I'm having trouble following you on this. I took your mention of how "the distinction between ideal and concrete vanishes" to be talking about the same thing as I've been calling abstract and concrete, so in your scenario 2, the distinction between abstract and concrete vanishes. With that distinction gone, then "There is no concrete, just the appearance of physical law arises from mathematical axioms" seems to trivially follow, if I take that use of "concrete" there to be the usual sense that is distinct from "abstract" as used by nominalists and platonists.
For an analogy, when talking about ordinary possible worlds, not necessarily mathematical-objects-as-worlds like we are, the usual modal anti-realist takes other possible worlds to be an ontologically different kind of thing than the actual world. On their account, only the actual world is real and other possible worlds are ontologically different kind of things than that actual reality. Modal realists like David Lewis, on the other hand, say there is only one kind of thing when it comes to types of worlds: possible worlds. The actual world is just one instance of that type of thing, not different or special except inasmuch as it is the one that we are in. Other possible worlds are also actual, to the people who are in them.
I'm saying basically the same thing about concrete vs abstract as Lewis says about actual vs possible. I'm not saying it's
the same distinction, but the relationship between the two sides of each distinction is the same -- it's analogous:
- Lewis says the actual world is just a possible world like any other possible world, and there is no special ontological status of "actuality", just the relationship this possible world has to us, namely that we're in it. Actuality is indexical, so any possible world is actual to anyone who's in it, and merely possible to anyone else who is not.
- 'm saying, analogously, that the concrete universe is just an abstract object like any other abstract object, and there is no special ontological status of "concreteness", just the relationship this abstract object has to us, namely that we're part of it. Concreteness is indexical, so any abstract object is concrete to anyone who is part of it, and merely abstract to anyone who is not.
I drew a picture to help:
