There is a long-standing tradition which requires that science deals only with natural explanations for natural phenomena, and thus can have nothing to say about the supernatural (defined as anything that exists outside of nature). While largely true, this way of thinking is all but useless in the real world. Sadly, we live in a society in which people are willing to believe the craziest bullshit imaginable--and much of this consists of supernaturalism.
We need a lot of people to fight against this decline of the intellectual climate. There are several groups of people qualified to do so: skilled investigative journalists, conjurors, and scientists (among others, but these are the primary movers and shakers in the skeptical community).
Investigative journalists are useful for two reasons. First, they have those investigative skills that allow them to get inside the scam organizations and find the truth at the bottom of these ridiculous notions. At least equally important is that they have the communicative skills to report their findings, in an understandable manner, to the public at large.
Conjurors are useful because many of the supernaturalists are, in fact, using age-old conjuror's techniques to achieve their so-called miracles. The psychics, for instance, use a method of cold reading in a majority of cases. And even when they aren't using well-known conjuror's tricks, they're often exploiting the same psychological principles that the legitimate entertainer makes use of to achieve certain effects. There is no group of people more qualified to detect trickery than professional tricksters.
But scientists are perhaps most important of all, because contrary to the common "science has nothing to say about the supernatural" humbug, these actually are scientific questions. The claim that science can't study the supernatural is true, but only in an esoteric sense. In any useful sense, science has a lot to say about these issues.
When people are talking about the supernatural, they're talking about events that operate outside of nature. However, in almost all cases, these supposedly supernatural events actually do (allegedly) have natural, physical manifestations. Anything that is detectable by human perception has some form of physical manifestation.
If the claim is that a house is haunted, there's going to be some physical manifestation. Either an apparition will show itself, or the ghost will create "cold spots" or knock on walls, or slam doors, or any other cliche from old horror films. These are all physical manifestations.
If the claim is that dowsing can detect water, that's not a supernatural claim. If true, it's a physical manifestation.
If the claim is that psychics can communicate with the dead, then something is interacting with the natural world.
If the claim is that there is a god, that's going to have physical manifestations. Some Deist gods may prove to be an exception, as they are not said to interact with the physical world. But the various gods that people actually worship certainly would have physical manifestations. Answering prayers, performing miracles, forgiving sins, creating universes: these are all physical manifestations.
My point is that, even if an event or being is said to be supernatural (whatever that is!), it has physical attributes. If it has no physical attributes at all, then no one is even going to be talking about it. It doesn't do anything for their life, it's impossible to detect, and makes no difference in human affairs. I don't believe that these things exist, but it's impossible for science to disprove them. We can call these "purely" supernatural phenomena, and the old adage that science has nothing to do with the supernatural actually does apply here.
But all the "supernatural" things people talk about in religions or New Age fairs, actually are well within the proper domain of science. Even if the being is supernatural (and thus, undetectable by science), it somehow interacts with the natural world. So its effects can be detected and can be studied by science.
For instance, if your claim is that there is a supernatural god who, say, answers prayers, how is that detectable by scientific means? The god may be supernatural, but the efficacy of prayer is within the natural realm and is certainly a matter for science to decide. In this case, all you have to do is run a statistical analysis to determine whether prayer significantly improves, say, the healing speed of hospital patients. When this experiment was performed by the Templeton Foundation, they had some interesting findings.
The patients were divided into three groups. One group was prayed for and not told about it. One group was not prayed for and not told about it. One group was prayed for and told so. The first two groups both demonstrated average recovery. The third group actually experienced a "nocebo" effect and had a prolonged recovery time.
This is a perfect example of science studying the supernatural. Of course Christian theologians were quick to criticize the study's research protocols (which, despite my dislike for the Templeton Foundation, were actually quite good), but they were just upset because someone had actually bothered to prove them wrong.
Related to the idea that science can't study the supernatural (whatever that is!) is the concept of NOMA, or nonoverlapping magisteria. As much as I respect and admire Stephen Jay Gould as a thinker and a scientists, I cannot forgive him for supporting and popularizing NOMA as a valid way of thinking--it is not! Gould wrote, "[T]he magisterium of science covers the empirical realm: what the Universe is made of (fact) and why does it work in this way (theory). The magisterium of religion extends over questions of ultimate meaning and moral value. These two magisteria do not overlap, nor do they encompass all inquiry (consider, for example, the magisterium of art and the meaning of beauty)."
On this point, Gould is dead wrong. He correctly identifies what science has to do with, but incorrectly gives ultimate meaning (which cannot actually exist) and worse, morality, to religion. After all that religion has done to society, I can think of fewer actions more misguided than allowing religion any more room to comment on morality. Religious morality promotes bigotry, stupidity, and murder.
But Gould's greatest mistake is in assuming that all religion does is "ultimate meaning and moral value." If that were the extent of religion, I would have no problem with it, and would agree with Gould's assessment. The problem is that ultimate meaning seems, to me, a red herring. Science can reveal the universe as it really is. Ultimate meaning, it seems to me, is simply what we as individuals and societies make of that universe. There is no "ultimate" meaning. There is only personal meaning. Science, it is true, does not have much to do with personal philosophy. It also doesn't have much to do with moral philosophy (though there are some minor points of overlap, despite Gould's assertion to the contrary). If religion weren't about supernaturalism or a magic man in the sky, Gould would be correct to give morality to it. However, religionists are not the most moral, nor the most intelligent people in the world. Any morality that modern religion (or any religion as it has ever existed in the history of the human race) gives us is guaranteed to be horribly skewed by supernaturalism. Gould argues for NOMA while considering the almost atheistic "religion" of many sophisticated theologians, forgetting that more than half of the American population still believes the Universe is less than 10,000 years old.
This debate over NOMA has created strange bedfellows. Many Christians, unsatisfied with the blind faith given them by their preachers and holy books, think that science should set out to prove their religion correct. These people are certainly opposed to NOMA. On the other hand, many other Christians realize that NOMA is their best protection from scientific scrutiny. They may not be satisfied with blind faith, but at least they're safe from falsification.
A lot of atheists and scientists (almost all scientists are atheists--food for thought) are on my side. They see NOMA for what it is--a last ditch effort to save religion from proper scientific scrutiny and debate. As such, we argue against it with all our might, because we know that the best way to kill religion is to expose it to the light of science, under which it cannot help but to shrivel.
On the other hand, such thoughts are not politically correct. There are those who think we need to take this battle one step at a time. For instance, American biologists are currently in a state of war against creationism. For these biologists, perhaps it is a safer tactic to make every attempt to keep science and religion separate. They are rightly concerned that many religious individuals will, if science and religion are forced into conflict, choose to ditch science and keep religion. It's a valid concern, and one I cannot answer to a particularly satisfying degree. Politically speaking, perhaps it is better to keep religion and science separate, if for no other reason than to keep funding and trick the religious IDiots into avoiding their conflicts with science.
And of course there are plenty of evolutionists who are also religionists, including some respected and noteworthy biologists. I don't understand how they can reconcile scientific truth with their Bronze Age mythologies, but they seem not to have a problem doing so.
But that still doesn't make NOMA true! We can discuss politics and tactics until the cows come home, if we want. But I actually care what is true, so I cannot support a proposition that goes against what I know to be true. Religion makes scientific claims, and should be subjected to scientific scrutiny. The same goes for all other forms of supernaturalism as well.
The controversy over evolution and creationism is but a single skirmish in a larger battle, I think. Perhaps in this skirmish, NOMA is a tactically sound position to defend. But in the larger battle, it will only cost us more in the future. It may be that we're best to leave NOMA where it belongs, accept the difficulty that causes in our present skirmish, and move on. If we do this, once our current fight against creationism has been won, we will have an easier time defeating religion, supernaturalism, and irrationality in general.
Unfortunately, many scientists disagree with me--at least publicly. In 1999, the National Academy of Sciences supported NOMA: "[S]cience and religion occupy two separate realms of human experience. Demanding that they be combined detracts from the glory of each." I'm not entirely convinced that they don't take this stance simply to protect their funding and political standing in a country dominated by mindless creationists. But the fact that they popularize this stance will not be useful to us in the future.
Science can indeed study the supernatural (as long as it has natural manifestations--as all supernatural phenomena in which people believe do). It's just that supernaturalists don't like what science discovers about them, and scientists don't like it when supernaturalists threaten their funding.
Keep it natural!