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On Formally Undecidable Propositions of Principia Mathematica and Related Systems
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Binding: Paperback
Dewey Decimal Number: 511.3
EAN: 9780486669809
ISBN: 0486669807
Label: Dover Publications
Manufacturer: Dover Publications
Number Of Items: 1
Number Of Pages: 80
Publication Date: April 01, 1992
Publisher: Dover Publications
Studio: Dover Publications
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Editorial Review:
First English translation of revolutionary paper (1931) that established that 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. Introduction by R. B. Braithwaite.
Customer Reviews
Average Rating: 
Rating:  - 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 notation
this is a very hard book. I had the benefit of the Kac-Ulam explanation.
I did find what might be problems with this proof.
1) One is the reliance on number theory proofs about prime numbers that are assumed true
in the Gödelization of the primes coding of the mathematical axioms.
2) The second ... Read More
Rating: - 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. My marking three stars regardless for this book is motivated by his extensive influence, but also by his fair admission later in life that his thesis could amount to hocus-pocus.
Indeed, I see it as one of the prominent mistakes in logical history, and I shall endeavor to explain as best I can. It should suffice to consider his Section 1, an outline of his proposed proof.
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Rating:  - 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). The proof consists in creating a statement that says "this statement cannot be proved", for then it follows that either this this statement can be proved and we have proved something false, or it cannot be proved but it is still true. In either case our formal system is flawed. This is in a way an instance of the liar paradox, which was of course well know long before, but no-one ... Read More
Rating: - 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 historical aspect of it. Godel himself is not a very good writer. If you want to study Godel's incompleteness theorems there are other books out there that prove his theorems in a much more refined, shorter, and easier fasion.
Rating: - Unbelievable theorem
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 ... Read More
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