Godel's Proof @ richardeward.com

Godel's Proof
by Ernest Nagel, James R. Newman
from NYU Press

Customer Reviews:

• Avg. Customer Rating: 4.5 / 5.0

• Godel's incompleteness theorems explained in non-technical language
  
  There is no question in my mind that the most misunderstood mathematical theorems of all time are Godel's incompleteness theorems. In essence, they state that no system powerful enough to do basic arithmetic is complete. Meaning that there will always be statements that are true in the system but that can never be proven in that system. These results have been seized upon by people with many different agendas and used to argue conclusions as significant as the existence of God and that human... more info

• Godel's incompleteness theorem, clearly explained
  Gödel's incompleteness theorem remains one of the most quoted, yet most misunderstood work in mathematics of the last century. Many non mathematicians had used the theorem (without understanding it, of course), to "prove" just about everything (generally it's been used to imply the limits of science, or stuff to that effect). The theorem, though, hardly implies that. This short book, written some 50 years ago, remains probably the best explanation of Godel's work available to the layman. The book... more info

• how i understand Godel
  Godel was able to construct a formula from the axioms of Principia Mathematica (PM, and related systems, due to Russell and Whitehead) that is (roughly) "There exists no proof for this formula". This IS the formula itself. now, we need to know if this is true or not. so we try to find a proof for it within PM. if it is possible to find the proof, that means the formula is correct. but the formula says you can't find it. if the proof cannot be found, that means the negation of the formula is correct, but... more info

• This is a strongly dissenting review
  My challenge would no doubt be viewed with contempt, despite the many justified challenges of the status quo in history. Somehow it is always thought that although profound mistakes were made in the past, the contemporary establishment has things straightened out. My contention is that what is called Goedel's proof is a fundamental embarrassment in the history of logic and mathematics.
  There are many particulars in this book that I can criticize which extend beyond Goedel. There is the formalization of... more info

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