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.
Preface 1. Validity Part 1: The Propositional Calculus: Elements and Decision Procedures 2. Some Simple Forms of Inference 3. Establishing Validity (Theory) 4. Establishing Validity (Practice) 5. Disjunction and Disjunctive Inference 6. Material Equivalence: ‘If and Only If‘ 7. Valid Inference and Proof 8. The Propositional Calculus 9. Truth-tables as a Decision Procedure 10. Equivalence Transformations 11. Another Decision Procedure Part 2: The Propositional Calculus: Axiomatic Systems 12. Operations of Inference 13. Axiomatic Systems 14. Formal Axiomatic Systems 15. The System PM (I) 16. PM (II) Substitution of Equivalents 17. PM (III) Some Further Theorems 18. PM (IV) Independence and Non-independence 19. Consistency and Completeness of PM 20. The System TB 21. Extensions of TB: The System W 22. Consistency and Completeness of W 23. The Elements of Formal Logic Part 3: The Lower Predicate Calculus Some General Remarks on Part 3 23. The Lower Predicate Calculus: Introduction 24. The System LPCl 25. LPCl: Decision Procedure I - The Truth-table Method 26. Universes of Discourse - Justification of Decision Procedure 27. LPCI : Decision Procedure II - Exposition 28. LPCI : Decision Procedure II - Justification 29. LPCl: Axiomatization 30. LPCl : Consistency and Completeness 31. The System LPC2: Introductory 32. LPC2: Decision Procedure I 33. LPC2: Decision Procedure II - Exposition 34. LPC2: Decision Procedure II - Justification 35. LPC2: Axiomatization 36. LPC2 and the Logic of an Empty Universe 37. Multiple Quantification I 38. Equivalence Transformations of Quantifiers 39. Multiple Quantification II 40. Multiple Quantification III 41. The Lower Predicate Calculus: Conclusion Part 4: Syllogistic Introductory Note 42. Résumé of Traditional Syllogistic Logic 43. Syllogistic and the Predicate Calculus 44. Syllogistic Moods under Interpretation 1: The Antilogism Theorem 45. Syllogistic and LPC1: Further Interpretations 46. Syllogistic and LPC1: Another Approach 47. The Validity of Syllogisms Reconsidered: An Extension of the Antilogism Theorem 48. Syllogistic: An Axiomatic Presentation 49. On the Meta-Iogic of AS. Appendices