Mr. Klingman,
I am looking forward to reading your essay, I am currently far behind on my reading. Thank you for reading my essay. There is no way to tell if counting can exist without logic since my would need logic to prove (or disprove) this point. Counting without logic seems impossible, but can you prove it?
The idea that the Universe is built on "logic" or "mathematics" is the same as saying the Universe is built on the English language or images we see. You can not start with the assumption that the model is the thing itself. The model must be outside the system to prove the system. We might never be able to prove the Universe, but a useful model is a wonderful thing. You cannot map a forest while chained to one tree in that forest.
All the Best,
Jeff