The reason is simply that, to some extent, science can give us information about what individual conduct, moral systems, laws, and so on are likely to lead to such plausible goals for all these things as individual and collective human flourishing, social survival, and reduction of suffering. Any source of information about what will lead to goals such as these has some moral authority.
Religion, Science, and Morality
Religion could have moral authority if it were actually a reliable source of information about the world. If religion could give us accurate information that acting in such and such way will lead to such and such consequences, then it could, at least to some extent, have moral authority. If the prophets and other authors of holy books were genuinely receiving information from a god or other supernaturally knowledgeable being, a being with an epistemic advantage over us, then we would be very wise to pay attention.
The difficulty is this: in the real world the holy books seem no more reliable about moral issues than they are about such matters such as the age of the Earth. Sophisticated religious adherents tend to interpret the holy books more in keeping with what they know from elsewhere about what conduces to human flourishing (or social survival, reduction of suffering, and so on). Far from being authoritative, the holy books end up needing to be interpreted in the light of secular wisdom about what actually conduces to, say, widespread human flourishing.
By contrast, various fields of science can now study many aspects of the world, including human nature, and the outcomes may have many implications for how we should act, what laws we should support, etc. As we learn more from science, this can feed back into popular moral understandings. Hume believed in moral progress, as understanding increased and civilization developed; and, in principle, I see no reason to think that he was wrong about this. As we know more, we can make better decisions in respect of moral issues.
To date, however, science is limited in what it can actually deliver. Given the current state of sciences such as psychology, the quality of any advice coming from science still leaves much to be desired. We do not have an exact science of what best contributes to, say, widespread human flourishing. In principle, we can develop this science, but for the moment we must rely to a large degree on such things as literature, historical experience, folk understandings of what makes people happy, and our own experiences as individuals. Moral philosophers need to reflect on all of these things; but at least in principle, science can deliver much useful information. We can expect it to get better and better.
Ultimate Values and Rational Reflection
What science can't do, even in principle, is tell us what our ultimate values or the totality of our values should be. Religion can't do that either.
We can, of course, reflect on our own values, trying to get them into some sort of order. Perhaps I place too much value on eating chocolate, given that I also value not developing obsesity. Okay, I can make a decision to try to lower the value I place on eating chocolate. At the least, I can try to think about the value of not developing obesity on the many occasions when I'd like to buy and/or eat chocolate. Maybe I can keep my chocolate consumption down that way, even though eating chocolate is still, all other things being equal, something that I value (and will indulge in from time to time). I don't have to be a slave to each particular value or desire that I find I have.
However, when I engage in this sort of rational reflection I try to sort out which values are really most important to me, what values I have about what values I want to retain, and so on. In doing that, I never step out of the entirety of my values at once. I always need more than just facts about the world, the "more" being my total system of values. Science cannot enable me to step out of all my values at once, though it can certainly give me some relevant information. Neither can religion. There's no substitute for my own rational reflection on what I value most.
Values and Facts
I agree, more or less, with Harris' story about how we should actually act, trying to create a world of widespread flourishing for human beings and other sentient creatures (by standards of flourishing that he and I would largely share). I disagree, however, with his claim that "values are facts". Nothing he said on that was convincing.
Sure, it can be a fact that "Person X values some particular thing." And Person X's valuing that thing, or having that value, may well consist (why not?) in Person X having a particular neurophysiology. Moreover, if I value Person Y being happy, it can be a fact that the thing I value exists -- i.e. that Person Y is (by some appopriate standard) happy. Moreover, Person Y's happiness may consist in some neurophysiological state.
So it can be a fact (even with a physical instantiation) that someone values something, and it can be a fact (even with a physical instantiation) that something I value actually exists. But the following are propositions which can be true or false: "Person X values such and such a thing" and "The thing that Person X values exists." Valuing, desiring, fearing, and so on are not the assertion of propositions.
The fact that the possession of a value or the act of valuing has a physical (neurophysiological) substrate does not mean that the valuing itself, or the having of the value, is the kind of thing that can be mistaken. When, for example, I value eating chocolate or desire to eat a chocolate, I am not making a claim that can be true or false. I want the world to be such that chocolate will continue to be available to me, or such that I can get chocolate now. I'm not claiming anything about how the world actually is -- the kind of thing that I could be wrong about.
What was more convincing in the Harris talk, though hardly surprising, was that there was widespread agreement on values in the audience. Apart from psychopaths, most people actually do agree a lot on values. Psychopaths basically lack sympathy for others, which is to say that they don't value others' non-suffering in the way that most of us do. (It's actually a bit more complicated than this, as they also tend to lack the normal capacity for prudence, and so they tend to get caught, but we can easily imagine somebody with the psychology of a cunning and prudent psychopath. If necessary, imagine it's an intelligent alien with no feelings of sympathy for human beings.)
I've never yet seen an argument that shows that psychopaths are necessarily mistaken about some fact about the world. Moreover, I don't see how the argument could run, since it's easy to imagine pointing out to the psychopath, as he tortures me, that I'm suffering extreme pain, terror, and so on. The psychopath can know all this, but simply not care. When the psychopath values being able to torture me, he (it will probably be a "he") is not making any factual claim. The fact that he has this value may consist in his neurological state. The fact that what he values exists may consist in mine. But he does not assert any mistaken proposition about the world such as, "Russell is not in pain." He knows all the facts, but he acts differently from a normal human being because he values different things. He's not mistaken about something ... but he's certainly dangerous to the rest of us, giving us a reason to lock him up.
There are also various differences in values among people who are not psychopaths, and again none of those people are necessarily making any mistake about facts about the world. They simply disagree in their settled wishes about how they want the world to be.
If one person, after full reflection, wants the world to be peaceful and gentle, and another wants it to be full of glorious battles and victories, that's a difference in their values, but it need not mean either is making a mistake about any matter of fact. Both may have very good knowledge of how things are, but they have different preferences as to how they want things to be. They will fail to convince each other because they don't disagree on the facts. Each will need to appeal to considerations that the other does not accept and cannot be compelled by reason to accept.
Rough Consensus
I don't think that Harris is going to overturn the standard Humean approach to the fact/value or reason/desire distinction any time soon. No one else has ever succeeded, and his argument here wasn't all that original. As I understood his point -- though maybe I got this wrong -- it was mainly that valued psychological states, such as a particular person's happiness, can actually exist and have physical instantiations. That is true, but it's not surprising, and it does not bridge the divide between fact and value.
That is true, but it's not surprising, and it does not bridge the divide between fact and value.Still, he doesn't need to do anything so dramatic. No fundamental advance in metaethics or moral psychology is required to demonstrate that we can obtain action-guidance from science (and could gain action-guidance from holy books if they were reliable sources of information about the world). What Harris said was, for all my quibbles, nonetheless a pretty good practical approximation to the truth about morality.
We can assume a great deal of consensus on what counts as flourishing and on the value in contributing to the widespread flourishing of others (not just ruthlessly seeking it for ourselves as individuals); on the self-defeating and socially-destructive outcome of a ruthless approach to seeking our own pleasure; and other such matters which, taken one by one, are not all that contentious. This is enough to get to a rough consensus or convergence on a rational moral system, and doubtless to overturn a lot of traditional religious morality in the process.
Incidentally, Harris is also correct in principle that more than one moral system might do the job. Moral systems are not arbitrary -- there is a largely-uncontroversial point to them -- but nor is there necessarily a "One Best System" that is fully determined by facts about the world. There may be many high peaks on a landscape of possible moral systems.
Simplicity and Approximation
I don't doubt that it would be rhetorically helpful if we could claim that values are objective in some stronger sense than I can accept.
As I watched the Harris video, I tried to imagine myself giving a similar talk, and it was obvious to me that if I even raised the issues where I'm disagreeing I'd get bogged down making subtle distinctions that might confuse the audience. You can be more forthright and straightforward and rhetorically effective if you have a simple story to tell. But alas, none of that entails that any simple story is more than an approximation.