| Preface | p. v |
| Glossary of Special Symbols and Abbreviations | p. xi |
| Mathematics, Formal Logic, and Names | p. 1 |
| Mathematics and mathematicians | p. 1 |
| Form and meaning | p. 4 |
| Use and mention | p. 9 |
| Statements about statements | p. 13 |
| The Statement Calculus | p. 17 |
| Statements and statement forms | p. 17 |
| Negation | p. 20 |
| Conjunction | p. 22 |
| Disjunction | p. 23 |
| The conditional | p. 26 |
| Statement formulas | p. 30 |
| Equivalence | p. 33 |
| Valid statement formulas | p. 35 |
| Notational conventions | p. 38 |
| Replacement | p. 41 |
| Substitution | p. 42 |
| Some useful valid formulas | p. 45 |
| A collection of valid statement formulas | p. 48 |
| Rules of inference | p. 49 |
| Collection of inference rules | p. 55 |
| Proof and Demonstration | p. 57 |
| Basic form of indirect proof | p. 57 |
| Special cases of the basic form of indirect proof | p. 61 |
| Proof by climination | p. 63 |
| Proof by cases | p. 68 |
| Converses | p. 71 |
| Conversion in classical logic | p. 73 |
| Inverses | p. 76 |
| Demonstration and proof | p. 78 |
| Trees | p. 83 |
| Abbreviated demonstrations as proofs | p. 83 |
| Deduction principle | p. 88 |
| Conventional proofs in geometry | p. 91 |
| Analysis of a conventional proof | p. 94 |
| Abstract Mathematical Systems | p. 100 |
| Mathematical models | p. 100 |
| A miniature geometry | p. 102 |
| Interpretations | p. 119 |
| The Restricted Predicate Calculus | p. 126 |
| Statement functions | p. 126 |
| Universal quantifier | p. 129 |
| Existential quantifier | p. 135 |
| Transformations of quantifiers | p. 137 |
| Free and bound variables | p. 139 |
| Inference rules for quantified statements | p. 141 |
| Inference of a statement function from a general statement | p. 142 |
| Inference rules of the statement calculus extended | p. 143 |
| Extension of the notion of valid statement formula | p. 144 |
| The generalization principle | p. 145 |
| Inference of a statement function from an existential statement: IE | p. 150 |
| Introduction of the existential quantifier | p. 153 |
| Use of the quantification inference rules | p. 154 |
| Statement functions of several variables | p. 157 |
| Extension of quantification inference rules | p. 162 |
| Final forms of the quantificational inference rules | p. 165 |
| Use of equality | p. 166 |
| Formal notion of equality | p. 173 |
| The scope of an assumption in a demonstration | p. 177 |
| Applications of Logic in Mathematics | p. 182 |
| Introduction | p. 182 |
| Abstract groups | p. 183 |
| Isomorphic interpretations | p. 189 |
| Abstract field system | p. 197 |
| Interpretations of the abstract system | p. 200 |
| Further development of the abstract field system | p. 201 |
| Types of informality in proofs | p. 202 |
| Solution of a linear equation | p. 205 |
| Further theorems in the abstract field system | p. 209 |
| Solution of a quadratic equation | p. 210 |
| Subtraction and division | p. 213 |
| Solution of simultaneous linear equations | p. 214 |
| Negation vs. negative number | p. 218 |
| Ordered fields | p. 220 |
| Absolute value | p. 227 |
| Inequalities and absolute value | p. 229 |
| Applications to notions of limit | p. 234 |
| Restricted quantification | p. 238 |
| Appendix: Symbolic Treatment of the Miniature Geometry | p. 243 |
| Index | p. 271 |
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