Dear Francisco Doria and Newton da Costa,
I will have to go through this essay with some care a few times before I can hope to sensibly comment, perhaps with an eye on the referenced works. I have in fact come across your work before, and wanted to understand it better---perhaps this essay will yield the needed impetus to really dig in.
I am particularly intrigued by the connection between undecidability and quantum physics---or rather, the lack thereof, in your terms, as if I understand correctly, you show that there are undecidable systems in classical mechanics, as well, and thus, it is not 'quantum magic' that leads to the emergence of undecidability.
I have been looking at the opposite direction---how undecidability of measurement outcomes, by means of Lawvere's fixed-point theorem, leads to quantum phenomena.
Rice's theorem, of course, can be understood in terms of Lawvere's, as well; I wonder if the same holds true of your extended version, or whether it derives from a different source.
Thank you for a challenging essay!
Kind regards
Jochen