I want to focus on a terminology point rather than re-fighting the reductionism war. But I think I need to spell out the context for my question. I'm trying to be fair to both sides, and this is as concise as I've been able to get it. Everything in italics is background, and suggestions on how to tighten it (what can be left out) are welcome though I don't promise to accept them.
Please remember that I'm an untrained amateur and gained much of my (mis) understanding of philosophy from this site. Deep historical references ain't something I can do, and terminology is my-best-current-understanding.
Background:
Reductionism get a bad rep because sheer complexity of real-world objects and events is often too great to work back from them to their precise causes. But any engineer knows precise/complete reverse-engineering is more of a pain in the ass than designing the thing from first principles. In fact, when designing, the best approach is generally divide-and-conquer: break the problem into simpler pieces, then partition those, until you hit something simple enough to implement directly; than build back up.
We may never be able to apply reduction to something as complex as a specific human brain; it's hard enough for the simple but chaotic Three-Body Problem. However, we can build a perfectly accurate model of how the three bodies interact, and understand why perturbation of the initial state alters the final state so much.
Non-physicalists (meaning those who believe the mind can't be fully accounted for by the body) complain that physicalism can't yet show how to reduce the mind to its components. (Though as I understand it their approach can't yet do so either.)
Physicalists counter that reduction is a red herring. it isn't necessary to reduce a magnificently intractable complex system if the model can be built up from components; that may not tell you the details of an individual mind or capture every last detail in a tractable form, but in time it should reach the same resulting model a successful reduction would, or one that is equivalent. And it's a much more practical research plan.
I'm looking for a name to call this bottom-up alternative to reduction, so I can answer "you can't reduce" with "So? That's the wrong approach for something this complicated. We can get the same end result more easily via XXXXX. And after all, that's closer to how evolution would have built the system in the first place, since mutation has no goals and selection works with what it gets."
Question:
What can I/we call this divide-and-conquer alternative to reduction? Composition? Conduction? Comduction or conposition? Compilation? Assembly? Integration? Summation? Engineering? A la carte?...
Is there an official term already in use which recognizes that the reductionism coin has an opposite face and names it?