Synopses & Reviews
Now much revised since its first appearance in 1941, this book, 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.
Review
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. Mind
Review
A masterpiece of clarity and analysis, setting forth at once briefly and comprehensively an introduction to formal logic that few can match. Philosophical Studies
Review
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
Review
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
Synopsis
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.
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