(Click here to continue on the main path)

But couldn't we just as easily say that 'treat equal cases equally and treat unequal cases unequally' implies that people should be treated differently unless the relevant similarities are found?

It looks to me as though 'treat equal cases equally' could be interpreted either way, and that neither interpretation is strictly implied. Each goes beyond what is implied by the original principle.

The rule doesn't give people a prima facie right to be treated the same any more than it gives them a prima facie right to be treated differently.

Look, I know this isn't a perfect analogy, but consider it. Suppose we had a rule that said we should paint all walls up to 6 feet high orange and all walls over 6 feet high purple. Now suppose someone said that this implied that by default we should paint all walls orange. Or suppose someone said that it implied that we should paint all walls orange until and unless we knew the wall was over 6 feet high. I think we would agree that this doesn't follow at all. In my opinion, you are doing something like that when you say that 'treat equal cases equally' implies that we should treat cases equally until and unless we can establish differences.

I think you seized upon the first formulation because it supports your politics. But as Vera suggested, that may be an illusion.