• First, there is agreement on at least some of the relevant variables. In other words, there was some agreement on what would make cases the same or different from the moral point of view. As Ayesha said, we had that much because the racist made the claim that blacks and whites differ in intelligence and in other ways. So we knew we could look for differences or similarities of intelligence to argue for or against racism.
• Second, the relevant differences that the racist claimed are the sorts of things that can be detected, at least in principle, by standard scientific methods.
  

But I also think we were lucky here. What if two parties who disagree can't agree on what the relevant differences are? One person might say that gender is a relevant difference and another might deny it. What kind of a question is that? For example, is it a scientific question? I suspect that in some cases it is but that in other cases it isn't. Then what?

What if two different moral systems entail (or assume?) two different sets of relevant differences? In that case, we may all agree that we should "treat equal cases equally" but we won't agree on what constitutes equal cases. Then what?

Have we come to a point at which rational argument comes to an end?