Shieva Kleinschmidt University of Southern California Many-One Identity and the Trinity The doctrine of the Trinity is, put simply, a conjunction of these three claims: (i) There are three distinct Divine Persons: the Father, the Son, and the Holy Spirit, (ii) each Divine Person is God, and (iii), there is exactly one God. However, if there are three distinct Persons that are each God, we should get the result that there are three Gods. It seems Trinitarian Christians are having trouble counting: they need 3 to equal 1. But is that such a tall order? Perhaps bizarre Mereology can give us a new way to count, to meet these many-one needs. Lately there has been a flurry of discussion about the claim that "composition is identity", i.e., that pluralities are identical to the things that they compose (if there is something they compose).1 Many can literally be one. In this paper, I argue that this claim is not helpful to Trinitarians. In §1 I present and discuss the many-one identity claim, and in §2 I apply the claim to the Doctrine of the Trinity, presenting how it might seem to help the Trinitarian. In §3 I argue that upon closer inspection it proves to not help at all, but instead leaves us with the same options that we began with. I also discuss the difficulties appeals to Composition as Identity generate for the intelligibility of monotheism. I conclude that, while it is an interesting metaphysical thesis, the Composition as Identity claim is not useful in helping reconcile the claims in the Doctrine of the Trinity.2 1. Many-One Identity Consider an apple and its two halves. The halves make up the apple; they are what it's composed of. The apple has each of the halves as parts, and has no parts that don't 1 Since it was defended by Donald Baxter (1988a and 1988b), the view has been discussed by David Lewis (1991), Peter van Inwagen (1994), Byeong-Uk Yi (1999), Trenton Merricks (1999 and 2005), Ross Cameron (2007 and forthcoming), Ted Sider (2007), Kris McDaniel (2008 and 2010), Raul Saucedo (unpublished), and Jason Turner (unpublished a and b), among others. 2 A quick note on my vocabulary before I begin: In the literature, there are varying accounts of what 'composition' and 'constitution' refer to. I'll follow Lewis (pp. 72-74) and van Inwagen (1994, p. 207) and use the standard account, that for the xs to compose y is for y to be a fusion of the xs, and for the xs to constitute y is for y to be a fusion of the xs and for there to be exactly one of the xs. So I'll take constitution to be a type of composition. 2 overlap either of the halves. There's an important sense in which the apple just is the halves. In some sense, the thing isn't anything beyond its parts. This intuition about the apple seems to generalize to all instances of composition. I just am the group of atoms that compose me, the table I'm writing at just is the top and legs that make it up. If we already posit the legs and top in this arrangement, it doesn't look like we're positing extra furniture in the world when we also claim there is a table. This intuition about composition has motivated David Lewis to claim that Mereology is ontologically innocent: when we have some objects, the positing of an object that is composed of them (i.e., an object that is their fusion) does not actually require any "further commitment"; we don't have to expand our list of what exists in any costly way.3 Describing the appeal of this claim, Lewis says: Given a prior commitment to cats, say, a commitment to cat-fusions is not a further commitment. The fusion is nothing over and above the cats that compose it. It just is them. They just are it . . . the cats are the same portion of Reality either way . . . if you draw up an inventory of Reality according to your scheme of things, it would be double counting to list the cats and then also list their fusion.4 The view expressed here is one on which things literally are identical to their parts. Lewis is following Donald Baxter in claiming that composition is an identity relation, or at least is analogous to one. The claim Baxter endorses (but which Lewis ultimately rejects) is: • Composition as Identity (CI): The predicate 'are' that is used to express composition expresses the same relation as the 'is' of identity.5 Of course, though this view claims that a whole is identical to its parts, it is not the view that wholes can be identical to each of their parts. If, for instance, an apple were identical to each of its halves, we would simply have two one-one identity relations; the apple = its right half, and the apple = its left half. This is not the view we're after. Instead, we want a one-many relation; the apple is identical to its right half and left half collectively.6 3 Lewis, p. 74. 4 Lewis, p. 81. 5 Yi, p. 145. 6 Some theorists may believe that composition as identity can only obtain when the composite is identical to each of its parts. This seems to be what motivates worries such as this one: "How can one thing be the same as two, neither of which is the same as the first? A cardboard disc is made up of two halves. Obviously the disc is not the same as the first half and not the same as the second." (Chandler, p. 314.) Obviously, it would be bad for the Composition as Identity theorist if they claimed that composites are identical to each of their proper parts. But they don't claim this, and they don't need to. The implicit 3 It's also important to note: the many-one thesis is also not merely view that wholes are identical to things like groups or sets of their parts (where groups and sets are taken to be individuals with other entities as members). This, too, would give us a oneone identity relation: the apple = the group of its parts, or the apple = the set of its parts. Many-one identity really is a single relation between one thing and many things. Lewis rejects Composition as Identity. Instead he endorses: • Weak Composition as Identity (WCI): The predicate 'are' that is used to express composition expresses a relation only analogous to the relation expressed by the 'is' of identity.7 In what follows I will discuss the strong version of Composition as Identity rather than the weak one. This is because Weak Composition as Identity is logically weaker than the strong one, and does not provide any extra tools for use in solving the puzzle of the Trinity. Further, the fact that it commits us to less doesn't end up rescuing it from any of the worries I raise in §4 against the strong version of Composition as Identity. And finally, it's not clear what Weak Composition as Identity amounts to. If a thing is distinct from its parts, how can we capture Lewis's intuition that it's "nothing over and above" them, when insisting on genuine ontological innocence? It matters for Lewis that this innocence entails that positing fusions in addition to pluralities of atoms involves no further commitments. But it's not clear what "no further commitment" means for him. It seems that people can (and many people do) posit objects without positing fusions of those objects; positing a fusion would, it seems, be a further commitment for them, at least in the straightforward sense of that phrase. One might claim, on Lewis's behalf, that he's merely asserting that Mereology doesn't require us to posit anything the existence of which is not entailed by what we currently posit. Forms of supervenience weaker than identity can produce this kind of redundancy. But we then lose the intuitive appeal of Lewis's claims – it's not the case that we'll be double counting when we list not only x and y in our ontology, but also z, whose existence is entailed by, but not identical to, x premise in Chandler's argument is that if the disc is not identical with each of the parts, it cannot be identical with the plurality of those parts; a similar argument is given by Byeong-Uk Yi (Yi, pp. 141-143). Wallace responds, rightly, by saying that what is true of x and y needn't be true of x and true of y -what is true of some parts needn't be true of each of those parts. And for the Indiscernibility of Identicals to hold when we assert that the parts collectively are identical to the fusion of those parts, all we need is that the parts collectively have the same properties as the fusion. We don't need that the fusion has the same properties as each of its parts. Thus, I see no reason to endorse Chandler's implicit premise. 7 Yi, p. 146. 4 and y's. For instance, I couldn't exist without, say, my singleton set's existence. Or perhaps not even without the existence of spacetime, or the number 4. In some sense, my existence entails the existence of those entities. But we certainly wouldn't be counting the same bit of reality twice if we included both me and the number 4 in our ontology. Weaknesses of Weak Composition as Identity aside, my goal in this paper is to establish that Composition as Identity is not helpful with the Trinity. If I'm successful, this will entail that Weak Composition as Identity is also not helpful. So, for the remainder of the paper I'll focus on the stronger of the two claims. To understand Composition as Identity we must know: what is it for composition to literally be a form of identity? It entails that if composition occurs, many entities can be identical to a single entity; namely, some parts collectively are identical to their fusion, and a fusion is identical to its parts. So an object, like our apple, really is identical to its parts, the halves that compose it. Lewis worries about allowing identity to be a many-one relation, saying, "What's true of the many is not exactly what's true of the one. After all they are many while it is one."8 That is, for some parts, A1, . . ., An, of an object, B: (i) A1, . . ., An are many, (ii) B is not many, and so, by Leibniz's Indiscernibility of Identicals and contrary to CI, (iii) it's not the case that A1, . . ., An and B stand in the identity relation.9 To find a way to avoid Composition as Identity's apparent violation of the Indiscernibility of Identicals we can turn to Frege,10 who presented a notion of relative counting according to which entities (including pluralities) have no cardinality simpliciter. Rather, the cardinality we ascribe to entities is indexed to the concept or sortal we are counting under. Frege says, "The Illiad, for example, can be thought of as one poem, or as twenty-four Books, or as some large Number of verses".11 The Composition as Identity theorist will say that the Illiad is identical to the twenty-four Books, which are identical to the large number of verses. The poem just is the verses, when counted under the concept poem rather than versus or books. This gives us one way to understand what Baxter means when he says, "the whole is the many parts 8 Lewis, p. 87 9 The predication over A1, . . ., An is not distributive. I.e., to say that A1, . . ., An are many is not to say that each of A1, . . ., An is many, and to say that it's not the case that A1, . . ., An stands in the identity relation to B is not to say that each of A1, . . ., An fails to stand in this relation to B. 10 Responding by appealing to Fregean counting is advised by Wallace. 11 Frege, §22, quoted in Wallace, p. 10. 5 counted as one thing"12 and it gives the Composition as Identity theorist a way to respond to Lewis's worry.13 Whereas before we may have said that the books are many but the poem is one, and thus the books and the poem are distinct, now we can say: the books qua books are many, and the books qua poem are one, and the poem qua books is many, and the poem qua poem is one. There's no incompatibility of properties pushing us toward distinctness of the poem and the books. A quick note on how we might understand Fregean sortal-relative counting: There are various options for relativising counting to sortals, brought to light when we ask what is meant by 'A1, . . ., An are many'. One option is to think that this is unanalysable, and so to take counting as both sortal-relative and basic. Another option is to analyze it as something like: !x, !y | (i) x " y, (ii) x is one of A1, . . ., An, and (iii) y is one of A1, . . ., An. Given this analysis, we can look for places to relativise; one of the expressions in the analysis must be sortal-relative. For instance, we can take is one of to be sortal-relative. Or perhaps instead we could claim that we must invoke a sortal when referring to entities, by making quantifiers or variables sortal-relative somehow. Or maybe distinctness should be taken to be sortal-relative. Though I haven't given a complete listing of them, I believe it's worth highlighting that there are a variety of options for cashing out the Fregean notion of sortal-relative counting. In what follows, however, I will treat them all in the same way, as the worries I raise in what follows apply to each of them. 2. Application to the Trinitarian Claims For Composition as Identity to help the Trinitarian, it must help us make sense of this (from the Athanasian Creed): We worship one God in the Trinity, and the Trinity in unity. Neither confounding the Persons, nor dividing the substance. For there is one person of the Father, another of the Son, another of the Holy Spirit. But the Father and the Son and the Holy Spirit have one divinity, equal glory, and coeternal majesty . . . the Father is God, the Son is God, and the Holy Spirit is God. However there are not three Gods, but one God.14 12 Baxter 1988a, p. 579. Though I should point out, Baxter does not accept Fregean counting. I'll elaborate on this below. 13 Not everyone thinks turning to Fregean counting is the best way to respond to this worry. In addition to Baxter, Ted Sider (2007) offers an alternative: don't deny that everything that's true of the many is true of the one, and vice versa. More on this option below. 14 Anderson, < http://www.creeds.net/ancient/Quicumque.html > 6 We can extract the three Trinitarian claims, that there are three distinct persons ("one person of the Father, another of the Son, another of the Holy Spirit"), one God ("there are not three Gods, but one God"), and that each Divine person is God ("The Father is God, the Son is God, and the Holy Spirit is God").15 Further, the Creed mentions not dividing the substance; though a bit obscure, this is perhaps promising for someone hoping to apply Composition as Identity to the Trinity. It suggests that God shares a single substance with the Persons. This means the case has a relevant similarity to cases in which we don't want to double-count: sharing substance and sharing "reality" seem to be the same thing. Remembering Lewis's example of the plurality of all cats, we can see that the plurality shares a single substance with the fusion of all cats (since they share "the same portion of Reality"16). The plurality of cats compose the fusion, and given Composition as Identity, the many cats are identical to one fusion. Likewise, the Trinitarian can say that in virtue of sharing a single substance with God, the Persons compose God, and so given Composition as Identity, the three Persons are identical to God. (Or, if we don't want to use 'God' as a name, we can instead say: in virtue of sharing a single substance with a god, the Persons compose a god, and so given Composition as Identity, the three Persons are identical to a god.) To cash this out this application of Composition as Identity to the Trinity a bit more, we can use Fregean relative counting and say that the three Divine entities are identical to the one, since when counting by Persons we find that we have three (the Father, the Son, and the Holy Spirit), and counting by Gods we find only one. Further, we can say that when Christians speak of their Trinitarianism they are counting by Persons, and when they speak of their monotheism they are counting by gods. There is no contradiction in worshiping three and one, because (to apply Megan Wallace's interpretation of Frege), there is no answer to the question "How many Divine entities are there?" until we specify what concept or sortal we're considering the Divine entities under. 15 The language of the Athanasian Creed can be read in various ways. In this paper, I will take 'God' to be a name, and 'god' to be a count noun. When I talk of there being "one God" I mean "for any x1, ... xn, and y1, ... yn, if x1, ... xn stands in the identity relation to God, and y1, ... yn stands in the identity relation to God, then x1, ... xn stands in the identity relation to y1, ... yn. (Where a plurality's standing in the identity relation to an entity does not entail that every member of the plurality stands in the identity relation to that entity. And of course, there might be only one member of x1, ... xn and y1, ... yn.) 16 Lewis, p. 81. 7 Finally, the identity between the Persons and God (or: the one god) will explain why in completely describing the Persons we completely describe God, and vice versa. The many are identical to the one. Thus it appears this strange Mereology is a useful tool in reconciling the claims of the Trinity. Unfortunately, this straightforward application of Composition as Identity faces problems that render it utterly unhelpful. 3. Problems First, I'd like to address a methodological question. The metaphysical view discussed in the previous section seems, at the very least, quite strange. What might our justification be for appealing to something so strange in order to reconcile the claims of Trinitarianism? Why ought Metaphysics bear this burden, perhaps at the cost of its own simplicity and intuitiveness? Why not think that Trinitarianism's apparent need for strange Metaphysics provides us with a reductio against Trinitarianism? My reasons for looking toward Metaphysics are twofold: first, the problem of the Trinity seems to be a Metaphysical puzzle. It involves all sorts of metaphysical issues, like: is identity transitive? Is it possible to have three people made of the same substance? What is Divine substance, anyway? It's difficult to see what other area of Philosophy let alone areas outside of Philosophy would be able to give us a solution (unless it is Logic telling us that contradictions can be true). Second, given that Metaphysics is the only hero available to save the day, it seems reasonable to let Metaphysics do so (at least, insofar as our reasons for endorsing Trinitarianism aren't themselves grounded in attempting to keep our Metaphysics simple and intuitive). For Trinitarians, the problem of the Trinity will be regarded in much the way many regard logical paradoxes like the Liar Paradox. The paradoxes are gripping because we have strong initial commitments to each of the claims that make up the paradox. Some regard the commitments to be so powerful, they'll go to dramatic lengths to be able to continue accepting all of the premises (e.g., by rejecting classical logic, positing hierarchies within languages, etc.). Similarly, the orthodox Christian takes the claims of the Trinity to each express something that's at the core of their Theology; preserving this is much more important to them than preserving their offhand metaphysical views. 8 The acceptability of this tradeoff is compounded by the relative accessibility of these claims. The claims of the Trinitarianism are individually pretty straightforward (at least, on some level): the Father is a Divine Person. And so is the Son. They are individuals. They're definitely distinct from one another. Each is God. (And, presumably, each is thereby a god, though I know that is contentious.) Nonetheless, there is only one god. We count them up, we get only one. Trinitarianism certainly raises a lot of questions, but the constituent claims seem accessible; we understand, at least in broad terms, how reality would be different if the truth-values of any of the above claims were different. The metaphysical underpinnings, however, are not nearly as straightforward. For instance, what really hinges on whether identity is always a one-one relation or is sometimes one-many? Or what would really be different if identity were sortal-relative? I certainly would never claim that issues like these don't matter: they're about the nature of some of the most fundamental features of the world. But the views about these topics are a bit inaccessible. All else being equal, it seems reasonable to complicate a bit of already strange, inaccessible theory in order to preserve a doctrine whose constituent claims all seem straightforward and which is taken by many to play an important role in their lives.17 The approach of appealing to (often very strange) Metaphysics to solve the problem of the Trinity is pervasive in the literature about the puzzle. Some examples include: Appeals to relative identity (from Peter van Inwagen and Peter Geach18), appeals to Aristotelian hylomorphic compounds (from Jeffrey Brower Michael Rea, 2005b), and even appeals to things being entirely located in more than one region at once (from Brian Leftow, 2004). An appeal to many-one identity follows neatly in this tradition. 17 I recognize that these "straightforward" Trinitarian claims are themselves metaphysical, and that if we had a deep understanding of them we would be getting into some of the more inaccessible Metaphysics I was describing. However, presumably Trinitarians will want to endorse their doctrine regardless of how the underlying Metaphysics works out. The doctrine at this metaphysically-neutral level is what I'm considering to be straightforward. Further, when I characterize the claims as "straightforward" I do so only in a relative sense, with obscure Metaphysics forming the rest of the relevant comparison class. 18 In addition to Geach and van Inwagen, there are many people who have written about this view (though not necessarily in defense of it). Among them: James Cain, G. E. M. Anscombe, Daniel Howard-Snyder, A. P. Martinich and Michael Rea. (Citations from Brower and Rea 2005b, p. 432) 9 Now, back to first-order Philosophy. What problems do we face in implementing the many-one identity solution? In the previous section, we saw that in order to apply Composition as Identity to the Trinity we need the Persons to stand in a parthood relation to God. (It's in virtue of the composition relation that Composition as Identity gives us the result that the Persons and God are identical.) But do we really want to claim that the Persons compose God? This will require that each of the Persons is part of God. If we take the composition relation in this case to be one-one rather than onemany, that is, saying that each of the Persons is an improper part of God rather than a proper part of God, positing a composition relation between the Persons and God isn't worrisome at all. Anyone who thinks God is a Person should posit a one-one composition relation between a Person and God. So: what if we claim that the Father, the Son and the Holy Spirit each stand in such a relation to God? 3.1. One-One Composition Unfortunately, Composition as Identity is not going to be doing any work in this case. It is already widely (though not universally) accepted that the one-one parthood relation is identity. Further, the claim that each Person is identical to God is nothing new for the Trinitarian! Recall, the Athanasian Creed tells us, "the Father is God, the Son is God, and the Holy Spirit is God."19 Many responses to the problem of the Trinity already endorse the identity of each Person and God. For instance, positing relative identity (saying the Father, Son and Holy Spirit qua gods are identical to one another, but qua persons are distinct), denying the transitivity of identity (saying that the Father and the Son can both be identical to God, but fail to be identical to one another), and endorsing Modalism. Accepting Modalism involves saying that the three Divine Persons are really all aspects of the same individual. So all of the apparently incompatible properties of the Persons (like being begotten, and also being neither begotten nor made) are had by the same individual. Though we might opt for doing something like relativising these properties to aspects (e.g., saying that God is begottonson and proceedingholy spirit), if we don't it looks like we'll have to deny the Indiscernability of Identicals.20 (And we might 19 Anderson, < http://www.creeds.net/ancient/Quicumque.html > 20 Even if Modalism did not require us to deny the Indiscernibility of Identicals, it seems that it would be a view that is congenial to the Composition as Identity theorist. This is because Composition as Identity 10 not want to relativise properties in this way, because we might think that some of these properties, like failing to be begotten, are sometimes had without relativisation to an aspect, so relativising them just sometimes would require that the properties have variable adicity.) It has been claimed that this is also required for making sense of the thesis that composition is identity. Donald Baxter advises against using Fragean counting to respond to Lewis's worry about the many having properties the one lacks; he denies that making counting relative to concepts or sortals under which we are thinking the object(s) is sufficient to account for the different cardinalities that we attribute to the object(s). He says, "Frege's suggestion fails, as mine does not, when whole and parts are homoeomerous, when they fall under the same sortal."21 (I'll return to this shortly.) Baxter's suggestion, to contrast with Frege's, is that the entities actually have different aspects, and in each aspect they have different properties (among which are some properties involving cardinality). Thus, he says: There are things true of an object in an aspect that are neither simply true of the object nor are entailed or explained by the concept used of the object. Someone as Senator might support a bill which she as citizen opposes. It is not simply true of her that she supports the bill. She does and she doesn't. Nor is her support entailed or explained by the fact that she falls under the concept of Senator. Thus talk of aspects is not just talk of individuals or concepts.22 When applied to the Trinity, this is Modalism with the denial of the Indiscernibility of Identicals. The Father, Son and Holy Spirit are aspects of the same individual, which has different properties in each aspect. In this way, Baxter asserts, we can discern between the identical.23 theorists put a lot of effort in trying to counteract assumptions that an entity in one aspect (or thought or counted under one concept) is not identical to that very entity when in another aspect (or thought or counted under another concept). For instance, the modalist asserts that the Father is just God in the aspect of (or when considered as) creator of the world, the Son is just God in the aspect of (or when considered as) the Word made incarnate, etc. This is much like thinking, going back to Frege, that the Illiad is one poem in the aspect of (or when counted under the concept of) literary work, twenty-four books in the aspect of (or when thought under the concept) homework assignments, etc. 21 Baxter, Forthcoming, p. 9. 22 Baxter, Forthcoming, p. 11. 23 One might here pause and wonder if we really have Modalism after all. Might discernibility be enough for distinctness (in a sense) of the persons? Suppose that we recognise, as David Brown would like us to, that at the time the Athanasian Creed was written, 'Person' did not mean what we usually think of as a person today, a "self-reflective and self-determining center of consciousness" (Brown, p. 526), but instead only meant 'the bearer of a referent.' Would this help? It seems not; the point of Baxter's claims is that the entities under discussion really are identical, even though they have different properties. Any inclination we have to see them as distinct is simply due to our (purportedly misguided) tendency to associate discernibility with (and perhaps even define it in terms of) non-identity. Modalism only requires that the 11 Does this give us something new and helpful? At the very least, we would need to have independent motivation for Composition as Identity, and also agree that Composition as Identity requires a denial of the Indiscernability of Identicals. However, Baxter is in the minority with respect to this second issue. Further, this would merely give us additional support for one way of endorsing a response to the Puzzle of the Trinity that we are already well aware of (i.e., Modalism with a denial of the Indiscernability of Identicals), and this solution will still face other problems, such as having been deemed heretical due to conflation of the Persons. So Composition as Identity isn't giving us any new alternatives. So, taking the composition relation between the Persons and God to be one-one is unhelpful. What of taking it to be many-one? 3.2. Many-One Composition Suppose we claim that the Persons stand in a many-one composition relation to God; that is, that they are each a proper part of God, and together compose Him. Now it seems we are simply left with a form of Social Trinitarianism. Michael Rea describes Social Trinitarianism as maintaining that "the relation between God and [each of] the Persons is not any sort of identity or sameness relation at all. Rather, it's something like parthood (God is a composite being whose parts are the Father, Son, and Holy Spirit) or membership (God is a community whose members are the Divine Persons)."24 Using parthood, the Social Trinitarian will claim there is one god, God, who is a composite being whose parts are the Father, Son, and Holy Spirit. This is exactly what we have when we require that composition is many-one in our application of Composition as Identity. So taking the many-one option requires that the Composition as Identity theorist endorse a response to the puzzle of the Trinity which can stand on its own. We might wonder, though, whether Composition as Identity can still contribute something to this solution. Social Trinitarians say there is only one thing identical to God, namely the community or fusion (or something relevantly similar) of the Persons. But we still want to preserve as much as possible the claim that each Person is a god. Monotheists cannot endorse both claims without appealing to one of the other responses Persons are identical; if there is only one referent, it does not matter that there are different senses or modes (via the individual's different aspects) of reference. 24 Rea, p. 432. 12 to the problem of the Trinity (like relative identity, Modalism, etc.). The only way in which the monotheist Social Trinitarian can claim the Persons are gods is via appeal to something like derivative Divinity. However, if we cared enough about the godhood of the Persons, we could combine our Social Trinitarianism with polytheism. We would still have only one God in the sense of having a single community of Divine Persons, but there would also be a god for each of the Persons to be identical to (so: there would be a total of four gods, one of whom is identical to God).25 Of course Social Trinitarians needn't be polytheistic.26 But endorsing polytheism along with Social Trinitarianism would provide a way to claim both that each Person is a god, and that there's only one God. One might hope that Composition as Identity can help the polytheist Social Trinitarian reduce the number of gods posited, so that our Social Trinitarian can claim that each Person is a god and the community is a god, but say nonetheless that there are not four gods. With the help of Composition as Identity, they could claim there are three gods when counting by Persons, and one when counting by communities (or counting by things identical to God); any higher number would be double-counting. We'd be including the same portion of reality in our ontology more than once. After all, consider an analogous example (presented by Baxter27 and discussed further by Wallace28): when counting a six-pack of beer, we want to say that there are six beers, one six-pack, etc. But when asked how many things there are in total, we should not simply sum these up, on pain of double counting. If we did, we would be counting the same entity more than once (first as beers, then as a six pack). Unfortunately, as Donald Baxter has noted, Fregean counting won't actually help us avoid double-counting in cases where the composite falls under the same relevant sortal as the parts. So it will not help us avoid double-counting with respect to gods, since each Person is a god, while the plurality is also identical to a god. To see why, imagine taking a bunch of dog statues, and making a larger dog statue out of them. When we want to know how many statues are there, we must count the composite statue, and 25 Unless, e.g., one of the Persons really is identical to the community of all of the Persons, somehow . . . 26 For instance, one could deny the claim that the Persons are God in any sense stronger than being proper parts of or members of God. My claim that applying Composition as Identity to the Trinity produces a form of Social Trinitarianism, however, still stands. And Social Trinitarianism, even in this form, can stand alone in reconciling the claims of the Trinity, independent of the thesis of Composition as Identity. 27 Baxter 1988. 28 Wallace, p. 12. 13 each of the statues that make it up. We seem to count the same portion of reality twice, in spite of sortal-relativization, and so end up with a number that's higher than it should be.29 One might claim that the dog statue case is not analogous to the case of the Trinity – after all, we have different sortals with the Trinity, which I've used throughout this paper: Gods and Persons. However, if we take the Trinitarian to be asserting that each Person is a god, and we claim that God is a god composed of the Persons, we have the result that a god is composed of gods. So when counting by gods, we must count the one god that Trinitarians posit, and the three gods that the fusion has as proper parts. (After all, all of the gods I've mentioned are numerically distinct; while the fusion may be identical to the plurality of gods, it is not identical with each god). This seems problematic: not only are we double-counting, but we seem to have an explosion of gods. Even the most enthusiastic proponents of the Divinity of the Persons probably don't think that there are four Christian gods. What can we do to escape these consequences? One option is to follow Baxter in rejecting Frege's way of counting and embracing the denial of the Indiscernibility of Identicals. This gives us a genuinely new option. We no longer have to count by gods when counting objects; we can say there are three gods, which just are identical to the one god. Polytheism allows us to have distinctness of the Persons while each of them is a god, and Composition as Identity gives us a relation between the Persons and God (i.e., the god that's identical to the community, according to Social Trinitarians) that does some work in explaining our Trinitarian leanings: Trinitarians, it can be said, emphasise a close relationship between the Persons; Composition as Identity gives us not only that they together compose a single entity, God, but also that they are identical to God. And the denial of the Indiscernibility of Identicals allows us to have a cardinality of gods that never exceeds 3. Unfortunately, this new option, of combining polytheism, Social Trinitarianism, the Indiscernibility of Identicals and Composition as Identity, does not warrant much excitement. First, polytheism requires an outright denial of monotheism, which is widely taken to be a component of Trinitarianism. Second, the denial of the Indiscernibility of Identicals undercuts the motivation for positing more than one Person: in the creeds, and especially in the Athanasian Creed, the claim that the Persons are distinct is supported by 29 This objection is based on: Baxter 2005, p. 9 14 pointing out that they have different properties.30 If we allow discernibility without distinctness, we undercut the motivation for denying Modalism (given that we're choosing between two heretical views, Modalism and polytheism). So while Strong Composition does give us a new option for asserting polytheism, once we reject the Indiscernibility of Identicals we won't have any need to endorse polytheism. It's also worth noting that, at best, this view will give us the result that there is one god (on one way of counting, or in one aspect) which is identical to three gods (on another way of counting, or in another aspect). But this isn't sufficient to satisfy the claims in the Athanasian Creed, for the Creed claims not only that there is one God, but also denies that there are three gods: it says, "there are not three gods, but one God". If we take the denial seriously, then there are no three gods for God to be identical to, and our application of the composition thesis is in trouble. Perhaps one could attempt to respond to this worry by saying something like this: of course it's true that there are not three gods, but one god, on one way of counting (or in one aspect of the entity). When we index all predications of cardinality to concepts or sortals we're counting under (or aspects in terms of which we're characterising the entity), any time we have a result that an entity e has a cardinality of n under sortal (or aspect) x, we get the result that it has a cardinality of exactly n under x, and thus, under x, it does not have a cardinality of n' (where n' is any number distinct from n). This response, however, has the downfall that inasmuch as its proponent was committed to the truth of the original claim in the Athanasian creed, they are committed to the truth of this statement about the Trinity as well: there is not exactly one god, but three gods. The statements are alike in all relevant respects, except for which sortal we are counting the Persons and their fusion under (or what aspect the entities are being characterised in terms of), and so the statements should be equally plausible. But it looks just like the denial of the original claim in the Athanasian creed; to interpret the original statement in a way that makes it compatible with what appears to be its denial seems problematic. So, to conclude: I've shown that if we take composition between God and the Persons to be a one-one relation, composition as Identity will be doing no work; we'll end up with identity between each of the Persons and God, and will have the standard 30 "The Father was not made, nor created, nor generated by anyone. The Son is not made, nor created, but begotten by the Father alone. The Holy Spirit is not made, nor created, nor generated, but proceeds from the father and the Son." 15 options available, like relativisation of identity, a denial of the transitivity of identity, and modalism. If we take the Persons to each be proper parts of God, and to together compose God, then we have a form of Social Trinitarianism. Composition as Identity is helpful to the Social Trinitarian who also endorses polytheism and the denial of the Indiscernibility of Identicals, but denying the Indiscernibility of Identicals undercuts the motivation for polytheism and so this is not a package anyone would have reason to endorse. Further, taking this option requires construing the claim that there are not three gods, but one god, as merely as plausible as what looks like it's denial, the claim that there is not exactly one god, but three gods. We must conclude that Composition as Identity, while a strange yet interesting Mereological claim, is of no use to the Trinitarian.31 31 I am very grateful to Donald Baxter, Daniel Howard-Snyder, Daniel Nolan, Ted Sider, and Dean Zimmerman for helpful comments on and discussion about this paper. 16 Works Cited: Anderson, Rev. Michael H. Creeds of Christendom. <http://www.creeds.net/ancient/Quicumque.html > Baxter, Donald. Forthcoming. 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