Steve, it is amazing to me that when I try to un-confuse you on basic logic, I get abused as some kind of arrogant rationalist. But I'll continue, for the sake of the less smug who may read this.
Actually, I hadn’t leveled that accusation. But since you bring it up, yes, there’s a sense in which you’re a rationalist, albeit a rationalist who takes intellectual shortcuts.
You also try to try to bully your opponents into submission. Maybe intimidation works in the classroom, but it has no effect on me.
For a relation to be symmetrical means that if A bears that relation to B, then also B bears it to A. A symmetrical relation doesn't have a direction, as it were.
You admitted at the outset that you know nothing about enantiomorphism.
See here sections 1&2.
I’m already acquainted with the Stanford entry on identity, which, of course, doesn’t address enantiomorphism. Nice bait-n-switch, though.
Geach's position is widely rejected…
I didn’t appeal to Geach, so that’s a red herring.
But I do claim that it is self-evident that there's such thing as =, and that L's Law is self-evident as well, and that these are part of our God-given common sense, and so, really don't need arguing for, for us to rely on them.
Since your unitarian god doesn’t exist, that appeal fails to inspire much confidence. Beyond that, there are several basic problems with your argument:
1. Does Isaian monotheism contradict the Trinity?
Tuggy likes to bandy this charge, but I have yet to see him even begin to rigorously derive that contradiction from Isaian prooftexts. If he’s going to allege a logical contradiction, then that’s a logically stringent allegation. He has to meet to meet a rigorous burden of proof. Just making facile appeals to the law of identity will hardly suffice.
This is what I derive from Isa 40-48:
i) Isaiah logically excludes the possibility that someone without Yahweh’s attributes could be truly divine.
ii) Isaiah logically excludes the possibility that someone with Yahweh’s attributes couldn’t be truly divine.
But I don’t see, by logical implication, how one validly infers from either or both of those propositions that the Trinity contradicts Isaian monotheism.
2. Tuggy has conceded if God is a Trinity, then that’s a necessary truth. In that event, he can’t simply invoke another necessary truth (or what he takes to be another necessary truth) to falsify the Trinity.
If we’re confronted with two apparent necessary truths which apparently contradict each other, what should we do about that? We can’t arbitrarily privilege one necessary truth over another. And a contradiction (real or apparent) doesn’t point in any particular direction regarding the possible resolution.
At best, that shifts to the issue of what’s our degree of warrant for believing that an apparent necessary truth is, in fact a necessary truth? In case of conflict, how do we weigh the comparative warrant for one with the comparative warrant for the other?
The warrant for believing the Trinity is a necessary truth involves the warrant for believing the Bible is inspired, as well as believing the Bible teaches the Trinity.
3. Tuggy says Leibniz law is self-evidently true whereas the Trinity is not self-evidently true.
Keep in mind that he hasn’t actually demonstrated the relevance of Leibniz law to his unitarian prooftexts.
But for the sake of argument, is it self-evident that Leibniz law is a necessary truth? Take the Stanford entry on psychologism:
I think psychologism is wrong, but a philosopher like Tuggy can’t just stipulate that psychologism is self-evidently wrong, for the arguments and counterarguments are quite complicated.
And this illustrates a larger problem for Tuggy: the status of necessary truths is worldview-dependent. Imagine if he were debating W. V. Quine rather than James Anderson. The presumption would be quite different.
On the one hand is the warrant for believing necessary truths like (arguendo) Leibniz law.
On the other hand, the warrant for believing there are no necessary truths given the warrant for believing in things like physicalism, psychologism, eliminative materialism, naturalistic evolution, &c.
I don’t believe those things myself, but as a philosopher, Tuggy can’t act as though his own position is a just a given.
4. Finally, Tuggy’s own position runs afoul of Leibniz law: