Moral realists think that there are mind-independent facts of the matter that ground the truth-values of claims like "killing small children for sport is wrong" and "playing Wii Golf is wrong." Whether one is the more austere kind of minimalist about truth or the most extreme, early-Wittgenstein-style correspondence theorist, or anything in between, if one is a moral realist, one will--at least on the most basic level of description--tell pretty much the same story about why "killing small children for sport is wrong" is true and "playing Wii Golf is wrong" is false. In each case, the type of event being referred to either is the way it is being described as being (in which case it's true) or it isn't (in which case it's false). For moral error theorists, again, regardless of their precise position on truth as long as it's within the usual range, the story about how to evaluate such statements is precisely the same as for the moral realist. The only difference is that, according to the error theorist, *both* of the statements just mentioned are false, since neither type of event has the property in question. According to the error theorist, after all, *no* type of event has that property, since there is no such property as (moral) wrongness.
(An important sidenote is that people sometimes speak as if the moral error theorist had to give up on *all* evaluative language, but that's absurd. The usual J.L. Mackie-style arguments against moral properties are obviously inapplicable to other sorts of evaluative properties--e.g. ones pertaining to epistemic matters--that can be reduced to ordinary, non-"queer" properties far more easily and less problematically than *morally* evaluative terms can. Anyone who thinks that the moral error theorist is saying something false-according-to-error-theory when she says "you shouldn't be a moral realist, since there's no evidence for the existence of moral properties" hasn't thought very hard about the variety of different things that the word "should" can do in different contexts. I'm not an error theorist, but I do take it a bit more seriously than all that.)
Moral "quasi-realists" argue that this story about truth only works for one kind of truth--"descriptive truth," and that it fails for another kind of truth--"evaluative truth." (Everyone else, of course, thinks that the very idea of a "non-descriptive" form of truth is deeply confused.) When it comes to "evaluative truths", the statement is true iff it (depending on one's preferred flavor of quasi-realism) expresses the speaker's moral attitudes, or the moral attitudes the speaker would have under certain sorts of idealized circumstances, or something like that.
Now, generally speaking, quasi-realists are realistic enough about human psychology to grant that there's no particular reason to believe that, even under idealized circumstances, we'd all have precisely the same moral attitudes, and of course, no one claims that we all have the same moral attitudes right now. As such, any form of quasi-realism about morality automatically adds up to a sort of relativism--not relativism about moral properties, mind you, but relativism about truth. If you and I have different deep moral attitudes, still would under idealized circumstances, etc., it's that from my perspective, killing small children for sport is right-for-me and wrong-for-you, but that, from my perspective, my claim that it's right is true and your claim that it's wrong is false, and the opposite is true from your perspective. Although few would like to put it quite like this, the quasi-realist avoids right-for-you and wrong-for-me at the expense of embracing true-for-you and false-for-me.
Now, relativism about truth might seem like an intuitively unappealing enough consequence on its own, but relativism about logical truth would take the quasi-realist to a really awkward place. After all, a big part of any story about "idealized circumstances" is presumably that, under these circumstances, one has, for example, chosen between moral claims and their negations in every case, made sure that all of their moral claims are consistent with each other, and so on. Logical matters are a key part of how quasi-realists can still make sense of criticizing claims that (according to them) aren't in the business of trying to correctly describe anything. You might not know what someone's deep attitudes are, but surely you can know that they're saying two things that are implicitly inconsistent with each other.
Moreover, they seem to be on solid ground here. It might seem like almost nothing is universally agreed on in the philosophy of logic. (After all, it's arguably the area of philosophy where the claims in dispute are the most basic.) Are contradictions ever true? Are instances of Excluded Middle always true, or should we sometimes simultaneously reject claims are their negations? What does it mean to say that one thing follows from another? Is there One True Logic, or should we be pluralists?
In all of this chaos, however, one of the few things that nearly everyone agrees on is what we could call the Universality of Logical Truth Thesis (ULTT). Dialetheists believe that some contradictions are absolutely, perspective-independently true no less than their orthodox opponents believe that all contradictions are are absolutely, perspective-independently false. Paracomplete theorist reject the view that, say, the instances of Excluded Middle that are relevant to the Liar Paradox are true for *anyone.* Even logical pluralists--e.g. Greg Restall and JC Beall, currently the best-known advocates of logical pluralism--generally focus on questions of validity. They argue that there are a plurality of genuine, legitimate logical consequence relationships, that that each one really does delineate a class of "valid" inferences is universally true and that these claims do not contradict each other. It's simply that some logical consequence relationships are appropriate for regulating our reasoning about some areas and that others are appropriate for regulating our reasoning about other areas. The truth of these appropriateness claims themselves will, again, be universal.
Of course, most philosophers believe in what we could call the UATT--the Universality of All Truth Thesis--and wouldn't bother thinking of the ULTT as a separate matter. The ULTT is important, though, because even quasi-realists, having rejected the UATT, still have good reason to cling tight to the ULTT. In fact, the ULTT looks like it's going to be absolutely central to their project, for cashing out what "idealized circumstances" look like, for making sense of why we should criticize people for having internally inconsistent moral stances, etc.
But there's a problem.
What about people who literally don't have *any* moral attitudes, and who are psychologically constituted in such a non-standard way that they're just totally incapable of forming any attitude of that type--they're morally color-blind? Parsing the existing scientific literature on people who have deeply non-standard psychological make-ups in ways that are morally relevant--say, psychopaths--raises all kinds of complicated conceptual and empirical problems that we don't need to get into here, but surely it's at least *possible* in principle for such people to exist.
From their perspective, no matter of expressing attitudes that they do have or under any circumstances would have could possibly decide between the truth of a moral claim and the truth of its negation. It seems like, given the overall story, the most natural thing to do would be to say that, from the perspective of the morally disengaged observer listening to a moral debate, either the person who says "killing small children for sport is wrong" and the person who says "killing small children for fun isn't wrong" are both saying true things, or neither of them is saying a true thing, or perhaps there's simply no fact of the matter about whether any such statements are true. All of these options, of course, get you logically heterodox general results.
And that seems to show that quasi-realists really aren't entitled to the full ULTT. The universality of logical truth at least can break down.
And, given the ULTT's apparently centrality to the quasi-realist's project, that seems like a problem.
*Remember, on a quasi-realist story, "killing children for fun" isn't a descriptive statement--it's not even a descriptive statement about the speaker's attitudes--but an expression of those attitudes. As such, "killing children for fun is always wrong" is *also* an expression of an attitude, so (at the very least) it's not entirely clear that one can take a classical way out here and claim that all negations of positive moral claims are true (for someone totally incapable of forming attitudes of the relevant type) according to the quasi-realist, the way that all such statements are true (for everyone) according to the error theorist.