> "mathematical objects directly" do not exist in the real world
Well, there's an influential minority that thinks mathematical objects are all that exists (Tegmark multiverse). I don't necessarily agree with them, but that's one way to rigorously define the domain for a utility function, in a way that is not obviously exploitable. Another way is to define utility in terms of an agent's perceptions, but that is exploitable by wireheading, and IMO that flaw is unfixable as the agent gets more powerful. I'm not aware of any other approaches that are different in principle from those two, so I'll stick with the lesser evil for now, and hope that someone comes up with a better idea.
And I'm very skeptical that mathematical Platonism is useful for AI: "mathematical objects directly" do not exist in the real world, and it is very much real-world things on which we want our software to operate. "Conceptual abstraction" simply refers to a learning algorithm that possesses a representation of, for instance, a chair, that is not composed entirely of a concrete feature-set (visual edges, orientations, and colors) and can thus be deployed to generatively model chairs in general.
Computational cognitive science is working towards this sort of thing, and the results should start to hit the machine-learning community fairly soon.