It seems to be an argument in favor of arithmetic being objective that almost everyone agree that a certain a set of axioms correctly characterize what natural numbers are (even if incompletely), and from that set of axioms we can derive much (even if not all) of what we want to know about the properties of natural numbers. If arithmetic were in the same situation as morality is today, it would be much harder (i.e., more counterintuitive) to claim that (1) everyone is referring to the same thing by "arithmetic" and "natural numbers" and (2) arithmetic truths are mind-independent.
To put it another way, conditional on objective morality existing, you'd expect the situation to be closer to that of arithmetic. Conditional on it not existing, you'd expect the situation to be closer to what it actually is.
In You Provably Can't Trust Yourself, Eliezer tried to figured out why his audience didn't understand his meta-ethics sequence even after they had followed him through philosophy of language and quantum physics. Meta-ethics is my specialty, and I can't figure out what Eliezer's meta-ethical position is. And at least at this point, professionals like Robin Hanson and Toby Ord couldn't figure it out, either.
Part of the problem is that because Eliezer has gotten little value from professional philosophy, he writes about morality in a highly idiosyncratic way, using terms that would require reading hundreds of posts to understand. I might understand Eliezer's meta-ethics better if he would just cough up his positions on standard meta-ethical debates like cognitivism, motivation, the sources of normativity, moral epistemology, and so on. Nick Beckstead recently told me he thinks Eliezer's meta-ethical views are similar to those of Michael Smith, but I'm not seeing it.
If you think you can help me (and others) understand Eliezer's meta-ethical theory, please leave a comment!
Update: This comment by Richard Chappell made sense of Eliezer's meta-ethics for me.