Predicts something that could happen in reality (e.g. we’re not rejecting math with 2+2=4 apples just because I only have 3 apples in my kitchen), or
Is an abstraction of other mathematical ideas.
Do you claim that (2) is no longer modeling something in reality? It is arguably still predicting things about reality once you unpack all the layers of abstraction—hopefully at least it has consequences relevant to math that does model something.
Or do you think that I’ve missed a category in my description of math?
It is arguably still predicting things about reality once you unpack all the layers of abstraction
I don’t see what abstraction has to do with it. The Standard Model has about 18 parameters. Vary those, and it will mispredict. I don’t think all the infinity of incorrect variations of the SM are more abstract.
I’d say that math either
Predicts something that could happen in reality (e.g. we’re not rejecting math with 2+2=4 apples just because I only have 3 apples in my kitchen), or
Is an abstraction of other mathematical ideas.
Do you claim that (2) is no longer modeling something in reality? It is arguably still predicting things about reality once you unpack all the layers of abstraction—hopefully at least it has consequences relevant to math that does model something.
Or do you think that I’ve missed a category in my description of math?
I don’t see what abstraction has to do with it. The Standard Model has about 18 parameters. Vary those, and it will mispredict. I don’t think all the infinity of incorrect variations of the SM are more abstract.