Like another reviewer, I started out agreeing with Huemer's basic claim, having concluded some forty-five years ago that the intuitionist position provided the most satisfactory explanation of normative beliefs. I read the book in part in the hope that he could provide better arguments than I had come up with, in particular a better rebuttal of what I view as the most serious challenge to our position. Unfortunately, he doesn't.
He does do a very good good job of demonstrating that ethical intuitionism is a defensible position and offering arguments to show that most of the alternatives, including ones that are much more widely accepted, are not. But he does not provide an adequate response to the one challenge I am concerned with, the view that combines ethical nihilism with evolutionary psychology.
The claim of that view is that there are no normative facts, that nothing is good or bad and there is no moral reason to do or not do anything. It explains our moral beliefs, the intuitions that Huemer views (and I view) as imperfect perceptions of normative facts, as explainable by evolution--they were beliefs that increased the reproductive success of those who held them in the environment in which we evolved, and so got hard wired into their descendants.
That approach challenges intuitionism in two ways. First, it explains the evidence, my ethical intuitions, on the basis of facts of reality I already believe to be true. Once we have one explanation there is no need for another. Second, it raises the question of how, if there are moral facts, we could have acquired the ability to know them, since at least some of them would presumably have led us to modify our behavior in ways that reduced our reproductive success--make us less willing, for instance, to slaughter the men of a neighboring tribe and take their women.
Despite these problems, I have not yet abandoned my current moral position, in part because the alternative position fails to answer the questions I want answered, indeed implies that they are unanswerable, that there are no actual oughts. In part also, I fail to adopt the nihilist position because I am unable to believe it. That inability is psychological, not logical. I cannot actually believe that there is nothing wrong with torturing small children for the fun of it or murdering large numbers of innocent people, both conclusions that follow from the view that nothing at all is wrong or right.