IV. Argument from science:
1. What science cannot discover, mankind cannot know.
2. Science cannot discover which moral values are correct and which are not.
3. Therefore, mankind cannot discover which moral values are correct and which are not.
4. If we cannot in principle discover what moral values are right or wrong, then we ought to view them as subjective and not objective.
5. Therefore, we ought to view moral values as subjective and not objective.
Here, too, the theist will disagree right at step (1). But so will, for instance, Michael Ruse, who suggests three areas in which we can have non-empirical knowledge: mathematics, morality, and "philosophical meta-questions."
I have trouble with Ruse's argument here. Morality, of course, is the issue at hand, so we can't bring it in here as an example without being guilty of circular argumentation. As far as mathematics, I think philosophers tend to underestimate the extent to which it is based on experience. Jason Rosenhouse makes the same point in his response to Ruse. If we think of "science" in its most general sense as "conclusions based on evidence and reason," then mathematics seems to fall under it.
And likewise for philosophical meta-questions: any discussion of these either brings in our observations and experience, or else is an exercise in pure logic. Either way, the discussion is, in the broad sense, a scientific one.
(You might object that I'm stretching the meaning of "science" beyond reasonable bounds. But I think the argument requires a very broad definition, or else (1) is indefensible. For instance, I know that I have a deodora cedar in my front yard, even though I haven't done a scientific investigation of that tree, and even though "my front yard" may not even have a scientific meaning, in the strict sense.)
Under this broad definition of science, the argument turns into something like Hume's is-ought problem: there is no way to go from a descriptive account of what is out there in the world to a prescriptive account of what we ought to do.
Hume's view is famously controversial. Let's suppose, though, that we can successfully argue for premises (1) and (2). I think we still run into a problem with premise (4).
Let's suppose that some version of utilitarianism is the "correct" morality: there is some quantifiable "greatest good for the greatest number." But suppose that, even though this greatest good is objectively defined and in principle calculable, it is in practice too difficult to actually determine. The consequences of any possible action ramify to such an extent that it becomes impossible to determine what combination of possible actions is the "right" one to choose. In this case, "science" would be unable to determine which moral values are correct, and yet morality would be completely objective.
So it seems to me that even if we accept that morality is unknowable (3), we need not accept that it is also subjective.