Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind.

The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.

chapter 1|6 pages


part I|1 pages

The Propositional Calculus: Elements and Decision Procedures

chapter 2|4 pages

Some Simple Forms of Inference

chapter 3|11 pages

Establishing Validity (Theory)

chapter 4|8 pages

Establishing Validity (Practice)

chapter 5|5 pages

Disjunction and Disjunctive Inference

chapter 7|4 pages

Valid Inference and Proof

chapter 8|9 pages

The Propositional Calculus

chapter 9|7 pages

Truth-Tables as a Decision Procedure

chapter 10|9 pages

Equivalence Transformations

chapter 11|9 pages

Another Decision Procedure

part II|1 pages

The Propositional Calculus: Axiomatic Systems

chapter 12|5 pages

Operations of Inference

chapter 13|4 pages

Axiomatic Systems

chapter 14|9 pages

Formal Axiomatic Systems

chapter 15|16 pages

The System PM (I)

chapter 16|8 pages

PM (II) – Substitution of Equivalents

chapter 17|6 pages

PM (III) – Some Further Theorems

chapter 19|6 pages

Consistency and Completeness of PM

chapter 20|6 pages

The System TB

chapter 21|8 pages

Extensions of TB: The System W

chapter 22|6 pages

Consistency and Completeness of W

part III|4 pages

The Lower Predicate Calculus

chapter 23|12 pages

The Lower Predicate Calculus: Introduction

chapter 24|4 pages

The System LPC1

chapter 27|7 pages

LPC1: Decision Procedure II— Exposition

chapter 28|6 pages

LPC1: Decision Procedure II- Justification

chapter 29|12 pages

LPC1: Axiomatization

chapter 30|5 pages

LPC1: Consistency and Completeness

chapter 31|4 pages

The System LPC2 : Introductory

chapter 32|4 pages

LPC2 : Decision Procedure I

chapter 33|4 pages

LPC2: Decision Procedure II–Exposition

chapter 35|6 pages

LPC2 : Axiomatization

chapter 36|9 pages

LPC2 and the Logic of an Empty Universe

chapter 37|10 pages

Multiple Quantification I

chapter 38|3 pages

Equivalence Transformations of Quantifiers

chapter 39|9 pages

Multiple Quantification II

chapter 40|11 pages

Multiple Quantification III

chapter 41|11 pages

The Lower Predicate Calculus: Conclusion

part IV|4 pages


chapter 42|11 pages

Résumé of Traditional Syllogistic Logic

chapter 43|4 pages

Syllogistic and the Predicate Calculus

chapter 46|5 pages

Syllogistic and LPC1: Another Approach

chapter 48|12 pages

Syllogistic: An Axiomatic Presentation

chapter 49|3 pages

On the Meta-logie of AS