I should not comment on anything that Ross Douthat ever writes. It's not a good practice to grant page views to misogynists with delusions of Thomistic philosophical chops. But sometimes I can't help myself, because Douthat is typical of a sort of intellectual* conservative that dresses up religious dogma and prejudice in the clothing of concern about social cohesian and mores.
I nearly found myself agreeing with Douthat on the subject of almost as odious Stephen Pinker. I agree that 'science' does not dictate any moral values (is versus ought, etc). But then I thought about what Douthat had written, and I realized he was wrong (even if Pinker was as well) and that all was right with the world once again.
Douthat makes an easy point in saying that 'science' does not endorse liberal cosmopolitanism. That is true. And Pinker makes it easy for Douthat in going on and on about the use of science as though evolutionary biology would provide to key to such questions as "what is justice?" But Douthat is still wrong. What you might call the humanist ethic does not come from science but from something deeper -- skepticism and compassion. When you read Montaigne, you see a aversion to cruelty (see "On Cannibals"). But you also see a profound skepticism of tradition and dogmatism. And this leads to that aversion to cruelty, since when you do not know if Huguenots are leading people into hell, burning them at the stake is mere murder. In general, a skeptical humanism strips away extraneous moral dictates (suffer not the witch to live, kill the heretic, let not man lie with man as with a woman) just by asking 'why?' And what you are left with at the end is a concern for your fellow human beings. The above is not a moral philosophy but a moral inclination, but people
follow their moral inclinations, not their moral philosophies. This does not need to be 'proven,' since no one actually needs to 'ground' their moral beliefs -- they simply follow their inclinations.
I would go further and say that I have see no evidence that moral philosophy has made people better. I have seen no evidence that attempts to logically 'ground' morality have improved our moral thinking and abolished slavery, liberated women or allowed gays to live openly. On the other hand I see the positive results of this moral inclination every time I see a same-sex couple walking openly down the street, or see a black man walk into a store and get service. This is why there is no crisis of 'relativism' in this country or any other. People will do what they think is right, even if they don't believe it was handed down from on high. Nietzche was wrong -- morality is only a 'problem' if you think it's a problem.
Now this inclination is not 'scientific' but skeptical curiosity about the world is also at the root of science. Thus while there is no -logical- connection between the two, they are similar inclinations, and it makes sense that they have grown in strength together. Moreover this inclination has been as active -within- religion as outside of it. It is why most Jews now believe that the welfare of women is more important than following the dictates of Leviticus, why Christians no longer torture one another because they disagree over the way in which Christ is present in the Eucharist.
A more specific complaint against Douthat is that he makes a characteristic leap employed by Kantians and Catholics alike -- the assumption that all morality based on the welfare of human beings is 'utilitarianism.' This is a crude not-quite ad hominem that states that if you don't believe that morality must have an inhuman origin (the dictates of God, the logic of a universal moral law) you therefore believe in throwing babies under buses if it will make more people happy. If you believe that morality seeks the good of human beings, you are a moral humanist. This does not mean that you believe that that good is the same as 'maximal happiness' and that happiness is synonymous with the absence of pain. For myself, I think that our knowledge is limited enough that any attempt to guide our actions by 'maximum happiness' in the abstract is hubristic at best. But this does not mean that I don't think that moral acts are those that benefit other human beings and the world we live in. To me, such a humanistic morality is the natural result of the skepticism that I mention above.
As a final thought, I should say where I'm coming from. I believe that 'Moral Law' is a bad metaphor. Worse than that, I think it is oppressive and monstrous to tell people that their actions, if they are to be just, should have an object -other- than the welfare of those around them and the world that they inhabit. But that's not my philosophy, just my inclination.
*I thought of adding quotation marks, but that seemed cheap. Douthat and his ilk can indeed use their brains; whether this effort is profitably employed is another story.