Now I'm not concerned with the actual content of Harris's talk, nor the arguments subsequent upon Carroll's comments, which you can find in the links from here and here.
My concern is to highlight the interesting proposition in moral philosphy that you can't derive an "ought" from an "is". This appears to have been first discussed by philosopher David Hume around 1739 and has become known as Hume's Guillotine. Wikipedia quotes book III, part I, section I of Hume's A Treatise of Human Nature:
In every system of morality, which I have hitherto met with, I have always remark'd, that the author proceeds for some time in the ordinary ways of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when all of a sudden I am surpriz'd to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is however, of the last consequence. For as this ought, or ought not, expresses some new relation or affirmation, 'tis necessary that it shou'd be observ'd and explain'd; and at the same time that a reason should be given; for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it.
In case you didn't follow that (yep, I struggled too!), here's Carroll's version from the final paragraphs of his Cosmic Variance piece (remember he's commenting on Harris's talk):
In the real world, when we disagree with someone else’s moral judgments, we try to persuade them to see things our way; if that fails, we may (as a society) resort to more dramatic measures like throwing them in jail. But our ability to persuade others that they are being immoral is completely unaffected – and indeed, may even be hindered – by pretending that our version of morality is objectively true [...]
The unfortunate part of this is that Harris says a lot of true and interesting things, and threatens to undermine the power of his argument by insisting on the objectivity of moral judgments. There are not objective moral truths (where "objective" means "existing independently of human invention"), but there are real human beings with complex sets of preferences. What we call "morality" is an outgrowth of the interplay of those preferences with the world around us, and in particular with other human beings. The project of moral philosophy is to make sense of our preferences, to try to make them logically consistent, to reconcile them with the preferences of others and the realities of our environments, and to discover how to fulfill them most efficiently. Science can be extremely helpful, even crucial, in that task. We live in a universe governed by natural laws, and it makes all the sense in the world to think that a clear understanding of those laws will be useful in helping us live our lives [...] When Harris talks about how people can reach different states of happiness, or how societies can become more successful, the relevance of science to these goals is absolutely real and worth stressing.
Which is why it's a shame to get the whole thing off on the wrong foot by insisting that values are simply a particular version of empirical facts. When people share values, facts can be very helpful to them in advancing their goals. But when they don't share values, there's no way to show that one of the parties is "objectively wrong". And when you start thinking that there is, a whole set of dangerous mistakes begins to threaten. It's okay to admit that values can't be derived from facts [...]
All of which seems about right to me; as is the corollary: you can't derive an "is" from an "ought", or in words of Flannery O’Connor "the truth does not change according to our ability to stomach it".