Epistemological Consequences of the Incompleteness Theorems - Raguní, Giuseppe (IJRDO -JOURNAL OF MATHEMATICS, 2015)
After highlighting the cases in which the semantics of a language cannot bemechanically reproduced (in which case it is called inherent), the main epistemological consequences of the rst incompleteness Theorem for the twofundamental arithmetical theories are shown: the non-mechanizability forthe truths of the rst-order arithmetic and the peculiarities for the model ofthe second-order arithmetic. Finally, the common epistemological interpretation of the second incompleteness Theorem is corrected, proposing the newMetatheorem of undemonstrability of internal consistency.