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arXiv · 1602.03390

Epistemological Consequences of the Incompleteness Theorems

Giuseppe Raguní
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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".

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Giuseppe Raguní. 2016-01-13. Epistemological Consequences of the Incompleteness Theorems. https://arxiv.org/abs/1602.03390

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