One of the more interesting arguments I have been in recently is whether scientific epistomology is limited and whether this implies that spiritual truth is somehow separate from scientific truth. The principle of separation has been labeled "Non-Overlapping Magisteria" or NOMA by the Catholic Church and the name has stuck. NOMA has been criticized as suggesting a false coexistance but I would argue that the issues with NOMA are due to both science and religion treading on eachothers' territory.
Of course, I am not a Catholic, or even a Christian. I expect my views here to ruffle quite a few feathers but I have done my best to make my argument solid.
The False Problem with NOMA:
A naive look at NOMA suggests that it is in fact a problematic principle because religions such as the Catholic Church have progressively given more and more of what was historically their domain over to science. Thus it is tempting to see NOMA as a drawn-out surrender where science gets to answer anything it can prove and religion gets to answer the rest. In this view, religion basically is there to offer certainty about things we can't be certain about and hence has no place in a scintific world is due to problems defining spiritual truth among both scientists and religious people.
Science does not Exist in a Vacuum:
Similarly, a lot of people water down science by suggesting that it is somehow fully self-contained, and that data inevitably leads to theory. The basic problem with this view is that the development of theory requires more than just a mathematical review of the data. Scientific theories arise from review of data, and by definition they are falsifiable (if some data is later discovered which disproves the theory) but they also contain elements of the theoritician's world-view beyond simply trying to put the pieces together. I suspect that this is why theoretical physicists who are deeply into phylosophy and spirituality are so well represented in the top tier of their field.
In short, as Werner Heisenberg pointed out, theory is developed by an individual reviewing data and applying ideas which pre-exist the review of the data to them (see "Physics and Philosophy"). I suspect that this was also behind Einstein's proclemation that imagination is more important than knowledge. Science is thus largely an area of applied philosophy where philosophical principles are applied to interpretation of data in the formation of theories much in the same way that engineering applies physics, chemistry, enad the like.
As such, science deprived of non-scientific ideas would also be denied the major breakthroughs that we have seen in every area.
The Limitations of Science:
Science is a methodology for a limited form of natural discovery which can provide some grounding for certain forms of philosophy but lacks any direction of itself-- even the direction of science is dictated by outside ideas as documented above.
Science is at its strongest where reproducible experimentation is possible. It is at most overextended where reproducible experimentation is not possible. For example, science probably cannot say much for certain about otherwise normal people who claim to have witnessed miracles, claim to have been abducted by aliens, etc except that "we don't know." Hence the hard experimental sciences in areas like particle physics and quantum mechanics are where it is strongest, and the soft sciences relating to subjects like psychology are where science is the weakest. In the middle are areas where limited experimentation may be possible but where the bulk of material to work from has to be unearthed-- areas such as paleontology, archeology, and historical linguistics. (Mathematics does not fit into this classification and is probably better described as a branch of deductive logic rather than science.)
Interestingly, what hamstrings scientific psychology is a scientifically valid observation argued first (in the field of modern psychology) by Carl Jung, that humans do not come into the world as blank slates, that we carry with us individual personalities (what he called the "a priori self") from a time before birth. This is observable in that some fetuses are more active than others, and display other behavioral differences as well. Since there is a portion of the psyche which is not reproducible, then you end up with a fundamental problem when looking for reproducible results-- at best results may show up in statistical analysis, but actual experimentation and repeatability is fundamentally limited even excluding ethical concerns.
The Valid Role of Science:
Science represents the best epistomology for seeking an understanding of mechanism of our current natural and (broadly-speaking) historical external world. It also provides more limited insight into older historical elements of the artificial world through archeology, historical linguistics. Finally there is even more limited value in areas such as clinical psychology (psychiatry is something different which is generally grounded in neural science and experimentation and is hence more scientific than clinical psychology).
However, science can never go from mechanism to goal-- it can never tell us what we as a society should value, and can never provide by itself any viable ethical principles (it can provide a method for validating actions we take in support of ethical principles, however).
Science can never be the guide to what is great artwork or music, and I believe it will ever be able to provide guidance for relating to the experience of the divine, which if my understanding of comparitive religion is accurate seems to be a near-universal aspect of the human condition. Science might be able to provide some insight into what makes certain pieces of art great or what the mechanism is in the brain for the sense of the divine, but cannot provide guidance beyond mechanism.
So science must remain concerned only with mechanisms and things which (necessarily spring from mechanism, such as chronology, age, and timing) of the natural and to a lesser extent the psychological and artificial world as well.
The Place of Religion:
If Science limited by its own epistomology, then the question becomes what of religion? Is there a place for religion alongside science and philosophy? I think that this problem, when approached rationally provides ample room to criticize and limit the scope of religious discourse. But I think that when one looks back it is clear that there is a place for religious belief.
The first issue is that religion must give up any claim of authority over mechanism (and hence chronology, age, timing, etc) of the natural world. This means that evolution for example exists in an area where religion has no claim of authority.
Most of the world's religions historically important religions developed at least in large part before the adoption of writing. Walter Ong ("Orality and Literacy") has documented a fundamental shift of thinking which occurs when one moves from oral-tradition-centered cultures to literacy-centered cultures. The literacy shift is, I believe, the core of the cognative shift which lead from the Renaissance to the "Enlightenment." However, as the Abrahamic religions developed in literary societies (including but not limited to Christianity, Islam, and Judaism), they have tended to have an emphasis more on the idea of literal truth. It is thus my belief that religion must step back and address issues more along the way that Hinduism or Platonism does-- as metaphores where the Ideas behind must be sought rather than mere simple pronouncements of literal truth.
Religious traditions thus end up being language-like structures for helping us relate to various aspects of our inner and outer world but exists in a way which is fundamentally does not overlap with science and yet provides immeasurable value (perhaps greater value than religions do today). In this view, science and religion could enhance eachother and coexist without conflict and both provide their best to society and eachother.
Ultimately, this means that most religions today must give up more than science, but in my view this is not a surrender but an act where religion refocuses itself on what it is really all about.
