Can science investigate the supernatural?

Good discussion going on about whether or not science can investigate the supernatural.

Occasional Sentient Developments blogger Russell Blackford stirred the pot with his article, Boudry, Blancke, and Braeckman on methodological naturalism:

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).

Blackford's article was followed by Christopher Schoen who asks, Is "dark matter" supernatural?:

At issue is the oldish question of whether science can probe into "supernatural" questions, the most famous of which is "Does God exist?" Traditionally, the question hangs on the distinction between two kinds of naturalism: methodological naturalism, which excludes supernatural phenomena as out-of-scope, (whether or not they actually exist), and philosophical naturalism, which assumes a priori that supernatural phenomena do not exist.

A number of scientists and philosophers are dissatisfied with these two options, since neither seems to permit the testing of the "God Hypothesis." The solution to this that both Russell and Jerry point to is presented in a new paper in Foundations of Science which proposes to further split Methodolological Naturalism into two more categories: Intrinsic Methodolological Naturalism (IMN) and Provisional Methodolological Naturalism (PMN). IMN is the old way of doing things; PMN the new, improved way, allowing for scientific study of supernatural phenomena, should they happen to pop up unexpectedly in the course of our research.

Nowhere do the authors of the paper define just what supernaturalism is supposed to mean. The word is commonly used to indicate that which is not subject to "natural" law, that which is intrinsically concealed from our view, which is not orderly and regular, or otherwise not amenable to observation and quantification. That right there should be a conversation-stopper, since these are science's stock and trade, and we've seemed to stumble on a simple logical end to the problem.

Also check out contributions to this discussion by Jerry Coyne, John Pieret, and Massimo Pigliucci and the Cosmic Variance blog. And of course the article that started it all, the paper by Maarten Boudry, Stefaan Blancke, and Johan Braeckman.