Epistemological Consequences of the Incompleteness Theorems

Abstract

After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental arithmetical theories are shown: the non-mechanizability for the truths of the first-order arithmetic and the peculiarities for the model of the second-order arithmetic. Finally, the common epistemological interpretation of the second incompleteness Theorem is corrected, proposing the new "Metatheorem of undemonstrability of internal consistency".

6 pages, IJRDO-Journal of Mathematics, Vol 2 Issue 12 December 2015. arXiv admin note: text overlap with arXiv:1206.2023