Integrating Science & Religion

"Nobody is integrating the sciences and spiritual knowledge with Wilber's scope and integrative power", asserts Michael Murphy - and I agree.
Because this topic is important, this post will include excerpts from: The Marriage Of Sense And Soul - Integrating Science And Religion. I enjoy promoting the work of brilliant minds, and it is my sincere wish that the subtlety of meaning couched within Ken Wilber's words resonate with you:

"We have seen that philosophers of science are in wide agreement that empirical science depends for its operation upon subjective and intersubjective strucures that allow objective knowledge to emerge and stablize in the first place. Put bluntly, knowledge of sensory exteriors depends upon nonsensory interiors, interiors that are just as real and just as important as the exteriors themselves. You don't get a message on the telephone, claim the message is real but the telephone is illusory. To discredit one is to discredit the other." If sensory-oriented science is not equipped to investigate these interior domains, it nontheless cannot deny their existence without denying its own operations. It can no longer claim that the xteriors alone are real. And that, very simpply, completely undercuts what we call objection number 1 (the belief that interior domains have no reality of their own). Precisely because empirical science is forced to acknowlledge interiors, it cannot dismiss Spirit merely on the basis that Spirit is interior. The first major objection falls.
Thus, if science wishes to continue to deny Spirit, it is forced to retreat to objection number 2 and attempt to deny, not all interiors, but only certain types of interiors, because, it is claimed, these other and "disreputable" interiors--such as spiritual experience--cannot be verified. They are at best private modes of knowing; at worst, hallucinations

The notion that there exists a single, straightford "scientific method" has long been discredited. It is almost unanimously acknowledged that there is no algorithm (not set method) for generating theories from data; the very notion was part of the myth of the given. Nonetheless, most philosophers--and certainly most working scientists--have a clear enough idea of what "doing science" actually means; enough, anyway, to differentiate scientific knowledge from poetry, faith, dogma, superstition, and nonverifiable proclamations. The scientific method might be slippery, but it still manages to get a lot of work done. . .

On the one hand, "empirical" has meant experiencial in the broadest sense. To say that we have some sort of direct experiential evidence, data, or confirmation. To be an "empiricist" in this borad sense simply means to demand evidence for assertions, and noot merely to rely on dogma, faiith, or nonveribiable conjectures.
I have a great deal of sympathy for that position. In fact, using "empirical" in the broad sense of "demand for experiencial evidence," I count myself a staunch empiricist. For the fact is, there is sensory experience, mantal experience, and spiritual experience--and empiricism in the very broadest sense means that we always resort to experience to ground our assertions about any of those domains (sensoory, mental, spiritual).

Here are what I believe are three of the essential aspects of scientific inquiry--what I will also call the "three starnds of all valid knowing.
1. Instrumental injunction. This is an actual practice, an exemplar, a paradigm, an experiment, an ordinance. It is always of the form "if you want to know this, do this."
2. Direct apprehension. This is an immediate experience of the domain brough forth by the injunction; that is, a direct experience or apprehension of data (even if the data is mediated, at the moment of experience it is immediately apprehended). William James pointed out that one of the meanings of "data" is direct and immediate experience, and science ancors all of its concrete assertions in such data.
3. Communal confirmation (or rejection). This is checking of the results--the data, the evidence--with others who have adequately completed the injunctive and apprehensive starnds.

These three strands, then, will be our guide through the delicate world of the deep interiors, the within of the Kosmos, the data of the Divine, where they will help us, as they do with the exteriors, to separate the dependable from the bogus."