This important paper (well, I've actually linked here to a publicly-available late draft that contains a few typos) in Foundations of Science merits careful reading. Authored by Maarten Boudry, Stefaan Blancke, and Josef Braeckman, it deals - very well, in my opinion - with the capacity of science to investigate the supernatural. It's refreshing to read something like this, which goes a long way towards setting the record straight.
Of course, science cannot investigate the supernatural if we define "the supernatural" as "whatever cannot be investigated by science"! But once we define the supernatural in some other plausible way it is by no means apparent that science can't investigate it, just as it can investigate things that no longer exist (such as dinosaurs), things that are very distant (such as the moons of Jupiter), and things that are very small (such as atomic nuclei). None of the latter can be perceived directly with our senses, but they can interact with our senses in other ways - by leaving traces on the world that we can perceive, by interacting with scientific instruments to create images that we can perceive, by affecting experimental apparatus in predictable ways, and so on. In the end, we can use distinctively scientific means to investigate many things that interact with our senses only indirectly. Depending on the situtation, we can sometimes establish a lot about those things. We do, in fact, know a lot about the moons of Jupiter, dinosaurs, and atomic nuclei, even though none of these things have ever been directly observed with our senses (the moons of Jupiter have been observed via scientific instruments such as telescopes, and we have various reasons to think that these are reliable, but they have not been observed by unaugmented human eyes).
For example, let's take a toy definition of the domain of "the supernatural": imagine that it relates to the existence, characteristics, and activities of disembodied intelligences. Can science investigate this domain? In principle, yes, at least sometimes.
If a disembodied intelligence such as a spirit or a demon is said to exist and to interact with the world in a certain more-or-less regular way (perhaps because this being has a particular power set and particular psychological dispositions), we can go and look for corroborating evidence. Of course, we may be caught short if we're told that this intelligence is capricious or is hiding or works in mysterious ways, or whatever, so that its existence ends up being compatible with any observations at all. People who posit capricious, etc., disembodied intelligences as explanations for phenomena are in fact making their claims immune to scientific investigation (and they are certainly not doing science, themselves!). But what makes their claims immune is reliance on the capricious, etc., nature of these beings, not the fact that they are said to be disembodied.
Hypotheses that refer to capricious intelligences or to intelligences that are described so vaguely that we can't get a handle on them at all, or to beings that are described in internally contradictory ways, are non-starters. And, indeed, there are many reasons why it is difficult to settle the truth of supernatural claims by scientific investigation. But that doesn't mean that all hypotheses about beings or intelligences or principles that meet some intuitively plausible definition of the supernatural are non-starters in principle. The practical difficulty in testing many of the claims made by, for example, Intelligent Design theorists is that they use immunization strategies. Again, that is a hallmark of non-science or pseudoscience (or at the very least science that is so fundamentally flawed that there can be no rational pedagogical purpose in teaching it to children).
Boudry and his colleagues make astute remarks about all this:
However, we have to be careful not to misconstrue the immunizing strategies and ad hoc amendments of creationists as intrinsic problems with supernatural claims. It is true that IDC proponents are guilty of immunization strategies, but as far as we can see, this unwillingness to take empirical risks is just an indication of the dismal state of their research programme. After all, resorting to immunization strategies is a typical feature of pseudo-science, supernatural or otherwise (Boudry and Braeckman 2010).
Thus, if only they chose to do so, IDC proponents could easily equip an alleged supernatural Designer with specific attributes and intentions in such a way that the design hypothesis would yield unexpected predictions and is not “compatible with any and all observations of the natural world”, as Scott claims (Scott 2004, 20; Richter 2002, 21). For example, if one supposes that the Designer is benevolent and has created the universe with good purpose, as almost any theist does, one is confronted with the problem of evil and suffering in the world (Hume 2007 ; Kitcher 2007, 130). As Reed Richter pointed out, in response to Scott’s defence of IMN, “‘[s]upernatural’ does not automatically imply arbitrary, capricious action as Scott implies”
Do consider the whole article, which contains plenty of detail to chew on. It won't escape long-term readers that Boudry and his colleagues are putting essentially the same view that I have long argued for (see here for example). They are giving it a more formal and concerted defence, and hopefully their argument will carry more weight than my occasional blog posts on the subject.
Of course science has learned over the years that explaining natural phenomena in terms of the actions of supernatural ones (e.g. disembodied intelligences) is not fruitful - that is because of the very poor track record of such hypotheses. The procedures of science now strongly discourage supernatural hypotheses, and a scientist resorting to them would, quite rightly, not be taken seriously. This is the practice of methodological naturalism.
But that does not mean that scientists must, in principle, have nothing to say if others advance claims about supernatural phenomena. If the claims are not sufficiently immunized, scientific investigation may even be able to show that they are false.
H/T to Jerry Coyne who has some interesting stuff of his own to say.