"Reflective equilibrium" is sometimes treated as the method of ethics (Rawls 1971 is the classic source). In reflective equilibrium, one considers one's judgments, beliefs, or intuitions about particular individual cases (e.g., in such-and-such an emergency would it be bad to push someone in front of an oncoming trolley?). One then compares these judgments about cases with one's judgments about general principles (e.g., act to maximize total human happiness) and one's judgments about other related cases (e.g., in such-and-such a slightly different emergency, should one push the person?). Balance them all together, revising the general principles when that seems best in light of what you regard as secure judgments about the cases, and revising one's judgments about specific cases when that seems best in light of one's judgments about general principles and related cases. Repeat the process, tweaking your judgments about cases and principles until you reach an "equilibrium" in which your judgments about principles and a broad range of cases all fit together neatly. In "wide" equilibrium, you get to toss all other sources of knowledge into the process too -- scientific knowledge, reports of other people's judgments, knowledge about history, etc.
How could anything be more sensible than that?
I am inclined to agree that no approach is more sensible. It's the best way to do ethics. But, still, our best way of doing ethics might be irredeemably flawed.
The crucial problem is this: The process won't bust you out of a bad enough starting point if you're deeply enough committed to that starting point. And we might have bad starting points to which we are deeply committed.
Consider the Knobheads. This is a species of linguistic, rational, intelligent beings much like us, who live on a planet around a distant star. Babies are born without knobs on their foreheads, but knobs slowly grow starting at age five, and adults are very proud of their knobs. The knobs are simply bony structures, with no function other than what the Knobheads give them in virtue of their prizing of them. Sadly, 5% of children fail to start growing the knobs on their foreheads, despite being otherwise normal. Knobheads are so committed to the importance of the knobs, and the knobs are so central to their social structures, that they euthanize those children. Some Knobhead philosophers ask: Is it right to kill these knobless five-year-olds? They are aware of various ethical principles that suggest that they should not kill those children. And let's suppose that those ethical principles are in fact correct. The Knobheads should, really, ethically, let the knobless children live. But Knobheads are deeply enough committed to the judgment that killing those children is morally required that they are willing to tweak their judgments about general principles and other related cases. "It's just the essence of life as a Knobhead that one has a knob," some say. "It's too disruptive of our social practices to let them live. And if they live, they will consume resources and parental energy that could instead be given to proper Knobhead children." Etc.
Also consider the Hedons. The Hedons also are much like us and live on a far-away planet. When they think about "experience machine" cases or "hedonium" cases -- cases in which one sacrifices "higher goods" such as knowledge, social interaction, accomplishment, and art for the sake of maximizing pleasure -- they initially react somewhat like most Earthly humans do. That is, their first reaction is that it's better for people to live real, rich lives with risk and suffering than to zap their brains into a constant state of dumb orgasmic pleasure. But unlike most of us, the Hedons give up that judgment after engaging in reflective equilibrium. After considerable reflection, they are captured by the theoretical elegance of simple hedonistic act utilitarianism. As a society, they arrive at the consensus that the best ethical goal would be to destroy themselves as a species in order to transform their planet into a paradise of happy cows. Let's assume that, like the Knobheads, they are in fact ethically wrong to reach this conclusion. (Yes, I am assuming moral realism.)
It seems possible that wide reflective equilibrium, even ideally practiced, could fail the Knobheads and Hedons. All that needs to be the case is that they are too implacably committed to some judgments that really ought to change (the Knobheads) or that they are insufficiently committed to judgments that ought not to change (the Hedons). To succeed as a method, reflective equilibrium requires that our reflective starting points be approximately well-ordered in the sense that our stronger commitments are normally our better commitments. Otherwise, reflective tweaking might tend to move practitioners away fromrather than toward the moral truth.
Biological and cultural evolution, it seems, could easily give rise to groups of intelligent beings whose starting points are not well-ordered in that way and for whom, therefore, reflective equilibrium fails.
Of course, the crucial question is whether we are such beings. I worry that we might be.
How Robots and Monsters Might Break Human Moral Systems (Feb 3, 2015)
How Weird Minds Might Destabilize Human Ethics (Aug 15, 2015)