Suppose for instance the answer to this question is "nothing." Unless one is an adherent of moral nihilism (which says there is nothing morally wrong) this encounters problems. If there is literally nothing that says how we ought to behave, then there is also nothing that says Hitler ought to have behaved differently when he decided to slaughter millions of Jews.

So we're back to the question at hand for the atheist. If God does not exist and moral principles are binding independently of whether we believe them to be so, who or what says how we ought to behave?

Interestingly enough, it seems almost self-evident to both the theist and the atheistic moral objectivist that objective morality is a fundamental part of reality. In the case of classical theism, God is the fundamental reality from which all existence and moral truths originate. Atheism faces a bit of a challenge however. Since moral statements are not analytic (true by definition, e.g. "hairless men have no hair"), it's more difficult for atheism to explain why morality exists so fundamentally, because in that case what would be morality's metaphysical basis? Let X be the basis of objective morality. X does not seem to be confined to any particular time or location. If we cut out any tiny space-time segment of the universe and destroyed the rest, morality would still exist in that segment.

What about humans? One interesting idea is that it is the existence of humans that somehow causes moral truths to exist, and if we took away humans moral truths would not exist. Upon closer examination however this does not appear to be the case. Take for instance the necessarily true statement "all bachelors are unmarried." This claim would hold true even if there were no bachelors, because what the statement is essentially saying is, "If there was one or more bachelors, any such bachelor would be unmarried." Similarly, the moral statement "It is morally wrong for a man to torture an infant just for fun" essentially means "If there was a man and an infant, the man should not torture the infant just for fun." Would this if-statement hold true in a universe without humans? It would appear so, because if we started with a universe without humans and the if-statement wasn't true, then even if we inserted a man and an infant into this previously uninhabited universe the statement "the man should not torture the infant just for fun" would not be true. This would mean "It is morally wrong for a man to torture an infant just for fun" is true without humans in the same way that "all bachelors are unmarried" is true without bachelors. But if that is the case, then the basis of objective moral truths cannot be the existence of humans.

The basis of morality would have a number of other interesting characteristics as well. Whoever or whatever it is that says how we ought to behave, this X must possess the following attributes.

Supremely transcendent authority. It is one thing to merely say what people should do, but X (the basis of objective morality) must be authoritative in that people really ought to obey it. Suppose for instance a Nazi commands a subordinate to kill Jews. Is it the case that the subordinate ought to obey the Nazi? No, the subordinate ought to obey the dictates of morality instead, because the dictates of objective morality ought to be obeyed over the orders of any human. The basis of morality must transcend the authority of other people's behavioral commands if its ought-statements are to be objectively truthful. This would include, for instance, transcending the authority of dictators who would order torture and genocide. Otherwise people ought to obey the dictator instead of morality. So the basis of objective morality not only says how we ought to behave but also does so with supremely transcendent authority (transcending e.g. Hitler's authority).

The existence of God would provide the foundation for objective morality as the eternal sovereign entity that everyone ought to obey. The problem for the atheistic moral objectivist would be trying to find a reasonable basis for objective morality that fits the above characteristics (e.g. eternal and omnipresent while being the supreme authority in the universe) but cannot reasonably be called God.

The answer to the question "Who or what says how we ought to behave?" need not be a literal mouth and voice or even necessarily anything that communicates to humanity. Rather, "Who or what says how we ought to behave?" is simply asking for the foundation of morality and the source of moral principles; i.e. the entity/thing/force that lays down these moral obligations and prohibitions.

The problem with "nothing says how we ought to behave" is that it is tantamount to saying "there are no rules of behavior." Something has to say how we ought to behave, whether it be God, mathematics or whatever.

Since moral statements are not analytic (true by definition, e.g. "hairless men have no hair")

So you say, but can you think of an alternative, one that you're willing to accept? If morality exists without God, who or what says how we ought to behave?

You said, "I reject the soundness, not the validity," but you yourself said that the Holocaust is morally wrong. You therefore believe the argument is sound.

When it comes to finishing the sentence "X is immoral if (the culture believes it? the individual believes it?)..." your answer is still a little vague.

What "evidence" are you talking about? We cannot empirically test for the immorality of stealing, for instance.

It is true we can test for the "benefit to harm ratio" at least if we define "benefit" as "pleasure and happiness" and harm as "pain and misery." Is that what you mean? It's almost as if you're saying "the principle that we ought to maximize benefit and minimize harm [using the same definitions of "benefit" and "harm" I mentioned earlier] says how we ought to behave." Is this what you mean?

Whether it's absurd depends on how you define "objective moral opinions." I'm not sure what you mean by that, and thus I'm also not sure why what you're saying would make "moral principles are valid, binding, and true independently of whether any of us humans think, feel, or believe them to be so" a false belief. Perhaps you could elucidate here?

This is precisely my point. If the Nazis succeeded in exterminating or brainwashing everyone who disagreed with them, they would still be wrong even if they thought otherwise, right? Wouldn't this imply that moral principles are valid, true, and binding independently of whether we believe them to be so?

Perhaps you mean their core beliefs (e.g. don't kill innocent people) weren't different and they were just ignorant that they were violating this principle. I'm not sure how plausible this is, at least with those Nazis who deliberately killed women and children, but let's ignore that for the moment.

Suppose a group of men called the Syndicate really did know they were killing innocent people solely for selfish gains (wealth, power) but believed there was nothing morally wrong with what they were doing (it could plausibly have happened before at last once; moral nihilists do exist).

Suppose the Syndicate succeeded in killing or brainwashing everyone who disagreed with them. Would the Syndicate be morally right here? Or would moral principles are valid, true, and binding independently of whether they believe them to be so?

Nothing. Nothing objective demands that I favor truth over lies, reason over unreason, or to get out of bed in the morning. This depends on my aims and goals. Once I accept certain drives, motivations, goals and aims however, much follows.