Culture-war rhetoric often assumes a fundamental opposition (even, inevitably a war) between something called STEM and something called The Humanities.

I'm hardly the first to point out that this is a large and rarely justified assumption, but since it's once more in the air...
First, neither label actually means much of anything in practice. Each is shorthand for a fluctuating and heterogeneous range of teaching disciplines and research fields.

Neither for STEM nor for The Humanities is there any single unifying methodology, subject, or goal.
Second, to the extent that there are antagonisms between practitioners in STEM fields and those in The Humanities, their practical import if not their vitriol pales in comparison to antagonisms within each, and those in turn pale in comparison to antagonisms within disciplines.
Third, the vitriol is greatly overstated -- or, perhaps, its source and nature are misunderstood. I regularly teach history of science, which usually means introducing it to Humanities students with no science backgrounds. Many are apprehensive about a course involving science.
But never (not once in ten years) have I encountered dismissal of science as unimportant, or false, or made up.

To the contrary, the prevailing sentiment is fear that it will be beyond their grasp. (This is a fear, incidentally, that culture-war rhetoric carefully cultivates.)
When we discuss current debates, students' overwhelming (I could almost say unanimous) view is that the authority of science matters fundamentally to our collective present and future. It's worth stressing that no amount of looking at science in historical context undercuts this.
Indeed, there is some anxiety on the part of some (Humanities) students that too sharp a public awareness of the social and political nature of scientific practice might undercut this authority. There's sometimes a hint of willingness to entertain noble lies on science's behalf.
But, obviously, that's a very far cry from Humanities students dismissing or devaluing science. And it's just as far from exposure to history of science (emphatically including constructivist approaches) weakening respect for scientific research. Quite the opposite.
On the other side, I do hear history and other Humanities subjects dismissed as unimportant, or false, or made up. Very occasionally I hear this from STEM colleagues or students in STEM fields, but that is -- at least in my experience -- quite rare.
But IME it comes largely from self-appointed defenders of Science who are not themselves scientists. To an extent it comes too from some practitioners of social science (economics, for example). Perhaps in their minds this serves to shore up their own scientific pretensions; idk.
And it comes from fringe figures pushing pseudoscience, whose own credibility rests on dismissing experts in their own fields as having been somehow captured and compromised by an unscientific or antiscientific agenda -- originating in, or having consumed The Humanities.
But, in terms of the actual research and teaching that actual scholars in fields labelled STEM and fields labelled The Humanities do, the idea of a fundamental conflict (or even a civilizational war) between the two makes little sense.
It would be closer to the mark, I think, to say that these loose labels can at best make handy weapons for those pursuing agendas outside the world of research and teaching.
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