| Preface | p. iii |
| Introduction | p. xi |
| Principles of Inference and Definition | |
| The Sentential Connectives | p. 3 |
| Negation and Conjunction | p. 3 |
| Disjunction | p. 5 |
| Implication: Conditional Sentences | p. 6 |
| Equivalence: Biconditional Sentences | p. 9 |
| Grouping and Parentheses | p. 10 |
| Truth Tables and Tautologies | p. 11 |
| Tautological Implication and Equivalence | p. 15 |
| Sentential Theory of Inference | p. 20 |
| Two Major Criteria of Inference and Sentential Interpretations | p. 20 |
| The Three Sentential Rules of Derivation | p. 25 |
| Some Useful Tautological Implications | p. 32 |
| Consistency of Premises and Indirect Proofs | p. 36 |
| Symbolizing Everyday Language | p. 43 |
| Grammar and Logic | p. 43 |
| Terms | p. 43 |
| Predicates | p. 45 |
| Quantifiers | p. 47 |
| Bound and Free Variables | p. 52 |
| A Final Example | p. 55 |
| General Theory of Inference | p. 58 |
| Inference Involving Only Universal Quantifiers | p. 58 |
| Interpretations and Validity | p. 64 |
| Restricted Inferences with Existential Quantifiers | p. 80 |
| Interchange of Quantifiers | p. 87 |
| General Inferences | p. 89 |
| Summary of Rules of Inference | p. 98 |
| Further Rules of Inference | p. 101 |
| Logic of Identity | p. 101 |
| Theorems of Logic | p. 108 |
| Derived Rules of Inference | p. 113 |
| Postscript on Use and Mention | p. 121 |
| Names and Things Named | p. 121 |
| Problems of Sentential Variables | p. 123 |
| Juxtaposition of Names | p. 125 |
| Transition From Formal to Informal Proofs | p. 128 |
| General Considerations | p. 128 |
| Basic Number Axioms | p. 129 |
| Comparative Examples of Formal Derivations and Informal Proofs | p. 131 |
| Examples of Fallacious Informal Proofs | p. 138 |
| Further Examples of Informal Proofs | p. 142 |
| Theory of Definition | p. 151 |
| Traditional Ideas | p. 151 |
| Criteria for Proper Definitions | p. 152 |
| Rules for Proper Definitions | p. 155 |
| Definitions Which are Identities | p. 161 |
| The Problem of Division by Zero | p. 163 |
| Conditional Definitions | p. 165 |
| Five Approaches to Division by Zero | p. 166 |
| Padoa's Principle and Independence of Primitive Symbols | p. 169 |
| Elementary Intuitive Set Theory | |
| Sets | p. 177 |
| Introduction | p. 177 |
| Membership | p. 177 |
| Inclusion | p. 181 |
| The Empty Set | p. 184 |
| Operations on Sets | p. 184 |
| Domains of Individuals | p. 187 |
| Translating Everyday Language | p. 189 |
| Venn Diagrams | p. 195 |
| Elementary Principles About Operations on Sets | p. 202 |
| Relations | p. 208 |
| Ordered Couples | p. 208 |
| Definition of Relations | p. 210 |
| Properties of Binary Relations | p. 213 |
| Equivalence Relations | p. 218 |
| Ordering Relations | p. 220 |
| Operations on Relations | p. 225 |
| Functions | p. 229 |
| Definition | p. 229 |
| Operations on Functions | p. 234 |
| Church's Lambda Notation | p. 242 |
| Set-Theoretical Foundations of the Axiomatic Method | p. 246 |
| Introduction | p. 246 |
| Set-Theoretical Predicates and Axiomatizations of Theories | p. 249 |
| Isomorphism of Models for a Theory | p. 260 |
| Example: Probability | p. 274 |
| Example: Mechanics | p. 291 |
| Index | p. 307 |
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