I think the answer is that we do not have have evidence against the supernatural. But then then we have no evidence for it. You could not find evidence for something that is seperate/ not interacting with our reality. We can speculate anything really and not find any evidence to contradict it.
I think the thing is that untill there is evidence to suggest something is there i.e. having an effect on the universe in a physical way, the only way this supernatural "thing" can effect the universe is in its role as an idea. That is to say the idea of the supernatural can affect the physical universe but only by existing in the imagination of a mind. No mind, no supernatural.
The supernatural can exist as a concept. If it does not interact with us on a physical level I would put that as near proof it does not exist independantly.
Yup.. That's pretty much what it comes down to IMO...
Imagine that we 'think' about two different supernatural things. One of them happens to really 'exist' (in the supernatural sense: it's there somewhere but has absolutely no effect on our reality), and the other has NO corresponding existence in the supernatural and is therefore pure fantasy.
There is absolutely no way for us to distinguish between the two. Furthermore, what is the CHANCE that something we make up, actually corresponds with a 'really existing' supernatural reality? One would think the chance is absolutely non-existing. Because anything we 'think' is probably somehow inspired by what we experience in our world. Thus, it sounds unlikely that we could think up something that is by definition not in any way relevant to our reality. But one could just as well say that we can't even say anything sensible about that probability.
I don't see how anything useful could come from this discussion, lol.