The Elements of Formal Logic

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. Resume 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