Mathematical Logic: Revised Edition

Willard Van Orman Quine

Book

Mathematical Logic

Revised Edition

Willard Van Orman Quine

Language: English

Published/Copyright: 1951

Published by

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About this book

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.”

Reviews

Every section of this book provides evidence of rare skill, both in research and communication; it deserves to be read and read again by all who have a serious interest in mathematical logic.
-- Max Black Mind

Combines exemplary clarity and precision with an unusual vividness and originality in style which actually makes the study of the work a fascinating adventure.
-- Carl G. Hempel Philosophic Abstracts

An excellent systematic presentation of mathematical logic… Because it is a clear, exact, and exhaustive treatment of the subject, Professor Quine’s book should serve well as a text in a course on mathematical logic.
-- Morton G. White Philosophical Review

Topics

Philosophy Philosophy of Science

Frontmatter Publicly Available Download PDF	i
PREFACE, 1981 Publicly Available Download PDF	iii
PREFACE TO THE REVISED EDITION Publicly Available Download PDF	vii
PREFACE Publicly Available Download PDF	viii
CONTENTS Publicly Available Download PDF	xi
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
CHAPTER ONE. Statelfzents
1. Conjunction, Alternation, and Denial Requires Authentication Unlicensed Licensed Download PDF	11
2. The Conditional Requires Authentication Unlicensed Licensed Download PDF	14
3. Iterated Composition Requires Authentication Unlicensed Licensed Download PDF	18
4. Use versus Mention Requires Authentication Unlicensed Licensed Download PDF	23
5. Statements about Statements Requires Authentication Unlicensed Licensed Download PDF	27
6. Quasi-Quotation Requires Authentication Unlicensed Licensed Download PDF	33
7. Parentheses and Dots Requires Authentication Unlicensed Licensed Download PDF	37
8. Reduction to Three Primitives Requires Authentication Unlicensed Licensed Download PDF	42
9. Reduction to One Primitive Requires Authentication Unlicensed Licensed Download PDF	45
10. Tautology Requires Authentication Unlicensed Licensed Download PDF	50
11. Selected Tautologous Forms Requires Authentication Unlicensed Licensed Download PDF	55
CHAPTER TWO. Quantification
12. The Quantifier Requires Authentication Unlicensed Licensed Download PDF	65
13. Formulae Requires Authentication Unlicensed Licensed Download PDF	71
14. Bondage, Freedom, Closure Requires Authentication Unlicensed Licensed Download PDF	76
15. Axioms of Quantification Requires Authentication Unlicensed Licensed Download PDF	80
16. Theorems Requires Authentication Unlicensed Licensed Download PDF	85
17. Metatheorems Requires Authentication Unlicensed Licensed Download PDF	89
18. Substitutivity of the Biconditional Requires Authentication Unlicensed Licensed Download PDF	96
19. Existential Quantification Requires Authentication Unlicensed Licensed Download PDF	101
20. Distribution of Quantifiers Requires Authentication Unlicensed Licensed Download PDF	105
21. Alphabetic Variance Requires Authentication Unlicensed Licensed Download PDF	109
CHAPTER THREE. Terms
22. Class and Member Requires Authentication Unlicensed Licensed Download PDF	119
23. Logical Formulae Requires Authentication Unlicensed Licensed Download PDF	123
24. Abstraction Requires Authentication Unlicensed Licensed Download PDF	128
25. Identity Requires Authentication Unlicensed Licensed Download PDF	134
26. Abstraction Resumed Requires Authentication Unlicensed Licensed Download PDF	140
27. Descriptions and Names Requires Authentication Unlicensed Licensed Download PDF	146
CHAPTER FOUR. Extended Theory of Classes
28. Stratification Requires Authentication Unlicensed Licensed Download PDF	155
29. Further Axioms of Membership Requires Authentication Unlicensed Licensed Download PDF	160
30. Substitutivity of Identity Requires Authentication Unlicensed Licensed Download PDF	167
31. Substitution for Variables Requires Authentication Unlicensed Licensed Download PDF	170
32. Further Consequences Requires Authentication Unlicensed Licensed Download PDF	175
33. Logical Product, Sum, Complement Requires Authentication Unlicensed Licensed Download PDF	179
34. Inclusion Requires Authentication Unlicensed Licensed Download PDF	185
35. Unit Classes Requires Authentication Unlicensed Licensed Download PDF	189
CHAPTER FIVE. Relations
36. Pairs and Relations Requires Authentication Unlicensed Licensed Download PDF	197
37. Abstraction of Relations Requires Authentication Unlicensed Licensed Download PDF	202
38. Converse, Image, Relative Product Requires Authentication Unlicensed Licensed Download PDF	208
39. The Ancestral Requires Authentication Unlicensed Licensed Download PDF	215
40. Functions Requires Authentication Unlicensed Licensed Download PDF	221
41. Abstraction of Functions Requires Authentication Unlicensed Licensed Download PDF	225
42. Identity and Membership as Relations Requires Authentication Unlicensed Licensed Download PDF	229
CHAPTER SIX. Number
43. Zero, One, Successor Requires Authentication Unlicensed Licensed Download PDF	237
44. Natural Numbers Requires Authentication Unlicensed Licensed Download PDF	241
45. Counter Sets Requires Authentication Unlicensed Licensed Download PDF	246
46. Finite and Infinite Requires Authentication Unlicensed Licensed Download PDF	250
47. Powers of Relations Requires Authentication Unlicensed Licensed Download PDF	253
48. Arithmetical Sum, Product, Power Requires Authentication Unlicensed Licensed Download PDF	259
49. Familiar Identities of Arithmetic Requires Authentication Unlicensed Licensed Download PDF	262
50. Ratios Requires Authentication Unlicensed Licensed Download PDF	266
51. Real Numbers Requires Authentication Unlicensed Licensed Download PDF	271
52. Further Extensions Requires Authentication Unlicensed Licensed Download PDF	275
CHAPTER SEVEN. Syntax
53. Formality Requires Authentication Unlicensed Licensed Download PDF	283
54. The Syntactical Primitive Requires Authentication Unlicensed Licensed Download PDF	287
55. Protosyntax Requires Authentication Unlicensed Licensed Download PDF	291
56. Formula and Matrix Defined Requires Authentication Unlicensed Licensed Download PDF	295
57. Axioms of Quantification Defined Requires Authentication Unlicensed Licensed Download PDF	299
58. Theorem Defined Requires Authentication Unlicensed Licensed Download PDF	302
59. Protosyntax Self-Applied Requires Authentication Unlicensed Licensed Download PDF	306
60. Incompleteness Requires Authentication Unlicensed Licensed Download PDF	312
APPENDIX. Theorem versus Metatheorem Requires Authentication Unlicensed Licensed Download PDF	319
List of Definitions Requires Authentication Unlicensed Licensed Download PDF	323
List of Theorems and Metatheorems Requires Authentication Unlicensed Licensed Download PDF	325
Bibliographical References Requires Authentication Unlicensed Licensed Download PDF	331
Index of Proper Names Requires Authentication Unlicensed Licensed Download PDF	339
Index of Subjects Requires Authentication Unlicensed Licensed Download PDF	341

Publishing information

Pages and Images/Illustrations in book

eBook published on:

July 1, 2009

eBook ISBN:

9780674042469

Pages and Images/Illustrations in book

Main content:

358

https://doi.org/10.4159/9780674042469

eBook ISBN: 9780674042469

Audience(s) for this book

Professional and scholarly;

Mathematical Logic

Overview

About this book

Reviews

Topics

Table of contents

Bibliographic data