This book is Nagel's Dewey Lecture on moral epistemology in 2015 and a follow up lecture to include also moral progress.
In the first lecture "Gut Feeling and Moral Knowledge", Nagel addresses the epistemic value of moral intuition, namely, how much our moral intuition in deciding right or wrong in ordinary situations give prima facie evidence into moral truth. Nagel believes that moral intuition is much more disadvantageous than empirical observation in scientific investigation which we know our empirical investigation is in direct causal interaction with the physical world. In moral intuition, when we try to establish that Rawlsian reflective equilibrium by test principles against judgments about particular situations, we aren't in any direct causal interaction with some moral reality to find the moral truths. The undertaking is a one-sided reflection by abstraction. There are two typical moral intuitions one uses to assess the right action to take in a given situation. One type is consequentislist which decides right or wrong based on the overall good or bad outcome an action results. The other is deontological which assesses whether an action is right or wrong based on some guiding principles applicable to that act, instead of the outcome of the action. Nagel mentions an approach from evolutionary psychology tends to see some shortcomings in a deontological approach if deciding merely on principle leads to more harm than good. But it seems a natural conclusion from evolutionary theory if its concern is survival for the collective. Nagel suggests looking at ourselves from the outside in a given situation may give further epistemic insight. We can come to see our attachments to right and deontology as an unnecessary cluttered outlook which grossly magnifies the claims of the person facing us that limits our rationality. Nagel thinks moral progress may favour a more consequential outlook than being stubborn in some deontology.
The second essay "Moral Reality and Moral Progress" proposes an account of the historical development of moral truth accessibility and moral progress. This account suggests a realism of moral truth independent of our beliefs so that a change in moral beliefs can be described as objectively correct or incorrect. Nagel suggests that moral intuition is dependent on the accessibility of a person's ability to understand the reason for action based on the knowledge he has. On this approach, moral progress is possible due to greater accessibility of reasons facts, and concepts of how one can act, leading to an historical progress. Nagel drew attention to views of homosexuality or sex not just for procreation as greater accessibility to knowledge, concepts, and understanding of facts surrounding the issues. He also suggests people in earlier days that had different views on these issues could hypothetically have views that modern people have, had such accessibility to knowledge was available to them. Nagel thinks such moral progress is not biologically innate but takes time from culturel development over time. This view of moral progress is historically developmental. Since he thinks views can be objectively right or wrong, moral progress involves progressively moving to moral perspectives that are more correct over history.
These two essays shed some original analysis on moral epistemology and the second essay is much more indepth into various moral issues. They both contributes to some original discussion in moral epistemology