But why do we value consistency? In science and in our everyday beliefs about the way things are, there is a straightforward answer. Inconsistent beliefs, taken together, form a contradiction: a proposition that has the form "p and not p." We assume that reality does not contain contradictions (an assumption first articulated by Parmenides). So we infer that an inconsistent set of beliefs cannot possibly be an accurate description of the way things are.
...To sum up: I'm not saying that we should stop caring at all about logical consistency in working out our positions on moral issues. But I think it is interesting and reasonable to ask why we do care. Moral philosophers, as theoreticians, naturally tend to focus on the theoretical coherence of statements and their implications. But morality isn't mathematics. It is perfectly rational, in one sense of the term, to prioritize practical consequences over logical consistency. Once we accept this, we will perhaps be more comfortable taking a pragmatic approach to moral problems, and feel free to do so without dissimulation or apology.
With Isaiah Berlin's concept of value pluralism never far from my thoughts, I was already receptive to this argument. To me, those two lines are key: "We assume that reality does not contain contradictions," and "morality isn't mathematics." Axioms themselves are often unexamined. At any rate, it's an excellent essay, well worth a careful reading.