It’s a materialist model in that there is only ordinary matter, nothing ‘extra’—no souls, no ghosts in the machine, no substance dualism. In calling it a variety of physicalism, I follow the usage of Strawson (link goes to pdf download), who distinguishes between physicalism and physics-alism. The former just means that everything in the universe is physical, whereas the latter includes a further commitment that everything can be made sense of by means of physical theories. This is a genuine further metaphysical hypothesis: even if everything is physical, there is no reason to think that everything should be captured by what a largely hairless primate on an unremarkable rock orbiting a small star calls a ‘theory of physics’.
The situation, as alluded to above, parallels that of mathematics. There, the theory of the natural numbers—the Peano axioms—fails to exhaustively describe its intended object, i.e. the natural numbers as a mathematical entity: there are statements that are true about the numbers, which the theory can’t decide. Likewise, I content that there are similar lacunae in physical theories, which thus fail to fully capture the nature of matter. But the natural numbers are still mathematical entities; likewise, matter still is physical. In this sense, my model is physicalist, but not physics-alist.
Well, I’m not appealing to Gödelian incompleteness directly, but to Löb’s theorem, which is a more general notion (in fact, Gödel’s second incompleteness theorem follows from Löb’s as a special case). This yields a sort of ‘upper’ boundary to what any given system could prove about itself, even in the limit of infinite computing time.
Essentially, these phenomena force a sort of threefold partitioning of the properties present in nature, if viewed through a theoretical lens (so this is just an epistemic, not an ontic, phenomenon: it’s only due to the limits of our theories that this splitting occurs, reality is—or can be, as far as the model is concerned—unifies). First, there are the structural, decidable (or computable) properties. These are, in the analogy to math, what can be proven from a set of axioms. Then, there are the undecidable properties. These are still on the level of structure in that they can be phrased in the language of the axioms, but can’t be decided on that level. Then, there are the properties of the object of the theory—of the natural numbers themselves, so to speak. If you had access to the natural numbers, you wouldn’t have any need to theoretically decide their properties; you could just see what’s true or false about them, in the same way you can just see a car is red, and don’t have to derive that fact from some axioms about it.
Hence, access to non-structural properties allows leapfrogging the boundary discussed above: the von Neumann replicator doesn’t have to prove that something is true about itself to itself, it just has to be true. Due to the self-referential nature of these statements, their truth is equivalent to access to their truth; hence, the von Neumann replicator knows things about itself that can’t be proven by any theoretical means.
I’m going to pull this discussion over to this thread, because it’s getting way off topic in the ChatGPT one.
First of all, I think it’s a category error to require testability for metaphysical notions. Testability is appropriate for scientific theories, but only because the attendant metaphysics is taken as given (and often enough, just accepted without examination). There’s no science without metaphysical baggage, there’s only science with unexamined metaphysical baggage, which it is typically all the worse for. And the metaphysical basis for statements like ‘all statements about the nature of reality should be testable’ is itself not testable, of course. This is the problem the positivists never quite got round to answering.
As for whether there’s a problem at hand, of course, opinions credibly differ on that front. I’m not convinced by the arguments of those that claim there isn’t, but if you are, that’s fine—you won’t have any need for something like my model, which really only arose out of a sort of desperation: wanting to keep what I think is good and right about metaphysical naturalism, while enabling it to confront the problem of consciousness head-on. I think that this is likely to be the most conservative way of achieving both goals; and anyway, it’s the only way I have seen so far that, to me, seems like it could actually work.
People seem to think that I’m introducing something mystical without need, but that’s the opposite of what I’m doing. I started out trying to find a naturalized theory of intentionality, and found that, in order to make it work, I had to find some way to go beyond the merely structural. Thus, the intrinsic properties I’m proposing answer a concrete need I have seen no other way to meet. If that doesn’t agree with a computationalist intuition, well, nobody has any guarantees that the universe should work according to their predilections—I had to be dragged away from it kicking and screaming myself, so I know what that’s like. Everything I’m proposing is there just because I saw no other way to make things work.