In my last post on ethical relativism, I argued that species categories are vague, and that ethical universalism must therefore be an empirical claim about the contingent constitution of members of Homo sapiens.
There are many examples of distinctively human cognitive abilities, but the most conspicuous (and relevant) of these is natural language.
Humans have language, nonhumans don't. And the language that humans
have is generally regarded as having a deep common structure, despite
the manifest variations at the surface.
The standard account of this linguistic commonality is Chomsky's concept of a universal grammar, which posits a set of innate cognitive rules that systematically order language. Some of the best evidence for the hypothesis comes from the existence of aphasias -- impairments in discrete kinds of linguistic cognitive functioning that correlate with damage to specific areas of the brain. Since aphasias can occur in the absence of general cognitive impairment, they are seen as evidence that basic language competence supervenes on specialized "organs" or "modules" in the brain, rather than simply being a product of a general-purpose learning function.
Is there an analogous "moral module" in the brain? Probably. In a recent study, for example, subjects with adult-onset damage to the prefrontal cortex apparently display abnormally utilitarian judgment in moral hypotheticals "that pit[ted] compelling considerations of aggregate welfare against highly emotionally aversive behaviours (for example, having to sacrifice one person’s life to save a number of other lives)," whereas their moral judgment in other kinds of hypothetical cases was normal.  (Deontologists and virtue ethicists: Insert pro forma joke about consequentialists and brain damage here.) As with aphasias and language, the inference here that there is a discrete organ underlying moral reasoning and decision-making is natural enough.
But does this form of "universal moral grammar" help the ethical universalist? No. For to whatever extent a moral module constrains what can count as "moral" in human communities, clearly it doesn't constrain it enough to give us anything resembling a meaningfully universal morality.  As Will Wilkinson pithily notes:
[I]t may be that Yanomamo warriors, queer-stoning Islamists and gay Dutch vegans are all living out various dialects of morality, but if so, then it turns out that morality is a pretty useless category.
Will's observation neatly suggests the kinds of success conditions any biology-based ethical universalism would have to meet. Namely, it would have to find a common biological basis for sanctioning some "culturally-approved" mores (say, veganism) while proscribing others (say, stoning homosexuals). And at least judging from the initial evidence coming out of the most recent studies, the prospects for finding a relevant biological commonality are poor. 
None of the above is to say that there isn't a
cross-culturally robust "normal" morality that might be grounded in
biological traits. But "robust" isn't "universal," and any theory of
morality grounded in the constitution or nature of the individual
organism has to deal with the fact that there is bound to be some
deviation from any postulated natural moral norms. In sum, ethical universalism does not seem to accommodate observed natural moral variation.
1. Koenigs, M., et al., "Damage to the prefrontal cortex increases utilitarian moral judgements." (Visited May 1, 2008.)
2. The existence of a common "moral grammar" might suggest to some that we all share the same basic morality. But this is a clear error, much like supposing that the existence of a universal grammar would show that English and and Finnish and Ekegusii and Tagalog are really all the same language. All a "universal grammar" means is that there are innate rules for structuring the relevant syntactical units. Precisely what those units are, and how they are cashed out "morphologically" or "semantically," will vary locally. This variation isn't vexing in the case of language precisely because language lacks the normative dimension that makes moral variation so vexing, viz., a felt universalism.
3. There is of course an even deeper problem lurking here: The very existence of moral "aphasias" or other deviant moral-cognitive characteristics runs more or less directly counter to the universalist premise. For if moral aphasias and the like create bona fide "deficits" in moral reasoning and action, then not all humans can be said to have "the same morality." One might appeal here to the biology of "normal" brains. But that move encounters obvious problems involving line-drawing (what kinds of "deficits" are "normal"?), normative authority (on what grounds is a "normal" morality "better" than a deviant one?), and general epistemology (when can we know that a deviant morality supervenes on a dysfunctional, innate biological structure?). Alternatively, one might argue the evidence for properly "moral" aphasias is ambiguous. (For instance, it might be argued that the study above only shows that moral decision-making is modulated by emotions.) But even if there were no empirical evidence of moral "aphasias," the hypothesis that there is a universal morality based in biological similarities effectively predicts that we should see moral aphasias, since damage to cognitive machinery dedicated to moral functioning should affect that functioning in systematic ways.