Document Type : Letter to Editor
Author
Assistant Professor, Department of Philosophy and Logic, Azarbaijan University of Tarbiat Moallem
Abstract
One of the most important applications of Gödel's completeness theorems is based on their roles the arguments of impossibility of formalization of human mathematical mind in capture of an algorithm or a finite formal system. Two main arguments have been proposed in this way of reasoning. In both of these arguments, it has been claimed that: the fact according to which human being can understand the truth of the unprovable Gödelian sentence, shows the superiority of human being’s ability in mathematical reasoning to all machines’. But there are some important debates on both arguments. After explaining these two arguments, we will investigate the extensive contentions and challenges between mechanists and anti-mechanists. By explaining and analyzing Gödel's incompleteness theorems and their connection to human arithmetical knowledge, we will show that there is no plausible argument, based on Gödel's incompleteness theorems, which can show the superiority of human being’s ability in mathematical reasoning to the machines’.
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