Categories, numbers, logic, grammar, etc. all map onto physical systems, but aren't necessarily directly linked. This is "metaphysics" in philosophy, and is essential in order to even reason about physical systems. Just the concept of a "physical system" is actually metaphysical, but without metaphysics, you can say nothing to anyone about anything. Metaphysics is just generally taken as a "given", but is worth evaluating itself.

Then you'll run into the "realism" vs. "nominalism" debate and you'll understand the philosophical underpinnings of the current culture wars in America.