I consulted this page at the Stanford Encyclopedia of Philosophy for this topic at http://plato.stanford.edu/entries/reflective-equilibrium/
There we find a good description of Reflective Equilibrium: " The method of reflective equilibrium consists in working back and forth among our considered judgments (some say our 'intuitions') about particular instances or cases, the principles or rules that we believe govern them, and the theoretical considerations that we believe bear on accepting these considered judgments, principles, or rules, revising any of these elements wherever necessary in order to achieve an acceptable coherence among them. . . . .
A 'reflective equilibrium' is the end-point of a deliberative process in which we reflect on and revise our beliefs about an area of inquiry, moral or non-moral. The inquiry might be as specific as the moral question, 'What is the right thing to do in this case?' or the logical question, 'Is this the correct inference to make?' Alternatively, the inquiry might be much more general, asking which theory or account of justice or right action we should accept, or which principles of inductive reasoning we should use. "
Note that this is a method for bringing a SET of beliefs into optimum coherence.
It is useful in many philosophic contexts from how to justify lines of inductive reasoning to evolving our moral and political principles. This method was first articulated it seems by Nelson Goodman in 1955 but was was named by John Rawls in A Theory of Justice from 1971.
t seems it's an idea that was in the air around the middle of the last century. I find it to be closely related to Quine's web of ideas where the meaning of any idea is determined by the web of other ideas with which it is immeshed. Or with Wittgenstein's ideas about language games from about the same time. It seems also related to Karl Popper's idea of an Open Society where people just solve their problems as they go along instead of looking for perfect utopias.
I suspect that with these ideas we are seeing darwinian ways of thinking finally starting to displace Platonic thinking. Instead of expecting crystal perfection underlying everything, a perfection only accessible via pure logic, philosophers turned to trying to understand how we really do think and decide.
The idea of equilibrium itself is interesting in the context of this shift away from platonic thinking. Plato was fascinated with forms; ie things that were permanent. Heraclitus recognized that some things like rivers were not static and ever changing.
Equilibrium is perhaps more subtle than Heraclitus' river - the river is visibly moving. But with equilibrium things seem still - but it's a stillness of forces in balance. When working towards a reflective equilibrium the idea is to do something, check out what happens, adjust things so that next time everything works out better. Repeat. When you reach the point where there is no change that will make things better then you have reached reflective equilibrium.
And when you reach the same circumstances you'll do the thing you know works best. But as soon as any of the elements of the system do change, then the process of reflective equilibrium shifts everything to find a new balance.
This flexibility has consequences. It's perfectly possible for different people to reach different reflective equilibria, since each person's personal reflection can lead to different conclusions. The idea of reflective equilibrium works at the individual level but it also works at a social level.
In a way, culture might be thought of the kind of equilibrium about what is acceptable social behavior. Within each culture most people are congenial to behaving in ways that have evolved locally, but there is no reason it seems for different cultures to evolve in the same way. But the reflective part of reflective equilibrium is hopeful perhaps when confronting the polarization that people are prone to. That is - we can reflect to each other and learn and gradually come to an equilibrium that includes us all.
What do you think?