More trinity

There's been some good comments on my last post. This is a continuation of that discussion.

In my original post, I treated "God" as a name, referring to a unique individual. The proposal on the table is that we treat "God" instead as a predicate (in the logical sense, not the grammatical sense): basically, "Jesus is God" does not mean "Jesus = God", but instead it means "Jesus is divine." It's a description, not an equation.

(This is not to say that "God" can't also function as a name; just that it isn't a name the way it's used in claim T1.)

On this reading, T1 could be paraphrased like this:

T1'.	(a) The Father is divine, (b) Jesus is divine, and (c) the H.S. is divine.

This is a sensible move, which smites both of my arguments in a single blow--because both of them treat "God" as referring to an individual. On this reading, the intermediate step "God is Jesus" (or "God is the Father", etc.) doesn't even mean anything--it's like saying "Human is Jeff".

So I agree that on this interpretation T1 and T2 are consistent. By T1, the Father, Jesus, and the H.S. are each divine. By T2, no two of these people (or "persons", if you prefer) are the same. So far so good.

But not so fast: the trinitarian also wants to make a third claim (which Eric was getting at):

T3.	There is exactly one God.

(This assumption was latent in my previous use of "God" as a name. But if "God" is a predicate, claim T3 needs to be made explicit.)

If we're using "God" in the same way as in T1, then we should be able to rephrase it:

T3'.	There is exactly one divine entity.

Now we have problems again. Let's give a name to that divine entity; say "Theo". Then we can conclude from T3':

P4.	If any entity is divine, then that entity is Theo.

And this "is" is identity--the equals sign. For any entity X, if X is divine, then X = Theo. But if I'm right so far, we can rewrite my first argument from before:

1.	The Father is divine	T1'(a)
2.	The Father = Theo	By P4
3.	Jesus is divine	T1'(b)
4.	Jesus = Theo	By P4
5.	Jesus = the Father	Identity is transitive and symmetric

We can also redo the second argument from before, provided that there are properties we can ascribe to Theo (like being a trinity) that don't apply to Jesus (or to one of the other two, for that matter).

So where might these arguments have gone wrong? What are our options?

1. We can deny T3: There are, in fact, three or more Gods.
2. We can deny that T3' is a good paraphrase of T3. There is only one God, but there are, in fact, three divine entities. In this case we need to tell a good story about what T3 really means.
3. We can deny that P4 follows from T3'. That is, we can deny the interpretation I gave to "There is exactly one". In this case we need to tell a good story about what "There is exactly one" really means here.
4. As with the original arguments, we can deny the transitive or symmetric properties of identity.
5. Or we can give up on T1 or T2, and either (a) become unitarians or (b) start over with our description of the trinity.

Now, options 2 or 3 seem feasible within the context of orthodox Christianity. Not easy, but feasible. Then again, nobody ever tried to say the trinity was easy.

Discuss.


[Footnote. Rebecca brought up an interesting point about Peter Geach's idea of "relative identity", which she represents as denying that identity is transitive. Here's my general position on that kind of move.

"Identity" is an abstract relation that philosophers and mathematicians introduced for speaking about things technically. As such, its defining properties are conventional. Now, you can say, "But wait! The conventions are bad! Here's a more useful set of conventions." There can be a lot of merit to an argument like that, but I don't think it's the best way of putting the point. Thing is, the conventions are very, very entrenched, and changing them is like trying to get people to use the "+" symbol to mean division--confusing.

That doesn't mean Geach's points are a waste of time, though: what is up for grabs is the semantics of non-technical ordinary language expressions like "Bush is the president", or "That is a good argument." There may be good reasons to think that the meanings of these sentences don't satisfy the formal conditions we conventionally put on identity. Now, one way to put that kind of complaint is to say something like "identity isn't transitive"; I would much rather say, "we don't actually mean identity (though we may mean something similar)".

(In fact, I haven't actually read Geach, but I think this is basically what he says; though he also adds the stronger claim that in fact we couldn't mean (absolute) identity, because its conventional properties aren't even coherent.)]

[PPS. I just found out that Peter Geach and Elizabeth Anscombe were married! Crazy.]