Again, I shamelessly plagiarize myself. This is a slightly adapted Usenet post. I promise to follow it with something light and uncontroversial.
But I'm going to go ahead and put a toe into into deep, unquiet waters with this post. I'm going to try to answer the question, "Which is more scientific, to be open minded about ghosts and ESP etc, or to dismiss the possibility?" How about if you replace 'ghosts and ESP' with 'God'? Is it consistent to give a different answer?
Assume for the sake of argument that we're not going to get any repeatable experiments demonstrating the existence of any of these. (If we ever do, science will demand that we take them seriously.)
But if we don't... Well, the whole point about the "supernatural" is that it's not limited by nature's laws. If you believe in the supernatural, it probably shouldn't bother you that it's not repeatable, and is inconsistent with the results of experiments we already have. The supernatural wouldn't operate on demand, presumably. But believers should acknowledge that they're never going to have any kind of scientific evidence for their claims, so they should never try to use scientific evidence as a tool of persuasion. And they should acknowledge that if they're right, it would mean that the universe does not in fact consistently obey the laws that scientists have uncovered -- in that sense we would have to throw those laws out. So long as they acknowledge that, there is nothing inconsistent about their position.
Is it possible to hold this position, to believe that the laws of nature are not without exception, and still do science?
I think history shows the answer is 'yes' -- but only to a certain extent.
In particular, some brilliant scientists are theists. Belief in God allows one to assume that the exceptions to (God's) laws are few and fit some still-larger pattern. The belief in any wider variety of supernatural powers and entities, however, seems to suggest that natural laws are of much more limited use, and thus makes science into pretty pointless pursuit. So I think one is much less likely to find a good scientist who believes in telekinesis and clairvoyance (both of which violate some principles that have been experimentally tested) than one who believes in a divine plan.
It's a question of what sort of rationality you expect from the universe. If you expect nothing more than consistency from the physical world, that the same conditions will produce the same results every time, then by definition you can't believe in miracles, or any other supernatural intervention. If, on the other hand, you expect events to serve some purpose, to be rational in the sense that they are a part of some larger plan, then you have no problem with miracles, since you believe that natural laws themselves are divine decrees, and can of course be suspended by divine will. You look for consistency at a higher level than the actual behavior of the universe, in the purpose that it serves. There is nothing irrational about this position (although it leaves theological problems to be solved -- why do bad things happen to good people, and so on.)
On the other hand, if the universe is neither purely mechanical nor operated in accordance with a single divine plan, then one can hope for very little consistency in the universe at all. Sometimes "laws" will work and sometimes they won't. A universe with ghosts and seers but no God is an irrational universe. Anything can happen. Now actually there is nothing self-contradictory about this position either. It could be that the universe is irrational. However, this is a universe in which many people would be deeply uncomfortable, which explains the hostility toward occultists and paranormalists from both scientists and religious believers.
Any of these three positions -- strict naturalism, "all-poweful" theism, or the belief that the universe is simply weird beyond comprehension -- is internally consistent, but they are not consistent with each other. Only if you're a strict naturalist, can you really hope to discover immutable natural laws through the scientific method. Monothesists have a different goal; discovering God's plan. (I don't know about polytheism. I suppose it would depend on the details.) Atheist mystics should not really expect much of the scientific method, or particularly trust in its results, since it relies on the assumption that the universe can be relied upon to behave in the same way everywhere and all the time.
I won't argue with people taking any of these positions, unless they try to take all of them at the same time. I'll also note that I haven't stated my own position -- it takes some maneuvering to force me to do that.