Year: 2024
Type: article
Abstract: This note clarifies the significance of the proof of Gödel’s first disjunct obtained through the formalisation of Penrose’s second argument within the DTK system. It analyses two formulations of the first disjunct – one general and the other restricted – and dwells on the demonstration of the restricted version, showing that it yields the following result: if by F we denote the set of propositions derivable from any formalism and by K the set of mathematical propositions humanly knowable, then, given certain conditions, F necessarily differs from K. Thus it is possible that K surpasses F but also, on the contrary, that F surpasses K. In the latter case, however, the consistency of F is humanly undecidable.
Source: Logic and Logical Philosophy
Authors: Antonella Corradini, Sergio Galvan
Institution: Università Cattolica del Sacro Cuore
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404300872