On Formally Undecidable Propositions of Principia Mathematica and Related Systems @ richardeward.com

On Formally Undecidable Propositions of Principia Mathematica and Related Systems
by Kurt Gödel
from Dover Publications

Customer Reviews:

• Avg. Customer Rating: 4.5 / 5.0

• 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 is... more info

• 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.
  Although that... more info

• 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... more info

• 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.

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