When two theories posit items playing structurally identical roles grounding identical truths, Leibniz's identity of indiscernibles implies the theories describe the same ontology under different terminology.

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Identity of indiscernibles(One of the conclusions Leibniz derives using the PSR.): The principle that no two distinct entities can share all the same properties — if two things are indiscernible, they are identical.
Leibniz: Leibniz is a German philosopher and mathematician from the 1600s-1700s who developed calculus (a powerful math tool for measuring change and areas) independently around the same time as Isaac Newton. He's famous for creating much of the notation we still use in mathematics today and for arguing that everything in the universe follows logical principles. His ideas profoundly influenced modern science, mathematics, and philosophy, making him one of history's most important thinkers.
Ontology(Carnap argues this enterprise is based on a mistake): The philosophical discipline that tries to answer hard questions about what there really is.
Structurally identical roles(describing how items in different theories might work the same way): When two things function in exactly the same way within a system—they have the same relationships and perform the same function, even if they have different names.

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