I like to draw a distinction between real and ideal.
I insist that math is ideal. it models reality ideally.
this distinction is important because otherwise we mix together something, and the ideas and concepts (e.g. symbols and rules) we use to describe and model said something.
the game is not real. people playing the game are real, the game getting played is real. the game on its own as may be described in symbols is ideal.
i suppose what it all is all about is the intersection between this reality and this ideality.
You can say that a certain axiom system models a certain part of reality in an ideal way. But whatever is ideal, is also real, because otherwise there is nothing that could model anything. So your intersection of reality and ideality is just ideality itself.
I insist that math is ideal. it models reality ideally.
this distinction is important because otherwise we mix together something, and the ideas and concepts (e.g. symbols and rules) we use to describe and model said something.
the game is not real. people playing the game are real, the game getting played is real. the game on its own as may be described in symbols is ideal.
i suppose what it all is all about is the intersection between this reality and this ideality.