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 rst incompleteness Theorem for the two
fundamental arithmetical theories are shown: the non-mechanizability for
the truths of the rst-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.
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