You can prove everything from a contradiction, but you can't prove everything from a false premise.
Correction accepted, thanks. (Will edit original comment.)
I take it that you mean that we can derive a contradiction from the assumption of moral realism.
I'm unsure about it now. I really did confuse contradictions and false beliefs.
I'd hesitate to call either moral realism or free will logically impossible
"Free will" means something different to everyone who talks about it. Some versions I've seen are definitely logically incoherent. Others are logically possible and are merely very complex theories with zero evidence for them that are retrofitted to formalize traditional human beliefs.
"Moral realism" is weirder. It seems to claim that, in the world of all moral claims, some are true and some are false. But since there are no universally compelling arguments, we don't know - we can't know - if we ourselves are even capable of recognizing, or being convinced by, the true moral claims if we were to encounter them. So it postulates some additional property of moral facts (truth) which isn't observable by anyone, and so does no predictive work. And it necessarily has nothing to do with the moral claims that we (or any other minds) actually do believe, and the reasons we believe in them.
But since there are no universally compelling arguments, we don't know - we can't know - if we ourselves are even capable of recognizing, or being convinced by, the true moral claims if we were to encounter them.
There seems to be something wrong with the argument in this sentence. There are no universally compelling arguments in mathematics and science either, yet we are capable of recognizing truth claims in those fields.
Continuing my quest to untangle people's confusions about Eliezer's metaethics... I've started to wonder if maybe some people have the intuition that the orthogonality thesis is at odds with moral realism.
I personally have a very hard time seeing why anyone would think that, perhaps in part because of my experience in philosophy of religion. Theistic apologists would love to be able to say, "moral realism, therefore a sufficiently intelligent being would also be good." It would help patch some obvious holes in their arguments and help them respond to things like Stephen Law's Evil God Challenge. But they mostly don't even try to argue that, for whatever reason.
You did see philosophers claiming things like that back in the bad old days before Kant, which raises the question of what's changed. I suspect the reason is fairly mundane, though: before Kant (roughly), it was not only dangerous to be an atheist, it was dangerous to question that the existence of God could be proven through reason (because it would get you suspected of being an atheist). It was even dangerous to advocated philosophical views that might possibly undermine the standard arguments for the existence of God. That guaranteed that philosophers could used whatever half-baked premises they wanted in constructing arguments for the existence of God, and have little fear of being contradicted.
Besides, even if you think an all-knowing would also necessarily be perfectly good, it still seems perfectly possible to have an otherwise all-knowing being with a horrible blind spot regarding morality.
On the other hand, in the comments of a post on the orthogonality thesis, Stuart Armstrong mentions that:
This is not super-enlightening, partly because Stuart is talking about people whose views he admits he doesn't understand... but on the other hand, maybe Stuart agrees that there is some kind of conflict there, since he seems to imply that he himself rejects moral realism.
I realize I'm struggling a bit to guess what people could be thinking here, but I suspect some people are thinking it, so... anyone?