“Whole numbers are abstractions”
But where do these abstractions exist? Whole numbers, rational and irrational numbers, mathematics, and all the associated symbols, only exist from the point of view of the human imagination. This is not to deny the “power of mathematics”, where mathematical symbols can be used to represent the real-world numbers and the real-world relationships that physics has obtained and deduced from experiments (despite some degree of error in the numbers).
Re the counting numbers: the number of planets in the solar system is not an actual real-world property (“what is common to”) of a collection of planets, a property that actually exists “out there” in the world. The number of planets in the solar system is something that only exists from the point of view of the human imagination. When analysed, counting is a many-step process, performed by people and some other living things, which also involves: 1) the ability of the counter to define the category being counted (e.g. first, define a planet); and 2) the ability of the counter to identify the category being counted (e.g. second, does a particular celestial object fit the agreed-upon definition? Is Pluto a planet?).
But, as opposed to what exists in the human imagination, there are numbers that actually exist in the real physical world “out there”. When particular categories of the real physical world are measured, e.g. relative position or mass, one gets a number, and this number is represented via the use of a number symbol. So real physical world numbers exist “out there” as opposed to the numbers that only exist in the human imagination.
“The power of mathematics comes from this ability to abstract”,
i.e. the power of mathematics comes from: 1) the human ability to invent and comprehend symbols; and 2) the human ability to represent the real physical world, and even imaginary concepts, with symbols. So, I guess that I agree with you about symbols.