Dale Tuggy's primary objection to the Trinity is that it (allegedly) violates the logical law of identity. However, one problem with his objection is that Tuggy is an open theist.
Open theism raises ancient philosophical questions, stretching back to Aristotle's naval battle, about whether propositions regarding the future (or future contingents) have truth value. There are two, perhaps related, issues:
i) In open theism, there is no actual future. The future does not yet exist (pace the B-theory of time).
ii) There is no one future. Rather, there are multiple possible futures. No particular alternate timeline is privileged in advance.
Considered either in isolation or combination, that raises the question of whether an open theist can make true statements about "the future".
If the outcome is open-ended until it eventuates, can statements about "the future" be either true or false? Like Schrödinger's cat, it could go either way.
That's not a problem for Calvinism. A Calvinist could be an A-theorist about time. Even if the future isn't real (as of yet), the future is still determinate. But in open theism, the future is indeterminate.
Some philosophers attempt to circumvent the problem by denying the law of bivalence. They espouse multivalent logic, viz. Łukasiewicz.
Perhaps that's Tuggy's position. If so, where does that leave his logical objection to the Trinity?