Chad M. sent me a paper of his in which he illustrates the distinction between the 'is' of predication and the 'is' of identity using the following examples:
1. Joseph Ratzinger is [the] Pope
2. Water is H2O
where the first sentence is proposed as an example of a predication and the second as an identity sentence. If I were to explain the distinction, I would use these examples:
3. Joseph Ratzinger is German
and (for consistency of subject matter)
4. Joseph Ratzinger is Pope Benedict XVI.
(2) and (4) are clearly sentences expressing strict, numerical, identity. Identity is an equivalence relation: reflexive, symmetrical, transitive. It is also governed by the Indiscernibility of Identicals: if x = y, then whatever is true of x is true of y, and vice versa. By these four tests, the 'is' in (4) is the 'is' of identity. The 'is' in (3) expresses a different relation. Frege would say that it is the relation of falling under: the object JR falls under the concept German. That relation fails each of the four tests. It is not reflexive, not symmetrical, etc.
Now my problem is that I don't find (1) to be a clear example of a predication in the way that (3) is a clear example.
Although 'The Pope' is a definite description, not a name (Kripkean rigid designator), (1) could be construed as asserting an identity, albeit a contingent identity, between the object picked out by 'JR' and the object picked out by 'the Pope.' After all, the sentence passes the four tests, at least if we confine ourselves to the present time and the actual world. The relation is reflexive, symmetrical, and transitive. For example, if JR is the Pope, and the Pope is the vicar of Christ, then JR is the vicar of Christ. Furthermore, whatever is true of JR now is also true of the Pope now, and vice versa. So the indiscernibility test is satisfied as well.
Why not then say that (1) expresses contingent identity and that the 'is' is an 'is' of identity, not of predication? The fact that one could maintain this, with some show of plausibility, indicates that Chad's example is not a clear one. That is my only point, actually.
I grant that the notion of contingent identity can be questioned. How could x and y just happen to be identical? For Kripke, identity is governed by the Necessity of Identity: if x = y, then necessarily x = y. This has the interesting implication that if it is so much as possible that x and y are distinct, then x and y are distinct. (Shades of the ontological argument!)
But there are philosophers who propose to speak of contingent sameness relations. Hector Castaneda is one. So I am merely asking Chad why he uses the puzzling and provocative (1) as illustrative of the 'is' of predication.
There is a labyrinth of deep questions lurking below the surface, questions relevant to Chad's real concern, namely the coherence of the Trinity doctrine and its (in)coherence with the doctrine of divine simplicity.