That seems to me more like an irreducible string of methods of interpretation. You have physics, whether you like it or not. If you want to understand the physics, you need math. And to use the math, you need logic. Physics itself does not require math or logic. We do, if we want to do anything useful with it. So it's not so much "reducible" as it is "interpretable"--physics is such that turning it into a bunch of numbers and wacky symbols actually makes it more understandable. But to draw from your example, you can't have a physical table with physically infinite apples sitting on it. Yet you can do math with infinities, but all the math in the world won't put more apples on that table.

...and since when is two apples sitting next to each other a pile??