Project

Proving Completeness of Arithmetic

Goal: Now we have to work in the positive direction. We have proven that there is no proof that it is not complete. Now we prove that it is complete.

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Marcia Ricci Pinheiro
added a research item
People normally believe that Arithmetic is not complete because Gödel launched this idea a long time ago, and it looks as if nobody has presented sound evidence on the contrary. We here intend to do that perhaps for the first time in history. We prove that what Stanford Encyclopedia has referred to as Theorem 3 cannot be true, and, therefore, if nothing else is presented in favour of Gödel's thesis, we actually do not have evidence on the incompleteness of Arithmetic: All available evidence seems to point at the extremely opposite direction.
Marcia Ricci Pinheiro
added a research item
In this paper, we investigate the concept of completeness. We studied the concept whilst still attending college, but that wasfrom a mathematical perspective. In 2000, we got to have contact with The Logicians' understanding of the concept through the hands of one of the most important modern icons of Philosophy, Dr. Graham Priest. We recently mentioned his ways of applying the concept, and that was in our last paper with the APM journal. There seems to be a bit of discrepancy. Because of that, it is worth studying the subtleties involved. It seems that reserved words should not be recreated in meaning, so that if there is any chance The Logicians' completeness does not coincide with The Mathematicians' completeness, the sense that last appeared should be dropped in favour of coherence.
Marcia Ricci Pinheiro
added an update
Now we have just proven that the concept of completeness that the nonclassicists have seems to be a bit equivocated.
With this, we are also investigating completeness a bit further.
 
Marcia Ricci Pinheiro
added a project goal
Now we have to work in the positive direction. We have proven that there is no proof that it is not complete. Now we prove that it is complete.