
The Invalidity of Godel's Incompleteness Work.
Posted:
Oct 4, 2013 11:47 PM


Two major theorems Godel's Incompleteness are:
 Incompleteness: Any formal system T that is consistent _and_ adequate enough to describe the concept of the natural numbers, would have G(T) as a statement that is true but not provable in T.
 Completeness: Any consistent formal system has to have a model.
On the Incompleteness, since the requirement that T be _informally_ adequate enough to describe the concept of the natural numbers is _not_ a syntactical notion [as that of a T's consistency], it's logically invalid to assume that T always be syntactically consistent, simply because we _informally assume_ T adequately describe the concept of the natural numbers. QED.
On the Completeness, since it's still entirely logically possible that it's impossible to know the truth value the formula cGC, or ~cGC, (defined below) in the natural numbers, it's still entirely logically possible that it's impossible to have a model for PA + cGC, or PA + ~cGC. Hence it's logically invalid to assert in meta level that a consistent formal system must necessarily have a model.
Note: cGC <> "There are infinitely many counter examples of Goldbach Conjecture".
Any constructive response would be welcomed.
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI

