[quote="MarcoPolo, post:1, topic:291042"]
More than once, and again recently, I heard a skeptic arguing against the validity of the supernatural on the grounds that you can't use science to prove it (reason, philosophy, deduction, etc... need not apply, I suppose). For example, he said if cancer goes into remission, there's no scientific way to determine the Virgin Mary's involvement [emphasis mine]. On the issue of "ghost" activity, he used the same argument that our inability to "explain" something scientifically does not allow us to draw supernatural conclusions.
One of the problems with such logic, as I see it, is that the skeptic's assertions themselves are unprovable by science. For instance, what scientific experiment can you conduct to make the claim "in order for something to be true, it has to be demonstrated by science"? The claim itself is unscientific. Thus, it is self-defeating. [emphasis mine]
What's the fallacy for such line of thinking?
Unless he maintains that (all) propositions must be scientifically verifiable, his position is not self-defeating.
Simply stating that, in the event of a seemingly miraculous event, science cannot invoke the non-empirical in its explanations of the said event, is not fallacious. For what it's worth, there are prominent Christian apologists that agree with this assertion.
Consider for example, reported near death experiences (or post-death experiences, a more accurate label).
There is a way to verify that a person was conscious after clinical death, (for example, if the patient can, upon recovering from death, report an incident that is not physically or tangibly possible for him to have knowledge of, e.g. details of an accident that occurred across the street from his hospital and during the time in which he was dead).
We can verify his post-death consciousness because we can verify whether the details of the accident are true/whether the accident occurred, and can, at least in theory, eliminate proposed physical and practical avenues through which the patient could have learned of the accident (e.g. hearing nurses in his room talk about it upon him recovering some brain activity).
However, if the person claims to have seen heaven and Christ during his dead-but-conscious phase, we cannot verify that claim -- that content of his post-death expierience would not be scientifically verifiable. All that science could conclude is that he was conscious post-death.
I recommend listening Christian apologist Gary Habermas on the subject of NEDs -- which ties into your OP.