We’re beginning to talk past one another. My main point is that RI does not committ one to views about ‘qua’.

Here is RI:

(RI): x and y are the same F but x and y are different Gs.

That’s from the Stanford Encyclopedia of Philosophy, an article on RI written by Harry Deutsch. It’s a good article.

If you can derive a view about ‘qua’ from that proposition alone, you are a rockstar. That’s my main point. Does RI-logic contain singular references? Now we are asking a new question. We went from talking about RI to RI-logic. Well, suppose it, that is, some particular version of it, doesn’t. Oh well, so much the worse for it if “singular reference” means reference to a single thing. I would have thought trinitarians thought they made singular reference to God. I would have thought that I made singular reference to the number one when I think “one is the loneliest number”. Similarly for “I exist”. Maybe RI-logic need not deny this, let’s hope, but that means looking at details that I’m not in a position to do (and it’s not the point of this post).

I won’t debate van Inwagen’s position since I don’t have his book and it was a long time ago that I read it. If he thinks RI is committed to something stronger than RI above, and if he gets rid of singular reference in his RI-logic, then okay for him. Doe he use the expession Jesus qua related is…? That would surprise me.

No, I don’t know anybody who accepts RI with identity, but then again, I don’t know anybody who accepts RI. Then again, I doubt anybody could really deny classical identity. It’s obvious as day, like “I exist”. Nobody could really think that and doubt it and nobody could think “the current president is identical to the current president” and doubt it, not seriously.

Anyway, it still seems to me an open question as to how to understand ‘qua’.

Van Inwagen does argue this. However, he begins the discussion by noting: “The language of RI-logic contains no singular references. Given our decision to be non-committal about the existence of classical, absolute identity, this is no accident. The philosopher who eschews classical, absolute identity must also eschew singular terms.” So, yes, this is a property of the RI-logic devoloped by van Inwagen, which makes no use of classical identity.

Still, as has been discussed, those who hold relative identity typically do not believe in classical identity – or at least they say that classical identity is only an approximation that works in everday cases. Do you know of any philosophers who accept relative identity without denying absolute identity?

At pp. 256ff., van Inwagen discusses the ‘subdominance’ of classical identity, noting that if classical identity is by definition subdominant (i.e. if, for any count noun N “x is the same N as y x is an N and x = y”) “then RI-logic is an interesting topic [i.e. describes something useful about the universe] only if classical identity does not exist.” But one can (and van Inwagen does) question whether classical identity is by definition subdominant. Personally, I rather suspect that it is, since x=y -> (for any predicate P, (Px -> Py)) implies the right-to-left direction of the operator, leaving only the left to right direction, and any questioning of the left to right direction would seem to make ‘absolute’ identity somewhat less than absolute.

Note that this is not RI, but RI and the claim that there is no classical identity. RI, itself, does not entail that there is no classical identity. As you say, vanInwagen himself develops a logic of relative identity, but is non-commital as to whether there is classical identity. He would not be non-commital if RI entailed that there is no classical identity.

“More relevant to our point, van Inwagen argues on pp. 259-260 that the logic of relative identity contains no absolute singular references.”

That’s not right. ‘One’ is a term with absolute singular reference. RI-theorists should not deny this. Instead, they will argue that the properties and individuals governed by RI cannot be expressed by terms with absolute singular reference. And the point is just that: they restrict RI to a certain class of predicates. This restriction, however, is defended not by appealing to RI, but rather, by appealing to something else. Incidentally, I haven’t heard a good defense of making a non-arbitrary restriction and that’s one reason why I fin RI to be implausible.

“The word sort does appear, repeatedly, in Richard Swinburne’s definition of RI in The Christian God.”

That’s fine. He can use the word if he wants to, but an RI-ist need not.

“If what you just said is true, then what on earth does ‘qua’ mean?”

Good question. I have no idea. That’s why I first indicated that it is important to state the logical form and entailments from sentences that contain ‘qua’. I wouldn’t be surprised though if ‘qua’ makes no single kind of semantic contribution, but that it’s use is various. The point is just that if we are to appeal to it to help make sense of the trinity, it needs to be clarified or it won’t help at all.

“In order for us to count differently given different sorts, the truth values of the != statements must be different for different sorts, which is the same as relative identity. So the “qua solution,” if interpreted this way, implies relative identity.”

That’s not the same as relative identity. Relative Identity does not tell us how to count things, although we might count things under sorts. First, this is because relative identity is consistent with classical identity and the claim that we count by classical non-identity. Second, nowhere in the formulation of RI does the word ‘sort’ appear, so it doesn’t imply anything about sorts.

You say “The idea is that there are different sort, like ‘being related’ and we can count something only with respect to a sort.” I say that this implies relative identity. The reason is that counting depends on the identity relation. That is, you only count the things that are not numerically identical to one another. To put it more formally, to say that there are three things is to say that (∃x,y,z)(x != y & x != z & y != z). In order for us to count differently given different sorts, the truth values of the != statements must be different for different sorts, which is the same as relative identity. So the “qua solution,” if interpreted this way, implies relative identity. Of course, the interpretation requires the possibly controversial claim that ‘related’ can function as a sortal, but that doesn’t strike me as too problematic in this context.

Does the qua solution require something stronger than relative identity? I’m not sure, but I would say that, at least on this interpretation, it does require relative identity, at least as a bare minimum.

Let me respond to your first point. You wrote:

“Christian – in this case, of course if some person P is a Christian philosopher, then P is comitted to holding some propositions by faith. What we are saying when we say that P qua Christian is so comitted is that he is comitted by virtue of his being a Christian, not by virtue of his being a philosopher.”

I understood defenders of the “qua solution”, to give it a name, would deny what you say above. They say:

(1) s qua F is G

does not entail

(2) s is G.

I take it they deny this in the case of the trinity so that:

(3) Jesus qua related is one in number.

does not entail

(4) Jesus is one in number.

The idea is that there are different sort, like “being related” and we can count something only with respect to a sort. There is no sort specified in (4), so it is incomplete and not truth-evaluable. But then (3) does not entail it.

You introduce an ‘in virtue of’ relation to help capture the “qua solution”. Maybe it helps, I’m not sure. As I understand you, if s is F qua G that entails s’s being G is explained by S’s being F. But, if that’s right, then s is F. And if s is F, then I no longer see how this strategy could help defenders of the trinity.

Are there grounds for denying the move from:

(5) God qua related persons is three in number,

to,

(6) God is three in number.

You then say:

“Relative identity basically says that it is possible for x qua S1 to have the property “is equal to y qua S1,” but for x qua S2 to have the property “is not equal to y qua S2.” This, I claim, is equivalent to, for instance, how Richard Swinburne defines relative identity.”

I don’t see the connection yet. I thought relative identity is just the claim that possibly, there is an x and y, such that x is the same F as y, but x is not the same G as y and x is not strictly identical to y. There is nothing in this thesis, by itself, which implies that some x can a property qua being an F. The ‘qua’ locution, and any explication of it, is left out entirely.

That is not to say that one cannot accept both views. And maybe even together they will help to explain away the inconsistency of the trinity. The point is just that these two views are very different and one could accept one view without accepting the other.

Relative identity basically says that it is possible for x qua S1 to have the property “is equal to y qua S1,” but for x qua S2 to have the property “is not equal to y qua S2.” This, I claim, is equivalent to, for instance, how Richard Swinburne defines relative identity: “the suggestion that it is possible for a substance a which is φ and ψ to be the same φ as b but not the same ψ as b is the suggestion of the possibility of ‘relative identity’” (The Christian God, p. 15 – note that Swinburne ultimately rejects relative identity). That is, relative identity claims that identity can be a ‘qua property’ and can have different values qua different sortals.

I think using ‘qua’ in English constructions makes sense, in some sense of ‘makes sense’. I’m interested in getting a better grip on the logical form of some of these constructions and also a better grip on their entailments. It is this deeper understanding I claim to lack, no surprise.

Kenny’s example: “The Christian philosopher qua Christian is comitted to holding to the truth of certain propositions by faith, but, qua philosopher, he is also comitted to holding to the truth of only those propositions for which he has epistemic warrant.”

So, I want to know what the phrase ‘The Christian Philosopher’, occuring as it does as a subject, contributes semantically. Does it refer to an individual? Something else? (I’m not asking for an account of phrases with its form, that’s hard, just tell me what you mean, that should be easier).

And then, I wonder, does it follow that if s is F qua G, then s is F? I take it that everybody wants to deny this. But in your example that would just mean that the christian philosopher is comitted to holding to the truth of certain propositions by faith. Now, you can say: wait! that is only true of christian philosophers ‘qua being Christian’.

But what is an individual qua being Christian except for a person who is a Christian? I’ll leave that question open to you.

Finally, I don’t think the ‘qua’ solution is the same as the relative identity solution, they really are very different.

JohnO,

Don’t some Christian’s look to creeds to defend the “Jesus is God” claim, and not the Bible? The Bible might be thought to be but one inspired source. And there is always the question: is Jesus God? We can then try to figure out what the world would have to be like for that question to get an affirmative. But the idea is just that by discussing the ‘qua’ strategy we don’t mean to be giving an exegesis of the bible, but are only trying out one strategy for making a creedal statement consistent and comprehensible. You might think: “but if it’s not scripture, then who cares?” If that’s the thought, I think many philosophy minded people will have a lot of long (long-winded) responses. The short one is that many people think Jesus is God and are motivated, for whatever reason, to assert this and we are interested in whether this belief is reasonable amongst a boackdrop of other beliefs they may have.

Does the Bible ever speak of the Jesus and God like this? I don’t think it does. And that is why I don’t think any of this is relevant to discussing the trinity. Jesus plainly affirms the Shema of Israel – showing us all that Jesus and the Pharisees have the same God (inequality between Jesus and God mind you). Jesus plainly says he has a God in John 17:3. Jesus plainly says he only does what God tells him to in John. Why is this such a big problem that you must think Jesus is God?

As for the qua, I think this does make sense in some cases. For instance, we might say: “the Christian philosopher qua Christian is comitted to holding to the truth of certain propositions by faith, but, qua philosopher, he is also comitted to holding to the truth of only those propositions for which he has epistemic warrant.” If this sentence is true and one can be at once a proper Christian and a proper philosopher (as we believe one can), then we must explain the compatibility of the two statements in one person.

What this means when applied to the Trinity statement is that the qua makes sense (more or less), but doesn’t do much to solve the problem, unless it is taken as grasping at the idea of relative identity: the Son qua God is the one and only God, but the Son qua Son bears a certain relationship to the Father and is therefore numerically distinct from the Father and is, as it turns out, one of three. Not to be overly pedantic, but this is the same as saying “the Father and the Son when both considered under the sortal term ‘god’ are numerically identical as the one and only being of that sort, but when considered under the sortal terms ‘father’ and ‘son,’ respectively, or both under the sortal term ‘person,’ are numerically distinct.”

Hmmm, that is interesting, I’ve never heard this before!

Sure – I believe that Moreland and Craig try just that. They take to talking of the Trinity “as a whole”, vs just those three divine Persons. Once we do that, though we’re pretty far from the mainstream, which I’m sticking to for the moment, which has pretty steadily maintained divine simplicity, and never wanted to say that Father and Son were parts of something greater.

Morris was the one that convinced me that this wasn’t going to be a useful strategy for explaining the trinity. His argument was basically that if we consider any conjunctive reduplicative proposition of the form “x as P is F and x as Q is not F” if the subjects of both conjuncts are the same, and our substitution of F is univocal, then the move only muddies the water because the contradiction of x being both F and not F holds. It’s stuck in my head all this time because Morris’s book was the first thing I was assigned to read in my first graduate seminar.

Doesn’t seem very plausible to me.

Hope all is well.

“They’re three qua related, and not-three qua separate individual(s). Does anyone see a problem with this?”

I do. I don’t understand it. And I don’t mean that as a coy philosopher’s move in an argument, I really, really do not understand it. One might try to understand by analogy. Say there is a book on the table. It is one qua book and 498 qua pages. If we are interested in books, there is one, pages, there are 498. But, what does the ‘it’ refer to? I said “It is one qua book”. I ask: what is ‘it’ that is one? I don’t know what the answer is.

It seems to me there are 498 pages. They are parts of a book. There is one book, it has 498 pages as parts.

It also seems to me that we mean “of a kind’ when we say ‘qua’. So, a brother (an individual) is stinky qua cousin just means that respect to the kind cousin, the individual is a lousy one of those. With respect to the kind individual, if there is such a kind, he is not a lousy one.

But that doesn’t help to make sense of counting. We are interested in the question, how many individuals are their in the trinity? If we accept the kind talk, then the view seems to be that the persons are three with respect to kind related, if there is such a kind, and one with respect to the kind God. But God is not a kind, he is an individual. And ‘related’ expresses an incomprehensible kind.

Or am I just naive about this?

Reforming Ontology and Logic in the Light of the Trinity: An Application of Van Til’s Idea of Analogy.
http://www.frame-poythress.org/poythress_articles/1995Reforming.htm