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Observational indistinguishability is not equality.

Hurkyl did not explained himself on the thread, plus the question is off-topic to that thread, hence this one.

So, suppose we have two models of the same thing, and all their predictions coincide. Why does it not make them equivalent?

More specifically, if these are mathematical models, could it be argued that predictions coincidence is only possible if actual math is the same (up to some kind of isomorphism, perhaps)?