Mathematical Logic (Dover Books on Mathematics) [Paperback]

Stephen Cole Kleene (Author), Mathematics (Author)

Book Description

ISBN-10: 0486425339 | ISBN-13: 978-0486425337 | Publication Date: December 18, 2002

Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.

Product Details

• Paperback: 416 pages
• Publisher: Dover Publications (December 18, 2002)
• Language: English
• ISBN-10: 0486425339
• ISBN-13: 978-0486425337
• Product Dimensions: 8.6 x 5.5 x 0.9 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #404,189 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

16 of 16 people found the following review helpful:

5.0 out of 5 stars Excellent Excellent Book, July 16, 2008

By 

Trenton F. Schirmer "Philosopher" (Fair Oaks, CA United States) - See all my reviews
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This review is from: Mathematical Logic (Dover Books on Mathematics) (Paperback)

This book was written by one of the great American mathematical minds of this century. I've read it cover to cover and it happens to be my favorite logic book for its scope, depth, and clarity. Kleene uses a combined model-theoretic and proof-theoretic approach, and derives many interesting results relating the two (he also gives mention to special axioms for Intuitionistic logic). Although his focus in the first part of the book is on a more or less mathematical treatment of standard first-order predicate logic (augmented later by functions and equality), he also spends considerable time discussing the ways in which formal logic can and should be used to analyze "ordinary language" statements and arguments. After setting the groundwork, he moves onto subjects such as set theory, formal axiomatic theories, turing machines and recursiveness, Godel's incompleteness theorem, Godel's completeness theorem, and just about every interesting subject relating to logic in the first half of the twentieth century.

For the mathematically inclined self-teacher, Kleene's exposition should not be difficult at all, in fact I found it remarkably clear compared to other mathematical treatments of the subject (which are necessary if one wants to understand the deeper results). I suppose less mathematically inclined readers could try Irving Copi's "Symbolic Logic" as a start, although even that requires some mathematical proficiency, and since it doesn't cover many of the things you will want to know about, you'll end up coming back to a book like Kleene's anyway. So to summarize, if you want to learn the hard stuff (from the first half of the twentieth century--which includes just about everything the layman/philosopher wants to know), there is no better or easier way.

42 of 59 people found the following review helpful:

3.0 out of 5 stars Not for the autodidact, July 19, 2004

By 

Christopher Schroen (Alexandria, VA) - See all my reviews
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This review is from: Mathematical Logic (Dover Books on Mathematics) (Paperback)

Ten years ago, I took an undergraduate course in symbolic logic. Wishing recently to refresh my (extremely rusty) memories of the propositional calculus and the first-order predicate calculus, I picked up this meaty text and was extremely dismayed to find myself soundly defeated within the first few pages. Kleene does not even make a pretense of holding the reader's hand: either you get it or you don't. There is nothing even remotely "user-friendly" about this book's presentation of its material.

If one were to read this book under the guidance of a teacher, I think it might be worthwhile. It may not be fair for me to blame the author for my inability to understand his writing. If you're smarter than I am, you might breeze right through it.

I cannot recommend this book, though, good though it may be, for anyone who wishes to teach him/herself logic, nor for anyone who wishes to brush up on the subject. There are exercises for the reader to test his/her understanding of the material, but no answer key is provided. This is heavy-duty stuff, and not well-suited to the self-teacher.

2 of 2 people found the following review helpful:

4.0 out of 5 stars Still very usefull, April 21, 2010

By 

Frederico Lopes (Brazil) - See all my reviews
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This review is from: Mathematical Logic (Hardcover)

There are many books on logic, but this, written by one of the chief logicians of the 20th century, deserves a place on your bookshelf. The informations and the exposition style are solid, clear and still new to many. The author also explains the historical motivations for each new concept he talks about, and this alone should make up your mind about buying this book.
But I have seen more modern approaches, and maybe better ones. It's possible to learn so much from this book, and so much that you'll need no other book, least you'd prefer a contemporary way to talk about those things. I would not adopt it for my classes, but I strongly recommend it to my fellows.