In my previous post I sketched Michael Rea and Jeffrey Brower's proposal for understanding the doctrine of the Trinity. In this post I want to consider some ways a critic might push on their proposal. In considering the case presented by Rea and Brower there appear to be at least two ways for the critic to proceed. One route would be to push against the account of numerical sameness without identity as a solution to the problem of material constitution. The second route would be to show that the analogy between the proposed solution and the doctrine of the Trinity is weak. In what follows I will make some remarks in regards to the former route.
In order for Rea and Brower's argument to go through it is important that their account of numerical sameness without identity provide a real solution to the puzzle of material constitution. If we don't have good reason to think that the account holds in the case of material constitution, then why should we think that it holds in the case of divine constitution? The argument by analogy proceeds by taking a case where we have clear understanding, and extend that understanding to a more distant case. So, what can be said for numerical sameness without identity?
Well, on thing that might be of concern is the degree to which numerical sameness without identity is counterintuitive. To be sure Rea and Brower grant that their argument for numerical sameness without identity is counterintuitive, but they assert that this is not a problem since every proposed solution to the problem of material constitution is counterintuitive. I'm happy to grant that any proposed solution to the problem is conunterintuitive, but we might be concerned that all claims of counterintuitiveness are not equal. Being the least intuitive account among competing counterintuitive accounts is certainly no advantage. I think it safe to assume that most metaphysicians consider numerical sameness without identity to be not just counterintuitive, but highly counterintuitive. Of course the number of metaphysicians who think a thesis false doesn't make it so. The point is that we should be suspicious that the account of numerical sameness without identity has not been neglected without good reason. If we are expected to adopt numerical sameness without identity as a solution to the problem of material constitution then more is going to need to be said as to why the account is preferable to other leading accounts.
Further, it is not clear why Rea and Brower are not committed to believing in Socrates’ weird objects like bent-tree. What is it that distinguishes the objects that seem to be significantly similar to the weird objects from the weird objects themselves? An obvious line of demarcation does not readily present itself. They acknowledge that this is an interesting and surprisingly difficult question, yet they offer nothing by way of explanation. This lack of explanation seems to leave the account of numerical sameness without identity on rather weak footing. The implication for the Trinitarian analogy is that if you could account for why an object can be simultaneously a tree and bent-tree you might have a stronger analogy, because this appears to be closer to the Trinitarian claim.
In my next post I'll grant numerical sameness without identity for the sake of argument to see whether it does the work Rea and Brower want of it.
Numerical Sameness Without Identity "counterintuitive"? I'd say "incoherent." It's like saying "Blueness Without Primary-Color-ness."
If identity is nothing else, it is numerical sameness. If that is false, then the only option left is relative identity. And actually, I'd say a RI approach to the Trinity, as van Inwagen has proposed (the last two essays in God, Knowledge, and Mystery: Essays in Philosophical Theology), is the only logically workable one on offer (although I think there is also such a thing as absolute, "numerical-sameness" identity, and that it can be expressed in terms of RI).
If one talks of "Numerical Sameness Without Identity," I can't see how one can fail to be "double-counting." If constitution is just coincidence, and coincidence is just overlap, then this account of constitution is subject to Ryan Wasserman's "deflationary" treatment (Noûs 38 (2004): 693–71)), and this will decidedly not give the desired result in explaining the Trinity.
Sorry; the title of the Wasserman paper cited above is "The Constitution Question."
Evidently Bono believes in numerical sameness without identity. In "One," he puts the view thus: "We're one, but we're not the same." (Of course, I'm taking "the same" here to indicate identity. Perhaps a tendentious reading. I'll ask Bono about it someday.)
More to the point, I'm not sure Micah's complaint is all that telling. I certainly grant that identity necessarily involves numerical sameness. And, although it's been a little while since I read Mike Rea's papers on this, I'm pretty sure he grants that, too. What he denies is that numerical sameness necessarily involves identity. Using Micah's analogy, Rea and Brower claim that you can have primary coloredness without blueness (sameness without identity)--but of course they _don't_ claim you can have blueness without primary coloredness (identity without sameness). The latter would be incoherent. The former is not obviously so.
I hasten to add that I am not a believer in sameness without identity, but I do think it's a pretty cool view that deserves more consideration. For that reason, I'm really glad that Matthew is doing these posts.
Okay, at first I thought my analogy came out backwards, but now I realize I just framed it wrong: the first sentence of my second paragraph should read "If numerical sameness is nothing else, it is identity." And then, actually, the next sentence would read "If it is nothing else—that is, there's no such thing,—then you're probably a Geachian."
And, certainly, it's worthwhile to look into what people might mean by such things—not trying to be a "crank" in both senses of the term! :-) But still, if someone's talking about "numerical sameness without identity," I find myself saying, agrave; la Peter van Inwagen, that "I do not understand him." Speaking of whom, here's perhaps a more apt analogy: It's like denying that identity is transitive; "The person who denies that identity is transitive does not understand the difference between the number one and the number two." (PvI, quoted loosely from memory, somewhere in one of the essays in Ontology, Identity, and Modality.)