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  • The Logic of Provability (Volume 0)

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George S. Boolos
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The Logic of Provability (Volume 0)

by George S. Boolos (Author) Format: Paperback
4.8 out of 5 stars (11)
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This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention.
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  1. ISBN-10
    0521483255
  2. ISBN-13
    978-0521483254
  3. Edition
    Revised ed.
  4. Publisher
    Cambridge University Press
  5. Publication date
    August 21, 2008
  6. Language
    English
  7. Dimensions
    6 x 0.79 x 9 inches
  8. Print length
    316 pages
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Editorial Reviews

Review

"The book contains an excellent combination of values: noble subject, fresh key results, and the gentle, friendly style of the author. It can be recommended as a textbook, as a handbook, or simply as high quality reading in logic." Sergei N. Artemov, Journal of Symbolic Logic

"I found it lively, lucid, and informative...Boolos' style of writing is unusually kind to the reader. When an argument becomes tricky, he breaks it down into a lot of small steps, showing the reader in detail just how to proceed. A result is that the book is remarkably easy to read." Vann McGee, Rutgers University

Book Description

Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.

Product details

  • Publisher ‏ : ‎ Cambridge University Press
  • Publication date ‏ : ‎ August 21, 2008
  • Edition ‏ : ‎ Revised ed.
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 316 pages
  • ISBN-10 ‏ : ‎ 0521483255
  • ISBN-13 ‏ : ‎ 978-0521483254
  • Item Weight ‏ : ‎ 15.8 ounces
  • Dimensions ‏ : ‎ 6 x 0.79 x 9 inches
  • Best Sellers Rank: #1,668,215 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.8 out of 5 stars (11)

About the author

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George S. Boolos

George S. Boolos

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Customer reviews

4.8 out of 5 stars
11 global ratings

Top reviews from the United States

  • V.
    5 out of 5 stars
    Lucid introduction and valuable reference
    Reviewed in the United States on September 26, 2004
    Format: Paperback
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    As the other reviewers note, this book is remarkable in that it both offers a reasonably gentle introduction to the subject even for those without too much mathematical background (logically-inclined philosophy students come to mind), and at the same time remains to this day an indispensable reference for the specialistâ€"this for example is the only source where you can find the proofs of Solovay's "other" modal completeness results for transitive models of set theory. George Boolos was (is) famous for, among other things, his gift of didactically brilliant exposition.

    There is only one other book on the subjectâ€"C.Smory'nski's "Self-Reference and Modal Logic", now out-of-print, which provides a nice complement to Boolos with surprisingly small overlap. For an introduction, I would not hesitate to recommend Boolos over Smory'nski.

    Since 1993 the "baton" has not completely "fallen out of Boolos' hands"â€"the interested reader can follow up on this via e.g. a couple of handbook-chapter expositions, easily found by googling around, that point to current research literature. However, no further textbook-level exposition appears to be forthcoming anytime soon.

    As a comment to galloamericanus' review, I would note that Boolos does not restrict his monograph exclusively or even primarily to his own results. The reader gets a fair overview of the research field by 1993 as shaped by many contributors.

    11 people found this helpful
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  • galloamericanus
    5 out of 5 stars
    Outstanding, but Difficult
    Reviewed in the United States on August 3, 2004
    Format: Paperback
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    George Boolos regrettably died too early, at age 56. He was a witty engaging writer, and a brilliant logician. This book,

    completed not long before his untimely death, is probably

    the high point of his career. The key insight, that modal logic

    can be interpreted as a sort of metamathematical algebra,

    is Godel's from the 1930s. And a key result is due to Martin

    Lob about 50 years ago. But Boolos built a towering edifice

    on this slim material. I think that the provability interpretation

    of the modal operator is the most philosophically and mathematically satisfying of all, and I hope someone comes

    along to pick up the baton that has fallen from Boolos's hand.

    18 people found this helpful
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  • ryotarounosuke
    4 out of 5 stars
    第二不完全性定理の部分だけでも貴重。
    Reviewed in Japan on November 22, 2003
    Format: Paperback
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    この本のはじめの方で、多くの本では「これらの議論を形式化すれば、～が出てきて、第二不完全先生定理が帰結する」というようになっている部分を、丁寧に追っている。可証性述語と様相論理の関係というのがこの本の一番のテーマであるから、こうした一部だけを取り上げてレビューするのは適当ではないかもしれないが、この点だけでも貴重な一冊なので挙げてみた。田中一之さんの本でも可導性性条件の証明は多少書いてあるが、やはりある程度丁寧に追った本を探していたので、この本はぴったりだった。特に、不完全性定理の議論を初めから形式化する方法が載っている本は少ない（と思う）のでかなり貴重。このやり方だと、第一不完全性定理を証明するのが通常より大変になるが、その代わり第二不完全性定理が自然に出てくる。ただし、Boolosは（論文でもその傾向があるように思われるが）本の書き方として、それほど分りやすくない点があり、それで四つ星にした。

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