That appears to involve a metaphysical assumption - the assumption of dualism.
It appears that way to you because you are a materialist. It does not involve an assumption of dualism. It
does entail that materialism is false, but that is not the same thing.
My own view is that I am part of the environment I observe and that it is part of me - that there is no fundamental difference between the inside and the outside. I don't assume the view is true but it is at least plausible and so I cannot accept that "external" is a meaningful way of describing me and not me.
So there's no difference between what you believe about reality and what is actually happening in reality? I don't understand.
So what does it mean in metaphysics?
Metaphysics and religion are a type of art. Correspondence in the arts works differently to science. In science, we have an attempt to accurately correspond to the a subset of reality we call "physical". In most of the arts there are attempt to correspond to various subsets of reality, usually related to humans, but in this case there is not usually any need to try to represent it accurately. At least, not since the invention of photography, anyway. Rather, it is understood that the correspondence will be imperfect and it is the nature of the imperfections which make the difference between one artistic statement and another. Art can also attempt to correspond to noumenal reality as well as physical reality, again usually in ways that are understood to be imperfect. Only during attempts at systematic metaphysics or related religious claims does art try to represent the entire system, and in this case there is once again a need to try to correspond correctly, even though this is impossible, hence "The Tao that can be described is not the eternal Tao", even though the Tao Te Ching then goes on to attempt a description of the Tao that cannot be described. This leads to an additional problem, because the one of the things these forms of art try to correspond to is the thing that words like "Tao" or "God" are supposed to refer to, and this thing is fundamentally paradoxical. That is why mystical texts tend to be full of what I'd call "absolute paradoxes" e.g. Wittgenstein claiming in the Tractatus that absolute solipsism can coincide with absolute realism.
Exactly, so you can't take any one metaphysical view and say that it is the metaphysics of science. Science is metaphysically neutral, even if individual scientists are not.
I am not trying to produce a metaphysics of science. We already have one of those. It's called "materialism". That is not to say that materialism is actually true, but that we must think like materialists when we are playing scientific language games.
So what is your definition of non-physical reality?
I'd define it as neutral, mathematical or informational.
How is something going to help you get at the truth if you don't know whether that thing is real or imaginary?
Coherency can help to inductively establish that it is real, or likely to be real.
so "internal" means your consciousness.
Which would make my consciousness external, wouldn't it?
Your consciousness is external to my consciousness.
But trying to reach correspondence between the model and "metaphysical or noumenal reality" would be a waste of time unless you could show the term to be meaningful.
Why? How can I show
any term to be meaningful?
So what kind of an explanation do you think your method would provide of any of these things that would be different to a scientific explanation and by what method would it reach that explanation?
The method is "by hook or by crook", although unlike Feyerabend I can't count such methods as scientific. There are no rules to art or mysticism.
The explanation would be metaphysical, which is to be understood as closely related to artistic and religious. The Tao Te Ching is artistic, metaphysical
and religious.