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| Preface to Revised Second Edition | |
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| Preface to Second Edition | |
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| Preface to Revised Edition | |
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| Acknowledgments | |
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| Introduction to Teacher | |
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| A Brief Introduction to Key Terms | |
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| Arguments | |
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| What is a Statement? | |
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| Premises and Conclusion | |
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| Putting Arguments into a Standard Format | |
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| Multiple Conclusions | |
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| Deductive Validity | |
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| Soundness | |
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| Missing Premises and Conclusions | |
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| Argument Forms and Propositional Logic | |
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| Formal Validity | |
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| Quotation Marks | |
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| Metalinguistic Variables | |
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| Non-formal Validity | |
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| The Need for Propositional Logic | |
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| Symbolic Notation | |
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| The Type/Token Distinction | |
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| Conjunction | |
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| Logical Conjunction | |
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| Distinguishing Deductive from Non-deductive Aspects of Conjunction | |
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| Phrasal Logical Conjunctions | |
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| Series Decompounding | |
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| Using 'Respectively' | |
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| Symbolizing Logical Conjunctions | |
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| Negation | |
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| Logical Negation | |
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| Some Other Negative Expressions | |
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| A Point about Methodology | |
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| A Point on Ambiguity | |
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| Symbolizing Logical Negations | |
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| Ambiguity and the Need for Groupers | |
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| Review of Symbols | |
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| Using 'Without' | |
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| Argument Forms Continued | |
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| Symbolizing Logical Negations Continued | |
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| Truth Tables | |
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| Well-formed Formulas | |
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| Scope | |
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| Main Connective | |
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| Truth Tables | |
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| Truth Table Analyses of Statements | |
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| Truth Table Analyses of Arguments | |
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| Disjunction | |
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| Logical Disjunction | |
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| Disjunction and Negation | |
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| Iterations and Groupers | |
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| Inclusive versus Exclusive 'Or' | |
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| Symbolizing Logical Disjunctions Continued | |
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| Conditionals | |
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| Conditionals with Constituent Statements | |
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| Conditionals without Constituent Statements | |
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| Logical Conditionals | |
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| Symbolizing Conditionals in PL | |
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| Necessary and Sufficient Conditions | |
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| Only If | |
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| Unless | |
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| Since, Because | |
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| Conditionals and Groupers | |
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| If and Only If | |
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| A Revised Grammar for Well-formedness in PL | |
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| Summarizing Truth Tables | |
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| Validity | |
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| Contradiction, Tautology, Contingency | |
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| Consistency | |
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| Logical Equivalence | |
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| Truth Trees | |
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| Reviewing Validity | |
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| Tree Trunks and Compound and Atomic Statements | |
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| Truth Tree Rules | |
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| Non-branching Rules | |
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| Branching Rules | |
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| Strategies | |
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| Truth Trees and Invalidity | |
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| Propositional Logic and Counter-examples (Counter-models) | |
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| Logical Properties and Relations Revisited | |
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| Consistency | |
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| Contradiction, Tautology, Contingency | |
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| Logical Equivalence | |
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| Property Predicate Logic | |
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| Limits of Propositional Logic | |
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| Singular Terms | |
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| Property Predicates | |
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| Quantifiers | |
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| Simple Existential Quantifier Statements | |
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| Symbolizing Simple Existential Statements | |
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| Simple Universal Quantifier Statements | |
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| Negations of Existentials | |
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| Complex Predicates | |
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| Well-formedness in PPL | |
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| Quantifiers Modifying General Terms | |
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| Existential Quantifiers and General Terms | |
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| Universal Quantifiers and General Terms | |
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| Evaluating Arguments in Property Predicate Logic | |
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| Quantifiers and Scope | |
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| The Truth Tree Method Extended | |
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| Quantifier Exchange Rule (QE) | |
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| Universal Quantifier Rule (UQ) | |
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| Existential Quantifier Rule (EQ) | |
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| Super Strategy | |
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| Property Predicate Logic and Counter-examples (Counter-models) | |
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| PPL Logical Equivalences and Non-equivalences | |
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| Other Logical Properties and Relations | |
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| Consistency | |
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| Logical Equivalence | |
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| Contradiction, Logical Truth, Contingency | |
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| Property Predicate Logic Refinements | |
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| Literal Meaning | |
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| 'Any' as an Existential | |
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| Restrictive Relative Clauses | |
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| Pronouns Revisited | |
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| Deixis and Anaphora | |
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| Quantification and Anaphora | |
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| Only | |
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| Restrictive Words in English | |
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| Evaluating Symbolizations of English in Logical Notation | |
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| Relational Predicate Logic | |
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| Limits of Property Predicate Logic | |
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| Convention 1: Number | |
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| Convention 2: Order | |
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| Convention 3: Active/Passive Voice | |
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| Convention 4: Single Quantifiers | |
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| Variables | |
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| Convention 5: Variables and Quantifiers | |
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| Convention 6: Variables and Property Predicates | |
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| General Comments about Variables | |
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| Relational Predicate Logic with Nested Quantifiers | |
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| Multiply General Statements | |
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| Universal Quantifier Procedure | |
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| Existential Quantifier Procedure | |
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| Double Binding Variables | |
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| Kicking Out | |
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| Systematic and Analytic Procedures | |
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| A Grammar for Well-formedness in RPL | |
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| Nested Quantifiers, Variables, and Scope | |
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| Order and Scope Refinements | |
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| The Order and Scope Procedure | |
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| Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL | |
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| Extending the Truth Tree Method to RPL | |
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| RPL Arguments without Quantifiers | |
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| RPL Arguments without Nested Quantifiers | |
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| RPL Arguments with Nested Quantifiers | |
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| Choosing Singular Terms to Instantiate | |
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| Infinite Truth Trees for RPL Arguments | |
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| Summary of Truth Tree Strategies | |
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| Relational Predicate Logic and Counter-examples (Counter-models) | |
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| Negation, Only, and Restrictive Relative Clauses | |
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| Negation | |
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| 'Only' as a Quantifier | |
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| Restrictive Relative Clauses | |
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| The Quantificational Restrictive Relative Clause Procedure | |
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| Quantifiers and Anaphora | |
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| Repair Algorithm | |
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| Anaphora and Restrictive Relative Clauses | |
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| Anaphora Across Sentences | |
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| Quantification in English | |
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| Relational Predicate Logic with Identity | |
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| Limits of Relational Predicate Logic | |
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| Extending the Truth Tree Method to RPL= | |
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| Identity-out Rule | |
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| Identity-in Rule | |
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| Sameness and Distinctness in English | |
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| 'Only' Again | |
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| Words of Distinction: Except, But, Other (than), Besides, Else | |
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| Numerical Adjectives | |
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| At Least n | |
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| At Most n (No More than n) | |
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| Exactly n | |
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| Counting Pairs | |
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| Combinatorics (optional) | |
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| Definite Descriptions | |
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| The Definite Description Quantifier Procedure | |
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| Definite Descriptions as Anaphors | |
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| Plural Definite Descriptions | |
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| Verbs and their Modifiers | |
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| Prepositional Phrases | |
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| The Event Approach | |
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| Indirect Support of the Event Approach | |
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| Fixing Referents and Binding Anaphoric Pronouns | |
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| Quantification over Events | |
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| Conversational Inferences and Events | |
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| Methodological Reflections | |
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| Adverbial Modification | |
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| Problems with the Event Approach | |
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| Appendix | |
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| Conjunction | |
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| Prepositional Phrases | |
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| Conversational Inferences and Deductive Validity | |
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| Relative Clauses | |
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| Negation and Disjunction | |
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| Modalities and Negation | |
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| Disjunction and Conversational Inferences | |
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| Conditionals | |
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| Explication of the Material Conditional Truth Table | |
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| Paradoxes of implication | |
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| Conditionals and conversational inferences | |
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| Paradoxes of implication revisited | |
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| 'If 's and 'Then's without Conditionality | |
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| Property Predicate Logic | |
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| Only | |
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| Conversational Inferences | |
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| Existential import | |
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| Scalar inferences | |
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| More on Literal Meaning | |
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| Adjectival Modification and Predication | |
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| A Non-standard Quantifier - Most | |
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| Relational Predicate Logic | |
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| Passive Voice: Another Argument for Variables | |
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| Passive voice for nested quantifier procedure | |
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| Properties of Relations | |
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| Symmetry, asymmetry, non-symmetry | |
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| Transitivity, intransitivity, non-transitivity | |
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| Total reflexivity, reflexivity, irreflexivity, and non-reflexivity | |
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| Relational Predicate Logic with Identity | |
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| 'Only' and Existential Import | |
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| Descriptions and Anaphora | |
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| Plural Anaphora | |
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| Plural definite descriptions as anaphors | |
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| Singular indefinite antecedents of plural pronouns | |
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| Partitives | |
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| Existence | |
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| Intensionality | |
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| Properties of the Identity Relationship | |
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| The Superlative | |
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| Identity and Predicative Adjectives | |
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| Verbs and their Modifiers | |
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| Infinitives and Gerunds | |
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| Reference to Events | |
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| The Logic of Perceptual Verbs | |
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| Answers for Selected Exercises | |
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| Appendix | |