TITLE:
Gödel and the Incompleteness of Arithmetic
AUTHORS:
Pinheiro
KEYWORDS:
Gödel, Arithmetic, Peano, Axiom, Classical Logic
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.8,
July
15,
2016
ABSTRACT: 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.