I do not think that natural "must mean that which we can explain using our physical notions of conservation, symmetry, action, etc. If we can't, then it's supernatural, in which case we can't explain it using physics."
A little clarification. I am talking about methodological naturalism (not metaphysical naturalism). Methodological naturalism is that we make our explanations of phenomena using naturalistic explanations.
I think [supernatural] should mean what most people think it means- something devine. Webster has as a first meaning (i)something outside the experience of man and as a second meaning (ii)something outside of the laws of nature. Nothing about it not being explainable. Even superconductors are outside the ordinary laws of nature. They are extraordinary, yet explainable.
No one would count superconductors as supernatural phenomena. The demarcation between natural and supernatural is the kind of explanation that one is offering (despite Webster's definitions).
I think your definition of the term supernatural as everything that cannot potentially be explained by physical notions would be acceptable to me if the set of supernatural things included superconductors and superfluids.
They cannot be included in the supernatural category since they can be accounted for using methodological naturalist explanations.
They are not found in nature, at least on earth. They are man made and then in some sense unnatural. But they are explainable.
That's right. Using methodological naturalism, we can account for their properties. However, supernatural things, we cannot account for using methodological naturalism (i.e., assuming things such things as principles of conservation, least action, least time, etc). That doesn't mean that supernatural things don't exist, it's just that we can't account for those kind of things in our explanations, so they are not useful to science. If we could explain something using methodological naturalism, then they would be useful to science, and in which case those things become natural phenomena.
Now, let me explain something. Methodological naturalism is not the same thing as metaphysical naturalism. The methodological naturalist can believe in the supernatural, whereas the methodological naturalist cannot. The thing is, the methodological naturalist will not introduce supernatural explanations into science. Science remains methodological naturalist by convention since this path has proven to be the most successful (since the 16th century it has been this way). However, if you want to be a methodological naturalist and believe in the existence of the supernatural, that is fine just as long as you speak in terms of methodological naturalist terms. To speak in methodological naturalist terms means that you adhere to naturalist principles. Sometimes those principles are challenged by 'spooky' things (like the quantum vesion of 'spooky' action-at-a-distance). This is acceptable as long as it doesn't become too unconventional (e.g., start suggesting that we can transport ourselves using action-at-a-distance transportation). In that case, the principles of methodological naturalism have been violated.
So if supernatural refers only to things that could never be explained by the notions you list, then I think nothing exists that is supernatural. That makes it a wasted word.
I want to avoid the confusion of mixing science up with theology. Science, I think, is methodologically naturalistic, and therefore will not get caught up into the metaphysical naturalist belief that the models of science show that nature is fully naturalistic at its most fundamental basis. Similarly, a metaphysical supernaturalist (i.e., someone who believes the supernatural really exists), can be a methodological naturalist (e.g., a scientist) as long as they accept the methodology of science. You can believe anything you want, just don't try to convince other scientists of it in your professional work.
I think this might clear up some of our confusion we are having. I'm not saying that the supernatural doesn't exist. I'm only saying that if you stick with a nomological perspective, then you are maintaining a methodological naturalist perspective, and it can be included in science if there is enough justification in doing so. If ya scientist really does hold to a metaphysical supernaturalist position, and a nomological account isn't part of that, then that scientist has to keep their metaphysical supernaturalist beliefs away from their methodological naturalist arguments (i.e., at a professional level). What they discuss with scientists on a non-professional level is their option. They can try to convert them to Christianity and that is their option. They just shouldn't submit Christian arguments to scientific publications. And, if they do, the articles should be rejected since they are not part of the methodological naturalist approach.
I guess it's a lot of terminology to throw around, I'm sorry if it's too much. But, I think these terms came into philosophical discussions for a reason, and it's very helpful sometimes to get familiar with them, especially as the conversations seem to keep coming up.