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G?del and the Incompleteness of Arithmetic

DOI: 10.4236/apm.2016.68042, PP. 537-545

Keywords: G?del, Arithmetic, Peano, Axiom, Classical Logic

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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.

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