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 what he's doing, 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?
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)?
Properly no they are not part of math, they are part of Computer Science, i.e. a description of how computations actually happen in the real world.
That is the missing piece that determines what axioms to use.
On Wei_Dai's complexity of values post, Toby Ord writes:
The kind of moral realist positions that apply Occam's razor to moral beliefs are a lot more extreme than most philosophers in the cited survey would sign up to, methinks. One such position that I used to have some degree of belief in is:
Strong Moral Realism: All (or perhaps just almost all) beings, human, alien or AI, when given sufficient computing power and the ability to learn science and get an accurate map-territory morphism, will agree on what physical state the universe ought to be transformed into, and therefore they will assist you in transforming it into this state.
But most modern philosophers who call themselves "realists" don't mean anything nearly this strong. They mean that that there are moral "facts", for varying definitions of "fact" that typically fade away into meaninglessness on closer examination, and actually make the same empirical predictions as antirealism.
Suppose you take up Eliezer's "realist" position. Arrangements of spacetime, matter and energy can be "good" in the sense that Eliezer has a "long-list" style definition of goodness up his sleeve, one that decides even contested object-level moral questions like whether abortion should be allowed or not, and then tests any arrangement of spacetime, matter and energy and notes to what extent it fits the criteria in Eliezer's long list, and then decrees goodness or not (possibly with a scalar rather than binary value).
This kind of "moral realism" behaves, to all extents and purposes, like antirealism.
I might compare the situation to Eliezer's blegg post: it may be that moral philosophers have a mental category for "fact" that seems to be allowed to have a value even once all of the empirically grounded surrounding concepts have been fixed. These might be concepts such as "would aliens also think this thing?", "Can it be discovered by an independent agent who hasn't communicated with you?", "Do we apply Occam's razor?", etc.
Moral beliefs might work better when they have a Grand Badge Of Authority attached to them. Once all the empirically falsifiable candidates for the Grand Badge Of Authority have been falsified, the only one left is the ungrounded category marker itself, and some people like to stick this on their object level morals and call themselves "realists".
Personally, I prefer to call a spade a spade, but I don't want to get into an argument about the value of an ungrounded category marker. Suffice it to say that for any practical matter, the only parts of the map we should argue about are parts that map-onto a part of the territory.