Since I asked these questions If magic is real, can it be true that rational scientific thought should exclude it? Science, Religion, Magic: Can they be maintained in equal and parallel opposition? I realized that I wanted something that went beyond "unscientific". I've asked this elsewhere, but didn't get a useful answer.
This is for an alternate world of roughly modern level of science. Magic exists, and it shouldn't be limited to subjective / unprovable effects. It is, however, intrinsically hostile to science because it is fundamentally irrational. I don't mean hostile in the sense that technological devices stop functioning in the presence of magic. I mean it in the sense that magic is not studied as a science.
My expectation of irrationalism goes beyond science. Magic is also not the prevalent means by which wealth and power are gained. It's not the main way wars are fought, and not because magic is useless as a weapon. My expectation is that only irrational people make (good) magicians. Developing a scientific mindset impedes one from working (understanding? Does anyone understand it?) magic. Because administrators tend to be logically minded, governments don't focus on organizing magic. Because strategists tend to be rational, militaries focus on non-magical methods.
Who do I expect to be magically inclined? Playing to tropes... A lot of people from 'primitive' cultures. It is not that they have any hereditary advantage, but that they have not institutionalized rationality to a great extent. There are many magically inclined people in industrialized cultures as well. The difference is that there isn't a recognized social place for them. They might be artists like Escher, Picasso and Dali, or just the hobo who says something oddly insightful and prescient and later says, "Told you so." Maybe I'll think of more likely places, but the common factor is obvious: they're all outsiders to the mainstream of industrialized civilization in some way. Magic is a disruptive force, something on the fringe.
For an example, how I expect magic to relate to warfare: Soldiers would sometimes carry charms to deflect bullets. Some of these actually worked. Yet national armies would not issue these as standard equipment. However, if a nation happened to be led by a crazed dictator, he might just send expeditions to discover sources of occult power...
My vision seems coherent, in a handwavey thematic sense. I'm not sure how to make it work on a... I guess "rational level" is the wrong thing to ask! Work with human nature, maybe. My vision implies some rather extreme assumptions: for example, that strongly rational people not only don't get magic, but are strongly resistant to even employing anyone who is irrational enough to be magicians. And I'm probably overestimating the rationality of the average person...