An Introduction to G?del's Theorems (Cambridge Introductions to Philosophy)

An Introduction to G?del's Theorems (Cambridge Introductions to Philosophy)
by Peter Smith

An Introduction to G?del's Theorems (Cambridge Introductions to Philosophy)
List Price: $29.99
Our Price: $21.21
You Save: $8.78 (29%)
Availability: Usually ships in 1-2 business days
Category: Book
See more book details and other editions


(Click here)
Buy this book at online book store in your country
Canada | UK | Germany | France

Book Summary Information

Author: Peter Smith
Edition: Paperback
Audio: English (Original Language); English (Unknown); English (Published)
Published: 2007-08-06
ISBN: 0521674530
Number of pages: 376
Publisher: Cambridge University Press

Book Reviews of An Introduction to G?del's Theorems (Cambridge Introductions to Philosophy)

Book Review: the best thing out there
Summary: 5 Stars

For a couple of decades now, students who had completed their first logic class and dabbled in a little bit of metatheory (perhaps soundness and completeness) were forced to avail themselves of Boolos and Jeffrey's (fourth edition with Burgess) "Computability and Logic." Unfortunately, the third edition presented much of the material in too brief a manner, resulting in a big jump from lower level logic to the material covered. The fourth edition is much longer, but no more easier to teach to talented undergraduates. More recently, Epstein's book on computability was an improvement in this regard, but its logical coverage was much less.

Smith's book should now be the canonical text. First, the discussion and proofs are astoundingly clear to students who haven't done much logic beyond their first class. Pick any topic from B & J and Smith, for example primitive recursiveness, the tie between p.r. axiomatizability and axiomatizability via Craig's theorem, etc. and the discussion and proofs in Smith will be clearer, more accessible, and more clearly tied to the other relevant concepts. Second, the coverage is exactly what is needed to understand both theorems and the most important consequences and extensions. Third, the way he ties the disparate topics together (for example the informal proofs through Chapter 5 and their rigorizaiton through Chapter 18) is just fantastic. This is really important for helping the reader develop a deeper understanding of things. If you just pile theorem upon theorem it's easy for the reader accept them as true without developing any logical insight and appreciation of the landscape.

I don't know if Cambridge would allow this, but in the next edition they should seriously think about adding exercise sections like B & J and Epstein. If they did, I think this book would eclipse the other two for classroom uses.

It's not just for students, either. A colleague and I were arguing about something and we picked up Smith's work rathern than either of Smullyan's to figure out a point relevant to the debate. I find that my grasp of the relevant proofs is much cleaer for reading Smith (my colleague is much, much better at logic than me, but with Smith's help I won the debate).

It is both extraordinary and a cause for celebration when someone can combine in a logic text this level of coverage, rigor, accessibility, and funness of read. I don't think there is a precedent actually. In short, Smith's work is a service to Lady Philosophy. Joe Bob says check it out.

Summary of An Introduction to G?del's Theorems (Cambridge Introductions to Philosophy)

In 1931, the young Kurt G?del published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. G?del also outlined an equally significant Second Incompleteness Theorem.?How are these Theorems established, and why do they matter?? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Logic & Language Books

Book Subjects
Most talked about in Logic : 2
Fundamentals of Mathematical Logic ImageFundamentals of Mathematical Logic
by Peter G. Hinman
A K Peters Ltd; Published: 2005-11-15; Hardcover; Book
Best price: $80.00
Price in other shops: $99.00
Mathematical Logic (Graduate Texts in Mathematics) ImageMathematical Logic (Graduate Texts in Mathematics)
by J.D. Monk
Springer; Published: 1976-09-07; Hardcover; Book
Best price: $31.87
Price in other shops: $69.95
Mathematical Logic ImageMathematical Logic
by Joseph R. Shoenfield
AK Peters, Ltd.; Published: 2001-01-15; Paperback; Book
Best price: $33.92
Price in other shops: $35.00
Introduction to Mathematical Logic ImageIntroduction to Mathematical Logic
by Alonzo Church
Princeton University Press; Published: 1996-10-28; Paperback; Book
Best price: $40.22
Price in other shops: $55.00
Introduction to Metamathematics (Bibliotheca Mathematica) (Bibliotheca Mathematica) ImageIntroduction to Metamathematics (Bibliotheca Mathematica) (Bibliotheca Mathematica)
by S.C. Kleene
North Holland; Published: 1980-01-01; Hardcover; Book
Best price: $100.80
Price in other shops: $126.00
Principles of Mathematical Logic ImagePrinciples of Mathematical Logic
by David Hilbert, W. Ackermann
American Mathematical Society; Published: 1999-07-01; Hardcover; Book
Best price: $28.42
Price in other shops: $29.00
Godel's Incompleteness Theorems (Oxford Logic Guides, No 19) ImageGodel's Incompleteness Theorems (Oxford Logic Guides, No 19)
by Raymond M. Smullyan
Oxford University Press, USA; Published: 1992-08-20; Hardcover; Book
Best price: $70.16
Price in other shops: $210.00
First-Order Logic ImageFirst-Order Logic
by Raymond M. Smullyan
Dover Publications; Published: 1995-01-30; Paperback; Book
Best price: $6.73
Price in other shops: $9.95
A Course In Mathematical Logic ImageA Course In Mathematical Logic
by John Bell, Moshe Machover
North Holland; Published: 1977-01-01; Hardcover; Book
Best price: $83.36
Price in other shops: $144.00
Mathematical Logic (Undergraduate Texts in Mathematics) ImageMathematical Logic (Undergraduate Texts in Mathematics)
by H.-D. Ebbinghaus, J. Flum, W. Thomas
Springer; Published: 1996-11-15; Hardcover; Book
Best price: $40.00
Price in other shops: $69.95
Similar Books and other products
Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) ImageTopoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
by Robert Goldblatt
Dover Publications; Published: 2006-04-28; Paperback; Book
Best price: $18.10
Price in other shops: $29.95
A Radical Approach to Lebesgue's Theory of Integration (Mathematical Association of America Textbooks) ImageA Radical Approach to Lebesgue's Theory of Integration (Mathematical Association of America Textbooks)
by David M. Bressoud
Cambridge University Press; Published: 2008-01-14; Paperback; Book
Best price: $32.39
Price in other shops: $39.99
Natural Deduction: A Proof-Theoretical Study ImageNatural Deduction: A Proof-Theoretical Study
by Dag Prawitz
Dover Publications; Published: 2006-02-24; Paperback; Book
Best price: $5.32
Price in other shops: $9.95
The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine ImageThe Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine
by Charles Petzold
Wiley; Published: 2008-06-16; Paperback; Book
Best price: $17.21
Price in other shops: $29.99
Godel's Theorem Simplified ImageGodel's Theorem Simplified
by Harry J. Gensler
University Press of America; Published: 1984-06-28; Paperback; Book
Best price: $24.58
Price in other shops: $31.50
Computability and Logic ImageComputability and Logic
by George S. Boolos, John P. Burgess, Richard C. Jeffrey
Cambridge University Press; Published: 2007-09-17; Paperback; Book
Best price: $26.96
Price in other shops: $29.99
Set Theory and Its Philosophy: A Critical Introduction ImageSet Theory and Its Philosophy: A Critical Introduction
by Michael Potter
Oxford University Press, USA; Published: 2004-03-11; Paperback; Book
Best price: $38.59
Price in other shops: $49.95
The Mathematics of Logic: A Guide to Completeness Theorems and their Applications ImageThe Mathematics of Logic: A Guide to Completeness Theorems and their Applications
by Richard W. Kaye
Cambridge University Press; Published: 2007-07-30; Paperback; Book
Best price: $32.91
Price in other shops: $39.99
Incompleteness in the Land of Sets (Studies in Logic) ImageIncompleteness in the Land of Sets (Studies in Logic)
by Melvin Fitting
College Publications; Published: 2007-02-19; Paperback; Book
Best price: $26.99
Price in other shops: $30.00
Godel's Theorem: An Incomplete Guide to Its Use and Abuse ImageGodel's Theorem: An Incomplete Guide to Its Use and Abuse
by Torkel Franzen
A K Peters, Ltd.; Published: 2005-05-25; Paperback; Book
Best price: $13.94
Price in other shops: $27.00
Book store. Illustrated catalog of books on different categories