When it comes to epistemology, I'm more of a pragmatic neo-Kantian than an empiricist. You can get a better sense of some major influences on the philosophy I work out in my writings, from the article linked below.
I wouldn't say mathematical order has no ontological reality. It's just that I'm a cosmicist about what Kant called noumena. If our concepts work, they uncover what Daniel Dennett called "real patterns," so we assume their subject matters figure into how things really are. Metaphysics is just a broad story we tell, or a model we formulate to organize our knowledge.
The difference we're having here is with our conceptions of truth. A Platonist says that math mirrors reality. On what I consider to be naturalistic, pragmatic grounds, I deny there's such perfect objectivity or semantic adequacy (links below). All our concepts simplify, and in some respects mathematical abstractions simplify the most. So Platonists mistake our ability to ignore aspects or details, for the supposed immaterial nature of reality.
It's not math that's to blame for the recent dead ends in physics, but the neo-Pythagorean reverence for "mathematical beauty" that leads physicists to mistake their speculations for testable, scientific models.
