First, I would like to restrict this discussion to duties or responsibilities, as opposed to good or bad states of affairs, for it seems plausible to me that states of affairs may be good or bad even if no one has a duty to bring them about or prevent their occurrence. For the purposes of this post, then, I will understand moral realism as the thesis that people really do have duties to each other.
Consider the following principle:
(1) Necessarily, if someone has a duty to do something, it is possible for them to find out or discover that they have a duty to do it.
(I say ‘find out or discover’ instead of ‘know’ to rule out externalist analyses of knowledge. This is because I think one can know one has a duty in an externalist sense even if one is unable to “tell from the inside” whether one has it. In my view this sort of knowledge of one’s duties is as good as none, for one cannot act on the basis of it.)
I think (1) is highly plausible. To see why I think so, consider what things would be like if (1) were false: If (1) were false, it would be possible for you to have a duty to do something and nevertheless not have even the slightest suspicion that this was so. And if, furthermore, you did not fulfill that duty, you would be morally responsible for violating it. Of course you would be completely ignorant of this—and so would everyone else, otherwise it would be possible for them to show you that you were in fact responsible (assuming the same evidence is available to all). No matter what you or anyone else did, you could never come any closer to discovering your duties than making a lucky guess.
I find this result intolerable, and I suspect many would agree. If the intuition supporting my view is correct, one’s duties must, in principle, be discoverable by one. From this it follows that moral skepticism—the idea that one could have duties that one could not discover one had—is incoherent; there cannot be any such thing as an undiscoverable duty. The only available options, then, are a form of moral verificationism and a form of moral nihilism: Either one has duties which are such that it is possible for one to find out that one has them, or one has no duties at all. So moral realism, understood as the thesis that people really do have duties to each other, entails that moral verificationism is true.