If I understand you correctly, then I think we agree.
Like the cogito ergo sum argument, ascribing axioms to the nature they describe conflates the subjective with the objective. For example, if I write a computer program that runs a simulation which calls for an abstract object or property - for example: one electron, or one topology, or one polygon of a given dimension within the defined scale of the program - every time it renders a thing or moves a thing, and that abstraction exists as a single entry in a single instance of a library in memory, then it’s more accurate to say that part of that thing is the same part as all other instances of the same part in all other things. Now, I’m not saying this is necessarily true. It could quite well not be. But the mere fact that it can’t be disproved casts doubt on the uniqueness of things. It could well be that the very axioms of mathematics which we’ve happened as a species to analyze the universe with are in no way special to the universe, and that there are other axiomatic systems which yield equally valid descriptions.
The question I would then have is whether there is a more fundamental logic that can show different mathematical systems to be logically related. If not, we’d have to face the possibility that different axiomatic mathematical systems describing what we think of as the same natural universe might be fundamentally incompatible, which then casts doubt on our concept of a unified reality. This is in fact what I was getting at months ago in the Simulation Argument thread, that our very understanding of what a simulation is and isn’t might be hopelessly naive…that, on one hand the things we call simulations which we make simple versions of in computers and on paper, and on the other hand the thing we call base reality or physical reality or even just not an artifact, might only be two simple categories in a much larger phase space of heretofore imagined alternatives.
We might eventually have to face the possibility that being finite and limited to subjective knowledge, we can never truly know the whole elephant. But in realizing that the part we’re grasping isn’t the whole elephant, we might at least expand our tool-set(s) for understanding more of the elephant.
