# Book:A.H. Basson/Introduction to Symbolic Logic/Third Edition

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## A.H. Basson and D.J. O'Connor:

## A.H. Basson and D.J. O'Connor: *Introduction to Symbolic Logic (3rd Edition)*

Published $1959$, **University Tutorial Press Ltd.**

- ISBN 0 7231 0456 5.

### Subject Matter

### Contents

- Preface to the Third Edition

- Chapter I. Introductory
- 1. Symbolic Logic and Classical Logic
- 2. The Use of Symbols
- 3. Logical Form
- 4. Inference and Implication

- Chapter II. The Calculus of Propositions
- 1. Propositions and their Relations
- 2. Truth-Functions
- 3. Basic Truth-Tables of the Propositional Calculus
- 4. Relations between Truth-Functions
- 5. Further Logical Constants

- Chapter III. The Calculus of Propositions (
*continued*)- 1. The Truth-Table Method of Testing the Validity of Arguments
- 2. Logical Punctuation and the Scope of Constants
- 3. The Construction and Application of Truth-Tables
- 4. An Indirect Method of Truth-Table Decision
- 5. The Classification of Propositions
- 6. Reference Formulae
- 7. Decision Procedures and Normal Forms
- 8. The Total Number of Truth-Functional Expressions
- 9. Derivation by Substitution

- Chapter IV. The Axiomatic Method
- 1. The Purpose of the Axiomatic Method
- 2. The Construction of an Axiom System
- 3. Derivable Formulae
- 4. Conditions for an Axiom System
- 5. Consistency
- 6. Independence
- 7. The Derivation of Formulae
- 8. Completeness

- Chapter V. Elements of the Predicate Calculus
- 1. Some New Forms of Inference
- 2. Singular Propositions
- 3. Further Remarks on Proper Names and Descriptions
- 4. Relations between the Propositional Calculus and the Predicate Calculus
- 5. The Particular Quantifier: Existence
- 6. Analysis of some Quantified Propositions
- 7. The Universal Quantifier
- 8. The Interpretation of Quantifiers as Conjunctions and Disjunctions
- 9. Free and Bound Variables: Constants
- 10. Interpretation and Satisfiable Formulae
- 11. Simultaneously Satisfiable Formulae
- 12. The Classical Syllogism

- Chapter VI. Elements of the Predicate Calculus
- 1. Extensions of the Class of Formulae
- 2. Formulae with more than one Quantifier
- 3. Two-termed Predicates
- 4. Satisfiability: Finite Domains
- 5. Finite Domains (
*continued*) - 6. Two-termed Predicates: Infinite Domains
- 7. Logical Truth
- 8. Decision Procedures
- 9. Axiom Systems

- Appendix
- 1. The Syllogism and the Algebra of Classes
- 2. Classes and the Relationships between them
- 3. The Boolean Algebra of Classes
- 4. The Boolean Algebra of Classes and the Syllogism

- Bibliography

- Exercises

- Index