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On Formally Undecidable Propositions of Principia Mathematica and Related Systems Paperback – Apr 1 1992
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Top Customer Reviews
(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.
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 ›
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.
Most recent customer reviews
I enjoyed this book very much. The only problem I had with it was that the material discussed was simply too elementary. Read morePublished on March 23 2002
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 morePublished on Jan. 8 2002
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 morePublished on Dec 12 2000 by Ben Rothke