The Logic of Provability [Paperback]

George S. Boolos (Author)

Book Description

Publication Date: April 28, 1995 | ISBN-10: 0521483255 | ISBN-13: 978-0521483254

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.

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

A completely rewritten and updated successor to the author's The Unprovability of Consistency (1979). This work's subject is the relations between probability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians.

Product Details

• Paperback: 316 pages
• Publisher: Cambridge University Press (April 28, 1995)
• Language: English
• ISBN-10: 0521483255
• ISBN-13: 978-0521483254
• Product Dimensions: 9 x 6 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,036,931 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

6 of 7 people found the following review helpful:

5.0 out of 5 stars Outstanding, but Difficult, August 2, 2004

By 

galloamericanus "galloamericanus" (Podunk, Iowa) - See all my reviews

This review is from: The Logic of Provability (Paperback)

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.

4 of 5 people found the following review helpful:

5.0 out of 5 stars Lucid introduction and valuable reference, September 25, 2004

By 

V. "quasimodo" (Denmark) - See all my reviews

This review is from: The Logic of Provability (Paperback)

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.

1 of 3 people found the following review helpful:

5.0 out of 5 stars Good reference., September 10, 2003

By A Customer

Amazon Verified Purchase

This review is from: The Logic of Provability (Paperback)

This book is an excelent reference for Logics of Provability.
I consider this book a "must have" for anyone in the field, or in the field of Modal Logics.

The author is a leader in the field, and this book is frequently cited in the bibliography of papers in the field.