Ms. Churchland is an eliminative materialist which is a fancy way of saying that she believes that everything that exists is either matter or a derivative of matter. There's nothing, she believes, that's independent of matter - no mind, no soul, no God - just atoms and energy and the phenomena comprised of these.
She was once interviewed by Sigal Samuel at Vox, and in the interview she says a number of things worth noting. Samuel's introduction suffices to give a sense of Ms. Churchland's views, but interested readers should read the transcript of the interview at the link.
Here are Samuel's introductory remarks:
For years, [Ms. Churchland has] been bothered by one question in particular: How did humans come to feel empathy and other moral intuitions? What’s the origin of that nagging little voice that we call our conscience?There's an important metaethical point to be made here. Let's suppose that everything she says about the origin of our moral sense is correct. If so, morality itself is a kind of illusion. Terms like morally right and morally wrong have no real force. They simply refer to whatever the community approves and disapproves.
In her new book, Conscience, Churchland argues that mammals — humans, yes, but also monkeys and rodents and so on — feel moral intuitions because of how our brains developed over the course of evolution. Mothers came to feel deeply attached to their children because that helped the children (and through them, the mother’s genes) survive.
This ability to feel attachment was gradually generalized to mates, kin, and friends. “Attachment begets caring,” Churchland writes, “and caring begets conscience.”
Conscience, to her, is not a set of absolute moral truths, but a set of community norms that evolved because they were useful. “Tell the truth” and “keep your promises,” for example, help a social group stick together. Even today, our brains reinforce these norms by releasing pleasurable chemicals when our actions generate social approval (hello, dopamine!) and unpleasurable ones when they generate disapproval.
Rooting morality in biology has made Churchland a controversial figure among philosophers. Some think that approach is itself morally repugnant because it threatens to devalue ethics by reducing it to a bunch of neurochemicals zipping around our brains.
A number of philosophers complain that she’s not doing “proper philosophy.” Other critics accuse her of scientism, which is when you overvalue science to the point that you see it as the only real source of knowledge.
Nor can there be any genuine moral obligation. We cannot be morally obligated to adhere to the communal norms, since if we were we'd have to approve the persecution of Jews if we lived in Nazi Germany or, if we lived in the Jim Crow South we'd have to favor discrimination against black Americans, even if we were black!
Nor could there ever be social progress since the moral consensus of the community would be right ab defino and the dissenter would likewise be wrong. And, if dissenters by definition must be wrong, why should anyone listen to them? Indeed, why should they not be punished if they refuse to accept what the community has established as right?
What Ms. Churchland has shown, if she's correct, is nothing more than why we feel certain things to be right or wrong, why we feel that we should do X rather than Y, but how could it be wrong to go against one's feelings? Or how could it be wrong if one's feelings predispose him to be kind and another's feelings incline her to be cruel?
If our moral sense has evolved as a result of genetic mutation and natural selection, if it's simply the product of dopamine levels in our brains, then how can we have genuine obligations to be kind rather than cruel? How can dopamine make an act right or wrong?
Moreover, the human species has evolved all sorts of feelings and behaviors - selfishness and selflessness, for example. If Ms. Churchland is correct the only way to arbitrate between these is to compare them to the norms of the community, but how can community consensus make something objectively right or wrong? If the community consensus is that slavery or child sacrifice is morally acceptable how could anyone insist that the community is wrong?
What gives the community consensus authority over an individual's moral intuitions? If the community consensus is that we should strive to eliminate our neighbors and seize all their resources, would an individual dissenter from this view be morally wrong? And what does it even mean to be morally wrong other than that one's brain chemistry isn't congruent with that of his fellow citizens?
Ms. Churchland's thesis that our moral sentiments are simply due to chemical processes in the brain may be of some interest to brain scientists and sociologists, but it's quite irrelevant to moral philosophy and ethics. It may explain why we behave in certain ways, but it has nothing to say about how we ought to behave, which is what moral philosophy is all about.