How would you model an abstract quality to the brain? What causes you to associate one with the other?
Our brains have evolved to assess sensory input and interpret the world external to the self so as best to survive and breed, the imperatives of evolution.
If you've ever watched an infant in the arms of his or her carer, you'll notice how the infant will look both at the face of the carer, and also where the carer points; and how, also instinctively, when the carer names the thing pointed to, the infant will repeat the name. Car. Plane. Daddy. Mommy. And how the infant will have no trouble with moving from category to example and back, the difference between 'a dog' and 'this dog', 'a car' and 'this car' &c.
Each of these categories exists as sets of abstractions in the brains both of carer and of infant. Some abstraction have real counterparts ─ Daddy ─ and some will be generalizations ─ (a) car ─ so that eg there's only one Daddy and only one "our car" but lots of adult males and lots of cars.
Thus the category 'car' doesn't exist anywhere but in a brain, whereas the item 'our car' is (at least in this example) real, has objective existence.
The question is does physics operate mathematically and why do they work so well together?
I don't know, but my ignorance doesn't bring Platoland into existence for me, or, I'd argue, for anyone else ─ I'd say Platoland was just as much a human abstraction as the elements and procedures of maths are. It may simply be that certain basics are constant or regular in nature, hence are describable in maths terms.
Is math merely a system designed to mimic what happens in the real world? Why are math discoveries preceding physics discoveries?
George Ifrah in his
Universal History of Numbers vol 1 suggests that the need for counting was more acute in some primitive situations than others, hence the shepherd would count his sheep (&c) out by transferring one pebble into a bag per passing sheep, and take one pebble out on their return, so that surplus pebbles represented sheep; or might notch a stick for each sheep out and run his thumbnail down the notches on their return; or &c. These systems are still found in various places, as I understand it. When it came to counting-systems, base 10 is from fingers, base 20 (Mayans, Aztecs, Celts, Basques) from fingers and toes. It's unclear (he says) why the Babylonians chose base 60. (I remember at school its divisibility was suggested. 2, 3, 5 give base 30; maybe they originally thought in semicircles.)
Yet we have an inner qualitative life that we can introspect on. How does that life map to the brain? Just the mere act of introspection itself with the ability to examine feelings, and to relate thoughts and memories within.
What about the fact of selves and self identity?
All of these are brain-states or brain processes, some very complex. Our understanding of how the brain works is itself a very large work in progress, of course.
If I were arguing for dualism, I'd be examining the reports of the researchers with great care, because I'd know there HAD to be a part of the brain where events with no physical cause were happening ─ the transferring of immaterial information into the material brain. (Though of course the absence of, or at least the failure to detect, such phenomena isn't the only problem dualism has.)
