Advances in Pure Mathematics

Volume 6, Issue 8 (July 2016)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

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Gödel and the Incompleteness of Arithmetic

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DOI: 10.4236/apm.2016.68042    1,685 Downloads   2,185 Views  
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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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Pinheiro,  . (2016) Gödel and the Incompleteness of Arithmetic. Advances in Pure Mathematics, 6, 537-545. doi: 10.4236/apm.2016.68042.

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