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I think you more or less described what I was aiming at but I'll re-word it a bit myself for further clarification in case others still find what I (or we) am attempting to convey.
Since Descartes, scientists have tended to view the Universe as a Great Machine consisting of material substances that contain properties as such that together they form interlocking relationships which remain absolute regardless of who is doing the measurement and when or where it is being done. This was the classical view, that underlying reality as it is perceived by us there are "objective" facts about the "external" world that we can know. Now, of course, much of this point of view was obliterated in the twentieth-century when the behavior of the "stuff" of matter began to appear, at its most basic level, completely dependent on its interaction with macroscopic objects, but I want to ignore QM for the moment as it's not necessary for my argument. My argument is basically this: When you say, in the one option, that mathematics is “simply a description of physical positioning,” I think I am in agreement with you that it indeed seems to be something more than that. The reason is that the description is not merely about movement, it’s about the rules to which movement must adhere. If it was about positioning and nothing more, there would be no reason to find absolute consistency in the behavior of matter (at least where classical objects are concerned). Now you can say that the rules are carved out by the properties of matter, for example, gravity is the result of the curvature of space, but there’s nothing in the matter (of space?) itself that suggests this something should have any necessary and universal consequences; the suggestion that there are innate properties of material substances basically affirms the coexistence of abstract “ideas” or “principles”, so that “this (matter) will always result in that (behavior).”
What are non-physical properties if not abstract entities?
(I don’t think E=MC^2, for example, can be called a physical property as there is nothing physical of which the description is about, i.e., the description is about how energy relates to matter/light/velocity, which are physical, but how these behave in conjunction with one another is not the same as the physical things themselves). QM, as I said, seems to cause bigger headaches in terms of what we can actually call objective or absolute in terms of our descriptions but even so it seems like there must be at least an abstract aspect to reality that is every bit, if not more, as real (though not concrete in a material sense) as material substances are.
Now, I’m not sure if I would go so far as to suggest disembodied consciousness, but if abstractions are “out there,” as fundamental properties of matter (e.g. in the necessity of their current and future positions) or something coexistence with matter, then I wonder if perhaps “mind” is not also itself an abstraction, as in a principle of physical structures like anything else (in the same way that E=MC^2 is a description about something essentially non-material, I mean, as in the relationship of physical objects at certain velocities), though in this case, particular structures, albeit due to their organization and/or chemical or organic components involved.
Hopefully I didn't make what I'm trying to convey more obscure. I should have probably just left it at what you already said.
Perhaps they are commonalities in composition of the particles which you interpret as some abstracted connection. A connection which they don't have.
Example:
You observe a yellow truck in Paris and a yellow truck in London. These items (by my hypothetical) have no association other than you have observed both to be yellow trucks. The connection occurs only because of your observation.
While there could be an underlying mind stuff in the universe, I see no evidence of it while I do see evidence connecting the experience of consciousness to the physical organization and chemical operations in the brain. Only systems of a minimum, apparently necessary, complexity in neuroanatomy exhibit behaviors characteristic of conscious individuals as experienced (me) or granted (to others by comparison with myself.) We do not yet have bottom up understanding of the design and operation of the wetware involved. I believe this will be obtained within a century and that once in hand, it will be replicated or simulated. At that point the question, "Are you there?" will have meaning and the answer must be believed to the same extent that it is when asked of another person.
There arises an interesting situation if the system under observation answers, "No."
So how, exactly, does God know that She's NOT a brain in a vat?
