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Set Theory and Its Logic, Revised Edition [Paperback]

W. V. Quine (Author)
5.0 out of 5 stars  See all reviews (1 customer review)

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Book Description

January 1, 1969

This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before.

Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.


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Editorial Reviews

Review

This revision of an important and lucid account of the various systems of axiomatic set theory preserves the basic format and essential ingredients of its highly regarded original...There have, however, been a number of important changes, generally in the interest of greater elegance and clarity...a generally improved version of an originally masterful and brilliant work. (Review of Metaphysics )

This is the masterpiece one would have expected it to be. For the expert it is a fresh and elegant treatise, brimming deliciously with new ideas and insights. For the beginner it is a brilliant gem of exposition, rendering a host of abstruse arguments crystal clear. For all it is a smooth and exciting journey to a vivid and comprehensive view of the alternative foundations of classical mathematics.
--Joseph S. Ullian (Philosophical Review )

Perhaps the most concise and readable general survey of axiomatic set theory at present available...Suitable reading not only for mathematics students...but also for philosophers with an interest in the foundations of mathematics. An excellent index and system of numbering formulae make it also a useful reference book.
--A. A. Treherne (Proceedings of the Edinburgh Mathematical Society )

This book is most remarkable for its way of presenting the subject matter. A definite system of set theory is offered, but at the same time alternative ways are indicated and partly explored at every turn...The book is also remarkable for its style. Pithy, with never an unnecessary word (but with every necessary one), at times witty, the book is written in a way that is a great relief from ordinary textbooks. Quine's books always have style, but I consider this as one of the most successful from this point of view.
--Jean van Heijenoort

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.

Product Details

  • Paperback: 380 pages
  • Publisher: Belknap Press of Harvard University Press; Revised edition (January 1, 1969)
  • Language: English
  • ISBN-10: 0674802071
  • ISBN-13: 978-0674802070
  • Product Dimensions: 8.1 x 5.4 x 1 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,061,934 in Books (See Top 100 in Books)

 

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15 of 16 people found the following review helpful:
5.0 out of 5 stars Masterwork, June 3, 2006
This review is from: Set Theory and Its Logic, Revised Edition (Paperback)
"Set Theory and It's Logic" has cast a long shadow since it's first appearance. It is quite simply the crowning work of one of the 20th century's most distinguished philosophers. Sober, clear, and direct (and yet unpretentious and very friendly), it is illuminating to anyone who has the patience to slowly sip it and consider the the way the arguments build up from line to line and page to page a seemingly indestructible house of cards. If one is unprepared for the rigors of the book, that can be easily remedied--Quine also wrote the best introductory book on Logic, "Methods of Logic", which he took through several editions before his death. That book assumes no backround in logic, and a beginner who works her way through the exercises will find herself well-prepared for the magic tricks in "Set Theory and its Logic". I wished we taught this stuff in the public schools, along with mathematics, and (to keep the old dialectic rolling) Homer, Shakespeare, Dante, Tolstoy, Dickinson--the great poets. I might be dreaming, but we may have, at the very least, more ethical scientists, more humane poets, or just plain old more interesting people--who know what the foundations of their thoughts actually assume. A classic.
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Inside This Book (learn more)
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
comprehension premisses, ancestral induction, noncommittal abstraction, numeration theorem, ordinal strength, impredicative theory, virtual theory, predicative attributes, ultimate classes, theorem schemata, comprehension assumptions, numbered formulas, transfinite recursion, cumulative types, inaccessible numbers, comprehension axioms, axiom schema, comprehension schema, finite classes, typical ambiguity, primitive notation, finite ordinals, existence assumptions, valid schema, schematic letters
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mathematical Logic
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