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

## 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.

### 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