Astronomer Phil Plait notes a webcomic addressing testability and the supernatural, and makes an odd endorsement of this position:
there’s no such thing as the supernatural. Either something is natural — that is, part of the Universe — or else it doesn’t exist.
If you posit some thing that has no perceivable or measurable effect, then it may as well not exist. And as soon as you claim it does have an effect — it can be seen, heard, recorded, felt — then it must be in some way testable, and therefore subject to science.
Not quite. The issue with the supernatural is not whether it’s part of the universe, but whether it is bound by the same laws as all the other elements of the universe. The bizarre claim about ghosts is that they somehow obey some laws but not others, for no obvious reasons.
Something supernatural could, in principle, interact with the universe sometimes but not at others. If it is operating outside of natural laws, that doesn’t obviously preclude it from sometimes interacting with things that do obey those laws, either by its own choice to obey those laws (“186,000 miles per second, it’s not just a good idea, it’s the law”), or by accident in the course of some random fluctuation of its supernatural nature.
Plait’s point, and the webcomic’s, is more about the transcendent than the supernatural. The explicitly miraculous could, in principle, exist and interact with nature, without being scientifically explainable or otherwise within the scope of science. Of course, if these miracles were common enough, we might detect some lawlike nature to them. If they could be reliably induced through prayer or other actions, that would itself be a law of nature, and would help naturalize those supernatural phenomena. That path has been followed before, with phenomena like gravity being seen first as supernatural (“spooky action at a distance”) to fully natural and lawlike.
The comic concludes with the thought that, if the supernatural exists but doesn’t interact with the world, “then why do we care?” That’s a fair question, but not one that serves atheists. It’s the reply of an apathist agnostic, who acknowledges that god(s) or other supernatural entities might exist, but are so uninteresting and irrelevant as to be unworthy of the time and energy so many people invest in either affirming or rejecting their existence.