Epistemological Consequences of the Incompleteness Theorems
General Mathematics
2016-02-11 v1
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".
Cite
@article{arxiv.1602.03390,
title = {Epistemological Consequences of the Incompleteness Theorems},
author = {Giuseppe Raguní},
journal= {arXiv preprint arXiv:1602.03390},
year = {2016}
}
Comments
6 pages, IJRDO-Journal of Mathematics, Vol 2 Issue 12 December 2015. arXiv admin note: text overlap with arXiv:1206.2023