A question came across my mind when I was watching a documentary on physics:
"Why is the Universe describable by mathematics?"
This puzzled me every now and then until I decided to formulate my own position on this matter. This is my position in the form of a syllogistic argument:
P1: "Physicality is intrinsically quantitative"
P2: "Universe is Physical"
C1: "Universe is Intrinsically quantitative"
P1B:"Mathematics is the symbolic abstraction of quantity"
C2:"Therefore, Universe can be represented by mathematics"
There are several things that needs to be addressed here: What does it mean for something to be "intrinsically quantitative"? What does it mean for mathematics to be a "symbolic abstraction of quantity?" I can answer both questions with a fairly moderate theory on the nature of quantity.
I want to make a distinction between two kinds of quantity: Dimensional Quantity and Numerical Quantity (or Individuated Quantity). The first kind of quantity is the quantity of spatial dimensions, in other words size. There are many qualities of dimensional quantity such as first dimension, second dimension, and third dimension. There are sub-qualities that subsume under each dimensions (as well as overlap) such as height, length, width, etc. The second kind is the individuated quantity in which it is not about measurement of size but counting individual separate things.
It seems here that while I can count different individual things, these individual things also have dimensional quantity. I can count individual trees and they all have height and width. Nonetheless, individuated quantity is different in so far as it is concerned with counting individual things. While it could be reduced to dimensional quantity it does not follow that the distinction between individuated quantity and dimensional quantity collapses. I can certainly reduce the content of the sentences into the number of letters of words that make up that sentence, but the distinction between the semantical meaning of the sentence and the number of letters and words that make up the sentence is still there.
So the Universe can comprehended mathematically through dimensional quantity and individuated quantity. This does not answer the question "What does it mean for mathematics to be a symbolic abstraction of quantity?" By "symbolic abstraction of quantity" I mean that our minds has the capacity to use arbitrary symbols along with the capacity to have understanding of the principle of quantity. Any kinds of symbols would as long as they are ideas of quantity (dimensional quantity and individuation quantity) along with the patterns.
There is another interesting question: "How is individuated quantity possible?" In another possible world it is possible that the universe has only dimensional quantity in which everything is homogeneously spread out like a peanut butter as opposed to being distributed or scattered. So why the latter rather than the former?
Perhaps it is possible that the dimensional quantity of space-time has the potential or capacity to allow individuated quantity of things simply because dimensional quantity of space-time consists of abstract points like coordinates in which an individual physical thing can possibly occupy. So when all individual things do exist in space time they are distributed by each occupying different point in space-time. So it is possible that individuated quantity supervenes on dimensional quantity of space time.
That's my rough outline of my view, not the most robust argument.
