If A and B are both rigid designators, and A = B, then A necessarily equals B (doesn’t it?)
If we can show that A does not necessarily equal B, then ( if they are rigid designators) we can say that A does not equal B.
But what if A or B is not a rigid designator? What can we take from that if someone is claiming this relationship of necessity? If one of them isn’t, then it seems to me that this relationship is destroyed. But we then can’t take the further step to say that A does not equal B.
How generic can a rigid designator be?