A well-written and well-argued account of a theory of moral progress. The writing is lucid, albeit a little too often rehashing the same points several times.
Starting with a morality based on reciprocity and cooperation in groups, the idea is that morality can expand from in-group/out-group thinking to include others as well, if certain conditions hold. The authors consider different examples and kinds of moral progress, but concentrate on the inclusion of additional moral agents, such as the argument of the 19th century abolitionists working against slavery that Africans have moral standing. The book uses human rights thinking as the main example.
The authors argue against what they call the evoconservative position: that humans are incorrigibly group-centered and that any attempts to greater inclusivity is an aberration which cannot be sustained. Importantly, the authors make the case that human moral psychology must be viewed in the light of the concept of plasticity, i.e. that the humans (and other organisms) have a range of possible behaviors which are activated depending on the concrete environment they encounter. If humans live in an environment of strife and strong competition, then in-group/out-group thinking becomes more dominant. When conditions favor cooperation and win-win scenarios, moral psychology can become more inclusive. Moral progress has a material, or naturalistic, foundation.
There are a few confusing points. In some places, the authors seem to argue that progress in moral thinking, e.g. arguments and debates about consistency in moral views, are insufficient to explain moral progress in general. Other times, the authors seem to suggest that it is exactly these debates that are being made possible by social developments. They say that their view is biological and naturalistic, and criticize cultural evolution as a concept. But if the logical content of moral argument has any force at all, then there must be cultural innovation and evolution, it seems to me.
One of the most interesting points of the book is that moral progress must entail epistemic humility. We should not try to formulate the ultimate morality, since we cannot know what innovations in morality might happen in the future. If we look back in history, there are many cases of social features that were considered moral, or non-moral, which we have now completely re-evaluated. Examples of features that have undergone fundamental changes in moral reasoning include slavery, dueling, sexual minorities, and the roles of men and women. We cannot presume to know what changes may occur in the future, so instead of trying to formulate the ultimate good, we should focus on improving morality, both the views of morality and its implementation.