Thank you for the latest of a long list of footnotes on Plato. I am reminded of Gregory Bateson's definition of "explanation"--the mapping of experience onto a tautology. And all mathematics is tautological. For example, 2+2=4, but only if you first (arbitrarily) define the two "things" you are counting as discrete integers. If an aspect of experience does not map onto the concept of discrete integers, then other possibilities arise:

-- 2+2 = 1 (if merging "clouds" are what you are counting)

--1+1 = anywhere from 3 to 15 (or more) if "human beings of opposite sexes" are what you are counting)

--1/1 = 2 (if "chalk" is what you are counting.)

And so forth. If the experiential element does not have the properties implied by the tautology, then the math is useless.