While it has been covered before,given Hope suggesting unexplained healing as evidence for a supernatural, it seems that this is a good time to look again at the problems of such claims.
First of all, it's worth realising that science is as stressed many times previously methodological naturalistic. Despite what some on both sides of the belief or not in the supernatural think, it offers no confirmation that the causes are naturalistic, just that if we make the assumption that they are, then the method appears to work. The point that dismissed by many when the likes of universe controlling pixies are mentioned as the cause of everything, is that this precisely applies to everything. All gravity, all cures all things. This causes an issue for those who want to claim two different set of causes natural/supernatural as the method they state covers the natural does not in a philosophical sense do this.
That, of course, makes it impossible to even suggest a distinction with other causes as it is a misrepresentation of the claim of science, but worse is that,they attempt to make this claim by ignoring actual precepts of science, e.g. that it is provisional to then further their case. One person on here who argues for conclusions that I do not agree with , does seem to get this, and that is Sriram when he argues that there is no such divide between natural and supernatural. The problem for those arguing for a supernatural cause is that they actually mistake the nature of science and imbue it with an objectivity it does not have.
This is then backed up by the classic god of the gaps approach which using the unjustified idea that science shows natural causes as being true, then argues that what doesn't seem to fit must be this other thing called supernatural. In so doing they, as noted already, ignore the provisionality of any scientific finding and add in their own incredulity as the determining method.
Oddly most of this has been implied by Vlad when he points out that philosophical naturalism cannot prove itself, but he fails to understand quite how deep the problem is, and this is why he ends up misrepresenting so many people who are not philosophical naturalists. At base this is our old friend the 'going nuclear' option as regards to method, and indeed logical conclusions. Once the relativism is introduced, it means you cannot rely on AMY of the indications from the method to show anything that is objective.
As a relativist, this causes me no problems because I donemake claims for objectivity. I"m aware of the various scenarios of brains in vat, the possibility that it's all just a hologram flowing from the information bleed from the event horizon of a black hole, that even the seemingly immovable object of the cogito may be a mirage for an emergent facility of quantum processes. But as a relativist nine of that really matters. For those who want objectivity and absolutes, it is fatal to the approach.