The PARTICULAR language you use to model reality, like the math you use, actually MODEL a reality that exists prior to your bias to experience and communicate those experiences to others. The language is what you are treating is the reference to the reality when it is only modeling the reality in the only way we are able to relay it in common between other people. That is, we ARBITRARILY select symbols, like the words and languages we use ONLY to communicate the reality we share in common. But the reality we subjectively experience is, in essence, unable to be shared in any sincerely "objective" way. So we are FORCED to use a set of symbols that we agree to only for the means of relaying back and forth agreement.Hobbes' Choice wrote:
Not sure what the problem here is.
We all of us had a rich experience of the world before we learned any maths, and we live most of our lives without daily reference to it.
Numbers are conceptual. Cups and apples exist without them. Does a cup need to know how many other cups in the cupboard before it can exist?
If no one had ever invented maths to count ONE world, would the world still have existed? Maths is a descriptive language.
The particular symbols we use for numbers and its relationships are still REFERRING to something 'real', even though the symbols are themselves NOT the actual things themselves. But this holds true for ANY reality we symbolize using language between each other. That is, just because you SEE something, while YOU can interpret it as 'real', communicating this to anyone or anything beyond yourself is still BEGGING, without any difference, that the words you use to reference and convey that experience to others is real as well.
So if you treat numbers as not real, nor is anything you can say is real, because all words, spoken or written, are themselves just SYMBOLS.
Now given ALL symbols to reference things, even if we may consider all unreal, Numbers are the MOST GENERAL inference we can be MOST CERTAIN of that is common between each and every person or thing.
Yet, unless you are a solipsist, all things you experience are symbols about the objective world to which you have no other choice but to infer are 'real'. So numbers are FROM the outside world, not simply something magically derived in and of you personally. The semantic meaning of some reality, such as, that "a coin has two sides", require that "twoness" is a property of the objective world, not your solipsistic invention. Thus numbers (the referents of the meaning, not the symbols) have a reality that we "DISCOVER".
I think the confusion DOES lie with confusing the difference between our "INVENTION" of the symbols that we use and to the referents of what those symbols denote by "DISCOVERY" in the real world. They are thus both true.