I've been swamped with paperwork the past several days, and since I needed to get passport photos for some ID-thingy or other, I went on a nice long walk from my apartment, just north of Trinity-Bellwoods park, to a good photo place on Yonge Street (you might have to zoom out one to see Trinity-Bellwoods Park). It was great to get out. On my way back I stopped by at Abelard Books on Queen Street and found two books I've been trying to find for some time: J.R.R. Tolkien's translations of Sir Gawain and the Green Knight, Pearl, and Sir Orfeo, and Dorothy Sayers's The Man Born to be King. They will certainly conduce to my reading pleasure for some time. I'm especially looking forward to the character development of Judas Iscariot in the Sayers book; she has an interesting dramatic approach to him.
I think I caught something, though, since I was feeling pretty bad last night; so I just finished my puzzlement post on Vallicella and went home rather than (as I was intending to do) staying up to finish some revisions on a chapter. In retrospect, it was probably not a good idea to write a post on the doctrine of the Incarnation while tired and feverish. So, having slept on it, here's a bit of clarification.
The triad is:
1. Necessarily, if two things are identical, they share all their (non-intentional)properties.
2. God the Son and Jesus do not share all their (non-intentional) properties.
3. God the Son and Jesus are identical.
Vallicella considers this to be an inconsistent triad; and then goes on to argue that (3) is false. All three statements of the triad are supposed to be part of orthodox Chalcedonian Incarnationalism (OCI).
(3) is to be understood as saying that God the Son and Jesus are numerically identical as persons, i.e., they are one and the same person. If this is so, however, (2) has to be interpreted in a certain way in order to create an inconsistency in combination with (1) and (3). That is, the properties under consideration have to be personal properties, properties necessary to being this person. But if this is how we interpret it, it seems (2) is not part of OCI.
There is a way (2) can be interpreted in order to apply to OCI, namely, if we interpret it as indicating natural properties. But then it will not generate inconsistency in combination with (3), unless we were to interpret the identity in (3) as stronger than just numerical sameness of person. I tended to slip into this interpretation in my original post; but it's ruled out by what Vallicella actually says in the article (and by his response to my original post).
So I'm puzzled about the argument.