We usually assume that the folk are objectivists about ethics, i.e. that they think that a question such as "Is incest (of a certain kind) morally wrong?" has a determinate and more-or-less factual answer ... in much the same way as a question like "Does 2 + 2 sum to 4?" or "How high is the Empire State Building?" The latter question might be ambiguous in certain ways, of course, but assuming we can specify more precisely what is meant, such as the height from street level on a particular side to the top of the tower, or whatever else we need to avoid any ambiguity, there is an answer that is independent of our tastes, desires, or anything else about us that we tend to think might legitimately vary. (I'll set aside any possible ambiguities in the arithmetical question.)
Conversely, answers to questions such as "Was Cleopatra beautiful?" or "Which taste nicer, cashews or maccadamias?" or "What is the best way to understand Hamlet?" seem rather different. Even if all human beings could agree that Cleopatra was beautiful (if we could reconstruct an accurate and precise image of what we looked like), there could be plenty of other intelligent beings in the universe that quite legitimately don't agree, even if they have similar senses to ours. And the likelihood is that even human beings could disagree about it quite reasonably. There is not an answer that is governed by facts that are independent of our standards of beauty, and there is nothing about reality that compels all rational beings to adopt the same standards on pain of being simply wrong.
Clearly, many questions do not have objectively correct answers. There are facts in the vicinity, but these facts will include the fact that someone with such and such standards of beauty will see Cleopatra as beautiful and someone with different standards will not. Even if human standards of beauty are genetically encoded to some extent, that does not make them objective in the sense under discussion, as there could be other rational beings that do not have the same genetic coding.
If the folk believe that there are objective answers to moral questions - moral facts that are somehow Out There to be discovered, and inescapably binding on all rational beings - then they are very likely wrong. It is difficult to see what these answers could be.
One can, of course, attempt to make morality objective by definition, such as by defining "is morally wrong" to mean "fails to maximise overall happiness". But that is hopeless. If that is all "is morally wrong" means, then there is a further question as to whether I should refrain from performing acts that are "morally wrong". Perhaps, for example, there are acts that fail to maximise overall happiness but are effective in saving my loved ones from danger; surely it makes perfectly good sense sense to ask whether I should perform the latter acts or not.
Similarly, someone can,in a moment of desperation, define "A should do X" to mean "of the acts available to A, X is the one that will produce most overall happiness." But if we start defining "should" in that way we are now stuck with someone being able to say "I should, by your definition of 'should', do X, but is it really what I ought to do?"
We can then redefine "ought"! But this still won't solve the problem. Our interlocutor will need to use new terminology, but it still remains open to her to convey that she is not going to do X, even though she "ought" to do so by a stipulated definition of "ought" and she can feel comfortable that she is not breaching any standard that binds her inescapably.
The lesson is that we can go on redefining "good", "should", "ought", or any other words we like, and it accomplishes nothing. These words have something extra that won't be captured by such definitions, the something extra being this component of a standard that is binding on the agent concerned. The person who wants to try to solve the problem can go on forever defining more and more words and expressions, but she will never be able to show that some standard of conduct is binding on me in a way similar to the way an empirical fact is binding on me (the Empire State Building just is a certain number of feet high, and there's nothing I can do to change it short of physically altering the building).
(Of course, a standard of conduct might be applied to me by others, such as the police. There are social facts about what standards of conduct people actually do apply to each other. I might not be able to escape the fact that the police apply a standard of a certain kind to my conduct. But what if I am in a position to escape detection by them? Am I still somehow inescapably bound to act in accordance with the standard on pain of being just mistaken, as if I think the Empire State Building is 2100 feet tall? Surely not!)
In the past, I've defended moral error theory: the idea that (1) moral judgments such as "Incest (of a certain kind) is morally wrong" are understood in our ordinary language to make objective claims, essentially because that's how the folk use words in their thought and speech ... but (2) there are no objective truths here. Taken literally, "Incest (of a certain kind) is morally wrong" might mean something like "Incest (of a certain kind) is forbidden by a standard that is inescapably binding on all rational creatures." In that case, such a claim will always end up being literally false. There are no such standards.
It's as if someone said: "Cashews are tastier than maccadamias by a standard that all rational creatures must accept" and hence that anyone who prefers maccadamias is objectively mistaken about the world.
In more recent times, though, I've come to think that error theory needs some extra work. In its usual formulations it may not be the whole story.
In particular, I've come to think that there is at least some merit in sophisticated relativist theories. Sophisticated relativists agree with error theorists that there are no objective moral truths in the sense that I've been attempting to describe, but they say that this does not render first-order thin moral claims simply false. These theories vary, but one way a sophsticated relativist theory might work is if it takes a claim such as "Incest (of a certain kind) is morally wrong" to mean "Incest (of a certain kind) is forbidden by a standard of conduct that is shared, or in question, in the context of our conversation." Other sophisticated relativists might try different tacks, but the overall approach is to offer a translation that could well be true. Spoken in a particular context, "Incest (of a certain kind) is morally wrong" might well be a true, if it conveys that incest of the kind in question is forbidden by a standard that the speaker and listener(s) share.
It seems that error theorists, at least as I'm characterising them, might disagree with sophisticated relativists, at least as I'm characterising them, only on an empirical matter: what do the folk actually have in mind when they make first-order thin moral judgments? What do the folk mean? Sounds simple enough, doesn't it? The problem, I think, is that the folk may be quite confused and inconsistent when it comes to points like this. Perhaps they don't really know what they mean, if asked to choose between the meaning given to moral language by an error theorist or by various kinds of sophisticated relativists.
Time for some empirical research, don't you think? We can maybe survey the folk about what they think they're saying. Maybe that will nail down which metaethical position is best, yes?
Alas, it might not be so simple. But that's a subject for another post.