Methods of logic

» This book undertakes both to convey a precise understanding of the formal concepts of modern logic and to develop convenient techniques of formal reasoning.» (Preface, p. VII). – This edition offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, – Contents : Introduction. – I. Truth Functions. 1. Negation, Conjunction, and Alternation; 2. Truth Functions; 3. The Conditional; 4. Grouping; 5. Truth-Value Analysis; 6. Consistency and Validity; 7. Implication; 8. Words into Symbols; 9. Equivalence; 10. Alternational Normal Schemata; 11. Simplification; 12. Duality; 13. Axioms. – II. General Terms and Quantifiers; 14. Categorical Statements;15. Venn’s Diagrams; 16. Syllogisms; 17. Limits of These Methods; 18. Boolean Schemata; 19. Tests of Validity; 20. Some Boolean Incidentals; 21. The Bound Variable; 22. Quantification; 23. Rules of Passage. Monadic Schemata; 24. Prenexity and Purity; 25. Validity Again; 26. Substitution. – III. General Theory of Quantification. 27. Schemata Extended; 28. Substitution Extended; 29. Pure Existentials; 30. The Main Method; 31. Application; 32. Completeness; 33. Löwenheim’s Theorem; 34. Decisions and the Undecidable; 35. Functional Normal Forms; 36. Herbrand’s Method; 37. Other Methods for Validity; 38. Deduction; 39. Soundness; 40. Deductive Strategy. – IV. Glimpses Beyond. 41. Singular Terms; 42. Identity; 43. Descriptions; 44. Elimination of Singular Terms; 45. Elimination of Variables; 46. Classes; 47. Number; 48. Axiomatic Set Theory. – Partial Answers to Exercises. – Bibliography – Index. M.-M. V.