiate 23314.5 Infinite Truth Trees for RPL Arguments 23414.6 Summary of Truth Tree Strategies 23614.7 Relational Predicate Logic and Counter-examples (Counter-models) 23915 Negation, Only, and Restrictive Relative Clauses 24415.1 Negation 24415.2 ‘Only’ as a Quantifier 24615.3 Restrictive Relative Clauses 24915.3.1 The Quantificational Restrictive Relative Clause Procedure 25015.4 Quantifiers and Anaphora 25215.4.1 Repair Algorithm 25415.5 Anaphora and Restrictive Relative Clauses 25715.6 Anaphora Across Sentences 26215.7 Quantification in English 26516 Relational Predicate Logic with Identity 26816.1 Limits of Relational Predicate Logic 26816.2 Extending the Truth Tree Method to RPL= 27016.2.1 Identity-out Rule 27016.2.2 Identity-in Rule 27116.3 Sameness and Distinctness in English 27316.3.1 ‘Only’ Again 27316.3.2 Words of Distinction: Except, But, Other (than), Besides, Else 27416.4 Numerical Adjectives 27616.4.1 At Least n 27616.4.2 At Most n (No More than n) 27916.4.3 Exactly n 28116.4.4 Counting Pairs 28316.4.5 Combinatorics (optional) 28316.5 Definite Descriptions 28416.5.1 The Definite Description Quantifier Procedure 28816.5.2 Definite Descriptions as Anaphors 28916.5.3 Plural Definite Descriptions 28917 Verbs and their Modifiers 29417.1 Prepositional Phrases 29417.2 The Event Approach 29617.3 Indirect Support of the Event Approach 29817.3.1 Fixing Referents and Binding Anaphoric Pronouns 29817.3.2 Quantification over Events 29917.3.3 Conversational Inferences and Events 30017.3.4 Methodological Reflections 30017.4 Adverbial Modification 30117.5 Problems with the Event Approach 304Appendix 308A1 Conjunction 308A1.1 Prepositional Phrases 308A1.2 Conversational Inferences and Deductive Validity 309A1.3 Relative Clauses 311A2 Negation and Disjunction 314A2.1 Modalities and Negation 314A2.2 Disjunction and Conversational Inferences 315A3 Conditionals 315A3.1 Explication of the Material Conditional Truth Table 315A3.1.1 Paradoxes of implication 318A3.1.2 Conditionals and conversational inferences 318A3.1.3 Paradoxes of implication revisited 320A3.2 ‘If ’s and ‘Then’s without Conditionality 321A4 Property Predicate Logic 321A4.1 Only 321A4.2 Conversational Inferences 322A4.2.1 Existential import 322A4.2.2 Scalar inferences 323A4.3 More on Literal Meaning 324A4.4 Adjectival Modification and Predication 325A4.5 A Non-standard Quantifier – Most 329A5 Relational Predicate Logic 330A5.1 Passive Voice: Another Argument for Variables 330A5.1.1 Passive voice for nested quantifier procedure 332A5.2 Properties of Relations 333A5.2.1 Symmetry, asymmetry, non-symmetry 333A5.2.2 Transitivity, intransitivity, non-transitivity 334A5.2.3 Total reflexivity, reflexivity, irreflexivity, and non-reflexivity 335A6 Relational Predicate Logic with Identity 337A6.1 ‘Only’ and Existential Import 337A6.2 Descriptions and Anaphora 338A6.3 Plural Anaphora 339A6.3.1 Plural definite descriptions as anaphors 344A6.3.2 Singular indefinite antecedents of plural pronouns 344A6.3.3 Partitives 346A6.4 Existence 347A6.5 Intensionality 348A6.6 Properties of the Identity Relationship 348A6.7 The Superlative 349A6.8 Identity and Predicative Adjectives 350A7 Verbs and their Modifiers 350A7.1 Infinitives and Gerunds 351A7.2 Reference to Events 353A7.3 The Logic of Perceptual Verbs 354Answers for Selected Exercises 356Chapter 1 356Chapter 2 357Chapter 3 358Chapter 4 361Chapter 5 363Chapter 6 364Chapter 7 366Chapter 8 373Chapter 9 378Chapter 10 381Chapter 11 392Chapter 12 397Chapter 13 398Chapter 14 400Chapter 15 413Chapter 16 419Chapter 17 426Appendix 427Logical Symbols 429Index 430

Select Guide Rating

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.

• Preface to Revised Second Edition xiii Preface to Second Edition xivPreface to Revised Edition xvAcknowledgments xviIntroduction to Teacher 11 A Brief Introduction to Key Terms 51.1 Arguments 51.1.1 What is a Statement? 61.1.2 Premises and Conclusion 61.2 Putting Arguments into a Standard Format 71.3 Multiple Conclusions 91.4 Deductive Validity 101.5 Soundness 131.6 Missing Premises and Conclusions 132 Argument Forms and Propositional Logic 172.1 Formal Validity 172.2 Quotation Marks 192.3 Metalinguistic Variables 212.4 Non-formal Validity 232.5 The Need for Propositional Logic 242.5.1 Symbolic Notation 252.6 The Type/Token Distinction 263 Conjunction 313.1 Logical Conjunction 313.2 Distinguishing Deductive from Non-deductive Aspects of Conjunction 333.3 Phrasal Logical Conjunctions 343.4 Series Decompounding 343.5 Using ‘Respectively’ 353.6 Symbolizing Logical Conjunctions 354 Negation 424.1 Logical Negation 424.2 Some Other Negative Expressions 434.3 A Point about Methodology 454.4 A Point on Ambiguity 454.5 Symbolizing Logical Negations 454.6 Ambiguity and the Need for Groupers 464.7 Review of Symbols 474.8 Using ‘Without’ 484.9 Argument Forms Continued 484.10 Symbolizing Logical Negations Continued 515 Truth Tables 565.1 Well-formed Formulas 565.2 Scope 575.3 Main Connective 585.4 Truth Tables 595.4.1 Truth Table Analyses of Statements 615.4.2 Truth Table Analyses of Arguments 646 Disjunction 686.1 Logical Disjunction 686.2 Disjunction and Negation 696.3 Iterations and Groupers 716.4 Inclusive versus Exclusive ‘Or’ 736.5 Symbolizing Logical Disjunctions Continued 767 Conditionals 797.1 Conditionals with Constituent Statements 797.2 Conditionals without Constituent Statements 807.3 Logical Conditionals 807.4 Symbolizing Conditionals in PL 827.5 Necessary and Sufficient Conditions 827.6 Only If 847.7 Unless 867.8 Since, Because 887.9 Conditionals and Groupers 897.10 If and Only If 907.11 A Revised Grammar for Well-formedness in PL 917.12 Summarizing Truth Tables 997.12.1 Validity 997.12.2 Contradiction, Tautology, Contingency 1027.12.3 Consistency 1047.12.4 Logical Equivalence 1058 Truth Trees 1098.1 Reviewing Validity 1098.2 Tree Trunks and Compound and Atomic Statements 1108.3 Truth Tree Rules 1118.3.1 Non-branching Rules 1118.3.2 Branching Rules 1128.4 Strategies 1148.5 Truth Trees and Invalidity 1178.6 Propositional Logic and Counter-examples (Counter-models) 1218.7 Logical Properties and Relations Revisited 1238.7.1 Consistency 1238.7.2 Contradiction, Tautology, Contingency 1248.7.3 Logical Equivalence 1269 Property Predicate Logic 1299.1 Limits of Propositional Logic 1299.2 Singular Terms 1309.3 Property Predicates 1329.4 Quantifiers 1349.4.1 Simple Existential Quantifier Statements 1359.4.2 Symbolizing Simple Existential Statements 1359.4.3 Simple Universal Quantifier Statements 1379.4.4 Negations of Existentials 1389.5 Complex Predicates 1399.6 Well-formedness in PPL 1429.7 Quantifiers Modifying General Terms 1459.7.1 Existential Quantifiers and General Terms 1459.7.2 Universal Quantifiers and General Terms 14710 Evaluating Arguments in Property Predicate Logic 15510.1 Quantifiers and Scope 15610.2 The Truth Tree Method Extended 15710.2.1 Quantifier Exchange Rule (QE) 15710.2.2 Universal Quantifier Rule (UQ) 15810.2.3 Existential Quantifier Rule (EQ) 16110.3 Super Strategy 16410.4 Property Predicate Logic and Counter-examples (Counter-models) 16610.5 PPL Logical Equivalences and Non-equivalences 16810.6 Other Logical Properties and Relations 17010.6.1 Consistency 17010.6.2 Logical Equivalence 17010.6.3 Contradiction, Logical Truth, Contingency 17111 Property Predicate Logic Refinements 17211.1 Literal Meaning 17211.2 ‘Any’ as an Existential 17311.3 Restrictive Relative Clauses 17511.4 Pronouns Revisited 17611.4.1 Deixis and Anaphora 17611.4.2 Quantification and Anaphora 17711.5 Only 18011.6 Restrictive Words in English 18211.7 Evaluating Symbolizations of English in Logical Notation 18512 Relational Predicate Logic 19112.1 Limits of Property Predicate Logic 19112.2 Convention 1: Number 19312.3 Convention 2: Order 19412.4 Convention 3: Active/Passive Voice 19512.5 Convention 4: Single Quantifiers 19712.6 Variables 19912.6.1 Convention 5: Variables and Quantifiers 20012.6.2 Convention 6: Variables and Property Predicates 20012.6.3 General Comments about Variables 20113 Relational Predicate Logic with Nested Quantifiers 20713.1 Multiply General Statements 20913.2 Universal Quantifier Procedure 21213.3 Existential Quantifier Procedure 21313.4 Double Binding Variables 21313.4.1 Kicking Out 21613.5 Systematic and Analytic Procedures 21713.6 A Grammar for Well-formedness in RPL 21813.7 Nested Quantifiers, Variables, and Scope 22013.8 Order and Scope Refinements 22113.8.1 The Order and Scope Procedure 22413.9 Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL 22614 Extending the Truth Tree Method to RPL 22914.1 RPL Arguments without Quantifiers 22914.2 RPL Arguments without Nested Quantifiers 23014.3 RPL Arguments with Nested Quantifiers 23214.4 Choosing Singular Terms to Instantiate 23314.5 Infinite Truth Trees for RPL Arguments 23414.6 Summary of Truth Tree Strategies 23614.7 Relational Predicate Logic and Counter-examples (Counter-models) 23915 Negation, Only, and Restrictive Relative Clauses 24415.1 Negation 24415.2 ‘Only’ as a Quantifier 24615.3 Restrictive Relative Clauses 24915.3.1 The Quantificational Restrictive Relative Clause Procedure 25015.4 Quantifiers and Anaphora 25215.4.1 Repair Algorithm 25415.5 Anaphora and Restrictive Relative Clauses 25715.6 Anaphora Across Sentences 26215.7 Quantification in English 26516 Relational Predicate Logic with Identity 26816.1 Limits of Relational Predicate Logic 26816.2 Extending the Truth Tree Method to RPL= 27016.2.1 Identity-out Rule 27016.2.2 Identity-in Rule 27116.3 Sameness and Distinctness in English 27316.3.1 ‘Only’ Again 27316.3.2 Words of Distinction: Except, But, Other (than), Besides, Else 27416.4 Numerical Adjectives 27616.4.1 At Least n 27616.4.2 At Most n (No More than n) 27916.4.3 Exactly n 28116.4.4 Counting Pairs 28316.4.5 Combinatorics (optional) 28316.5 Definite Descriptions 28416.5.1 The Definite Description Quantifier Procedure 28816.5.2 Definite Descriptions as Anaphors 28916.5.3 Plural Definite Descriptions 28917 Verbs and their Modifiers 29417.1 Prepositional Phrases 29417.2 The Event Approach 29617.3 Indirect Support of the Event Approach 29817.3.1 Fixing Referents and Binding Anaphoric Pronouns 29817.3.2 Quantification over Events 29917.3.3 Conversational Inferences and Events 30017.3.4 Methodological Reflections 30017.4 Adverbial Modification 30117.5 Problems with the Event Approach 304Appendix 308A1 Conjunction 308A1.1 Prepositional Phrases 308A1.2 Conversational Inferences and Deductive Validity 309A1.3 Relative Clauses 311A2 Negation and Disjunction 314A2.1 Modalities and Negation 314A2.2 Disjunction and Conversational Inferences 315A3 Conditionals 315A3.1 Explication of the Material Conditional Truth Table 315A3.1.1 Paradoxes of implication 318A3.1.2 Conditionals and conversational inferences 318A3.1.3 Paradoxes of implication revisited 320A3.2 ‘If ’s and ‘Then’s without Conditionality 321A4 Property Predicate Logic 321A4.1 Only 321A4.2 Conversational Inferences 322A4.2.1 Existential import 322A4.2.2 Scalar inferences 323A4.3 More on Literal Meaning 324A4.4 Adjectival Modification and Predication 325A4.5 A Non-standard Quantifier – Most 329A5 Relational Predicate Logic 330A5.1 Passive Voice: Another Argument for Variables 330A5.1.1 Passive voice for nested quantifier procedure 332A5.2 Properties of Relations 333A5.2.1 Symmetry, asymmetry, non-symmetry 333A5.2.2 Transitivity, intransitivity, non-transitivity 334A5.2.3 Total reflexivity, reflexivity, irreflexivity, and non-reflexivity 335A6 Relational Predicate Logic with Identity 337A6.1 ‘Only’ and Existential Import 337A6.2 Descriptions and Anaphora 338A6.3 Plural Anaphora 339A6.3.1 Plural definite descriptions as anaphors 344A6.3.2 Singular indefinite antecedents of plural pronouns 344A6.3.3 Partitives 346A6.4 Existence 347A6.5 Intensionality 348A6.6 Properties of the Identity Relationship 348A6.7 The Superlative 349A6.8 Identity and Predicative Adjectives 350A7 Verbs and their Modifiers 350A7.1 Infinitives and Gerunds 351A7.2 Reference to Events 353A7.3 The Logic of Perceptual Verbs 354Answers for Selected Exercises 356Chapter 1 356Chapter 2 357Chapter 3 358Chapter 4 361Chapter 5 363Chapter 6 364Chapter 7 366Chapter 8 373Chapter 9 378Chapter 10 381Chapter 11 392Chapter 12 397Chapter 13 398Chapter 14 400Chapter 15 413Chapter 16 419Chapter 17 426Appendix 427Logical Symbols 429Index 430

Select Guide Rating

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.

• Preface to Revised Second Edition xiii Preface to Second Edition xivPreface to Revised Edition xvAcknowledgments xviIntroduction to Teacher 11 A Brief Introduction to Key Terms 51.1 Arguments 51.1.1 What is a Statement? 61.1.2 Premises and Conclusion 61.2 Putting Arguments into a Standard Format 71.3 Multiple Conclusions 91.4 Deductive Validity 101.5 Soundness 131.6 Missing Premises and Conclusions 132 Argument Forms and Propositional Logic 172.1 Formal Validity 172.2 Quotation Marks 192.3 Metalinguistic Variables 212.4 Non-formal Validity 232.5 The Need for Propositional Logic 242.5.1 Symbolic Notation 252.6 The Type/Token Distinction 263 Conjunction 313.1 Logical Conjunction 313.2 Distinguishing Deductive from Non-deductive Aspects of Conjunction 333.3 Phrasal Logical Conjunctions 343.4 Series Decompounding 343.5 Using ‘Respectively’ 353.6 Symbolizing Logical Conjunctions 354 Negation 424.1 Logical Negation 424.2 Some Other Negative Expressions 434.3 A Point about Methodology 454.4 A Point on Ambiguity 454.5 Symbolizing Logical Negations 454.6 Ambiguity and the Need for Groupers 464.7 Review of Symbols 474.8 Using ‘Without’ 484.9 Argument Forms Continued 484.10 Symbolizing Logical Negations Continued 515 Truth Tables 565.1 Well-formed Formulas 565.2 Scope 575.3 Main Connective 585.4 Truth Tables 595.4.1 Truth Table Analyses of Statements 615.4.2 Truth Table Analyses of Arguments 646 Disjunction 686.1 Logical Disjunction 686.2 Disjunction and Negation 696.3 Iterations and Groupers 716.4 Inclusive versus Exclusive ‘Or’ 736.5 Symbolizing Logical Disjunctions Continued 767 Conditionals 797.1 Conditionals with Constituent Statements 797.2 Conditionals without Constituent Statements 807.3 Logical Conditionals 807.4 Symbolizing Conditionals in PL 827.5 Necessary and Sufficient Conditions 827.6 Only If 847.7 Unless 867.8 Since, Because 887.9 Conditionals and Groupers 897.10 If and Only If 907.11 A Revised Grammar for Well-formedness in PL 917.12 Summarizing Truth Tables 997.12.1 Validity 997.12.2 Contradiction, Tautology, Contingency 1027.12.3 Consistency 1047.12.4 Logical Equivalence 1058 Truth Trees 1098.1 Reviewing Validity 1098.2 Tree Trunks and Compound and Atomic Statements 1108.3 Truth Tree Rules 1118.3.1 Non-branching Rules 1118.3.2 Branching Rules 1128.4 Strategies 1148.5 Truth Trees and Invalidity 1178.6 Propositional Logic and Counter-examples (Counter-models) 1218.7 Logical Properties and Relations Revisited 1238.7.1 Consistency 1238.7.2 Contradiction, Tautology, Contingency 1248.7.3 Logical Equivalence 1269 Property Predicate Logic 1299.1 Limits of Propositional Logic 1299.2 Singular Terms 1309.3 Property Predicates 1329.4 Quantifiers 1349.4.1 Simple Existential Quantifier Statements 1359.4.2 Symbolizing Simple Existential Statements 1359.4.3 Simple Universal Quantifier Statements 1379.4.4 Negations of Existentials 1389.5 Complex Predicates 1399.6 Well-formedness in PPL 1429.7 Quantifiers Modifying General Terms 1459.7.1 Existential Quantifiers and General Terms 1459.7.2 Universal Quantifiers and General Terms 14710 Evaluating Arguments in Property Predicate Logic 15510.1 Quantifiers and Scope 15610.2 The Truth Tree Method Extended 15710.2.1 Quantifier Exchange Rule (QE) 15710.2.2 Universal Quantifier Rule (UQ) 15810.2.3 Existential Quantifier Rule (EQ) 16110.3 Super Strategy 16410.4 Property Predicate Logic and Counter-examples (Counter-models) 16610.5 PPL Logical Equivalences and Non-equivalences 16810.6 Other Logical Properties and Relations 17010.6.1 Consistency 17010.6.2 Logical Equivalence 17010.6.3 Contradiction, Logical Truth, Contingency 17111 Property Predicate Logic Refinements 17211.1 Literal Meaning 17211.2 ‘Any’ as an Existential 17311.3 Restrictive Relative Clauses 17511.4 Pronouns Revisited 17611.4.1 Deixis and Anaphora 17611.4.2 Quantification and Anaphora 17711.5 Only 18011.6 Restrictive Words in English 18211.7 Evaluating Symbolizations of English in Logical Notation 18512 Relational Predicate Logic 19112.1 Limits of Property Predicate Logic 19112.2 Convention 1: Number 19312.3 Convention 2: Order 19412.4 Convention 3: Active/Passive Voice 19512.5 Convention 4: Single Quantifiers 19712.6 Variables 19912.6.1 Convention 5: Variables and Quantifiers 20012.6.2 Convention 6: Variables and Property Predicates 20012.6.3 General Comments about Variables 20113 Relational Predicate Logic with Nested Quantifiers 20713.1 Multiply General Statements 20913.2 Universal Quantifier Procedure 21213.3 Existential Quantifier Procedure 21313.4 Double Binding Variables 21313.4.1 Kicking Out 21613.5 Systematic and Analytic Procedures 21713.6 A Grammar for Well-formedness in RPL 21813.7 Nested Quantifiers, Variables, and Scope 22013.8 Order and Scope Refinements 22113.8.1 The Order and Scope Procedure 22413.9 Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL 22614 Extending the Truth Tree Method to RPL 22914.1 RPL Arguments without Quantifiers 22914.2 RPL Arguments without Nested Quantifiers 23014.3 RPL Arguments with Nested Quantifiers 23214.4 Choosing Singular Terms to Instantiate 23314.5 Infinite Truth Trees for RPL Arguments 23414.6 Summary of Truth Tree Strategies 23614.7 Relational Predicate Logic and Counter-examples (Counter-models) 23915 Negation, Only, and Restrictive Relative Clauses 24415.1 Negation 24415.2 ‘Only’ as a Quantifier 24615.3 Restrictive Relative Clauses 24915.3.1 The Quantificational Restrictive Relative Clause Procedure 25015.4 Quantifiers and Anaphora 25215.4.1 Repair Algorithm 25415.5 Anaphora and Restrictive Relative Clauses 25715.6 Anaphora Across Sentences 26215.7 Quantification in English 26516 Relational Predicate Logic with Identity 26816.1 Limits of Relational Predicate Logic 26816.2 Extending the Truth Tree Method to RPL= 27016.2.1 Identity-out Rule 27016.2.2 Identity-in Rule 27116.3 Sameness and Distinctness in English 27316.3.1 ‘Only’ Again 27316.3.2 Words of Distinction: Except, But, Other (than), Besides, Else 27416.4 Numerical Adjectives 27616.4.1 At Least n 27616.4.2 At Most n (No More than n) 27916.4.3 Exactly n 28116.4.4 Counting Pairs 28316.4.5 Combinatorics (optional) 28316.5 Definite Descriptions 28416.5.1 The Definite Description Quantifier Procedure 28816.5.2 Definite Descriptions as Anaphors 28916.5.3 Plural Definite Descriptions 28917 Verbs and their Modifiers 29417.1 Prepositional Phrases 29417.2 The Event Approach 29617.3 Indirect Support of the Event Approach 29817.3.1 Fixing Referents and Binding Anaphoric Pronouns 29817.3.2 Quantification over Events 29917.3.3 Conversational Inferences and Events 30017.3.4 Methodological Reflections 30017.4 Adverbial Modification 30117.5 Problems with the Event Approach 304Appendix 308A1 Conjunction 308A1.1 Prepositional Phrases 308A1.2 Conversational Inferences and Deductive Validity 309A1.3 Relative Clauses 311A2 Negation and Disjunction 314A2.1 Modalities and Negation 314A2.2 Disjunction and Conversational Inferences 315A3 Conditionals 315A3.1 Explication of the Material Conditional Truth Table 315A3.1.1 Paradoxes of implication 318A3.1.2 Conditionals and conversational inferences 318A3.1.3 Paradoxes of implication revisited 320A3.2 ‘If ’s and ‘Then’s without Conditionality 321A4 Property Predicate Logic 321A4.1 Only 321A4.2 Conversational Inferences 322A4.2.1 Existential import 322A4.2.2 Scalar inferences 323A4.3 More on Literal Meaning 324A4.4 Adjectival Modification and Predication 325A4.5 A Non-standard Quantifier – Most 329A5 Relational Predicate Logic 330A5.1 Passive Voice: Another Argument for Variables 330A5.1.1 Passive voice for nested quantifier procedure 332A5.2 Properties of Relations 333A5.2.1 Symmetry, asymmetry, non-symmetry 333A5.2.2 Transitivity, intransitivity, non-transitivity 334A5.2.3 Total reflexivity, reflexivity, irreflexivity, and non-reflexivity 335A6 Relational Predicate Logic with Identity 337A6.1 ‘Only’ and Existential Import 337A6.2 Descriptions and Anaphora 338A6.3 Plural Anaphora 339A6.3.1 Plural definite descriptions as anaphors 344A6.3.2 Singular indefinite antecedents of plural pronouns 344A6.3.3 Partitives 346A6.4 Existence 347A6.5 Intensionality 348A6.6 Properties of the Identity Relationship 348A6.7 The Superlative 349A6.8 Identity and Predicative Adjectives 350A7 Verbs and their Modifiers 350A7.1 Infinitives and Gerunds 351A7.2 Reference to Events 353A7.3 The Logic of Perceptual Verbs 354Answers for Selected Exercises 356Chapter 1 356Chapter 2 357Chapter 3 358Chapter 4 361Chapter 5 363Chapter 6 364Chapter 7 366Chapter 8 373Chapter 9 378Chapter 10 381Chapter 11 392Chapter 12 397Chapter 13 398Chapter 14 400Chapter 15 413Chapter 16 419Chapter 17 426Appendix 427Logical Symbols 429Index 430

Select Guide Rating