That’s an interesting question. What I do know is that science cannot verify if a physical object has a mind or not. Science assumes that physical objects don’t have a mind. Instead, it assumes a mechanistic worldview where objects in nature act according to certain regularities that can be comprehended by humans. Because this is an assumption, not a discovery, science cannot judge whether something has a mind or not. Even if the object does have an immaterial mind, science is only analyzing the material, non-mind part of it.
I did not say that the “material” are things that can be defined mathematically. Rather, they are things that can be modeled using mathematics. And this is merely a sufficient, not necessary criterion, as some sciences, like biology, don’t always use mathematics in all their theories. What I actually mean is the material is that which can be explained in terms of regularly occurring mechanisms.
I agree with you that it is an odd definition, but it seems the best solution I can think of right now to avoid circularity. But my definition is motivated by the fact that I think the defining feature that differentiates a spirit vs. material is that the former behaves in ways that are unpredictable. Thus, one cannot treat a spirit as one would atoms in a lab. I touched upon this in a reply in another thread.
It would be nice to come up with a definition of the material which is both non-circular and explains the nature of its existence. How would you define the material vs. immaterial?