Stanley Fish has now responded with a post which reveals that he has completely misunderstood the argument.
Here I'll just point out one particularly egregious misunderstanding. Boghossian wrote:
Pinning a precise philosophical position on someone, especially a non-philosopher, is always tricky, because people tend to give non-equivalent formulations of what they take to be the same view. Fish, for example, after saying that his view is that “there can be no independent standards for determining which of many rival interpretations of an event is the true one,” which sounds appropriately relativistic, ends up claiming that all he means to defend is “the practice of putting yourself in your adversary’s shoes, not in order to wear them as your own but in order to have some understanding (far short of approval) of why someone else might want to wear them.” The latter, though, is just the recommendation of empathetic understanding and is, of course, both good counsel and perfectly consistent with the endorsement of moral absolutes.
Fish merely responds that his two claims are not "contradictory", and so totally misses the point that he has been caught in the classic pomo bait-and-switch of oscillating between a radical-sounding claim and an utterly uncontroversial platitude. We can all agree to the platitude, without any need for the more radical claim.
Fish now clarifies that he "denies nothing except the possibility (short of force or torture and they don’t count) of securing universal assent". But who does he imagine himself to be arguing against here? This isn't "relativism", unless the impossibility of reasoning with convinced counterinductivists likewise qualifies us as "epistemic relativists" about whether the sun will rise tomorrow. (What is it with non-philosophers and their bizarre attributions of magical beliefs about the causal powers of arguments?)
Contra Fish, acknowledging the limited causal powers of moral argument is not "a way of denying moral absolutes", any more than acknowledging the limited causal powers of scientific argument (when faced with, e.g., committed creationists) is a way of denying the theory of evolution. I suppose he could just stipulate that he's going to start using these words differently from the rest of us, but nothing is gained by such needlessly obscurantist behaviour. (Or nothing of intellectual merit, at least; I guess Fish has shown that one can make a career out of redefining provocative-sounding phrases to express trivial platitudes.)