Our model is talking about some aspect of an observer independent reality; that is, the mathematical structure of the theory refers to or represents something that there is in the world independently of our mathematical theories.
The "stuff" that exists in reality, independent of our models, is EXPERIENCE. The representational models we make are NOT models of an observer-independent reality; they are models that parse, consolidate, and systematize human experience. It is, of course, very important for me to concede that the productive modeling of experience, which is the basis of Reason and is exemplified by science, only works because experience demonstrates tremendous CONSISTENCY.
But I simply and categorically refuse to assign any
a priori fundament to explain the existence of this consistency. I consider the presupposition of observer-independent reality to be -- at best -- irrelevant (and at worst, inimical) to the exercise of reason and science. It is sufficient and responsible to acknowledge that consistency of experience
happens and is the basis for all epistemological construction.
Naturally I wonder
why experience is consistent, but since I am a holist, I consider the idea of a reality independent from humans to be a contradiction in terms. Nothing is independent of anything except in the cognitive schemata of sentience that has reached a state of complexity sufficient to yield self-reflection and a sense of spatio-temporal extension, allowing for delineation, disambiguation, and identification. Since cognitive schemata circumscribe all attempts to explore the basis for consistency, I accept that humans are not equipped to "step outside" of reality in order to objectify it (mystical experience notwithstanding; but that's not for the science forum).
Even if I did feel disposed to grant an independent existence to reality, with not a sentient mind in the universe to consider it, such a reality offers no insight or solution to the issue of reality's ontological status. It just adds another layer to the issue.
There are physicists like Tegmark who do subscribe to that Platonic, 'mathematical universe' picture but I think they are confusing the map for the territory.
I have no regard for Platonism, so if Tegmark believes in the Platonic existence of numbers and numeric operators then I feel he is wrong, same as you.
And one surely can be a realist and have no difficulty with the idea of spacetime as emerging from some non-spatiotemporal structure (e.g. non-locality), that we may not be able to presently or perhaps ever conceptualize. As Gisin points out:
It might be interesting to remember that no physicist before the advent of relativity interpreted the instantaneous action at a distance of Newton’s gravity as a sign of non-realism (although Newton’s nonlocality is even more radical than quantum nonlocality, as it allowed instantaneous signaling).
It sounds like Gisin makes the same mistake as Maudlin (whom you cited earlier) in thinking that non-realism implies non-existence. It doesn't. Non-realism implies that existence (i.e., ontological status) is outside of science's purview, on science's own terms.
Personally, I feel science should always continue forever to look for cause-and-effect, reductionistic modeling to explicate new phenomena because these are paradigms with excellent track records for utility. But it is a mistake to give up testability just so we can continue to confine ourselves to such models. If Bohm models a non-spatiotemporal quantum potential or full-blown "Implicate Order" we must have testability, otherwise such models just stand in the way of scientific progress by insulating science from that which science is not yet prepared to explain. I hate to say it, but that is exactly what dogma does.