Morality is a natural phenomenon. Its roots lie in our needs and our capacities for sympathetically imagining the feelings of others, for inventing co-operative principles, for being able to take an impersonal view of our own doings. We have what Adam Smith called a “man within the breast” monitoring our feelings and actions in the name of those with whom we live. Imagining their admiration, we feel pride; imagining their anger, guilt, their contempt, shame.
Next on the list: showing that reasoning is a natural phenomenon whose roots lie in our natural ability to make judgments and draw conclusions, that religion is a natural phenomenon rooted in our natural ability to engage in religious practices, and that going to bed is a natural phenomenon whose roots lie in our need for sleep.
Seriously, though, I actually don't know of anyone spends much time talking about the subject who doesn't think that morality is a natural phenomenon in at least something like this sense, even if they have weaker sentimentalist inclinations than Blackburn; even the very strongest forms of divine command theory hold that we have natural moral capacities -- they just think that consistent atheism is inconsistent certain things that moral capacities require, or that it enervates their effectiveness, or that these natural capacities culminate or find their best organization when combined with the belief that their demands are actually truly authoritative commands. If William Warburton can agree with your moral naturalism, you don't really have much of a moral naturalism.
But it is nice to see Adam Smith's impartial spectator, even if Blackburn doesn't acknowledge how controverisal he is. Plus I'm experimenting with using Blackburn's Think as a textbook for a course this summer (I've wanted to try it out for years now, and my usual course structure isn't suitable for the particular kind of course I'll have to be teaching this summer, due to the way it's scheduled); I can add this review as a supplement to the "What to Do" chapter.