Compositionalism, Nestorianism, and the principle of no co-member parts

Abstract Compositionalists hold that God the Son became human by acquiring all the parts that ordinarily compose a human being (his ‘human nature’). To be orthodox, though, they must deny that Christ's human nature is a person, even though it has all the parts that human persons ordinarily have. One way to do this is by appealing to the principle that no member of a natural kind can have another member of the same kind as a proper part. Since Christ is a person, he cannot have another person as a part, so if his human nature is a part of him, it cannot be a person. This principle is defended on the grounds that it can resolve metaphysical problems involving apparently multiple individuals of the same natural kind that share the same space. I argue that this is a weak strategy. First, it leaves unanswered key questions about how and why the principle applies to the incarnation. Second, counter-examples to the principle exist, suggesting that it is not true. Third, there is a better solution to the kinds of metaphysical paradoxes for which this principle is usually invoked, but this solution cannot be applied to the case of Christ. Consequently, compositionalists should not rely on this principle as a means of avoiding Nestorianism.


Concretism and compositionalism
A 'concretist' model of the incarnation is one which holds that God the Son became human by 'assuming' the parts that make up a human being 1what Brian Leftow calls a 'full natural endowment of a human being' (Leftow (2002), 278). For example, suppose that substance dualism is true, and that each human being consists of a soul and a body. Then a concretist would say that the Son became human by acquiring a human soul and a body, which were united to him. Or alternatively, suppose that physicalism is true, and each human being consists only of a body, which has both physical and mental properties (perhaps the mental properties are wholly distinct from the physical properties, as property dualists think, or perhaps notit makes no difference for our purposes). Then a concretist would say that the Son became human by assuming such a body. In other words, it makes little difference exactly what the 'full natural endowment of a human being' actually iswhat matters is that the Son acquired one. In what follows, I will follow convention in writing as if dualism is true and a 'human endowment' consists of a body and a soul, but nothing important depends on this.
Models of this kind have been by far the most common for most of Christian history. Typically, when ancient or medieval theologians write about Christ's 'human nature', they mean it (for the most part) in a 'concretist' sense: it refers not to a set of properties but to a concrete particular, namely the 'human endowment' that the Son assumes. It is easy to see why a model of this kind would appeal to anyone committed to anything like classical theism: if divine persons are necessarily atemporal and immutable, then a divine person cannot be transformed into a human being or anything else. But a divine person could exist in a relation to something that is temporal and mutable, and perhaps such a relation could be close enough that the divine person could genuinely count as being human in virtue of it. 2 'Compositionalist' models of the incarnation are a subset of concretist models. 3 On these models, when the Son assumes Christ's human nature, Christ's human nature becomes a part of a greater whole, namely Christ. Moreover, what it is a part of is not simply a mereological sum, but a genuine unity. What that genuine unity is, and what makes it a genuine unity, varies according to the model. Different concretists explain the assumption of the human nature by the Son in terms of different relations that may obtain between them. One might think that compositionalists identify the relation of part-to-whole as holding between the Son and the human nature, while other concretists identify alternative ones. However, it is not this simple.
To illustrate: one common idea that many concretists have used is that of instrumentality. On this view, the Son uses Christ's human nature like an instrument or tool: it is through the human nature that the Son acts upon the world. It is possible to construct a model of the incarnation like this that is not compositionalist in the sense defined above. Iain Torrance (1988,(92)(93)(94)(95) gives a helpful illustration of one way of doing this in the course of explaining Severus of Antioch's model of the incarnation. Severus (on Torrance's interpretation) thinks of Christ's human nature as like the stick used by a blind man to find his way around. Just as the blind man's attention is on the objects around him, which he perceives by using the stick, so too the Son's attention is on the human world, which he perceives by using Christ's human nature. However, the stick is clearly not part of the blind man; the implication, at least in Torrance's version of the model, is that Christ's human nature is not part of the person of Christ. This, then, is a concretist model, but not a compositionalist one.
However, other theologians have used the same notion of instrumentality in a compositionalist way. There are two ways of doing this. 4 The first is to keep the Son and Christ's human nature distinct, but to see them both as parts of a greater whole, namely Christ. One author who does this is Katherin Rogers. Her analogy for the incarnation is a boy, Nick, playing a video game. In the game there is an avatar which Nick controls. Both Nick and the avatar are parts of a composite she calls 'Nick playing'. Similarly, the Son acts through Christ's human nature, and because of this, the Son and Christ's human nature are both parts of a whole. This whole is, however, not a composite person, but a composite state of affairs (Rogers (2013), 254).
The second way of using instrumentality in a compositionalist way is to suggest that, when the Son assumes the human nature, the human nature actually becomes part of the Son. The situation is rather like an organ transplant, in which something that is by nature not part of the patient becomes a part. Thomas Aquinas articulates a model of this kind when he distinguishes between external instruments (such as an axe) and internal ones (such as a hand). I can use an axe to act on the world, and I can use my hand to do so, and in both cases I am (in a sense) using an instrumentbut my hand is part of me in a way in which an axe is not. God the Son uses Christ's human nature in a similar way, but like a hand, not an axe (Summa contra gentiles IV.41.11). On this view, God the Son is, in the incarnation, a composite person: he consists of the pre-incarnate Son plus Christ's human nature. 5 So while many theologians have proposed concretist models of incarnation that appeal to the relation of instrumentality, some of these models are compositionalist and some are not; and those that are compositionalist can be constructed in different ways. Something similar can be said about other relations which theologians have argued hold between God the Son and Christ's human nature: any such relation could, at least in theory, be understood as uniting God the Son and Christ's human nature in such a way as to make them both parts of a greater whole; or as uniting them in such a way as to make Christ's human nature part of God the Son; or as uniting them in a non-mereological way. 6 The Nestorian problem and a compositionalist response A common objection to concretist models of incarnation is that they are Nestorian. Normally, each human individual consists wholly of a single human endowment. I, for example, consist of a human body and soul. So ordinarily, any given human endowment just is a human person. One would think, then, that the same applies to the human endowment assumed by the Son. But this cannot be, for then Christ's human nature would be a person in its own right, distinct from the person of the Son, making two personsone human, one divineand that is the Nestorian heresy. Any Christian who wants to be orthodox must avoid saying anything that entails this.
One of the key tasks facing concretists, then, is to explain why Christ's human endowmentuniquely among all known human endowmentsis not a person. There are various ways in which concretists may try to do this. One way is to point to the unique nature of the union in Christ. On this view, there is something very special and unusual about the relation which holds between God the Son and Christ's human nature, such that it blocks the human nature from being a person. This is the approach typically taken by medieval philosophers. According to them, the divine Son acts as the 'supposit' of the human nature. Ordinarily, any human endowment is a substance, acting as its own supposit. But because Christ's human nature is united hypostatically to the Son, it cannot act as its own supposit. This means that it is not a substance, and therefore not a person, because a person is classically defined as a kind of substance. Just how this works is, of course, subject to many different interpretations, and medieval theologians disagreed over the details. Some, such as Aquinas, thought that the hypostatic union means that Christ's human nature lacks something that it needs in order to be a substance. Others, such as Scotus, thought that the human nature lacks nothing, but merely being assumed by the Son blocks it from being a person. 7 All agreed, however, that this is something extraordinary. The hypostatic union is a unique relation which uniquely blocks the personhood of the thing assumed.
A number of modern compositionalists, however, have given a different answer to the Nestorian problem, and it is this answer that I want to focus on in this article. 8 They point not to the extraordinary nature of the hypostatic union but simply to the fact that the human nature is part of a composite person. On this view, any person (whether divine or not) cannot contain another person as a proper part. Since Christ's human nature is a proper part of Christ, and Christ is a person, the human nature is automatically blocked from being a person. 9 This approach typically involves an appeal to the following general principle, which we can call the Principle of No Co-Member Parts, or NCP: NCP: For any two objects x and y that are both members of the same natural kind f at time t, x cannot be a proper part of y at t. 10 If this principle holds, then the fact that Christ's human nature is a proper part of a person automatically prevents it from being a person. 11 It is important to note how this approach differs from that of the medieval philosophers. They pointed to something unusualeven uniqueabout the way in which Christ's human nature was united to the divine Son. The modern compositionalists, by contrast, do not appeal to any special features of the hypostatic union. Instead, they point to a general rule of mereology, namely NCP. If we accept this rule, then Christ's human nature is straightforwardly blocked from personhood even if the relation between the human nature and the composite Christ is a relatively mundane one. As long as the former is part of the latter, we have the desired result.
But why suppose that NCP is true? Those who make use of it point to the fact that, if it is true, then undesirable metaphysical problems can be solved, quite apart from the incarnation. They point, in particular, to a cluster of problems of identity that arise from apparently overlapping individuals. 12 Imagine a cat, Tibbles. Consider one of Tibbles's hairs, h. Now consider the rest of Tibbles, without h, which we can call Tib. Tib and h jointly compose Tibbles. Is Tib a cat?
It seems that Tib is a cat, because Tib has all the parts needed for cathood (if Tibbles lacked that one hair, h, Tibbles would certainly still count as a cat; but Tib is exactly the same as Tibbles in that alternative scenario). But Tib is not identical with Tibbles, because Tib is a proper part of Tibbles. Therefore, it seems we have two cats occupying almost exactly the same space.
Worse, we can tell a similar story for every hair on Tibbles's body. If Tibbles has 1,000 hairs, there are 1,001 cats sitting on the mator indeed far more, because we can imagine parts of Tibbles that have various numbers of these hairs. These cats all overlap with each other, but they are not identical with each other, because they are not all composed of precisely the same set of parts. This is evidently a metaphysically unpalatable situation. And if the prospect of innumerable cats doesn't give us pause for thought, consider that everything that has been said about Tibbles could also be said about any human being. Are there thousands of distinct people sitting in my chair? If so, which one am I? Clearly, it would be highly desirable to be able to explain why there was only ever one cat sitting on the mat, despite the reasoning given above that suggests otherwise. 13 A number of solutions have been proposed to try to secure this result. 14 The most popular is to appeal to NCP, the principle that a member of a natural kind cannot have another member of that same kind as a proper part. If this principle holds, then Tib cannot count as a cat, because it is a proper part of a cat. It follows that there is only one cat on the mat, which is the desired outcome. 15 Applying this to Christ, we can say that the human nature cannot count as a person, because it is a proper part of Christ, who is a person. Once again, we have the desired outcome.
The most influential philosopher of religion to appeal to this reasoning is Brian Leftow. He writes: One wants to avoid the 1,001 cats, of course . . . The way to do so is clearly to adopt some principle ruling it out that cats have cats as proper parts. Surely this is true: there is just one cat, Tibbles, on the mat . . . More generally, given a set of parts composing at time t a member of a natural kind (e.g. cat), no subset of that set composes at t a member of the same natural kind. Well, then: persons are a natural kind . . . And so even if the created parts of the incarnate Christ would on their own have constituted a person, a human being, they actually only join with the Son to constitute a 'larger' person and human . . . (Leftow (2002), 281-282) 16 The reasoning, then, is that we can block both Tib's claim to cathood and Christ's human nature's claim to personhood by appealing to NCP.
In what follows, I will argue that this solution is unsound. My argument will consist of three parts. First, I will raise some issues with the application of NCP to incarnation: even if we grant that NCP is true, work needs to be done in explaining why and how it can be applied in this context. Second, I will consider counter-examples to NCP that suggest that it is false. Third, I will consider the primary argument for thinking the principle to be true, which is based on the assumption that it is the only reasonable way of resolving Tibbles-type problems. I will undermine that argument on the basis that a better way of resolving those problems existsbut this way does not help to protect compositionalism from the charge of Nestorianism.

NCP and incarnation: initial problems
Suppose that NCP is true, and is the correct way to resolve the Tibbles problem. Can it be applied to the incarnation as straightforwardly as Leftow suggests? There are two complications here. 17 The first is this strategy's reliance on natural kinds. If there are such things as natural kinds, biological species are the most obvious candidates. Two cats, then, are plausibly members of the same natural kind, and so if NCP is true, we can reasonably say that no cat can have another cat as a proper part. But it is far from clear that 'persons' are a natural kind. It is easy to imagine science-fiction thought experiments that call it into question. Elliotta human beingand E.T.an extra-terrestrial life-formare both persons, but it is not at all obvious that they are both members of the same natural kind. It is even less obvious if we range beyond the organic: Captain Picarda human beingand Commander Dataan androidare both persons, but androids are artefacts and not members of any natural kind, let alone the same one as humans. And it becomes harder still if we turn to theology. Can I really be said to belong to the same natural kind as, say, God the Fathera divine person who Christian tradition says not only exceeds me to an infinite degree in rationality, knowledge, and power, but is not even really an individual being at all? To classify God in any 'natural kind' is surely a category mistake. God is not among the items of the universe, but that which makes the universe possible; God is not a being, but Being Itself in its purest and infinite form. 18 To say that any created object shares a natural kind with God seems absurd. But if the compositionalist is to appeal to NCP to avoid Nestorianism, it seems this is what she must say.
One might reply by appealing to the doctrine of the imago Dei: human beings are made in 'God's image', so there is a fundamental similarity between them. This does not seem convincing to me, because an image is not, usually, of the same natural kind as the original. A picture of a giraffe is not a giraffeit is not even an animal. To use the idea that human beings resemble God in some way as justification for assigning them to the same natural kind is to make an unwarranted leap.
Oliver Crisp gives a different answer to this worry, by suggesting that even if the composite Christ is not a member of a natural kind, something like NCP could still apply: it could be said that the parts making up the person of Christ are such that no collection of those parts less than the total number of parts composes another thing of the same sort as the parts that together make up the person of Christ. (Crisp (2007), 65-66) This addresses the worry by avoiding mention of 'natural kinds', but it does so at the cost of abandoning whatever intuitive appeal NCP has. For consider the following version of NCP that avoids mentioning natural kinds: NCP ′ : For any two objects x and y that both fall under the same category f at time t, x cannot be a proper part of y at t. NCP ′ is clearly false: a machine can be a proper part of another machine, for example, and a community can be a proper part of another community. But then it is very hard to see why something like NCP ′ should apply in the case of the incarnation.
Suppose we overlook this, or provide some account of how divine and human persons are indeed members of the same natural kind or are subject to some principle that parallels NCP. A second problem arises. NCP is supposed to explain why Christ's human nature is not a person. It is not a person because it is a proper part of a person. But NCP, by itself, is not sufficient to yield this conclusion. Suppose we are presented with an apparent situation in which two objectsa and bboth belong to natural kind F, and a is a proper part of b. If NCP is true, then it cannot be the case that all of these things are true. At least one of the following must be false: (1) a is a proper part of b; (2) a is an F; or (3) b is an F. However, the truth of NCP alone does not tell us which of these is false. 19 Perhaps all of them are. Now consider the incarnation. Christ's human nature and God the Son both appear to be persons, and Christ's human nature is a proper part of God the Son. Assuming the truth of NCP, and assuming that persons are a natural kind, we conclude that at least one of the following is false: (1) Christ's human nature is a proper part of God the Son; (2) Christ's human nature is a person; or (3) God the Son is a person. Compositionalists tell us that (2) is false. But why?
Well, (3) cannot be false, on theological grounds: God the Son is definitely a person. Moreover, one might point to the fact that before the union, the Son exists as a person, whereas the human nature does not exist at all. And if something that is a person gains a new part, then it remains a person with the new part (unless the new part somehow destroys another element essential to personhood). 20 So it is not unreasonable to think that, in this case, the whole blocks the part from personhood, rather than vice versa. How, then, to choose between (1) and (2)? The compositionalist might say that we know (2) to be false, because affirming it would be Nestorianism. But this would be compatible with (1) being false too. That is, perhaps Christ's human nature is not a person and it is not part of God the Son. What reason do we have for thinking that the human nature is a part of God the Son, other than that the compositionalist wants it to be?
To put it another way, Christ's human nature certainly appears to be a person. Not only does it consist of exactly similar components to things we normally consider persons, but it behaves just like them, toowalking and talking and so on. So the claim that it is a person seems very plausible. By contrast, the claim that Christ's human nature is a proper part of God the Son is much more mysterious (as opposed to, say, the mere claim that God the Son makes use of Christ's human nature, which as we have seen is neutral on the question whether one is a part of the other). The compositionalist says that NCP stops Christ's human nature from being a personbut wouldn't it be more reasonable to say that NCP stops it from being a part of God the Son? We can't just appeal to orthodoxy and say that we know that Christ's human nature isn't a person and therefore it can be part of God the Son, because the whole point of bringing NCP in is to explain why it isn't a person. In other words, the appeal to NCP does not really explain what it is supposed to explain.
So a successful use of NCP to defend compositionalism needs to do two things. First, it needs to be shown that it is plausible to suppose that God the Son and human beings both belong to the same natural kind, despite the tremendous difference between themor, failing that, that a principle similar to NCP still applies to them. Second, it needs to be shown how an appeal to NCP can explain why Christ's human nature is not a person rather than why Christ's human nature simply isn't a part of God the Son at all. However, none of the compositionalist uses of NCP that I know of has done either of these two things.

Counter-examples to NCP
Suppose for the sake of argument we ignore these problems, or assume that solutions to them can be found. A more fundamental issue remains: is NCP true? In this section, I argue that it is not, given that counter-examples to it can be found. I will focus on one actual example and a couple of thought experiments.
First, consider angler fish of the suborder Ceratioidei. Some families of this suborder famously exhibit extreme sexual dimorphism. The female is a large fish that ambushes prey with an illuminated lure and an enormous mouth. The male, by contrast, is small and lives independently only as an adolescent. When the male encounters a female, he attaches himself to her and becomes fused permanently onto her body, merging his bloodstream with hers to derive nutrients, and functioning only to fertilize her eggs. 21 Here, it seems we have a case of a fish that acquires another fish of the same species as a body part. If biological species are natural kindsand if anything is a natural kind, a biological species isthen this is a clear counter-example to NCP.
One might object that in this case, the male is not really a part of the female, because he is genetically distinct from her. 22 However, there are many cases where we would accept that we are dealing with a single individual despite genetic diversity within it. An obvious one is organ transplants. If I receive a new heart, it is genetically distinct from the rest of my body, but it would be odd to deny that it is really a part of my body because of that. Genetic mutations offer another case. If one of my cells undergoes a mutation, its DNA is now different from the DNA in the rest of my body, but it does not cease to be a part of me because of that. A third casewhich to my mind is the most persuasiveis that of chimeras. A chimera, in the biological sense of the word, is an organism that has two or more genetically distinct populations of cells. There are a number of ways in which this can happen, but one of the most dramatic is when two fraternal twin zygotes merge with each other at an early stage in the womb, and go on to develop as a single individual. The result is an individual with some parts of her body derived from one of the original zygotes, and the rest derived from the other, though they may be merged so perfectly that there is no apparent abnormality. Consequently, she has one set of DNA in some parts of her body, and another set of DNA in the rest. The frequency of such casesparticularly in humansis uncertain, given that they are usually only detected if they result in some observable physiological condition (such as having eyes of different colours, though this can have other causes too). There have been cases where women discovered they were chimeras only when genetic tests seemed to show that they were not the mothers of their own children: further investigation revealed that the initial tests had sampled cells from one 'half' of the mother's body but the child had inherited DNA from the other. 23 Clearly, if a person is found to be a chimera, that does not disqualify parts of her body from being genuinely parts of her simply because of their genetic diversity. But the angler fish is, effectively, a chimera, though it is formed in an unusual way. If this is so, then it is indeed a fish with another fish of the same species as a body part.
If we want to consider counter-examples to NCP involving persons rather than biological species, real examples are harder to come by, but one might point to the octopus, the only known invertebrate (other than close relatives such as cuttlefish) whose intelligence rivals that of mammals. An individual octopus has a central brain (more or less), but each tentacle also has a semi-independent nervous system of its own, such that tentacles can act partly on their own initiative and partly under the control of the central brain. 24 Here already we have something like a person with other persons as parts, though at a level of intelligence well below personhood (at least as far as the tentacles are concernedthe octopus itself may be a different matter). But suppose we imagine a more intelligent version of the octopus, such that it can be considered a personand grant a similar level of intelligence to each individual tentacle. 25 We could even imagine a version where each tentacle has its own conscious experience, distinct from that of the central octopus; but the central octopus's consciousness includes those of its tentacles. Now a compositionalist might say that, in this scenario, the tentacles do not constitute persons in their own right, even though they have their own conscious experience, because having conscious experience is not sufficient for personhood. (Christ's human nature has conscious experience, after all.) But consider a corollary of NCP. If a putative member of a natural kind does not count as a true member of that kind on account of being a proper part of another member of that same kind, what happens if it ceases to be such a proper part? It would seem that it suddenly does become a member of that kind after all. 26 But this opens up deeply implausible possibilities. Suppose we extend the super-octopus scenario by imagining that each tentacle is capable of breaking away from the octopus and survivingand thinkingentirely independently. Perhaps each tentacle has its own eyes and mouth, and can speak; we can give individual tentacles whatever features we think essential to personhood. Perhaps the tentacle can break away from the octopus quite casually, mid-sentence, without any interruption to its stream of consciousness. Would we really want to say that the tentacle does not count as a person one moment, and then suddenly counts as a person the next, even without any change at all in its conscious experience? Maybe this weird alternativeworld octopus can detach and re-attach its tentacles repeatedly without any interruption to their conscious experience; it would be perverse to insist that they pass in and out of personhood.
For me, this thought experiment yields the intuition that whether or not something is a person depends on its internal properties, not upon its environment. Whether or not I would be inclined to call a tentacle a person has nothing to do with whether it is operating as part of a wider system which is also a person, and has everything to do with what properties it has in itself. 27 To see this more clearly, imagine another thought experiment, involving a hundred billion people all arranged in a phone network in which they communicate with each other in a way that mimics the connections between neurons in the brain. If one accepts a functionalist account of the mind, one could plausibly suppose that a single enormous person would emerge from this system. But the people who compose the network would still be persons. Setting up this system would not mean a hundred million people had ceased to be people, and shutting down the network would not cause them to become people again. And this is because whether or not something is a person does not depend upon what is going on outside itwhether, for example, it is acting as part of an enormous simulation of a neural network. 28 While some of these cases are obviously fanciful, their apparent coherence suggests to me that it is perfectly possible, at least in theory, to have an individual of a natural kind that has other members of that same natural kind as proper parts. Consequently, NCP seems to be false.
There is an objection to arguments of this kind. Oliver Crisp considers another possible counter-example to NCPthe papal triple crown, which is a crown that is made of crowns. 29 He writes: this analogy is only partial. The three crowns were all members of the same kind prior to the assembly of the triple tiara. The various 'parts' of Christ, on this version of a three-part Christology, are not clearly instances of the same kind prior to their assembly. (Crisp (2007), 65 n. 42) However, this seems to me to be begging the question. Why does it make any difference whether the crowns existed independently as crowns before becoming parts of a larger crown? The only answer I can think of to that is that being parts of a larger crown precludes them from counting as crowns at all, and so they never had a chance at crownship, so to speak. But that presupposes that being parts of a larger crown does preclude them from counting as crowns, which is exactly the point at issue.
More generally, Crisp seems here at least implicitly to entertain the notion that a part of a member of a natural kind could be a member of that same natural kind after all, if it previously existed as a member of that natural kind without being a part of a larger member. So the component crowns are crowns, even though they are parts of a larger crown, precisely because they were once independent. This yields the following modified version of NCP: NCP ′′ : A member x of a natural kind f at time t2 cannot have another member y of that same natural kind f as a proper part of x at t2, unless y previously existed at an earlier time t1 as a member of f without being a proper part of a member of f. This is even harder to find a rationale for than the original NCP. Why would the fact that the component crowns once existed independently make any difference to whether they count as crowns now? We can imagine two exactly similar papal tiaras, one of which was made by taking already existing crowns and stacking them together, and the other of which was made from scratch, with its component crowns never existing beforehand. It would be odd to say that one of these had crowns as proper parts and the other didn't. If the components of one tiara count as crowns, the components of the other should do as well, because they are exactly similar.
Moreover, we have already seen that if NCP were true then parts that become detached could suddenly begin to count as members of the relevant natural kind. Now imagine a scenario in which the second tiara's component crowns are not crowns (because they never existed independently); but then the tiara is disassembled, at which point the components do become crowns because they exist independently; and then the tiara is reassembled again. If NCP ′′ were true, then the components are not crowns before the tiara is disassembled, but they are crowns after it is reassembledeven though the post-assembly tiara is exactly the same as the pre-disassembly one. This seems absurd.
And even if we do accept the formulation of NCP ′′ over the original NCP, we can easily recast our counter-examples to meet it. We could suppose, for example, that the hundred billion people who compose the enormous neural network are born into the role; or imagine an angler fish variant where the male is born attached to the female. In the super-octopus example, the tentacles already come into existence as parts of the greater whole. Yet they still seem to be counter-examples to NCP ′′ .

An alternative to NCP
We seem, then, to have strong reasons to think NCP false, despite the fact that if it were true we could resolve paradoxes of the Tibbles variety in a straightforward way. But some view the fact that NCP yields desirable metaphysical results as a kind of argument for the truth of NCP. Indeed, Robin Le Poidevin describes Leftow's formulation of it as 'a convincing argument for the principle that no parts of a person can themselves be persons' (Le Poidevin (2009), 174, my italics). Perhaps we can best interpret Leftow's account as relying on the following implicit argument: (1) If it is possible for a member of a natural kind to have other members of that natural kind as constituent parts, there are multiple cats on the mat. (2) There is only a single cat on the mat.
(3) Therefore, it is not possible for a member of a natural kind to have other members of that natural kind as constituent parts.
Tibbles-type paradoxes call (2) into question, but let us take it for granted for now. Leftow gives no argument to support (1), which is effectively an assertion that NCP is the only way to stop there being multiple cats. Indeed, he does not explicitly state (1), beyond stating that appealing to NCP is 'clearly' the right way to resolve the Tibbles paradox, but I take it to be a hidden premise that is required for his argument to work. 30 It is equivalent to: (1 ′ ) There is at most one cat on the mat only if it is impossible for a member of a natural kind to have other members of that natural kind as constituent parts.
We can undermine (1 ′ ), and with it (1), if we can point to an alternative way of showing that there is only a single cat on the mat. Here is a way of doing so that seems to me to be plausibly correct. 31 Suppose we introduce the concept of 'kind-essential parts', or KEPs. We are familiar with the notion of essential propertiesthese are properties that an individual has to have in order to count as a member of a particular kind. Kind-essential parts, by contrast, are parts that an individual has to have in order to count as a member of a particular kind. For example, suppose that the property of having a brain is essential to human nature. The brain itself will therefore be a kind-essential part, and anyone who is a human being will be a human being partly in virtue of having a brain as a part. Now we can articulate a new principle, which I will call No Co-KEP Individuals, or NCI: NCI: Two distinct individuals of the same kind f at any time t cannot share numerically the same KEPs at t.
So think again of Tibbles. What are the KEPs for cats? It is hard, precisely, to say; certainly some common cat parts, such as tails, are not essential parts for cats, since there are some that lack them. But suppose we say that, at least, a head and a central body (the cat equivalent of a torso) are essential for cats. 32 Anything that lacks one of these is not a cat. 33 Now consider Tib: Tib has all the KEPs needed for cathood, but they are the same KEPs that Tibbles has. Tib does not have a head or a body distinct from the head and body of Tibbles. And the same thing applies to all of the other putative cat-candidates within Tibbles. None of these therefore counts as a different cat from Tibbles. Either they are cats, but the same cat as Tibbles, or they are not cats at all. NCI is neutral on which of these is the case. The latter seems more probable to me, but fortunately we do not need to resolve this question for our purposes here. Either way, we are dealing with only a single cat. NCI therefore solves the Tibbles paradox. And it does so, I think, better than NCP does. As I have argued, it seems possible to think of counter-examples to NCP, where a member of a natural kind does contain other members of the same natural kind as proper parts. But none of these is a counter-example to NCI. For example, the KEPs in virtue of which the male angler fish is a fish are distinct from the KEPs in virtue of which the female angler fish is a fish, even though the male angler fish is a part of the female. So NCI allows the male to be a fish even though he is a proper part of a larger fish. And I cannot think of any case where two things share the same KEPs in virtue of which they both belong to the same natural kind, and yet are distinct members of that natural kind. 34 Moreover, NCP has the appearance of an arbitrary principle invented to avoid unpalatable consequencesthere aren't any good reasons, apart from a desire for it to be true, to think that it is true. But NCI does not have this ad hoc feel to itat least, speaking for myself. I think that there is only one cat because I think that NCI is true, not vice versa. It seems inherently plausible to suppose that if the KEPs are what make an individual a member of a certain kind, you have exactly as many members of that kind as you have KEPs. 35 So in the case of Tibbles, there is one cat precisely because there is only one set of KEPsone head and one body, or whatever the KEPs are. Consequently, the first premise in the argument for NCP is underminedit could be (and, if I am right, actually is) the case that there is only one cat on the mat even though NCP is not true.
How does this apply to incarnation? Unfortunately, NCI is not going to help compositionalists. It is easy to see why: Christ's two natures have their own sets of KEPs for personhood. As I have already indicated, if 'person' is going to cover both human and divine individuals it must be a very broad category. But to be a person must presumably involve (perhaps among other things) having parts that allow you to think, reason, will, and have conscious experiences. Now Christ's human nature has such a part. Whether it is his brain, his whole body, his soul, some combination of these, or something else, makes no difference to us. God the Son also has such a partor, perhaps more properly, just is such a thing. Again, the details do not matter, as no orthodox Christian could deny that the Son, minus the human nature, has whatever is required for personhood (the Father and the Holy Spirit are persons too, despite never being incarnate). Therefore, both the divine Son and the human nature have their own sets of KEPs in virtue of which they qualify as persons. Therefore, we cannot appeal to NCI to say they are distinct persons, even if one is part of the other.
To put it another way, it is true (given compositionalism) that the divine Son and the human nature 'overlap', in the sense that one is a part of the other. However, their person-making parts do not overlap. They remain distinct.
So it seems that if NCI is the correct way for resolving the Tibbles paradox, the compositionalist Christ still turns out to be two persons. Christ is not analogous to Tibbles after all, because Christ has two sets of KEPs for personhood, while Tibbles has only one set of KEPs for cathood.

Conclusion
To sum up, then, we have three problems for the compositionalist who wants to rely on NCP to avoid Nestorianism. First, there are key questions that need to be answered about precisely how NCP blocks Christ's human nature from being a person. Second, and more fundamentally, NCP is probably false, since counter-examples to itboth actual and imaginedare possible. Third, there are better ways to solve the metaphysical puzzles for which NCP has been introduced, but these ways cannot be applied to the compositionalist Christ to avoid Nestorianism.
I conclude, therefore, that compositionalism is in a worse position than is commonly supposed. Those who appeal to NCP to defend compositionalist accounts of the incarnation may need to find an alternative way of avoiding Nestorianism.
Conflict of interest. None. Notes 1. The term 'concretism' has become standard following Plantinga (1999), 184. 2. For this reasoning in Aquinas's model of incarnation, see Gorman (2000), 146-145. 3. The terms 'concretist' and 'compositionalist' are sometimes used interchangeably, reflecting the not-entirely generally agreed status of the terminology surrounding this topic. For our purposes, however, I will take them to be distinct in the way described here. Recent authors who have defended versions of compositionalism in this sense include Freddoso (1983), Leftow (2002), Stump (2003), Crisp (2007), Loke (2011), Flint (2011), and Rogers (2013. 4. These two ways are what Flint (2011) calls 'Model T' (the Aquinas-type model) and 'Model A' (the Rogers-type model). 5. 'Pre-incarnate' must of course be understood non-temporally here, as Aquinas holds the Son to be atemporal. 6. I emphasize this point here because it is important to recognize that the fact that a theologian appeals to some relation R other than that of part-to-whole as holding between God the Son and Christ's human nature does not, in itself, mean that that theologian holds a non-compositionalist model. It could be (and at least sometimes actually is) the case that that theologian thinks that the relation of part-to-whole holds between God the Son and Christ's human nature precisely becauseor partly because -R does. Consequently, it is not always easy to tell whether a concretist model of the incarnation is compositionalist or not. 7. On this, see Pawl (2020), 19-21. 8. These authors include Leftow (2002), 281-282;Stump (2003), 199;Crisp (2007), 65 and(2011) 58-59;and Le Poidevin (2009), 174. I have also appealed to it myself, together with Marmodoro and Hill (2010), 483-486. 9. Stump argues that a limited version of this principlethat a substance cannot contain a substance as a proper partfollows from Aquinas's view 'that a substantial form configures prime matter ' (2002), 199. A similar argument for the principle on the basis of Aristotelian metaphysics can be found in Marmodoro and Hill (2010), 483-486. However, although such a principle could be grounded upon Aristotelian metaphysics, Aquinas never articulates such a principle in his discussions of the incarnation. Certainly he denies that Christ's human nature is a substance, but he does not base this denial upon a version of NCP. 10. There are less sweeping versions of this principle, in which it is made to apply only to some natural kinds. In such versions, these natural kinds are sometimes said to be 'maximal'. So if one holds only that no person can be a proper part of another person (while perhaps remaining neutral about other natural kinds), one holds persons to be maximal. Olson (1997), 261, for example, in a paper heavily criticizing the notion that persons are maximal, still allows that organisms are maximal. In this article, for the sake of simplicity, I do not directly address the claim that persons (and perhaps only persons) are maximal, which would be the version of the principle relevant to the incarnation; but much of what I say about NCP in general applies to it. 11. Evidently, the principle depends upon there actually being natural kinds. I am inclined to doubt that there are, but I will not press this point here, since I take it that a commitment to the existence of at least some natural kinds is implicit in the doctrine of incarnation itself. If 'humanity' is no more than a nominal essence, then to say that Christ shared in our humanity means no more than that we are inclined to call him 'human', but surely it must mean more than that. Why, if humanity is only a nominal essence, would it matter so much that he share in it at all? 12. These puzzles go back to the Stoic philosopher Chrysippus, who used the example of Dion (a human being with the usual number of limbs) and Theon (that part of Dion that consists of all of him other than his left foot); see Burke (1994), 129-123. Most modern discussions of these puzzles take their cue from Geach (1980), who recasts them in terms of Tibbles the cat. However, different authors vary the thought experiment (sometimes it is Tibbles's tail that is detached, sometimes a hair), and they vary the terminology too (with different names being given to the portion of Tibbles that is not detached). For the sake of simplicity, I will use the version (and names) used by Crisp (2011), 58-59. 13. Note: this is just one of a number of puzzles about Tibbles. The original form of the puzzlethat of Theon and Dion, as posed by Chrysippuscan be translated into Tibbles-speak like this: Tibbles and Tib both exist and are distinct from each other. But suppose we cut off hair h. Now one of the following things must be true. Either (1) Tibbles has ceased to exist and Tib alone remains; or (2) Tib has ceased to exist and Tibbles alone remains; or (3) Tibbles and Tib both continue to exist as distinct entities; or (4) Tib and Tibbles are now identical with each other although they were distinct before the removal of h. All of these are problematic. If (1) is correct, then removing any particle, however small, from a composite object will cause it to cease to exist. If this is so then every time a cell in my body is replaced, I cease to exist. If (2) is correct, then Tib can pass out of existence even though nothing about Tib itself has actually changedfor the removal of h occurs outside Tib. (Chrysippus himself favoured this solution, and was criticized for it by Philo of Alexandria; for a modern defence, see Burke (1994).) If (3) is correct, then it is possible for two distinct objects to occupy exactly the same space at the same time, having all their parts in commonwhich is not only contrary to common sense but raises the question: how many such objects might there be at any one time in any given place, including sitting in my chair right now? If (4) is correct, then a statement of the form 'a is identical with b' can be contingently true, because although Tibbles is now identical with Tib, it wasn't always. Moreover, it would follow that the indiscernibility of identicals doesn't always hold, because Tib has some properties that Tibbles lacks, such as the property of having once been a proper part of Tibbles, and yet Tib is supposed to be now identical with Tibbles. (On this last issue, see Gallois (2005); for this paradox more generally applied to compositionalist models of incarnation, see Le Poidevin (2009), bearing in mind that although he is discussing the same theological topic with reference to the same metaphysical thought experiment, he is concerned with a different paradox from the one we are concerned with.) Fortunately, all of this is quite distinct from our problem, which is concerned with the cathoodor otherwiseof Tib while hair h remains in place. What happens to Tib (and Tibbles) when h is removed does not come into our problem. 14. One is Peter Geach's appeal to 'relative identity', according to which Tibbles and Tib might be different 'masses of feline identity' but the same cat (see Geach (1980), 216). Few philosophers, however, have accepted the notion of relative identity; see Wiggins (1980), 15-44. A second strategy is van Inwagen's denial (1981) that entities such as Tib are things at all, because they are just 'arbitrary undetached parts' that do not track real divisions in the whole. This also has not attracted widespread acceptance. And indeed, whether or not this solution is acceptable in the case of Tibbles, it does not help us with the incarnation. Christ's human nature, on a compositionalist model, is not an arbitrary undetached part. On the contrary, there is a very clear distinction between the human nature on the one hand and the divine Son on the otherand even if this were not apparent, it is required by orthodoxy. The Chalcedonian definition states that the two natures are unmingled and remain distinct. So the human nature should still count as a genuine part of Christ even if Tib is not a genuine part of Tibbles. 15. For an appeal to this principle in the context of Theon and Dion, see Burke (1994), 136-138. 16. Note that Leftow envisages both the human nature and the Son as proper parts of the composite Christ, in a rather similar way to Rogers's account (Flint's 'Model T'see note 4). This leads to the somewhat odd result that Christ is not identical with the Son (the latter is a proper part of the former); it also means that only one out of Christ and the Son can be a person, at least if NCP holds. (Indeed, if the human nature is supposed not to be a person because it is part of a larger one, then Christ must be a person, in which case the Son is not, which seems deeply problematic; see Senor (2007), 56.) For more discussion of these problems with Leftow's version of compositionalism, see Flint (2011). For our purposes, I will ignore these issues and assume what I think is the more common version of compositionalism, according to which the Son is not a proper part of the composite Christ but is instead identical with the composite Christ (Flint's 'Model A'). On this version, when the Son becomes incarnate, he gains the human nature as a new part. This seems to me to be the most natural context for an appeal to NCP: it is, supposedly, because it is a part of the Son that the human nature cannot be a person. 17. One other complication may be mentioned: to what extent is compositionalism to be understood literally? In De unione Verbi incarnati 2, Aquinas states that the human nature should be seen 'not properly as a part in a whole'. Some modern writers on compositionalism cite this passage sympathetically: see Freddoso (1983), 305 n. 16 andFlint (2001), 5. One may therefore ask: if a compositionalist is to appeal to NCP, does this commit them to a literal understanding of compositionalism? After all, if Christ's human nature is not literally a part of the divine Son, then NCP might seem not to apply. Alternatively, perhaps the incarnation is sufficiently similar to mereological compositionthough distinctfor NCP or a similar principle to apply to it. In which case, some explanation of why this principle applies is in order. However, I do not want to focus on this issue here, since as far as I can tell, those compositionalists who have appealed to NCP or a similar principle have not claimed that their compositionalism should be taken non-literally. 18. For some authors, one should talk instead of divine persons constituting a 'supernatural kind', which is analogous to, but distinct from, natural kinds. On this, see Senor (1991). 19. On this, see Olson (1997), 262, who makes the similar point with regard to Dion and Theon: we may want to say that Theon (a proper part of Dion, without one foot) is not a person because he is part of Dion, but we might just as well say that Dion is not a person because he has Theon as a part. Olson repeats this point in a slightly different context later (2002), 194-195. 20. I am grateful to an anonymous reviewer for Religious Studies for this point. 21. On this, see Pietsch (2005). 22. I am grateful to an anonymous reviewer for Religious Studies for raising this objection. 23. For more on natural chimeras and their prevalence among humans, see Wenk (2018). 24. On the complexity of the relation between the central nervous system and the tentacles, see Gutnick et al. (2020). 25. I assume here that it is a lack of intelligence that blocks both octopuses and their tentacles from personhood, but in a thought experiment of this kind one can always add other properties as well.