In the famous graphic novel Watchmen by author Alan Moore, Dr. Manhattan is able to duplicate himself and simultaneously be three distinct places at once. He can, for example, have one body standing in the doorway and one body sitting on the bed (both of which are talking to his girlfriend) as well as another body working in the laboratory in a separate room, who is aware of the conversation the other bodies are having. And yet, each particular figure is identical to him. Thus, Body 1 could make a certain indexical claim: “I am a numerically distinct body, but identical to the person Dr. Manhattan.” Body 2 could make the same statement.
In the soft-Latin conception of the Trinity advocated by Scott Williams, the formulation is a “flipped” versions of Dr. Manhattan. The divine Logos thinks: “I am the Father,” which translates: “I am numerically the same but not identical to the Father.” And the Father thinks: “I am the Father,” which translates: “I am numerically the same and identical to the Father.” Through means of these indexical phrases, one is able to preserve the Trinitarian aspect of God, but also preserve a robust monotheistic conception.
One obvious point to remember is that such as conception of God is probably quite a bit anthropomorphic. I doubt God thinks in English, so these propositions should not be taken in a strictly univocal sense. And although the case of Dr. Manhattan is weird, I find myself with enough imagination to think about the subject of his identity without dismissing it as completely meaningless. I wonder whether or not Dr. Manhattan provides any sort of useful thought experience for theologians and philosophers contemplating the Trinity. Please feel free to share your thoughts in the comments.