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Hi Michael,
Thank you for a very well written description of Agent vs Object physics. However, I wondered about one thing you wrote:
> Instead, the natural-number basis of physically-real scientific theories of object state changes identifies such theories as being exactly the type of arithmetic systems considered by Gödel [13]... Given its significance it should be taught to all aspiring physicists and philosophers, many of whom haven't grasped that Gödel's incompleteness is a feature of discrete logic over arithmetic natural-number systems.
Gödel states that the systems he is considering are those for which the axioms of Principia Mathematica hold. In a footnote he explicitly states that he is including the axiom of infinity. Such systems are sufficient to do arithmetic (addition and multiplication) but most importantly, to do arithmetic for *any* natural number (no matter how large).
Every actual computer does not meet this test because it has a finite memory size (as well as finite word size). Instead, actual computers can be models for Primitive recursive arithmetic, which is provably consistent in Peano arithmetic. Therefore, finite systems can be consistent. It is only the abstract infinite logical systems that come to grief by Gödel's hand.
> The computational universe paradigm implicitly raises issues of mathematical completeness and computability.
My essay Software Cosmos constructs an example of a (closed) computational universe (that appears as open), and shows how that this answers several puzzles in observational cosmology.
In such a computational model, your "Agent Physics" can be distinguished from "Object Physics" in terms of software architecture: they occur at different layers. The philosophical question that arises is whether the Agent layer is higher or lower than the Object layer; put another way, does Life emerge from Matter, or does Matter emerge from Life?
I am curious how you would place your Object Physics and Agent Physics within the model I describe. I hope you get a chance to read it.
Hugh