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| ""Not"" and ""If"" | |
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| Symbols and sentences | |
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| From symbols to English and back | |
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| Derivability and validity of symbolic arguments | |
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| Validity of English arguments | |
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| Fallacies | |
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| Theorems | |
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| Historical remarks | |
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| Appendix | |
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| ""And,"" ""Or,"" ""If and Only If"" | |
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| Symbols and sentences | |
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| Translation and symbolization | |
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| Inference rules and derivability | |
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| Theorems with unabbreviated proofs | |
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| Abbreviated derivations | |
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| Theorems with unabbreviated proofs | |
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| Arguments | |
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| Truth-value analysis of sentences | |
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| Truth-value analysis of arguments | |
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| Historical remarks | |
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| Appendix: list of theorems of chapters I and II | |
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| Appendix: solutions to selected exercises | |
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| ""All"" and ""Some"" | |
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| Variables, quantifiers, formulas | |
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| Bondage and freedom | |
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| Informal notational conventions | |
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| Translation and symbolization | |
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| Inference rules | |
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| Derivations | |
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| Theorems with unabbreviated proofs | |
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| Abbreviated derivations | |
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| Fallacies | |
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| Theorems with abbreviated proofs | |
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| Arguments | |
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| Invalidity: truth-functional expansions and models | |
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| Historical remarks | |
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| Appendix: list of theorems of chapter III | |
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| Appendix: solutions to selected exercises | |
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| Appendix: summary of the system of logic developed in chapters I-III | |
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| ""All"" and ""Some,"" continued | |
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| Terms and formulas | |
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| Bondage and freedom | |
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| Informal notational conventions | |
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| Translation and symbolization | |
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| Revised inference rules | |
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| Theorems | |
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| Invalidity: truth-functional expansions and models | |
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| Invalidity: false arithmetical translations | |
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| Arguments of English | |
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| Historical remarks | |
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| Appendix: list of theorems of chapter IV | |
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| Appendix: solutions to selected exercises | |
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| ""Is"" (in one sense) | |
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| Terms and formulas | |
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| Translation and symbolization | |
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| Inference rules | |
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| Theorems | |
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| Invalidity | |
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| Historical remarks | |
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| Appendix: list of theorems of chapter V | |
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| Appendix: solutions to selected exercises | |
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| ""The"" | |
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| Descriptive phrases, terms, formulas | |
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| Bondage and freedom | |
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| Informal notational conventions | |
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| Translation and symbolization | |
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| Inference rules | |
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| Theorems | |
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| Invalidity | |
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| Arguments of English | |
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| Historical remarks | |
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| Appendix: list of theorems of chapter VI | |
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| Appendix: solutions to selected exercises | |
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| Additional Derivational Procedures | |
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| Alphabetic variance | |
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| Substitution | |
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| Abbreviated derivations reconsidered | |
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| biconditional derivations | |
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| Formulas without overlay and prenex normal form, again | |
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| Abbreviated derivations justified | |
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| generalized priciples of interchange | |
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| Historical remarks | |
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| Appendix: list of theorems of chapter VII | |
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| Appendix: solutions to selected exercises | |
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| Appendix: summary of the system of logic developed in chapters I-VII | |
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| ""The"" again: A Russellian Theory of Descriptions | |
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| The Fregean theory of chapter VI reconsidered | |
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| A Russellian theory of descriptions | |
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| Historical remarks | |
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| Appendix: list of theorems of chapter VIII | |
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| Appendix: solutions to selected exercises | |
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| Appendix: summary of the Russellian system of logic developed in chapter VIII | |
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| Automatic Procedures | |
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| Introduction | |
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| Tautologies reconsidered | |
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| Tautological implication | |
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| generalized indirect derivation | |
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| A proof procedure for prenex formulas | |
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| A derivation procedure for prenex arguments | |
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| Conversion to prenex form | |
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| A derivation procedure for arbitrary symbolic arguments | |
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| A decision procedure for certain prenex formulas | |
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| A decision procedure for certain prenex arguments | |
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| Historical remarks | |
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| Definitions: Formal Theories | |
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| The vocabulary of formal languages | |
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| Bondage and freedom | |
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| proper substitution | |
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| alphabetic varianc | |
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| Informal notational conventions | |
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| Derivability | |
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| Formal theories | |
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| the theory of commutative ordered fields | |
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| Extensions of theories | |
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| the theory of real numbers | |
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| |
| Definitions | |
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| Variable-Binding Operators | |
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| Definitions reconsidered | |
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| |
| The theory of convergence | |
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| A sketch of further developments | |
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| |
| Historical remarks | |
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| |
| Appendix: list of constants used in chapters X and XI | |
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| Appendix: list of axioms, definitions, and theorems of chapters X and XI | |
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| Bibliography | |
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| Index of Proper Names | |
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| Index of Subjects | |