One of Dale Tuggy's dilemmas is his unsuccessful attempt to compartmentalize numerical identity. He makes allowances for personal identity which he disallows in the case of numerical identity. He's too bullheaded to appreciate that personal identity is just a special case of numerical identity. Numerical identity is the general principle, of which personal identity is one example.
For instance, Tuggy himself seems to think personal identity requires numerical identity. Tuggy the militant unitarian is numerically the same person as Tuggy the social Trinitarian. Yet Tuggy is a methodist about numerical identity, but a particularist about personal identity. Where numerical identity is concerned, he begins with criteria: Leibniz's Law! A necessary truth! Or his a priori stipulation that "numerical identity doesn't come in degrees."
But where personal identity is concerned, he begins with examples: "Don’t things change? e.g. Last year you weighed 200, and now you weight 210 lbs. But does this mean that the you of 2010 is not numerically the same as the you of 2011? Ridiculous! Things can qualitatively change while remaining numerically the same. That’s just common sense."
Here he just stipulates that qualitative change is consistent with numerical identity because "that's just common sense." So he has two contrary standards for defining identity. And yet he tries to merge the two when it serves his purpose.
Consider two hypotheticals:
i) What would I be like if my mother had died when I was five?
ii) What would I be like if I were a giraffe?
The first hypothetical is realistic. We may not know enough to answer that question, but that was possible, and if it happened, I would turn out differently.
But the second hypothetical is basically nonsense. A giraffe is so different from a human that it wouldn't be the same individual in any appreciable sense.
That's why a standard move in discussions of transworld identity is to take the nearest possible world as the frame of reference. A possible world most like the real world. But that means counterfactual identity is based on similarity rather than sameness. And similarity is a matter of degree. Degrees of similarity and dissimilarity.
That's why the first hypothetical is realistic. It posits that I and my counterpart have the same personal history up to the age of 5, at which point, due to a family tragedy, our paths begin to diverge. But because we were the same person with the same history up to that point, and because we remain human, have the same surviving parent, and so forth, there's a meaningful basis of comparison. Those could be alternate outcomes for the same individual.
By contrast, a giraffe is so unlike a human that a giraffe can't be your counterpart in a possible world. There is no sense in which you could be identical to a giraffe.
But if counterfactual identity is a matter of degree, then why not diachronic identity? Suppose we recast the counterfactual scenario in chronological terms: What would I be like if I turned into a giraffe tomorrow? Here issues of diachronic and transworld identity intersect. It's about past and future identity, as well as counterfactual identity. And the comparison fails for the same reason. Lack of adequate, salient similarity.
Tuggy's objection to the Trinity is especially ironic considering the fact that he maintains a temporalist view of God. So for Tuggy, personal identity and diachronic identity intersect in God's case no less than man's case. Tuggy's God undergoes change. And change is a kind of difference. Clearly, then, there's a sense in which Tuggy's God is not uniformly the same God from t1 to t2.
Likewise, Tuggy is a freewill theist. Tuggy's God has counterparts in possible worlds, where God said or did something different. Where God's experience is different. Clearly, then, there's a sense in which Tuggy's God is not uniformly the same from w1 to w2.
Even in reference to divine personal identity, Tuggy makes allowance for differentia concerning that individual. So why does he refuse to make allowance for differentia concering the Trinity? Why does he measure the Trinity by the yardstick of strict identity, but use a rubber ruler for his own God when it comes to transworld identity or identity over time? Flexible theories of identity for unitarian open theism, but inflexible theories of identity for Trinitarian theism.
Sure, Tuggy can dictate that certain kinds of change or difference are somehow consistent with numerical identity; sure, he can dictate that certain kinds of change or difference are consistent with his denial that numerical identity admits degrees of identity, but is there anything beyond his arbitrary stipulation to show how that's consistent?
He can attempt to distinguish between intrinsic and extrinsic properties, but that presumes rather that proves consistency with numerical identity. For unless you can already establish that the intrinsic/extrinsic distinction is compatible with numerical identity, you can't invoke that distinction to salvage numerical identity. Whether distinctions like that are consonant with strict identity is the very issue in dispute. And if that's consistent with numerical identical, why not other kinds of differentia?
This is a central tension in his position. He doesn't begin with Leibniz's law when he clears space for personal identity. When push comes to shove, he makes ad hoc modifications to Leibniz's law to accommodate whatever personal identity demands. His unyielding definition of numerical identity in relation to the Trinity becomes very yielding when he turns to the ambiguities of personal identity. He regards the "law of identity" as a necessary truth, but contingent truths shape his view of personal identity. As a result, you notice the gearbox smoke and grind when he tries to mesh the two.
There are philosophers like McTaggart who are far more uncompromising when it comes to strict identity. McTaggart is a consistent methodist. Tuggy, by contrast, has a makeshift position. He's a methodist when attacking the Trinity, but a particularist on personal identity. Yet his views on personal identity infect his views on numerical identity. By introducing fudge factors into personal identity, his theory of numerical identity becomes chocolate-coated in the process. There's no uniform principle driving his theories of identity.