Poll – How many divine Persons?

Dale,

Well, I certainly don’t think it’s transparent to everyone that numerical identity, i.e., the identity required to be counted as one, requires Leibniz’s Law. For instance, I am not, by the indiscernibility of identicals, identical to myself one-trillionth of a second ago, but it isn’t obvious to everyone why this should count against numerical identity (even if LL is required for self-identity), since I have to consider myself now and myself one-trillionth of a second ago as the same exact thing for all sorts of reasoning. Either I am doing so purely as a pragmatic convenience, or I really am the same exact thing. The problems raised on either side are complicated and not fully resolved.

Further, even if we appeal to Leibniz’s Law, that doesn’t help as much as it would seem. Quantification is always relative to a universe of discourse; you can appeal to Leibniz’s Law either for an unrestricted domain or a restricted one. For instance, if x and y differ on some properties G but are exactly equivalent for some properties F, restricting the domain to the relevant properties F would yield us the result that, for that domain, x and y are numerically identical. So you need not just Leibniz’s Law, but an unrestricted domain — you have to be quantifying over everything. But that’s a tricky issue. To quantify over everything, we know we can’t be quantifying over the set of everything, because that leads straightforwardly to contradictions. Then what are we doing? Can we really quantify over everything, or do we simply do so for relevant practical purposes? (This is the flip side of the previous problem; and shows that you can’t get out of the normativity problem by appeal to LL, since the same problem arises here unless you have an account of universal quantification that doesn’t appeal to a set of everything.)

On the parallel argument, while I think one might question the formulation of (1), I don’t think there’s anything puzzling at all about its meaning. I can be unique visitor x, y, and z, for instance, by using three different computers to view the website. So that’s the least puzzling thing about the parallel. The rest of the argument is much harder to interpret. I don’t think there’s any such thing in natural language as “wearing its logic on its sleeve”; for one thing, it depends on which logic you use and how you’ve used it. For instance, you’ve chosen to treat ‘Father’, ‘Son’, and ‘Holy Spirit’ as constants rather than as predicates, which is a controvertible move, since it’s unclear whether this is the best way to treat proper names. I think we’ve argued that question before. You’re right about your diagnosis if we really can convert ‘Father’ to logical constant f without loss of logical functionality; but there are other positions (for instance, I’m inclined to think that proper names virtually never function logically as constants because they are predicable and constants are not; but there are other positions besides my own on which it would arise).

I suspect one issue people are having with both 2 and 3 is what it means to say x is ‘numerically identical’ to y; usually we understand it to presuppose that (among other things) x maps numerically to y. Understood in that way 3 would be puzzling. On the other hand, you might not think of numerical identity as requiring such a presupposition; in which case (2) might be puzzling. Numerical identity, after all, has no well-established and rigorous definition, which is why it has tended to be a hot topic in analytic philosophy.

I think a way to highlight the general character of the problems people are (probably) having is to use an argument of similar form. Consider the following argument:

(1) x, y, and z are three unique visitors to the website in one person.
(2) Therefore neither x, y, nor z are numerically identical to that one person.
(3) This one person is numerically identical to a unique visitor.
(4) Therefore there are at least four unique visitors.

Now, this turns out to be a very puzzling argument in many ways. Unique visitors don’t map onto to persons in any regular way; the two are intimately related, but they are counted differently. So a website counter can identify as a single unique visitor many people (e.g., they could all be looking at the website together on one computer), or as two unique visitors one person (e.g., he could look at the website from two different computers). Suppose we set aside the unique visitor as many persons case, and assume that every unique visitor is one and only one person. Then it is true that every unique visitor is a person, and that in each case this person is numerically identical to the thing that that unique visitor is. Thus (2) is ambiguous between “Neither the thing that is x (i.e.,, the referent of ‘x’), nor the thing that is y, nor the thing that is z, is numerically identical to a person,” which is false; and “Neither the thing that is (i.e., the referent of the description) x, qua (description) x, nor the thing that is y, qua y, nor the thing that is z, qua z, is numerically identical to a person,” which is true. A similar ambiguity arises with (3); and (4) doesn’t follow from any of the interpretations of the premises except where (2) and (3) are both interpreted so as to be false. Likewise, someone might question the particular formulation of (1).

I’m not saying that this is a rigorous parallel, but they are parallel in terms of the questions they raise. For that reason and others, I’m less inclined to think that the rejection of (4) has to be a mistake; it may just have arisen due to the ambiguities of (2) and (3) — (4) doesn’t manifestly follow from (2) and (3) because both are ambiguous, and so someone could quite reasonably not see how (1)-(3) put together would yield (4), even though (1)-(3) might all sound right. It would have to involve some confusion; but the confusion might more a matter of interpreting the premises than drawing the conclusion, and as much due to the argument itself as to the person interpreting it.