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: |