Michael Blasco
As I keep repeating, but not all the time because it gets a bit boring, I keep repeating that we represent the underlying low-level real-world system with mathematical symbols; and so I, and others, call the real-world system a mathematical system.
But we call the real-world system a mathematical system because we symbolically represent the underlying low-level world in terms of categories, relationships/ equations, and numbers (and I contend that algorithmic symbols are also required).
And the term "mathematical system" is justified because physicists have measured the world in terms of categories, and the measurements have resulted in numbers, and physicists have looked at the numbers and found relationships between the categories.
Actual measured reality, and the relationships that have been found, is why we can justifiably call the real-world system a "mathematical system". The term is nothing to be scared of: it is a way of seeing and analysing the world.
The next issue is: What is a (moving) mathematical system?
And it is clear that categories, relationships/ equations and numbers are not sufficient to represent a moving mathematical system. For a start, as physicists have pointed out: “There’s nothing deader than an equation”; “equations can’t fly”, https://ncatlab.org/nlab/show/John+Wheeler .
I'm saying that what is initiating and reinitiating movement in the numbers in a mathematical system is "quantum number jumps", BY matter (where matter is defined as small parts of the universe). And I'm saying that this moving mathematical system can only be symbolically represented via the use of algorithmic/ logical connective statements, plus the abovementioned equation-statements.