I am asking about the simpler version of Löb's Theorem, not the Generalized Löb's Theorem. That is, if a system can derive "S is provable implies that S is true", then that system can derive S. I am looking for interesting applications in realms outside of Mathematics: for example, Gödel's Incompleteness Theorems have tremendous philosophical implications, but I do not see analogous applications for Löb. I found an anti-mechanistic argument in a paper "Löb’s Theorem as a Limitation on Mechanism" by Michael Detlefsen at http://www.public.iastate.edu/~dfade...against_ai.pdf, but the arguments appear either dubious when he is being precise and fuzzy in the rest of the paper. Any leads, links, or summaries of arguments would be appreciated.