>(as opposed to other abstract objects such as patonician ideas, or more commonly gods)
Well neither of those two deal with counting... We already know (historically, empirically) that counting & manipulating 'stuff' is what works for making applicable theories. Mathematical abstraction preserves those "traits", & makes the object more general - ie more flexible. Chess for example is about counting, but it's not explicitly written in a form that allows you to drop it in a theory.
I think the important thing is the traits aren't arbitrary. They were forced on people, eg you need to learn counting if you want to keep track of your goats.
Well neither of those two deal with counting... We already know (historically, empirically) that counting & manipulating 'stuff' is what works for making applicable theories. Mathematical abstraction preserves those "traits", & makes the object more general - ie more flexible. Chess for example is about counting, but it's not explicitly written in a form that allows you to drop it in a theory.
I think the important thing is the traits aren't arbitrary. They were forced on people, eg you need to learn counting if you want to keep track of your goats.