| Preface |
| Introduction |
| Principles of Inference and Definition / Part I： |
| The Sentential Connectives / Chapter 1.： |
| Negation and Conjunction / 1.1： |
| Disjunction / 1.2： |
| Implication: Conditional Sentences / 1.3： |
| Equivalence: Biconditional Sentences / 1.4： |
| Grouping and Parentheses / 1.5： |
| Truth Tables and Tautologies / 1.6： |
| Tautological Implication and Equivalence / 1.7： |
| Sentential Theory of Inference / Chapter 2.： |
| Two Major Criteria of Inference and Sentential Interpretations / 2.1： |
| The Three Sentential Rules of Derivation / 2.2： |
| Some Useful Tautological Implications / 2.3： |
| Consistency of Premises and Indirect Proofs / 2.4： |
| Symbolizing Everyday Language / Chapter 3.： |
| Grammar and Logic / 3.1： |
| Terms / 3.2： |
| Predicates / 3.3： |
| Quantifiers / 3.4： |
| Bound and Free Variables / 3.5： |
| A Final Example / 3.6： |
| General Theory of Inference / Chapter 4.： |
| Inference Involving Only Universal Quantifiers / 4.1： |
| Interpretations and Validity / 4.2： |
| Restricted Inferences with Existential Quantifiers / 4.3： |
| Interchange of Quantifiers / 4.4： |
| General Inferences / 4.5： |
| Summary of Rules of Inference / 4.6： |
| Further Rules of Inference / Chapter 5.： |
| Logic of Identity / 5.1： |
| Theorems of Logic / 5.2： |
| Derived Rules of Inference / 5.3： |
| Postscript on Use and Mention / Chapter 6.： |
| Names and Things Named / 6.1： |
| Problems of Sentential Variables / 6.2： |
| Juxtaposition of Names / 6.3： |
| Transition From Formal to Informal Proofs / Chapter 7.： |
| General Considerations / 7.1： |
| Basic Number Axioms / 7.2： |
| Comparative Examples of Formal Derivations and Informal Proofs / 7.3： |
| Examples of Fallacious Informal Proofs / 7.4： |
| Further Examples of Informal Proofs / 7.5： |
| Theory of Definition / Chapter 8.： |
| Traditional Ideas / 8.1： |
| Criteria for Proper Definitions / 8.2： |
| Rules for Proper Definitions / 8.3： |
| Definitions Which are Identities / 8.4： |
| The Problem of Division by Zero / 8.5： |
| Conditional Definitions / 8.6： |
| Five Approaches to Division by Zero / 8.7： |
| Padoa's Principle and Independence of Primitive Symbols / 8.8： |
| Elementary Intuitive Set Theory / Part II： |
| Sets / Chapter 9.： |
| Membership / 9.1： |
| Inclusion / 9.3： |
| The Empty Set / 9.4： |
| Operations on Sets / 9.5： |
| Domains of Individuals / 9.6： |
| Translating Everyday Language / 9.7： |
| Venn Diagrams / 9.8： |
| Elementary Principles About Operations on Sets / 9.9： |
| Relations / Chapter 10.： |
| Ordered Couples / 10.1： |
| Definition of Relations / 10.2： |
| Properties of Binary Relations / 10.3： |
| Equivalence Relations / 10.4： |
| Ordering Relations / 10.5： |
| Operations on Relations / 10.6： |
| Functions / Chapter 11.： |
| Definition / 11.1： |
| Operations on Functions / 11.2： |
| Church's Lambda Notation / 11.3： |
| Set-Theoretical Foundations of the Axiomatic Method / Chapter 12.： |
| Set-Theoretical Predicates and Axiomatizations of Theories / 12.1： |
| Isomorphism of Models for a Theory / 12.3： |
| Example: Probability / 12.4： |
| Example: Mechanics / 12.5： |
| Index |
| Preface |
| Introduction |
| Principles of Inference and Definition / Part I： |
図書
