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The Algebra of Logic by Louis Couturat ISBN: 0486446387 Dover Publications Price: $37.50 click here to see this book In an admirably succinct form, this volume offers a historical view of the development of the calculus of logic, illustrating its beauty, symmetry, and simplicity from an algebraic perspective. Topics include the principles of identity and the syllogism, the principles of simplification and composition; the laws of tautology and of absorption; the distributive law and the laws of duality, double negation, and contraposition; the formulas of De Morgan and Poretsky; Schröder's theorem; sums and products of functions; solution of equations involving one and several unknown quantities; the problem of Boole; Venn diagrams; tables of consequences and causes; and formulas peculiar to the calculus of propositions. 1914 ed. Table of Contents for The Algebra of Logic Preface Bibliography 1. Introduction 2. The Two Interpretations of the Logical Calculus 3. Relation of Inclusion 4. Definition of Equality 5. Principle of Identity 6. Principle of the Syllogism 7. Multiplication and Addition 8. Principles of Simplification and Composition 9. The Laws of Tautology and of Absorption 10. Theorems of Multiplication and Addition 11. The First Formula for Transforming Inclusion into Equalities 12. The Distributive Law 13. Definition of 0 and 1 14. The Law of Duality 15. Definition of Negation 16. The Principles of Contradiction and of Excluded Middle 17. Law of Double Negation 18. Second Formula for Transforming Inclusion into Equalities 19. Law of Contraposition 20. Postulate of Existence 21. The Developments of 0 and 1 22. Properties of the Constituents 23. Logical Functions 24. The Law of Development 25. The Formulas of De Morgan 26. Disjunctive Sums 27. Properties of Developed Functions 28. The Limits of a Function 29. Formula of Poretsky 30. Schröder's Theorem 31. The Resultant of Elimination 32. The Case of Indetermination 33. Sums and Products of Functions 34. The Expression of an Inclusion by Means of an Indeterminate 35. The Expression of a Double Inclusion by Means of an Indeterminate 36. Solution of an Equation Involving One Unknown Quantity 37. Elimination of Several Unknown Quantities 38. Theorem Concerning the Values of a Function 39. Condition of Impossibility and Indetermination 40. Solution of Equations Containing Several Unknown Quantities 41. The Problem of Boole 42. The Method of Poretsky 43. The Law of Forms 44. The Law of Consequences 45. The Law of Causes 46. Forms of Consequences and Causes 47. Example: Venn's Problem 48. The Geometrical Diagrams of Venn 49. The Logical Machine of Jevons 50. Table of Consequences 51. Table of Causes 52. The Number of Possible Assertions 53. Particular Propositions 54. Solution of an Inequation with One Unknown 55. System of an Equation and an Inequation 56. Formulas Peculiar to the Calculus of Propositions 57. Equivalence of an Implication and an Alternative 58. Law of Importation and Exportation 59. Reduction of Inequalities to Equalities 60. Conclusion Index

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