Science operates in the natural, not the supernatural. In fact, I go so far as to state that there is no such thing as the supernatural or the paranormal. There is just the natural, the normal, and mysteries we have yet to explain by natural causes. Invoking such words as "supernatural" and "paranormal" just provides a linguistic place-holder until we find natural and normal causes, or we do not find them and discontinue the search out of lack of interest.
This is what normally happens in science. Mysteries once thought to be supernatural or paranormal happenings -- such as astronomical or meteorological events -- are incorporated into science once their causes are understood. For example, when cosmologists reference "dark energy" and "dark matter" in reference to the so-called "missing mass" needed to explain the structure and motion of galaxies and galaxy clusters along with the expansion of the universe, they do not intend these descriptors to be causal explanations. Dark energy and dark matter are merely cognitive conveniences until the actual sources of the energy and matter are discovered. When religious believers invoke miracles and acts of creation ex nihilo, that is the end of the search for them, whereas for scientists the identification of such mysteries is only the beginning. Science picks up where theology leaves off. When a theist says "and then a miracle happens," as wittily portrayed in my favorite Sydney Harris cartoon of the two mathematicians at the chalkboard with the invocation tucked in the middle of a string of equations, I quote from the cartoon's caption: "I think you need to be more explicit here in step two."
To our bronze-age ancestors who created the great monotheistic religions many millennia before the rise of science, an invisible intentional agent in the form of a god was the best explanation they could think of to explain the world. Today we can explain much (but not yet all) of the workings of the natural world, such that the realm of the unexplained requiring gods is shrinking as the sphere of science expands into the great unknown. Although an expanding sphere of science comes into contact with an ever increasing surface area of the unknown (thus, the more you know the more you know how much you don't know), recall the mathematical principle of surface area to volume ratio: as a sphere increases the ratio of its volume to surface area increases. Thus, in this metaphor, as the sphere of knowledge increases, the ratio of the volume of the known outpaces to the surface area of the unknown increases. It is only a matter of time before there will be no place left for God to stand.
Now, one may postulate a supernatural God who exists outside of space and time and is not knowable to science because He is not part of the natural world, thus obviating my expanding sphere of knowledge metaphor. But if that is so, then how are we to know whether or not this God exists? What is the difference between an invisible God and a nonexistent God? As corporeal beings who form beliefs about the world based on percepts (from our senses) and concepts (from our minds), how can we possibly know a being who by definition lies outside of both our percepts and our concepts? At some point doesn't God need to step into our spacetime to make himself known in some manner -- say through prayer, providence, or miracles? And if so, why can't science measure such divine action? If there is some other way of knowing, say that of the mystics or the faithful through deep meditation or prayer, why couldn't neuroscience say something meaningful about that process of knowing? If we came to understand -- as studies with meditating monks and praying priests have shown -- that a part of the parietal lobe of the brain associated with the orientation of the body in space is quiescent during such meditative states (breaking down the normal distinction one feels between self and non-self and thus making one feel "at one" with the environment), wouldn't this imply that rather than being in touch with a being outside of space and time, it is actually just a change in neurochemistry?
So the answer to the question on the table turns on what, precisely, is being claimed in the name of religion? If no empirical claim is made that science can address, then there is little more to be said on the matter. If specific claims are made in the name of God and religion then let's hear them and put them to the test.
Until then, I believe that it is time to step out of our religious traditions and embrace science as the best tool ever devised for explaining how the world works, and to work together to create a social and political world that embraces moral principles and yet allows for natural human diversity to flourish. Religion cannot get us there because it has no systematic methods of explanation of the natural world, and no means of conflict resolution on moral issues when members of competing sects hold absolute beliefs that are mutually exclusive. Flawed as they may be, science and the secular Enlightenment values expressed in Western democracies are our best hope for survival.
