This might seem far away from the Platonic political philosophy of Leo Strauss. But in fact, I see a fundamental agreement between the Straussian reading of Plato and the Churchlandian account of the neurobiology of morality--particularly, in the theme of human care within an uncaring universe.
Plato is well known for teaching a moral cosmology that shaped the Western intellectual tradition--"The Great Chain of Being"--for almost 2,000 years. According to this view, the moral order of human life depends on a cosmic moral order in which everything has been intelligently designed for the Good, and thus the human good requires that human beings imitate somehow the cosmic good.
Remarkably, Strauss and his followers argue that a careful reading of Plato shows that this is his exoteric teaching, the teaching for the unphilosophic multitude, but not the esoteric teaching, the teaching for the philosophic few. The philosophic teaching of Plato's Socrates suggests that the cosmos is morally neutral--that the cosmos does not care for human beings. Thus, Plato is not a Platonist.
It follows then--as indicated by Joseph Cropsey, Catherine Zuckert, and other followers of Strauss--that the moral and political order of human life depends on human "care": human beings care about their existence within an uncaring world of nature and without any divinity to care for them.
Churchland elaborates the same theme and indicates how modern neuroscience is beginning to explain the evolved neurobiological mechanisms supporting human care. As shaped by evolutionary history, nervous systems are organized to take care of the body. Animals with neural adaptations inclined to care for themselves and for their well-being are selected over those that neglect their self-preservation. In mammals, this caring for oneself is extended into care for others--for one's offspring, for one's mate, for one's kin, and for others in one's group. We are now beginning to explain how this works through the neurochemistry of oxytocin and vasopressin, which support attachment and bonding. This sustains the basic social desires or sentiments that lead to human morality.
This is not a satisfying view of morality for those people who want their morality grounded in cosmic standards of right and wrong, as in the moral commands of a divine lawgiver. An evolved human morality is purely human in being adapted to human needs and desires, and thus it has no cosmic support. For many contemporary moral philosophers, this would mean that human morality is an illusion because it lacks "normativity" in so far as it lacks any support by a cosmic God, cosmic Reason, or cosmic Nature.
Platonism is associated with the idea of moral cosmology--the Idea of the Good. But Strauss and his students see in Plato's Socrates an implied skepticism about any moral cosmology.
Churchland sees this as well. In her comments on Plato's Euthyphro, she writes:
Always modest, Socrates confesses ignorance of the answer to his own questions concerning the source of morality. The pattern of questioning strongly hints, however, that whatever it is that makes something good or just or right is rooted in the nature of humans and the society we make, not in the nature of the gods we invent. There is something about the facts concerning human needs and human nature that entails that some social practices are better than others, that some human behavior cannot be tolerated, and that some forms of punishment are needed. This does not mean that moral practices are mere conventions, on par with using a fork or wearing a hat to a funeral. (196)
This suggests a fundamental continuity between Straussian Platonic naturalism and Churchlandian Darwinian naturalism.
A few of the relevant blog posts can be found here, here, and here.