A friend of mine who is quite an aggressive Nominalist told me the other day:
"Mathematics and numbers are arbitrary; they can accurately predict physical systems in real life only because they are consistent, but any consistent framework will do."
I'm curious as to what other examples of "consistent frameworks" he is talking about. Perhaps there are alternative definitions of addition? Of subtraction, or multiplication?
Different things you can do to numbers that have a "mapping" (isomorphic) to real-world, physical phenomenon? (Such as mathematical addition isomorphically mapping to, say, putting together two groups of apples, or differentiation of position mapping to velocity)
Are there any examples of this?
There might not be; this is somewhat of a vague question and it might end up being very stupid. But I'm interested in what other completely different frameworks of "math" might exist that are meaningful in describing/modeling physical events.