Again, this is a description that could arguably fit quantum physics. It's eerie and strange and doesn't exactly match our picture of what reality should be, and yet we consider it natural. I wonder why that is?
The term "supernatural" only applies to things that have not been demonstrated to exist. If they were shown to exist, they would not be considered supernatural, no matter how much difficulty we might have fitting it into our previously existing picture of science.
No, it's not. The fact that there's no coherent definition for "natural" is the problem, since I don't even know what a supernatural framework entails without that. Two hundred years ago, modern physics would have been quite the supernatural framework.
Insofar as naturalism is a methodology, it's quite clear. Insofar as it is more than a methodology, it's practically incoherent. Given your focus on falsifiability, I don't know what a "naturalistic universe" would be except for one where the tools of empirical science could conceivably provide a full ontological picture of reality, and it's clear that they do no such thing.
Epistemic structural realism seems to be the best way to go, but I see no way to reconcile that with a genuine naturalistic ontology (assuming one could be conceptualized).
Pretty sure quantum physics is generally noted even by experts to be hypothetical at this point, not something we can reasonably test anymore than what's beyond a black hole (I like to think it's a wormhole, but we don't know). It doesn't fit into nature in the same fashion and if it does, it would be predictable, even if the rules are going to be more stochastic than, say, gravity on a universal scale that takes into accounts the mass of various astrological objects
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Just because something would seem bizarre to ancient peoples doesn't make it less true, the arguments stand on their own merit, supernatural arguments don't have merit because they're basically trying to avoid being investigated by science and falling into nature, because that would render them mundane.
Also, the supernatural is not presumed along with the natural except in concept at best, but you don't need the supernatural to make sense in the same vein as the natural, which makes sense sufficiently on its own without need to treat the supernatural as anything but conceptual
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Metaphysics doesn't necessarily require an absolute and complete assessment of reality, to say nothing of the distinctions to be made between the material and conceptual as both being real, but one having more practical reality, while the other is demonstrable as physically present and tangible.
Falsifiability doesn't assume absolute knowledge as the goal, it's self correcting in seeking out the most precise and accurate view of reality
Ontology is a subset of metaphysics, naturalism and physicalism/materialism are arguably distinct, to say nothing of having to account for things that wouldn't fit into a structure where everything is material unless they're emergent properties (minds from brains, for instance)
Naturalistic ontology is not making an absolute statement, it's saying that the best explanation is that model where the nature of things is such that it's not a system that just has utterly random miraculous events happening except in our limited understanding of them. Our understanding is always provisional, we cannot have full knowledge, particularly with an expanding universe and the scale always changing in terms of understanding things like gravity not being the same in the galaxy versus our planet or moon. Understanding nature as a consistent system that we can understand even if sometimes it doesn't seem like it is being both intellectually honest and humble
If I narrowly avoid getting struck by lightning, someone could say that's supernatural intervention, but that assumes something we don't have a basis for beyond speculation without substance. Anything supernatural tends to boil down to a credulous attempt to account for things we're ignorant of and would generally change if evidence shows it, unless it's such a thing that's unfalsifiable by nature (God in particular)