A self-evolving system seems to require a "loop" and
not a "tower of turtles, ad infinitum".
> When I wrote "self-evolving" I didn't mean evolution in the biological
> sense, where cycles of generation and selection of entities are necessary.
> I meant the generation of all possible theorems in a formal system, a process
> which is not recursive as a whole, and can proceed indefinitely.
Well, I'm thinking about it. For sure I'm not so smart. But this is a difficul issue.
In example, the "outside" perspective is different from the "inside" perspective.
You must also take in account: Haussdorff theorem ["Grundzuge der
Mengelehre", 1914] and Banach & Tarski [Fundamenta Mathematicae,
6, (1924), p. 244-277] and Mycielski & Steinhaus ["A mathematical axiom
contradicting the axion of choice", Bull. of Polish Acad. of Science, 10, (1962),
p. 1-3]. And the action-entropy (-> information) equivalence. And the 3 entropies
relation (physical, shannon, algorithmic). And, as a matter of fact, that "some"
entity (the "prior" question) must prove all those "possible theorems". And the
"no laws" suggestion, and the relativistic (and also Hawking's) "block universe"
hypothesis. And some time-like looping such as that suggested by Huw Price,
and Lebowitz & Bergmann & Aharonov, and Goedel (which was injured by
the "big bang" argument, but not mortally wounded), in connection, of course,
with the halting problem.
In other words: "Hinc Sunt Leones".
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