Mathematical Logic, Revised Edition
Revised Edition
1st Edition
Published on 30. June 2009
359 pages
978-0-674-04246-9 (ISBN)
Description
W. V. Quine's systematic development of mathematical logic has been widely praised for the new material presented and for the clarity of its exposition. This revised edition, in which the minor inconsistencies observed since its first publication have been eliminated, will be welcomed by all students and teachers in mathematics and philosophy who are seriously concerned with modern logic. Max Black, in Mind, has said of this book, "It will serve the purpose of inculcating, by precept and example, standards of clarity and precision which are, even in formal logic, more often pursued than achieved."
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Content
- Intro
- CONTENTS
- Introduction
- CHAPTER ONE. Statements
- 1. Conjunction, Alternation, and Denial
- 2. The Conditional
- 3. Iterated Composition
- 4. Use versus Mention
- 5. Statements about Statements
- 6. Quasi-Quotation
- 7. Parentheses and Dots
- 8. Reduction to Three Primitives
- 9. Reduction to One Primitive
- 10. Tautology
- 11. Selected Tautologous Forms
- CHAPTER TWO. Quantification
- 12. The Quantifier
- 13. Formulæ
- 14. Bondage, Freedom, Closure
- 15. Axioms of Quantification
- 16. Theorems
- 17. Metatheorems
- 18. Substitutivity of the Biconditional
- 19. Existential Quantification
- 20. Distribution of Quantifiers
- 21. Alphabetic Variance
- CHAPTER THREE. Terms
- 22. Class and Member
- 23. Logical Formulæ
- 24. Abstraction
- 25. Identity
- 26. Abstraction Resumed
- 27. Descriptions and Names
- CHAPTER FOUR. Extended Theory of Classes
- 28. Stratification
- 29. Further Axioms of Membership
- 30. Substitutivity of Identity
- 31. Substitution for Variables
- 32. Further Consequences
- 33. Logical Product, Sum, Complement
- 34. Inclusion
- 35. Unit Classes
- CHAPTER FIVE. Relations
- 36. Pairs and Relations
- 37. Abstraction of Relations
- 38. Converse, Image, Relative Product
- 39. The Ancestral
- 40. Functions
- 41. Abstraction of Functions
- 42. Identity and Membership as Relations
- CHAPTER SIX. Number
- 43. Zero, One, Successor
- 44. Natural Numbers
- 45. Counter Sets
- 46. Finite and Infinite
- 47. Powers of Relations
- 48. Arithmetical Sum, Product, Power
- 49. Familiar Identities of Arithmetic
- 50. Ratios
- 51. Real Numbers
- 52. Further Extensions
- CHAPTER SEVEN. Syntax
- 53. Formality
- 54. The Syntactical Primitive
- 55. Protosyntax
- 56. Formula and Matrix Defined
- 57. Axioms of Quantification Defined
- 58. Theorem Defined
- 59. Protosyntax Self-Applied
- 60. Incompleteness
- APPENDIX. Theorem versus Metatheorem
- List of Definitions
- List of Theorems and Metatheorems
- Bibliographical References
- Index of Proper Names
- Index of Subjects
