Dear Marni Dee Sheppeard,
Since MacLane and Birkhoff I have avoided the square logic map diagrams, but I nevertheless managed to find quite interesting remarks in your essay.
Your abstract states "all we can really do is count." I begin my essay (and other essays) based on counting as the prototypical logic machine, constructed from NOTs and AND 'gates' which are ubiquitous in physical reality and manifest at all levels, RNA/DNA/proteins to telomeres, to insects, crows, neurons, silicon, etc. It is also the case that the key quantum field theory operator is the Number operator, or counter. So, with Kronecker, counting seems to be the sufficient basis for "all the rest" of math.
You note of the Standard Model, which is poorly understood, that enormous effort went into maintaining locality, while quantum physics would abandon it. My essay offers a novel analysis of this problem, which a recent comment on my thread describes as having a "self-concealing nature", thus making it extremely hard for physicists to see the error in logic. It is not a mathematical error, but a mapping error.
I do not believe classical physics requires distinguishability of particles as you seem to suggest, although, as you further suggest "for truly non-separable concept of existence, we must reinterpret the continuum of C."
I'm sure I've missed some of the more subtle issues of your essay, but I hope you will read my essay and try to understand the subtlety within it.
Best regards,
Edwin Eugene Klingman