There must be an opposing critique by now about physics having all the mathematizing one could hope for and yet no clear ontology of QM. Petabytes/day at CERN, several dozen QM interpretations with math and statistics, and yet the most popular take on QM is operational, and the others are so beyond experimental capability it won’t be settled in our lifetime.
At least other domains have ontology as primary (physics used to too!)
Ontology was central to past physical theories like of Newton or Aristotle though. Why is ontology inherently philosophical? (I mean in the natural philosophy way it is sure, but I don’t think you mean just that). I don’t see biologists getting by with operational theories for a hundred years. It seems less “by design” and more like without choice. A retreat. Even GR has light cones and events as real physical objects of the theory.
> Ontology was central to past physical theories like of Newton or Aristotle though
Yes, physics has origins in philosophy. Philosophical notions that could be formulated mathematically and tested experimentally became physics, and the rest became metaphysics. And, in the 21st century, metaphysics is of zero importance to working physicists. Only a few physicists would even be able to accurately describe what "ontology" is.
> Even GR has light cones and events as real physical objects of the theory.
Events and light cones are just convenient words/phrases for mathematical definitions, e.g., an event being the 4-vector (t, x, y, z). They don't have any further philosophical significance.
It’s no coincidence the discoverer of nonlocality John Bell insisted on clear beables (ontology) of the theory. It’s not philosophy to posit what exists. Be careful because doing it your way may require future disentangling as mathematical existence and physical existence are usually quite dissimilar. Only using mathematical definitions for physical theories is bound to create future tangles. And who knows when the next Bell will come along to disentangle the operational mess.
Engineering, at least the ME and EE kind, is kind of a middle ground. Some physics/math envy in the sense that we usually have to use fudge factors to make our designs work in real life.
Of course we're too busy making stuff to spend a lot of time on envy...
"These chemicals crystallize into the same shapes, what should I call my exciting new observation? I know, I'll translate the concept into Ancient Greek, let's see. 'Isomorphism' hey? That sounds very respectable and grand - perfect!".
Both times it was like: we define it this way in this paper. I didn't get the feeling it was a general usage thing. The definitions given were plenty rigorous, it's just that there weren't any other morphisms lying around that the author needed to disambiguate between. "Equivalence" would've done just as well.
I think the humanities are important, I just think it would be a better PR move to resist the urge to style them after anything else.
I think this phenomenon detracts from important debates about what kind of mathematics is most appropriate in certain fields. I think there's certain predictable regularities to be found in different fields, but the way they might best be modeled isn't always the same, and holding up more "reduced", lower level fields as examples becomes sort of a red herring in a lot of ways. It's one thing to point out that certain types of math are inappropriately reductionistic, or cannot be applied due to inappropriate axiomatic assumptions; it's another to outline an alternative.
One of the use cases of studying math is the ability to quickly identify and fend off mathematical complications. In one example I could help a student of medicine tear down a wall of inappropriate statistical nonsense.
At least other domains have ontology as primary (physics used to too!)