Comment by zmgsabst
The structure that most words describe is objective, so you haven’t distinguished math as a language. (Nor is mathematics entirely “objective”, eg, axiom of choice.) And the number of terms in your chosen language with your chosen basis isn’t objective: that’s an intrinsic fact to your frame.
The complexity of terms is not fixed — that’s simply wrong mathematically. They’re dependent on our chosen basis. Your definition is circular, in that you’re implicitly defining “non-degenerate” as those which make your claim true.
You can’t make the whole class simplified at once, but for any state, there exists a basis in which it is simple.
This is getting tedious. The point about mathematics was simply that it carries and objectivity that natural language does not carry. But the point about natural language was always a red-herring; not sure why you introduced it.
>You can’t make the whole class simplified at once
Yes, this is literally my point. The further point is that the relative complexities of two systems will not switch orders regardless of basis, except perhaps in degenerate cases. There is no "absolute" complexity, so your other points aren't relevant.