It is, after all, simply a fact that many of what we take to be the plain and evident elements of universal morality are in reality artifacts of cultural traditions. Today we generally eschew cannibalism, slavery, polygamy, and wars of conquest because of a millennial process of social evolution, the gradual universalization of certain moral beliefs that entered human experience in the form not of natural intuitions but of historical events. We have come to find a great many practices abhorrent and a great many others commendable not because the former transparently offend against our nature while the latter clearly correspond to it, but because at various moments in human history we found ourselves addressed by uncanny voices that seemed to emanate from outside the totality of the perceptible natural order and its material economies.
One certainly may believe that those voices in fact awakened us to “natural” truths, but only because one’s prior supernatural convictions prompt one to do so. To try then to convince someone who rejects those convictions nevertheless to embrace those truths on purely “natural” grounds can never be much more than an exercise in suasive rhetoric (and perhaps something of a pia fraus).
The process of writing my dissertation (about a figure erroneously placed in the natural law tradition) brought me around to this point: if one is not convinced that natural law exists as an abstract category whose contents can be deduced, one is stuck attempting to induce natural law principles from observed behavior. But, since human beings are products of culture no less than nature, and culture itself has transformative impact on each person from birth, and on mankind as a whole for tens of thousands of years, it will be impossible to sort out the 'cultural' from the 'natural,' as any good state-of-nature theorist will admit. Natural law then becomes a kind of shell game, smuggling in prejudices derived from religion in content-neutral packages. Karl Barth, in Part I of the Church Dogmatics, criticizes this approach for two closely related reasons: first, it opens itself to accusations of bad faith. Those who argue for natural law are only going to see in nature those things which are compatible with their religious beliefs, so acting as though the conversation were really a disinterested series of observations about nature will be hard for the non-religious conversational partner to believe. The second problem is that it induces, ever so slightly, a tendency to actually argue in bad faith on the part of the religious believer, to engage in self-deception about the aims and purposes of conducting a conversation on natural law in the first place.
The only concern I have that Hart omits is a Foucaultian one: appeals to nature are immensely powerful. That's why everyone makes them: the claim is being harnessed for its epistemological and rhetorical power, as a way of benefitting the side making it and preemptively disparaging opposition.