So, how do we ground moral reasoning? This is the province of a whole area of inquiry known as metaethics, and I suggest that Harris would benefit from reading about it....Just as we don't need a good answer to the question of where mathematics comes from to engage in mathematical reasoning, so it is not very productive to keep asking philosophers for "the ultimate foundations" of what they do (if this sounds like an easy way out to you, remember that neither math nor science itself have self-justifiable foundations).
Well, yes, but this sounds as if Pigliucci seems to realize that as an atheist he has no grounds for making moral judgments, especially those which involve anyone but himself, and doesn't want anyone taking the trouble to point this out.
He's also confusing apples and oranges in comparing the grounds for one's ethical judgments with the grounds for mathematics. We don't keep asking for an explanation for the ultimate foundations of mathematics because the assertions in mathematics are self-evident or derived from self-evident axioms. It is these that form the ultimate foundation of the discipline, and, unlike the ultimate foundation of many ethical theories, they're neither arbitrary nor subjective preferences. They're objective and universally accepted. There's no dispute about them, but it's not so with the grounds for our ethical claims.
It's silly to ask someone who has just pointed out that 1 + 1 = 2 to explain why he believes that, but it's not at all silly to ask someone who insists, for instance, that families should limit themselves to two children to give an account of what he's basing this moral adjuration upon.
No general ethical claim is self-evident. There are some, of course, that have powerful intuitive appeal, like the assertion that it's always wrong to torture children, but intuitive appeal doesn't make the claim self-evident in the sense that 1 + 1 = 2 is. To see this, consider that in any possible world 1 + 1 would still equal 2, but there are possible worlds, as unpleasant as they may be to imagine, in which torturing children would not be wrong. For example, such behavior would not be wrong in a world in which there are no moral duties, which is precisely the sort of world this world would be were there no God.
To request that a person making a moral judgment explain the foundations upon which the judgment rests is to safeguard against having them bind the rest of us to their own arbitrary, personal preferences. It's also a guard against allowing them to persuade us that they're really saying something meaningful about the world - as opposed to merely telling us something about their own subjective tastes - when they declare a particular behavior right or wrong.
Perhaps Pigliucci wants to be able to make moral judgments without having to defend the fact that his judgments are either hanging in mid-air or piggy-backing upon a theistic understanding of morality, but, if so, he really shouldn't be permitted to get away with it.RLC