Can Science and the Supernatural coexist?

Should science be limited to the study of the known natural world and its systems? Or is the job and goal of science to seek knowledge no matter where that may take the searcher? In other words, do we limit scientific study to the natural only?

I can hear the cries of researchers studying the paranormal as they scramble to justify their grant monies! Creation scientists and those who fall into the Intelligent Design category will immediately disagree.

Let's look at this logically. What is the definition of science?

From Dictionary.com:

n.

1. The observation, identification, description, experimental investigation, and theoretical explanation of phenomena.
2. Such activities restricted to explaining a limited class of natural phenomena.
3. Such activities applied to an object of inquiry or study.
4. Knowledge, especially that gained through experience.


So only item 2 mentions the necessity of confining one's studies strictly to the supernatural. And what is the supernatural?

The same source yields:
adj.
1. Of or relating to existence outside the natural world.
2. Attributed to a power that seems to violate or go beyond natural forces.
3. Of or relating to a deity.
4. Of or relating to the immediate exercise of divine power; miraculous.
5. Of or relating to the miraculous.


The first two definitions of "supernatural" do not mention a deity at all, simply some power or existence beyond what is known to be natural.

Doesn't it follow that the best scientist would not turn away from evidence that pointed in a supernatural direction? To do so makes for bad science, for in so doing the scientist is failing to make every effort to pursue all possibilities. Ignoring evidence that points to supernatural activities or powers from prejudice or religious preference is undoubtably an everyday occurence in the scientific community but that does not make it best practice. You can be sure that Stephen Hawking and Albert Einstein never thought in that way. Great thinkers allow for all possibilities so as not to miss the truth.

My conclusion is as follows: One looks to natural processes to explain all phenonmenae first, but one must be willing to follow evidence into the realm of the supernatural if that is where the evidence leads. Those who are unwilling to do so are allowing their prejudices to diminish their effectiveness as researchers.