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| Preface | |
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| Introduction | |
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| Principles of Inference and Definition | |
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| The Sentential Connectives | |
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| Negation and Conjunction | |
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| Disjunction | |
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| Implication: Conditional Sentences | |
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| Equivalence: Biconditional Sentences | |
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| Grouping and Parentheses | |
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| Truth Tables and Tautologies | |
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| Tautological Implication and Equivalence | |
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| Sentential Theory of Inference | |
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| Two Major Criteria of Inference and Sentential Interpretations | |
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| The Three Sentential Rules of Derivation | |
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| Some Useful Tautological Implications | |
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| Consistency of Premises and Indirect Proofs | |
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| Symbolizing Everyday Language | |
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| Grammar and Logic | |
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| Terms | |
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| Predicates | |
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| Quantifiers | |
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| Bound and Free Variables | |
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| A Final Example | |
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| General Theory of Inference | |
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| Inference Involving Only Universal Quantifiers | |
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| Interpretations and Validity | |
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| Restricted Inferences with Existential Quantifiers | |
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| Interchange of Quantifiers | |
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| General Inferences | |
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| Summary of Rules of Inference | |
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| Further Rules of Inference | |
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| Logic of Identity | |
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| Theorems of Logic | |
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| Derived Rules of Inference | |
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| Postscript on Use and Mention | |
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| Names and Things Named | |
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| Problems of Sentential Variables | |
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| Juxtaposition of Names | |
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| Transition From Formal to Informal Proofs | |
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| General Considerations | |
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| Basic Number Axioms | |
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| Comparative Examples of Formal Derivations and Informal Proofs | |
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| Examples of Fallacious Informal Proofs | |
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| Further Examples of Informal Proofs | |
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| Theory of Definition | |
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| Traditional Ideas | |
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| Criteria for Proper Definitions | |
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| Rules for Proper Definitions | |
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| Definitions Which are Identities | |
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| The Problem of Division by Zero | |
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| Conditional Definitions | |
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| Five Approaches to Division by Zero | |
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| Padoa's Principle and Independence of Primitive Symbols | |
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| Elementary Intuitive Set Theory | |
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| Sets | |
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| Introduction | |
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| Membership | |
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| Inclusion | |
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| The Empty Set | |
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| Operations on Sets | |
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| Domains of Individuals | |
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| Translating Everyday Language | |
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| Venn Diagrams | |
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| Elementary Principles About Operations on Sets | |
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| Relations | |
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| Ordered Couples | |
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| Definition of Relations | |
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| Properties of Binary Relations | |
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| Equivalence Relations | |
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| Ordering Relations | |
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| Operations on Relations | |
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| Functions | |
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| Definition | |
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| Operations on Functions | |
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| Church's Lambda Notation | |
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| Set-Theoretical Foundations of the Axiomatic Method | |
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| Introduction | |
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| Set-Theoretical Predicates and Axiomatizations of Theories | |
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| Isomorphism of Models for a Theory | |
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| Example: Probability | |
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| Example: Mechanics | |
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| Index | |