Actually, I guess it could be a bit less clear if you’re not already used to thinking of all math as being about theorems derived from axioms which are premise-conclusion links
But that’s not all that math is. Suppose we eventually prove that P!=NP. How did we pick the axioms that we used to prove it? (And suppose we pick the wrong axioms. Would that change the fact that P!=NP?) Why are we pretty sure today that P!=NP without having a chain of premise-conclusion links? These are all parts of math; they’re just parts of math that we don’t understand.
ETA: To put it another way, if you ask someone who is working on the P!=NP question, he is not going to answer that he is trying to determine whether a specific set of axioms proves or disproves P!=NP. He’s going to answer that he’s trying to determine whether P!=NP. If those axioms don’t work out, he’ll just pick another set. There is a sense that the problem is about something that is not identified by any specific set of axioms that he happens to hold in his brain, that any set of axioms he does pick is just a map to a territory that’s “out there”. But according to your meta-ethics, there is no “out there” for morality. So why does it deserve to be called realism?
ETA2: Perhaps more to the point, do you agree that there is a coherent meta-ethical position that does deserve to be called moral realism, which asserts that moral and meta-moral computations are about something outside of individual humans or humanity as a whole (even if we’re not sure how that works)?
But that’s not all that math is. Suppose we eventually prove that P!=NP. How did we pick the axioms that we used to prove it? (And suppose we pick the wrong axioms. Would that change the fact that P!=NP?) Why are we pretty sure today that P!=NP without having a chain of premise-conclusion links? These are all parts of math; they’re just parts of math that we don’t understand.
ETA: To put it another way, if you ask someone who is working on the P!=NP question, he is not going to answer that he is trying to determine whether a specific set of axioms proves or disproves P!=NP. He’s going to answer that he’s trying to determine whether P!=NP. If those axioms don’t work out, he’ll just pick another set. There is a sense that the problem is about something that is not identified by any specific set of axioms that he happens to hold in his brain, that any set of axioms he does pick is just a map to a territory that’s “out there”. But according to your meta-ethics, there is no “out there” for morality. So why does it deserve to be called realism?
ETA2: Perhaps more to the point, do you agree that there is a coherent meta-ethical position that does deserve to be called moral realism, which asserts that moral and meta-moral computations are about something outside of individual humans or humanity as a whole (even if we’re not sure how that works)?