Dear Bruno, I would like to start a new thread to discuss the nature and existence of the "many non computational things" that you have mentioned in your posts. Could you find a few moments to write some remarks on these? In particular I wonder if their proposed non-computability can be expanded into disjoint classes such that we have some kind of taxonomy of properties. Can they be represented approximately by a finite language? Other than the restriction of recursive enumerability (modulo homeomorphisms of their topological duals), what is it, in your opinion, that makes such things "non-computable"?
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