I think it would be best to just not use the word supernatural. We could just say that science deals with what we can observe. If it can be observed then science can deal with it.
Saying science deals with what we can observe is really just saying science does not deal with the supernatural. All supernatural means is above, or beyond the natural, i.e. that which conforms to the laws of physics, biology, etc. The Oxford American Dictionary defines supernatural as
quote:
(of a manifestation or event) attributed to some force beyond scientific understanding of the laws of nature
While we can muse on some ways in which the supernatural can be scientifically tested (Taq's dollar-giving Ubergod) in general I don't really think it's true. Unless the supernatural being manifests itself in ways that we can directly observe it and the actions it does, there's no way to test for it. Being supernatural, and thus not subject to the laws of nature, we have no way to predict anything about it. How do you predict the whims of an all powerful being that can somehow affect the universe without using any of the known natural forces, or leaving any trace of its action? E.g. We can scientifically determine that planes stay in the air due to specific forces having to do with fluid dynamics and such because these are predictable laws, but there's no way to test if it's really just because a god is holding it with is invisible hand that leaves no fingerprints.
I guess my whole point is that the word supernatural is nothing special, it just means something outside that which we can observe.
We have many intuitions in our life and the point is that many of these intuitions are wrong. The question is, are we going to test those intuitions?
-Dan Ariely