Bob, regarding distinct entities, think of a clone or a pair of identical twins. They share the same physical features such that A=B, but it is not the same as A=A. If one of the twins were to get into an accident or we re-arrange a gene in the clone, it would violate the first equation and have no effect on the second as this effect won't be translated into the second individual. So, it would no longer be such that A=B, it would be A=/=B, but A=A would still be true for each individual. (You could also define A as being the set of the two, in which case any change in one will not effect the truth value of A=A). If you start with A being one individual, then everything that you apply to one would have to happen to the other (twin/clone) by definition. If there is some disconnect, then you started with the proposition A=B and then showed that A=/=B. With the alternative universes, if they are in fact identical (A=A), then they can't differ. If they can differ then you have started with A=B. This wouldn't undermine the law of identity, but it would undermine deterministic and possibly in-deterministic accounts of physics.