If so, does it have a name? I'm especially interested in search terms that I can use for further reading.
In physics, we're familiar with the distinction between "relations of ideas" and "matters of fact." It's especially useful to be clear about what derives from premises and what has been established experimentally, as we usually work in both directions to meet in the middle.
But some arguments seem to straddle both categories and others seem to be neither. For the first type, consider a scientific model, like the Standard Model of particle physics. It is a mathematical model—the first questions we should ask of it is whether it is logically valid. But it is also built to represent facts—the next questions we should ask is whether it agrees with measurements. No one believes the Standard Model as a fact about the world: we expect it to be replaced by successively better matches to empirical fact. A scientific model seems to be a composite thing, judged by the methods of both categories.
But beyond the criteria of logical consistency and agreement with experiment, we also apply criteria that are neither of the above. For lack of better words, these are called "beauty" and "simplicity." Despite the consistency and accuracy of the Standard Model, we distrust it because it has more ad-hoc parameters than we'd expect nature to have.
I can be clearer with an older (more established) example: Ptomley's solar system model of circular orbits with circular epicycles is logically consistent and can be made an arbitrarily good fit by adding epicycles upon epicycles. Kepler's solar system model of elliptical orbits reaches the same precision with fewer parameters. The argument that picks between them doesn't rely on an a priori proof (first prong) or agreement with experiment (second prong) because they both pass both tests. The argument comes from somewhere else. Some people say, "simplicity," but I would call it something more like "insight." Kepler's model makes it easier to discover Newton's, because Newton's gravitation can directly explain ellipses, but has nothing to say about an infinite sequence of epicycles (unless that sequence happens to converge to an ellipse).
"Relations of ideas" and "matters of fact" have different methods for determining truth—mathematical proof and experiments. This "beauty," "simplicity," or "insight" seems to be neither of the above, but it's also not sophistry or nonsense. It seems to belong to a third category that I don't know the name of.
My question is: what's the name of the thing that I'm taking about? Even if Hume didn't discuss it, what's the modern name so I can read up about it?