Elementary Logic: Revised Edition

by Willard Van Orman Quine

Overview

Much revised since its first appearance in 1941, Willard Van Orman Quine’s Elementary Logic, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truth-function logic along with a complete proof procedure for the logic of quantifiers.

Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters.

Product Details

ISBN-13:	9780674244511
Publisher:	Harvard University Press
Publication date:	10/15/1980
Edition description:	Revised Edition
Pages:	144
Product dimensions:	5.50(w) x 8.20(h) x 0.50(d)

About the Author

W. V. Quine was Edgar Pierce Professor of Philosophy, Harvard University. He wrote twenty-one books, thirteen of them published by Harvard University Press.

Table of Contents

Preface to the Revised Edition

Preface to the 1941 Edition

1. Introduction

PART 1: STATEMENT COMPOSITION

2. Truth Values

3. Conjunction

4. Denial

5. 'Or'

6. 'But', 'although', 'unless'

7. 'If'

8. General and Subjunctive Conditionals

9. 'Because', 'hence', 'that'

10. Reduction to Conjunction and Denial

11. Grouping

12. Verbal Cues to Grouping

13. Paraphrasing Inward

PART 2: TRUTH-FUNCTIONAL TRANSFORMATIONS

14. Substitution in Truth-Functional Schemata

15. Instances

16. Equivalent Schemata

17. Truth-Functional Equivalence

18. Replacement

19. Transformation

20. Proofs of Equivalence

21. Alternation and Duality

22. Normal Schemata

23. Validity

24. Truth-Functional Truth

25. Inconsistency and Truth-Functional Falsity

26. Implication between Schemata

27. Truth-Functional Implication

PART 3: QUANTIFICATION

28. 'Something'

29. Quantifiers

30. Variables and Open Sentences

31. Variants of 'Some'

32. 'Some' Restricted

33. 'No'

34. 'Every'

35. Variants of 'Every'

36. Persons

37. Times and Places

38. Quantification in Context

PART 4: QUANTIFICATIONAL INFERENCE

39. Quantificational Schemata

40. Predicates

41. Restraints on Introducing

42. Substitution Extended

43. Validity Extended

44. Equivalence Extended

45. Inconsistency Proofs

46. Logical Arguments

47. Identity and Singular Terms

48. Membership

Index

Editorial Reviews

For Quine, of course, the territory of logic seems but an extension of his own back yard, so assuredly does he walk there where others tread only with brainracking caution. And as he is both master innovator and master explicator, with a masterful prose style to boot, any work of his is a painless necessity.

Choice

Combines exemplary clarity and precision with an unusual vividness and originality in style which actually make the study of the work a fascinating adventure—no small achievement in the reputedly dullest and most barren field of scientific research.

Philosophic Abstracts - Carl G. Hempel

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. Viewed as a whole, the system of logic explained in this book comes nearer than any previous attempt to conforming with the regulative ideals of the mathematical logician… This advance in unification and deductive elegance is not achieved at the expense of rigour; while the striking nature of the gain in the conciseness of the whole may be verified by any reader who will compare the length of this book with that of the corresponding sections in Principia… 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.

Mind - Max Black

A masterpiece of clarity and analysis, setting forth at once briefly and comprehensively an introduction to formal logic that few can match.

Philosophical Studies

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. Viewed as a whole, the system of logic explained in this book comes nearer than any previous attempt to conforming with the regulative ideals of the mathematical logician... This advance in unification and deductive elegance is not achieved at the expense of rigour; while the striking nature of the gain in the conciseness of the whole may be verified by any reader who will compare the length of this book with that of the corresponding sections in Principia... 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"

A masterpiece of clarity and analysis, setting forth at once briefly and comprehensively an introduction to formal logic that few can match.-- "Philosophical Studies"

Combines exemplary clarity and precision with an unusual vividness and originality in style which actually make the study of the work a fascinating adventure--no small achievement in the reputedly dullest and most barren field of scientific research.--Carl G. Hempel "Philosophic Abstracts"

For Quine, of course, the territory of logic seems but an extension of his own back yard, so assuredly does he walk there where others tread only with brainracking caution. And as he is both master innovator and master explicator, with a masterful prose style to boot, any work of his is a painless necessity.-- "Choice"

From the Publisher

Combines exemplary clarity and precision with an unusual vividness and originality in style which actually make the study of the work a fascinating adventure—no small achievement in the reputedly dullest and most barren field of scientific research.
— Carl G. Hempel

Philosophic Abstracts

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 . Viewed as a whole, the system of logic explained in this book comes nearer than any previous attempt to conforming with the regulative ideals of the mathematical logician...This advance in unification and deductive elegance is not achieved at the expense of rigour; while the striking nature of the gain in the conciseness of the whole may be verified by any reader who will compare the length of this book with that of the corresponding sections in Principia... 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