Mathematical logic / by Willard Van Orman Quine.

Format:

Book

Author/Creator:

Quine, W. V. (Willard Van Orman)

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Mathematics.

Physical Description:

1 online resource (xii, 346 pages)

Edition:

Rev. ed.

Place of Publication:

Cambridge, MA : Harvard University Press, c1981.

Language Note:

English

Summary:

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."

Contents:

Frontmatter

PREFACE, 1981

PREFACE TO THE REVISED EDITION

PREFACE

CONTENTS

Introduction

CHAPTER ONE. Statelfzents

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. Formulae

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 Formulae

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

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliography and index.

ISBN:

9780674042469

0674042468

OCLC:

923117190