If two universes have a perfect 1:1 correspondence, can they be both identical and distinct?
In philosophy, can two things be completely indistinguishable from one another, and yet still be two separate things?
Let's assume there exists an exact replica of our universe, but in which the value of every property is inverted in some way. Temperature would be one of these properties. However, the properties which contribute to a sense of hotness and coldness have themselves been inverted, as have the meanings associated with those properties. Something which is hot in our universe would be cold in the other, but the traits which contribute to coldness in our universe are those which contribute to hotness in the other, and vice versa.
Each universe maintains a perfect 1:1 correspondence for every property and relation. The flipped universe would appear completely normal to its inhabitants, because the relations between concepts are preserved.
If every property, concept and relation corresponds perfectly between the two universes, what would distinguish them? Would they be considered different universes, or just two different ways of referring to the same one?
Could they somehow be both identical and distinct, or is that a logical impossibility? Is there a concept in philosophy which deals with this?