The doctrine of the trinity maintains that God exists in three persons. The doctrine is not found explicitly in the Bible. Rather, it has been inferred from biblical claims and formulated as official doctrine in various Christian creeds and confessions.3 The earliest creedal formulations of the doctrine—in the Creed of

3 For a useful discussion of the biblical support for the doctrine, see Gerald O'Collins, SJ, The Tripersonal God (Mahwah, NJ: Paulist Press, 1999).

Nicaea (325), the Nicene-Constantinopolitan Creed (380/1), and the Athana-sian Creed (c.500) tell us in a limited way what it is for God to exist in three persons; but problems still remain.

The limited characterization we have is this: In God, there are three genuinely distinct persons, Father, Son, and Holy Spirit. The persons are not to be viewed as mere manifestations or aspects of a single substance; rather, each is a substance, and is consubstantial with the Father.4 To say that the persons are consubstantial is at least to say that they share a common nature. Whatever else it means, then, it means that all three persons are equally divine: no one is superior to or any more divine than any of the others. Thus, Father, Son, and Holy Spirit are three distinct divine beings. And yet, says the Athanasian Creed, they are not three gods, but there is one god.5

In light of all this, the doctrine of the trinity may fruitfully be viewed as the conjunction of three theses, along with some constraints. The theses are T1—T3:

(T1) There is exactly one god.6

(T2) Father, Son, and Holy Spirit are not identical to one another.

(T3) Father, Son, and Holy Spirit are consubstantial.7

The (primary) constraints are that T1—T3 are to be interpreted in such a way as to avoid the following three errors, or heresies: modalism (the view that the persons are mere manifestations or aspects of something), subordinationism (the view that the divinity of one or more is subordinate to that of another), and

4 The consubstantiality of the Son with the Father is explicit in the creeds of produced by the First Council of Nicaea in 325 and the First Constantinopolitan Council in 380/1. (It is the latter creed that is nowadays usually referred to by the label 'the Nicene Creed'.) The consubstantiality of the Spirit with the Father is affirmed in the Synodical Letter of the First Constantinopolitan Council. The Greek term, which appears in a lot of the relevant literature, is homoousion

5 This translation is from the essay by Brower and Rea, Chapter 6 in this volume, but with the capitalizations removed from the word 'god'. I have done this to make it clear that 'god' in this context functions not as a name but rather as a kind-term. It's a rather weak monotheism to say 'There is exactly one God', with 'God' functioning as a name. For, after all, that claim is consistent with the claim that there is exactly one Zeus and with the claim that there are gods superior to God.

6 As indicated in note 5, I think that what is essential to the doctrine of the trinity is not the claim that there is exactly one bearer of the name 'God', but rather that there is exactly one substance of the kind god. So, to avoid various confusions, I'll restrict the capitalized 'God' for proper-name uses. I do this for the sake of convenience here, not on principle. (Elsewhere I have been happy to mark the relevant distinctions and so on in other ways.)

7 It is more common nowadays to claim that the central tenets of the doctrine are these three: (i) there is exactly one God; (ii) the Father is not the Son, the Son is not the Spirit, and the Father is not the Spirit; and (iii) the Father is God, the Son is God, and the Spirit is God. This way of characterizing the doctrine more closely follows the Athanasian Creed. But the language of (iii) is less clear than the language of T3 above (due to the fact that the predicate 'is God' can be, and has been, assigned a variety of different meanings). Just as importantly, this formulation obscures the centrality of the notion of consubstantiality in the doctrine—the very notion that lay at the centre of some of the most important controversies surrounding the First Nicene Council. My own formulation of the doctrine is more in accord with formulations found, for example, in the systematic theologies of Louis Berkhof and Charles Hodge.

polytheism (the view that it is not the case that there is exactly one god). This is the heart of the doctrine of the trinity.

But problems linger. The most notable problem, and the one that has dominated the attention of contemporary philosophers, is the apparent threat of contradiction. (Thus it is usually called the logical problem of the trinity..) There are various ways of trying to demonstrate the inconsistency. The one I favour focuses on the fact that two divine beings who are consubstantial are identical with respect to their divinity (so that neither is any more or less of a god than the other). Thus:

(1) There is exactly one god, the Father Almighty. (From T1)

(3) The Son is consubstantial with the Father but not identical to the Father. (From T2 and T3)

(4) If there are x and y such that x is a god, x is not identical to y, and y is consubstantial with x, then it is not the case that there is exactly one god. (Premise)

(5) Therefore: It is not the case that there is exactly one god. (From 2, 3, 4)


The only way out of the contradiction is either to give up one of the tenets of the doctrine of the trinity or to give up Premise 4.

Most philosophers working on this problem have tried to solve it in one (or a combination) of the following three ways: (i) by oflEring a model or analogy that helps us to see how it might be coherent to say that there is one god but three divine persons, (ii) by oflEring an account of what it means to say 'there is exactly one god' that doesn't imply that all divine beings are the same god, or (iii) by defending a view according to which numerically distinct beings might nonetheless be the same god. The models are heuristic devices aimed at making the doctrine intelligible. They solve the problem, however, only if they help us to see our way clear to rejecting Premise 4. Strategies (ii) and (iii) are more directly aimed at that task. In particular, each is aimed at helping us to see how the following claim might be coherent:

claim: There are three divine beings but there is exactly one god. If 'there is exactly one god' doesn't imply that all gods are the same divine being, then 'there is exactly one god' doesn't imply that there is exactly one divine being, and so claim is unproblematic. Likewise, if distinct beings can be the same god, then it might be that there are three divine beings who nevertheless count as one god. Hence, again, claim is unproblematic. And if claim is true, then Premise 4 is false.

Until recently, it has been common in the literature to try to force solutions to the problem of the trinity into one of two camps: Social Trinitarianism (ST) and Latin Trinitarianism (LT). Supposedly, ST represents a way of thinking about the trinity that has its roots in the Eastern Church, most notably in the work of the fourth-century Cappadocian Fathers (Gregory of Nyssa, his brother Basil of Caesarea, and their friend Gregory Nazianzen). LT, on the other hand, is supposed to be a substantially different way of thinking about the trinity which has its roots in the Western Church and is paradigmatically exemplified in the work of Augustine and Aquinas. According to the common lore, ST takes the threeness of the persons as given and tries to explain their unity, whereas LT takes the unity of God as given and tries to explain the threeness of the persons. Accordingly, social trinitarians are commonly charged with erring on the side of polytheism whereas Latin trinitarians are often accused of slipping into modalism.

Note, however, that the difference between ST and LT is not at all obviously the same as the difference between strategies (ii) and (iii) mentioned above. Nor is it clear what exactly it means to take either the threeness of the persons or the unity of God 'as given' and to try to explain the other (while somehow not also explaining what one allegedly takes as given). This should make us suspicious of the utility of this standard way of dividing the literature. Moreover, the LT/ST classificatory scheme has recently come under heavy attack for historical reasons as well.8

That said, though, much of the most important contemporary literature presupposes the standard ST/LT classificatory scheme. In terms of that scheme, the essays in Part I by J. P. Moreland and William Lane Craig and by Peter Forrest exemplify the ST approach whereas the essay by Brian Leftow exemplifies the LT approach. The essay by Peter van Inwagen seems to me to transcend the LT/ST categories. Richard Cross's paper offers some of the historical reasons for thinking that the LT/ST classificatory scheme ought simply to be rejected; and the paper by Jeffrey Brower and myself presents a view roughly in line with van Inwagen's which is fleshed out in a way that I think is well in keeping with models offered by the most prominent fourth- and fifth-century writers on the doctrine of the trinity (including both Augustine and Cappadocian Fathers).9

Elsewhere, I have suggested that contemporary social trinitarianism is committed to the following central tenets:

8 See esp. Lewis Ayres, Nicaea and its Legacy: An Approach to Fourth-Century Trinitarian Theology (New York: Oxford University Press, 2004) and Michel Rene Barnes, 'Augustine in Contemporary Trinitarian Theology', Theological Studies 56 (1995): 237—50, and 'De Regnon Reconsidered', Augustinian Studies 26 (1995): 51—80.

9 For further details on the contemporary literature, see Michael Rea, 'The Trinity', in Flint and Rea (eds.), Oxford Handbook of Philosophical Theology. For an excellent and thorough overview of the 4th-cent. controversies over the doctrine, see Ayres, Nicaea and its Legacy. Useful collections on the doctrine of the trinity include Stephen T. Davis et al. (eds.), The Trinity: An Interdisciplinary Symposium on the Doctrine of the Trinity (New York: Oxford University Press, 1999) and Thomas McCall and Michael Rea (eds.), These Three are One: Philosophical and Theological Essays on the Doctrine of the Trinity (Oxford: Oxford University Press, 2009).

1. Father, Son, and Holy Spirit are not numerically the same substance. Rather, the persons of the trinity are consubstantial only in the sense that they share a common nature; and the sharing is to be understood straightforwardly on analogy with the way in which three human beings share a common nature.

2. Monotheism does not imply that there is exactly one divine substance. Rather, it implies at most only that all divine substances—all gods, in the ordinary sense of the term 'god'—stand in some particular relation R to one another, a relation other than being the same divine substance.

3. The persons of the trinity stand to one another in the relation R that is required for monotheism to be true.

Different versions of ST might then be distinguished in accord with differences over what relation R amounts to.

There are many candidates in the literature for being monotheism-securing relations, but the most popular are the following:

(a) Being parts of a whole that is itself divine.

(b) Being the only members of the only divine kind.

(c) Being the only members of the community that rules the cosmos.

(d) Being the only members of a divine family.

(e) Being necessarily mutually interdependent, so that none can exist without the others.

(f) Enjoying perfect love and harmony of will with one another, unlike the members of pagan pantheons.

Most social trinitarians in fact opt for a combination of these, and most (but not all) of the combinations include at least (a), (b), and (c).10 William Lane Craig and J. P. Moreland focus primarily on (a). On their view, God is composed of the divine persons in a sense analogous to the way in which the three-headed dog Cerberus, guardian of the underworld in Greek mythology, might be thought to be composed of three 'centers of consciousness'. On their view, the three conscious parts of Cerberus are not dogs; there is only one full-fledged dog— Cerberus. But the centres of consciousness are canine, just as any other part of Cerberus is (derivatively) canine. One dog, then; three derivatively canine individuals. Likewise in the trinity: one full-fledged god; three derivatively divine individuals. Monotheism is thus secured by the fact that the persons are parts of a single fully divine being.

■0 See, for starters, Richard Swinburne, The Christian God (Oxford: Oxford University Press, 1994); David Brown, The Divine Trinity (La Salle, IL: Open Court, 1985); and Cornelius Plantinga, Jr., 'Gregory of Nyssa and the Social Analogy of the Trinity', Thomist 50 (1986): 25—352; 'The Threeness/Oneness Problem of the Trinity', Calvin Theological Journal 23 (1988): 37—53; and 'Social Trinity and Tritheism', pp. 21—47 in Ronald Feenstra and Cornelius Plantinga, Jr., Trinity, Incarnation, and Atonement (Notre Dame, IN: University of Notre Dame Press, 1989). Additional references may be found in the essays that follow.

Peter Forrest, on the other hand, develops a model according to which the persons are 'quasi-individuals' who are the products of divine fission. To say that they are quasi-individuals is to say (i) that they lack individuating properties, and so (ii) there is a unique lowest correct answer to the question 'how many are they?' but no unique correct answer. To get a handle on what this means, consider a world about which we may correctly say 'there is nothing in the world except for two perfectly indiscernible spheres'. If the spheres are perfectly indiscernible, then they have no individuating properties (no 'thisness'). But if they have no individuating properties, then, really, there is no fact of the matter how many spheres there are. It is appropriate to say that there are two; but one might just as well say that there is one (presumably bi-located) sphere. Likewise, he thinks, one might also correctly say that there are three, or four, or however many you like. There is, therefore, no correct answer to the question of how many spheres there are, but (since there is at least one sphere) there is a lowest correct answer. He then suggests applying this metaphysic to the trinity: The lowest correct answer to the question 'How many (primordial, pre-fission) gods are there?' is one; but, due to divine fission, the lowest correct answer to the question 'How many divine persons are there?' is three. Much of the paper is devoted to arguing that this way of thinking of things provides a model of the trinity that preserves a great deal of what we (adherents of orthodoxy) want to say about the trinity.

Pursuing a related idea, Brian Leftow argues that the persons of the trinity might be thought of on analogy with a time traveller who appears thrice located at a single time.11 Toward developing his model, Leftow oflErs us the example of Jane, a Rockette who is scheduled to dance in a chorus line but, at the last minute, discovers that two of her partners have failed to show up. Jane goes on stage and dances her part, then later enters a time machine (twice) so that she can (twice) go on stage with herself and dance the leftmost and rightmost parts as well. According to Leftow, there is a very clear sense in which Jane's part of the chorus line contains three of something; and yet there is just one substance (Jane) in that part. Likewise in the case of God. The three persons are analogous to the three simultaneously existing 'segments' of Jane's life. According to Leftow, '[e]ach Rockette is Jane. But in these many events, Jane is there many times over.' And, apparently, what we say about Jane and the three Rockettes is also to be said about God and the three divine persons.

The papers by van Inwagen and by Jeffrey Brower and myself aim to solve the problem in a very different way: by explicitly pursuing strategy (iii) above. Pursuing strategy (iii) is a matter of trying to show that distinct beings might nonetheless count as the same god. How would one do this? The most

11 I say that Leftow's idea is related to Forrest's because I think that there is an interesting resemblance between divine fission as Forrest characterizes it and the sort of splitting into three 'life events' that Leftow seems to have in mind. Whether the similarities should call into question Forrest's characterization of his own view as a form of ST, or Leftow's characterization of his view as LT, is an interesting further question.

straightforward way is to endorse the doctrine of relative identity. There is a weak version of this doctrine, and a strong version. The weak version says:

(RI1) States of affairs of the following sort are possible: x is an F, y is an F, x is a G, y is a G, x is the same F as y, but x is not the same G as y. The strong version is just the weak version plus (RI2):

(RI2) Either absolute (classical) identity does not exist, or statements of the form 'x = y are to be analysed in terms of statements of the form 'x is the same F as y' rather than the other way around. RI2 is not needed for solving the problem of the trinity; but some philosophers—notably, Peter Geach—endorse it for other reasons, and it serves as independent motivation for RI1.12

Defenders of the relative identity solution have mostly occupied themselves with working out the logic of relative identity in an effort to show that the doctrine of relative identity itself is coherent, and to show that the doctrine of the trinity can be stated in a way that is provably consistent given the assumption of relative identity. The most important paper of this sort is Peter van Inwagen's (highly technical) 'And Yet They Are Not Three Gods, But One God'." The paper included in this volume is a shortened and somewhat simplified presentation of the same line of reasoning.

RI2 in particular is widely rejected as implausible; and I have argued elsewhere that invoking it in a solution to the problem of the trinity implies that the diflErence between the persons is theory-dependent, and so merely conceptual. 14 But without RI2, RI1 is (at first glance, anyway) unintelligible. The reason is simple: sameness statements are naturally interpreted as identity statements. So, the claim that 'x and y are the same F' seems logically equivalent to the claim that 'x is an F, y is an F, and x = y. RI1 is inconsistent with this analysis of sameness statements. But on its own, it doesn't supply any replacement for that analysis. Thus, it renders sameness claims utterly mysterious. Appealing to RI1 without a supplemental story as a way of solving the problem of the trinity, then, simply replaces one mystery with another. That is hardly progress.

The paper by Jeffrey Brower and myself supplies the relevant supplemental story: a story according to which, in short, to say that x and y are the same god is just to say that x and y do something analogous to sharing all of the same matter in common. At the heart of our view is the idea that the divine persons are to be thought of on the model of Aristotelian matter-form compounds. Their constituents are a shared divine nature which plays the role of matter and a

12 See e.g. Peter Geach, 'Identity', Review of Metaphysics 21 (1967): 3—12, and Reference and Generality, 3rd edn. (Ithaca, NY: Cornell University Press, 1980), secs. 30, 34, and 110.

13 pp. 241—78 in Thomas V. Morris (ed.), Philosophy and the Christian Faith (Notre Dame, IN: University of Notre Dame Press, 1988).

14 'Relative Identity and the Doctrine of the Trinity', Philosophia Christi 5 (2003): 431—46.

person-defining property (like being the Son, or being Begotten) that plays the role of form. Thought of this way, however, our view is quite similar to the view that Richard Cross identifies as the fundamental point of agreement between Eastern and Western views of the trinity. According to Cross, East and West agreed that (a) the divine nature is a property, and (b) that one and the same divine nature is a constituent of each of the divine persons—i.e., it is the point at which they overlap. If this is correct, then the view that we defend has some claim to being a development of a way of thinking about the trinity that was held in common by the most important fourth- and fifth-century defenders of Nicene orthodoxy in both the East and the West.15

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