On Formally Undecidable Propositions of Principia Mathema... and over one million other books are available for Amazon Kindle. Learn more

Sorry, this item is not available in
Image not available for
Image not available

To view this video download Flash Player


Sign in to turn on 1-Click ordering
More Buying Choices
Have one to sell? Sell yours here
Start reading On Formally Undecidable Propositions of Principia Mathema... on your Kindle in under a minute.

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

On Formally Undecidable Propositions of Principia Mathematica and Related Systems [Paperback]

Kurt Gödel
4.6 out of 5 stars  See all reviews (15 customer reviews)

List Price: $8.95
Price: $8.50 & FREE Shipping on orders over $35. Details
You Save: $0.45 (5%)
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
Only 9 left in stock (more on the way).
Ships from and sold by Amazon.com. Gift-wrap available.
Want it tomorrow, July 15? Choose One-Day Shipping at checkout. Details
Free Two-Day Shipping for College Students with Amazon Student


Amazon Price New from Used from
Kindle Edition $5.99  
Hardcover --  
Paperback $8.50  
Mass Market Paperback --  

Book Description

April 1, 1992 0486669807 978-0486669809

In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.
The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.
This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

Frequently Bought Together

On Formally Undecidable Propositions of Principia Mathematica and Related Systems + Gödel's Proof + Introduction to Mathematical Philosophy
Price for all three: $23.18

Some of these items ship sooner than the others.

Buy the selected items together

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: German

Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 80 pages
  • Publisher: Dover Publications (April 1, 1992)
  • Language: English
  • ISBN-10: 0486669807
  • ISBN-13: 978-0486669809
  • Product Dimensions: 8.3 x 5.1 x 0.2 inches
  • Shipping Weight: 2.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #115,960 in Books (See Top 100 in Books)

More About the Authors

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

4.6 out of 5 stars
4.6 out of 5 stars
4 star
2 star
1 star
Most Helpful Customer Reviews
207 of 219 people found the following review helpful
3.0 out of 5 stars Unbelievable theorem August 3, 2004
Reading through the reviews of self-proclaimed math geniuses (see some of the below unhelpful reviews for examples) is hardly edifying, so I feel compelled to lend a hand. Here are a few comments about this publication:

First, the introduction does a poor job in explicating the theory. I suppose it gives you the basic idea, but this is hardly the first account of the theory one should read. Brathwaite does not connect all of the dots, and it will take a long time to figure out how the proof works from his intro, if you can do it all. (And that's not a challenge or insult; it simply isn't that well written.)

Second, forget about wading through Godel's proof on your own. The reviewer who claimed to do so with two years of algebra and a really good dictionary is simply lying. You do not wade through difficult theorems in mathematical logic without the appropriate tools. And the appropriate tools include having done similar but simpler proofs on your own and having a solid background in mathematical logic. Without this background, it doesn't matter whether you have the ability to be a mathematics professor at Princeton or place top five in the Putnam - you simply will not understand the proof in a rigorous manner. By all means, take a look at it to get a general feel for what's going on, but if you want a semi-technical account read Smullyan's "Godel's Incompleteness Theorems."

Third, as one reviewer pointed out, there are multiple errors in this printing of the proof. This makes what was a tall task virtually impossible.

So what did Godel do that was so interesting?

He proved that there were certain arithmetical statements about whole numbers that were not provable but true.
Read more ›
Was this review helpful to you?
90 of 98 people found the following review helpful
Anyone who wants to trace this proof is free to do so. Though the formal logic can be formidable, and must be learned before tackling the proof, only the basic structure is necessary and it is not difficult to learn. It is also necessary to know a little about prime numbers, specifically that every composite number can be decomposed into some unique group of prime factors. Otherwise, all the technical aspects of the proof (barring the conclusion of theorem VI and a bit of the recursion) can be perfectly understood by someone outside of the world of formal mathmatics.
The proof itself is meant for a professional mathmatician. If you are interested and willing this will not dissuade you. To say Godel was not a master of exposition is misleading for he is ,if nothing else, just that. I have heard working through the proof compared to a mystical experience and the proof itself to a symphony. It is truly beautiful to even the mere math enthusiast. Godel is not, however, a college professor and does not wish to explain what need not be explained. This will not be of much consolation when he prefaces a statement with, "of course," for the twentieth time and you have no idea what he is talking about. But if you are not afraid to go ahead when you have tried and failed to understand, and are not afraid to return when you have gained some small piece of the puzzle and try again, everything will come clear. This is the original. All the commentaries are great, and some are even helpful before you get to the conclusion, but they are not the proof and should not be taken as a substitute. They do not suffice the way a generic drug does. There is no way to understand the full scope of the proof if you are not willing to immerse yourself in it and the language it uses.
Read more ›
Was this review helpful to you?
38 of 39 people found the following review helpful
5.0 out of 5 stars A profound paper, but difficult to read September 26, 2000
By A Customer
This book is a translation of one of the most important papers in 20th-century mathematics. It's wonderful that Dover has published it at such a cheap price, so everyone interested in the incompleteness theorems can take a look at it. However, I should warn potential readers that it is _not_ the best introduction, for three reasons:
(1) Goedel was not the world's greatest expositor.
(2) We now have nearly 70 years worth of insight Goedel didn't have when writing this paper.
(3) Goedel never intended the paper to be read by anyone but professional mathematicians.
Non-mathematicians who really want to understand this material should also take a look at "Goedel's Proof" by Nagel and Newman (and perhaps Hofstadter's "Goedel, Escher, Bach: An Eternal Golden Braid" for cultural background). Mathematicians can find lots of more technical expositions.
The original paper should not be the only source one tries to learn from, but I think it can be very valuable to take a look at it side-by-side with more modern treatments to get a feeling for how the ideas really arose. In principle one could learn everything straight from the source, but it just isn't the most efficient way. (I say this as a professional who has read the original paper and lots of other accounts of the proof, as well as written one of my own.)
Net recommendation: this book is so cheap that one should buy it and a modern treatment.
Comment | 
Was this review helpful to you?
32 of 35 people found the following review helpful
5.0 out of 5 stars Read the masters! October 31, 2001
Format:Paperback|Verified Purchase
THE proof as Goedel wrote it (plus typos). I have seen modern proofs of this theorem which are much easier to follow (as an example, a Mir book on mathematical logic by a Russian mathematician whose name I cannot recall), but this one is the REAL thing.
Modern proofs can be much clearer, but the original always has an added value. The writing style is not the best, but by reading this version you get a clearer idea of how Goedel came up with his theorem and the many difficulties he faced. Remember, by the time most of us read or heard about this for the first time, mathematical logic had advanced quite a few decades.
Was this review helpful to you?
Most Recent Customer Reviews
5.0 out of 5 stars Impress your friends
For math gnurds only. If you don't understand the symbolic logic, no big deal. Your friends probably won't understand it either.
Published 10 months ago by Peter Schwartz
5.0 out of 5 stars Important insight into Godel's thinking
As other reviewers have noted, there are numerous easier expositions of the work Godel reports in his 1931 paper. Read more
Published on March 2, 2011 by Victor A. Vyssotsky
3.0 out of 5 stars Mathematical Rationalism has limits
It is very hard to find faults in what may be the most famous proof of the 20th century.

For those not familiar with the Russell-Whitehead Principia Mathematica... Read more
Published on March 16, 2007 by Roger Bagula
3.0 out of 5 stars The following is a dissenting view
As indicated in two other reviews of mine here, my comprehension of Goedel's work is opposite to the general one. Read more
Published on October 24, 2006 by Paul Vjecsner
5.0 out of 5 stars Gödel's proof of the inadequacy of formalism
Gödel proves that a formal system containing arithmetic must be incomplete (i.e. incapable of proving all true statements). Read more
Published on October 15, 2006 by Viktor Blasjo
5.0 out of 5 stars One of the Best Books You Should Never Read
Godel's incompleteness theorem's are without a doubt genious. However, this day in age, no logician actually reads Godel's original work unless they are only interested in the... Read more
Published on July 23, 2005 by steve
5.0 out of 5 stars From the horse's mouth, 'le text'
Speaking not as a math specialist but one disposed to read a number of the popular explications of Godel's famous proof I can say that it was Godel's original text that did it for... Read more
Published on August 2, 2003 by John C. Landon
5.0 out of 5 stars A Breeze
I enjoyed this book very much. The only problem I had with it was that the material discussed was simply too elementary. Read more
Published on March 23, 2002
5.0 out of 5 stars Fascinating but not good for the recreational reader
I read this over my winter break (2001) from my second year of medical school at UCSF. This is a fun book to try to grasp, but unless you are extremely mathematically gifted (like... Read more
Published on January 8, 2002
5.0 out of 5 stars One of the most influential treatises of all time
This is indeed one of the most influential treatises of all time. In a nutshell, Godel's Undecidability Theorem proved that within a formal system, there are questions that exist... Read more
Published on December 12, 2000 by Ben Rothke
Search Customer Reviews
Search these reviews only

What Other Items Do Customers Buy After Viewing This Item?


There are no discussions about this product yet.
Be the first to discuss this product with the community.
Start a new discussion
First post:
Prompts for sign-in

Look for Similar Items by Category