Is Objective Moral Truth Possible?

Over at Balkinization, Brian Tamanaha has posted a "pragmatic view of natural law."  Here's an excerpt:

Opponents castigate pragmatists for being moral relativists. The charge seems to fit the pragmatists, except for this consideration: criticizing someone as a “relativist” is meaningful only if it is possible to be a non-relativist.

These critics—let’s call them “objectivists”—deny that their position is a relativist one because objective natural principles really do exist. When making this claim, objectivists are saying not only that they believe that these principles exist, but more so that they do in fact exist.

The pragmatist will respond that, while the belief of objectivists in natural principles is sincere and has consequences (when they act on this belief), the claim itself is wrong—there are no such things as universal, objective, absolute principles. The referent of the claim does not exist. If it is meant by the objectivist as a factual claim, it is false. If it is a metaphysical claim, then it is a myth or fiction on a par with belief in the existence of ghosts.

Assuming these responses are correct (a big assumption, which cannot be discussed here), the charge of relativism senseless. It has no bite because objectivists are in exactly the same position as pragmatists—they too have no objective, universal grounding for their principles. One could say that we all are relativists—and the objectivists just don't know it—but a better understanding is that the term relativism is misleading and inapt because it posits an alternative position that is not available.

I'm in the process of trying to work through these questions as part of my ongoing project on conscience.  Steve Smith has argued that conscience claims seem to depend "on metaethical objectivism -- on a commitment to the idea that morality is in some sense natural, or given, or objectively true."  I'm open to being persuaded otherwise, but I'm inclined to agree with Steve on this point.  And I don't think moral objectivism is so far-fetched -- if a moral claim is "objectively" true to the extent that its truth is a quality that exists apart from the fact of my belief in it.  And I'm not sure that it depends on our belief in God.

If there are certain observable truths about human nature (whether it's a created nature or an accidental nature that has taken hold at this stage of our evolution), those truths have moral implications, don't they?  For example, from what we know about our social nature in terms of human bonding and relationships, the practice of breaking apart slave families to sell members as separate commodities is immoral, isn't it?  (I'm even putting aside the question of slavery itself.)  I don't know anyone who will say "that practice is immoral because I believe it is immoral" (which is what the non-objectivist has to say, right?).  They're much more likely to say, "that practice is immoral because it is immoral."  Moral judgments, it seems to me, are grounded outside ourselves -- not necessarily in universal divine revelation, but perhaps in what we know about the human person.  I recognize that "is" does not generally lead to "ought," but aren't there circumstances where the gap between "is" and "ought" is so small as to be irrelevant outside the academy?  If so, aren't we then in the realm of moral objectivism?