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Foundations of Mathematical Logic
Haskell B. Curry
Table of Contents
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Preface; Explanation of Conventions
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| Chapter 1. Introduction | ||||||||
| 1. The nature of mathematical logic | ||||||||
| 2. The logical antinomies | ||||||||
| 3. The nature of mathematics | ||||||||
| 4. Mathematics and logic | ||||||||
| 5. Supplementary topics | ||||||||
| Chapter 2. Formal Systems | ||||||||
| 1. Preliminaries | ||||||||
| 2. Theories | ||||||||
| 3. Systems | ||||||||
| 4. Special forms of systems | ||||||||
| 5. Algorithms | ||||||||
| 6. Supplementary topics | ||||||||
| Chapter 3. Epitheory | ||||||||
| 1. The nature of epitheory | ||||||||
| 2. Replacement and monotone relations | ||||||||
| 3. The theory of definition | ||||||||
| 4. Variables | ||||||||
| 5. Supplementary topics | ||||||||
| Chapter 4. Relational logical algebra | ||||||||
| 1. Logical algebras in general | ||||||||
| 2. Lattices | ||||||||
| 3. Skolem lattices | ||||||||
| 4. Classical Skolem lattices | ||||||||
| 5. Supplementary topics | ||||||||
| Chapter 5. The Theory of Implication | ||||||||
| 1. General principles of assertional logical algebra | ||||||||
| 2. Propositional algebras | ||||||||
| 3. The systems LA and LC | ||||||||
| 4. Equivalence of the systems | ||||||||
| 5. L deducibility | ||||||||
| 6. Supplementary topics | ||||||||
| Chapter 6. Negation | ||||||||
| 1. The nature of negation | ||||||||
| 2. L systems for negation | ||||||||
| 3. Other formulations of negation | ||||||||
| 4. Technique of classical negation | ||||||||
| 5. Supplementary topics | ||||||||
| Chapter 7. Quantification | ||||||||
| 1. Formulation | ||||||||
| 2. Theory of the L systems | ||||||||
| 3. Other forms of quantification theory | ||||||||
| 4. Classical epitheory | ||||||||
| 5. Supplementary topics | ||||||||
| Chapter 8. Modality | ||||||||
| 1. Formulation of necessity | ||||||||
| 2. The L theory of necessity | ||||||||
| 3. The T and H formulations of necessity | ||||||||
| 4. Supplementary topics | ||||||||
| Bibliography; Index | ||||||||