Is there a thing called absolute morality? Or is it all subjective? Or do they coexist?
This is a complex topic that deserves a complex answer; but I should be clear that though I'm an atheist, I'm not speaking for atheism (as there are many moral realists that are atheists, and I'm about to argue against it).
I'm a moral noncognitivist. I don't think there are moral propositions (that moral statements have truth values). I don't think that makes any sense because I use Correspondence Theory of truth. For a statement to be propositional (to have a truth value), it has to be able to correspond in some way to reality. I don't think we cognize anything if we attempt to find content in moral statements that corresponds to reality, because at the end of the day, the content of moral statements are "ought" statements.
I don't know what it means to say that an ought corresponds to reality, and I don't think anybody else really does either. Moral statements seem to behave more like preferences to me. Consider the following statements:
1) Mushrooms are the best pizza topping.
2) Erin thinks mushrooms are the best pizza topping.
3) One ought not to punch babies.
4) Erin thinks one ought not to punch babies.
Which of these statements are propositional, and why?
I think we will easily all agree that (1) is not propositional: there's no truth content to a preference statement, right? Nothing about "being the best" corresponds to reality if "being the best" is just a vague preferential attitude.
However, I think I can convince folks that (2) is propositional. (2) has a truth value because the statement is really just saying that its content (Erin) has a particular property (she likes mushrooms on pizza), and this is either true or false in reality. This
corresponds to reality.
So, (3) is a typical moral statement, so moral realists would say that (3) is propositional. But I don't see it: what about (3) corresponds to reality? If you ask me, (3) looks like it behaves an awful lot like (1) does. The content doesn't seem to produce a cognitive picture in my mind of a correspondence: what does it mean for an ought to exist in mind-external reality?
Moving on to (4), I think I can again convince folks that we have a proposition again. Much like with (2), here it's really just being said that "Erin has a particular property," and that property is "having the belief that one shouldn't punch babies."
So Erin does have a moral belief, but said moral belief isn't propositional (even if a proposition can be made
about it); it's not absolute. It's not
exactly a preference, but it
behaves like a preference philosophically.
I think the onus is on moral realists to either demonstrate a better theory of truth than Correspondence Theory, and/or to demonstrate how an "ought" translates to an "is" in a cognitive way.
Moving on to another point: even if we can't form naked moral propositions (if my non-cognitivism is correct), we can still form objective propositions with moral properties using hypothetical imperatives (if/then statements). For instance, this is a proposition with a truth value: "If I value people not being hungry, then I should help feed the homeless." People in reality can have the property of being hungry, and I can have the property of valuing their wellbeing. If that is the case, then it follows that I should help.
The reason these hypothetical imperatives never get us to naked moral propositions or to moral realism is because we will never be able to explain the "if" portion: it's true that "if Erin values preventing suffering, then Erin should not punch babies," but why ought Erin value preventing suffering? There will never be an answer to that (at least until the moral realists make their case).
So, I think that doxastic voluntarism is false when it comes to values (we do not consciously choose them, I can't just will myself to have different values than I do; and I didn't choose my values consciously in the first place. It has been some combination of nature and nurture that gave me my values). We just happen to value the things that we value, and don't value the things that we don't. We build our moral beliefs on these values using hypothetical imperatives. I value life, so I don't cause death. I value altruism, so I don't behave maliciously selfishly. I can't just will myself to change these values, so all these old canards about "well if moral realism is false, then people would just behave like animalistic hedonists" is false.
I think this is what everybody does, even moral realists, who are simply wrong in their beliefs that moral realism is cognitive.
Edit: On a re-read, I wanted to be more clear by what I mean by a "naked moral proposition." That would be a supposed moral statement that is propositional without needing a hypothetical imperative to be propositional.