So far, we've basically determined that Barth isn't a moral realist. Which, it's important to remember, isn't the same as metaphysical realism—Barth is certainly an epistemological realist, which is quite a different thing. That was, in fact, why I started with moral realism, and the whole attractiveness of the concept as far as I'm concerned. So: God is real, but Barth does not hold to any set of naturally or ideally available objects in the world to which our moral concepts might correspond. God, as our Object, is irreducibly an agentic Subject.
If Barth is not a moral realist, we're left to take the other horn, which has been creatively named "moral anti-realism." Trust me, it sounds worse than it is. Anti-realism generally has to do with disbelief in reified constructs. Disbelief that the rational is necessarily real. Like when we say that our concept of goodness has an objectively real counterpart independent of theory. It isn't necessary to believe this to have a concept of goodness. It doesn't make moral theory more or less plausible.
So, if Barth is a moral anti-realist, are we out of the woods? Not quite yet. This clearing has more woods on the other side.
"Anti-realism" depends a great deal on what someone might be a realist about. You can be a realist about science, and still be an anti-realist about the Higgs boson—which is to say, "Our methodological system (physics) works to describe the function of the world, but I don't feel bound to believe that there are actually these specific little bits of matter that do the whole "mass" thing. What's important is that the model works, and that when it doesn't, we are free to come up with better placeholders to describe the phenomena."
Now, with the new data from the LHC, it's getting harder to be an anti-realist about the Higgs, but it's even harder to be an anti-realist about something like the electron, for example—unless you're a string theorist. It is, on the other hand, entirely appropriate to be an anti-realist about disproven concepts like phlogiston and the four-element cosmos.
You might say I'm a theological anti-realist of this sort, for example. I believe in the existence of God, but I am unwilling as a theologian to put too much trust in the things we believe about God. Immutability and impassivity, for example. I don't believe these are correct, but I don't believe in the opposite of them, either. And if you look at the patristic positions on them, as opposed to trying to define the terms philosophically, you will see that the Fathers were generally anti-realists about them, too.
The point is to have a suitable set of constructs to define God's faithfulness and fidelity and trustworthiness, which involves understanding God as the kind of a thing that we can therefore trust. It isn't about the objective verifiability of our statements with respect to the external reality of God; it's about the objective reality of God. The important thing about immutability and impassivity is not that there is a being of whom these are absolutely defining characteristics. These are placeholders for a value, and their objective truth is unnecessary as long as the subjectivity that they represent is upheld. It's not a question of non-reality; it's a question of what grounds the reality.
So a moral realist is not merely someone who says, "yes, there is a real basis for morality"—a moral realist draws the conclusion that because there are real moral values, we can therefore make real, valid statements about them that can be validated by correspondence. This is what a moral anti-realist opposes. There is a real basis for morality, generally, in moral anti-realisms—but it isn't objective. And it doesn't generally issue in objectively validatable general moral propositions.
Now, I've already claimed that we can't agree with Barth and also be realists about the existence of generally valid moral propositions. Even if the ground of our ethics is a non-natural real, the material of our ethics is not propositionally available from it in any direct and permanent sense. So Barth's might be a form of moral anti-realism.
Let's go a step further in defining realism for a moment, to get some better leverage. Moral realism may also be defined as the understanding that moral values are "mind-independent." This may not be the best statement of moral realism, but it makes for a more useful definition of moral anti-realism. As such, moral anti-realism is a contention that morality is not independent of cognition, and so is dependent on or constituted by mental activity. We speak here of moral judgments, or moral evaluations, not moral values as such.
The relevance here comes in the fact that the moral judgments need not be yours for you to obey them. They may belong to your community, your family, or another individual you respect ... whether that person is human or divine. What is good, is good because it seems good, to someone. What is right, is right because it seems right with respect to the good, to someone. Here we have piety: obedience conditioned on relationships. Subjective rather than objective authority.
This is in no way a declaration that there is no moral ground; it only states that the moral ground is personal and interpersonal. There can still be moral absolutes in such a system. What a moral absolute says, in much the same way as in moral realism, is that in all circumstances X is always good, and effective action toward X is therefore always right. For the moral anti-realist, it just says this on the basis of personal and interpersonal authority, rather than the authority of an objective state of the universe. This changes the qualifications for whether it is a right or wrong statement.
If, as a moral realist, I refuse to accept a genuine moral absolute, I am wrong because my personal moral perception does not align correctly with the universe. If, as a moral anti-realist, I refuse to accept your genuine moral absolute, I may simply be subject to a different moral authority. You would have to prove me wrong Socratically, by reference to my own system, or convince me as to yours. Of course, both realism and anti-realism can just as easily include moral relativism, such that what is good and right depends upon what the circumstances are. The realist will claim that there is an objective good, and right actions with respect to it, for every situation; the anti-realist permits disagreement on what those are without one of us necessarily being wrong.
Now, that's condensed a lot into one generalization, and I have left out error theory, in which moral judgments do attempt to make objectively true statements, but cannot. Generally, any realism accepts that many of its statements will be false, but that some will be true, and these will be true because they correspond to reality. Error theory would be a form of cognitive realism subject to inevitable failure. It is an anti-realism because it takes the assertion of correspondence truth and negates the correspondence. There remains the possibility of an objective moral basis, but our moral judgments simply do not reach it. There's a lot of go-round on this one, but as a Barthian I find it uninteresting. Besides which, both error theory and forms of non-cognitive anti-realism tend to lead back to a sort of quasi-realism.
Next up: Divine command theory as an anti-realism.