In a 2013 talk at Ryerson University’s “God and the Multiverse” workshop, Timothy O’Connor presented a materialist account of the Incarnation, which, he claimed, was “free of demonstrable incoherence.”  Here I’ll briefly lay out an argument for incoherence that can be assembled from various claims made in the talk, and then suggest that O’Connor’s proposed “way out” isn’t wholly attractive.
Materialism and Compositionalism
To begin with, how does O’Connor understand materialism? As follows:
I hold that human persons are wholly, materially composed individuals, who have a kind of unity not had by garden-variety material composites. This unity is conferred by our having strongly emergent mental capacities and properties...
The idea of a mental property is familiar enough, I suppose. To say that a mental property is emergent is, at least in part, to say that it is a “causal consequence” of a “specific threshold of organized complexity”  being reached in the physical organism. Then, in some fashion, the emergent mental properties bestow unity on the human body, resulting in a human person.
Fair enough. Next, how does O’Connor understand incarnation? He is a compositionalist—a position he describes in this way:
On my preferred version of compositionalism, when God the Son became incarnate, he simultaneously created and absorbed into himself a human embryo, which as it matured expressed increasingly significant cognitive capacities and properties...
That developing embryo, fetus, newborn, youth, adult was--and according to orthodox doctrine, eternally is--not a distinct person from God the Son...It was and is an instance of human nature—a living, fully intact human body…It is a part, the human part, of the one person, God the Son, latterly known as “Jesus Christ” in virtue of the incarnational event.
So the basic idea is that God the Son, who was a simple, disembodied Self, took on a human nature (i.e., “absorbed” a human body into himself), and became a composite whole, consisting of two parts: a human body and, presumably, an immaterial divine person.
An Argument for Incoherence
Now my tentative claim is that these remarks don’t seem to fit together well. In fact, they might even be demonstrably inconsistent. Consider this argument:
Every properly formed and functioning human body is an autonomous experiencing subject [i.e., a human person]. (O’Connor)
The human part of God the Son is a properly formed and functioning human body. (O’Connor)
So, the human part of God the Son is a human person. (1 and 2)
The divine part of God the Son is a divine person. (premise)
So, God the Son contains two persons: one human, one divine. (3 and 4)
But: there is exactly one person who is God the Son. (premise)
Let’s quickly survey the crucial premises, leaving out (3) and (5) which are simply valid inferences. (1) seems to follow from O’Connor’s emergent materialism. Thus, in the talk, he says: “A properly formed and functioning human body is sufficient for the emergence of an autonomous experiencing subject and agent at the center of a dynamic, phenomenal, intentional manifold of experience.”
(2) is equally secure. O’Connor notes: “That developing embryo, fetus, newborn, youth, adult...was and is an instance of human nature—a living, fully intact human body.” This certainly seems to suggest that Jesus’ body was properly formed and functioning.
What about (4)? It assumes, of course, that God the Son has more than one part—more than the human part. And if so, I take it, this other part would be a divine part. But surely that part would be a person in its own right. It would be the (pre-incarnate) person who became embodied in the incarnation—the body being the other part.
Lastly, (6) is something of an a priori theological truth. At any rate, O’Connor has no qualms with it: “It [i.e., the body of Jesus] is a part, the human part, of the one person, God the Son, latterly known as ‘Jesus Christ’ in virtue of the incarnational event.”
To my mind, the premises seem to be in fairly decent shape.
O'Connor's Way Out?
If you listen carefully to the talk, you’ll see that O’Connor has his sights set on denying (3). He wants to say that the human part of God the Son is not a human person; it is a non-personal, human part. Here’s what he says of that part: “It was and is an instance of human nature—a living, fully intact human body, but one that is not in itself a person at all.” That means that O’Connor will have to deny one of the premises leading to (3): either (1), (2), or perhaps both.
It seems to me that O’Connor will deny (1). “Typically,” he says, “an instance of human nature will include in itself a proprietary center of subjectivity and agency.” I assume that to say something is typically the case means that it isn’t always the case. That's fair. But note that there is a plausible reason for thinking that on emergent materialism there is a human person involved.
Consider the human embryo that God the Son “absorbs” (whatever that comes to; it's not clear). This physical part is said to mature “increasingly [in] significant cognitive capacities and properties.” But then surely, at some point, we will be confronted with “the emergence of an autonomous experiencing subject,” in which case even if there is only one (divine) person present at the point of “absorption,” a second human person will emerge later on, simply as a “causal consequence” of a “specific threshold of organized complexity” being reached in Jesus’ human body.
How does O’Connor avoid what seems to be this obvious implication of his view? By drawing an analogy. Just as for the materialist it’s not the brain that experiences things, but rather the whole material person, so too only the composite whole—God the Son—experiences things qua subject; his parts (post-incarnation) do not. Thus O’Connor:
But I do not think that orthodox Christology faces a deep problem here. Consider that the brain is not the subject of the experience of an ordinary human person--the whole person is...the subject is the larger whole…
In the unique case of the incarnate Christ, human nature is embedded within a larger individual--a divine human composite. It is that composite that is the experiencing agent.
Problem solved. In short, properly formed and functioning human bodies are persons unless they are embedded in larger composite wholes.
Incarnation at What Price?
Is O’Connor’s way out successful? It’s rather hard to say. There just aren’t enough details on the table. I think he needs to say something about why being embedded strips what would otherwise be a person—this bodily, human part—of its personhood. This is very unclear, and appeals to mystery here (O’Connor isn't averse) don’t really help.
Just take the case of the human embryo that eventually becomes the adult man, Jesus. It’s interesting that O’Connor picks that entity as the candidate for “absorption.” Why not the body baptized by John the Baptist? (cf. Matt 3). Why couldn’t the incarnation have taken place at that point? The problem, I suspect, would be this. Let ‘HB’ denote Jesus’ human body prior to reaching the so-called “threshold of organized complexity.” By the time of Jesus’ baptism, HB would have become a full-fledged human person. Once the threshold is achieved, a complete set of mental properties has emerged, thereby providing unity to and conferring personhood upon HB. So let HB+ stand for this resulting human person.
Now ask yourself: what would have happened if God the Son (pre-incarnate) had “absorbed” HB+ into himself? Well, it would have become a part of him; that much seems clear. What kind of a part? Personal or impersonal? It has to be one or the other. If we say it’s personal, then it looks like (5) is true. But this scarcely seems intelligible. How could there be two persons—or even just a single human person—inside a “larger” divine person?
On the other hand, if HB+ loses its superscript upon “absorption,” there has to be a sufficient reason for that. To lose the ‘+’, you have to lose those emergent mental properties. They would have to be removed during the embedding. But isn’t that a problem? For O’Connor also wants to say:
The one person—the Son—somehow operates through his human intellect, experiencing as subject the purely human phenomenal, intentional manifold...It is that composite which is the experiencing agent.
But there is no human intellect, if those mental properties aren’t there. All you’d have left would be HB, which presumably isn’t to be confused with a human intellect. To have intellect, you must have mental capacity and properties; but on this scenario you wouldn’t. The Son couldn’t “somehow operate” though his human intellect because he just wouldn’t have one. In short, there wouldn’t be any incarnation to speak of.
Perhaps now we can see why O’Connor’s preferred candidate for “absorption” is the embryo. For on his gradualist definition of human personhood, the embryo quite obviously isn’t a person. Mental properties emerge, but not of course all at once. It’s a gradual process. At the front end, however, at conception, nothing mental has yet emerged; and thus HB isn’t unified. Consequently, at best it’s a mere human body but nothing like a person. It’s perfect for “absorption” without incoherence; not so perfect for other purposes (e.g., as they relate to unborn human life).
There is a price to be paid for any theory of the incarnation, I suppose. The question is whether O’Connor's theory is priced right, if it divests human embryos of personhood. Here you might think (as I do) that the Incarnation has rather enough to do without taking on unnecessary metaphysical baggage. Indeed, one wonders whether starting from scratch without those materialist assumptions isn’t in fact the better (and less costly) way forward here.
— Richard Brian Davis
 Timothy O’Connor and Phil Woodward, “Trans-Universe Identity: Incarnation and the Multiverse.” [video]
 Timothy O’Connor and Jonathan D. Jacobs, “Emergent Individuals.” [link].