The paper was presented at the 2018 conference "Analytic Theology and the Tri-Personal God: the Trinitarian Renewal in Analytic Tradition" at Université catholique de Louvain Publication is forthcoming in a volume in Bibliotheca Ephemeridum Theologicarum Lovaniensium What Exactly Are the Intra-Trinitarian Relations? I. WHAT IS A TRINITARIAN MODEL? In his Invitation to Analytic Christian Theology, Thomas McCall claims that analytic theology should be a "retrieval theology" – that it should examine and critically engage various theological proposals from Christian tradition. McCall insists that such a retrieval is especially wanted in the contemporary analytic discussions of the doctrine of the Trinity, which have been "fairly loose" in their use of the tradition 1 . It is true that the majority of analytic debates over social vs. Latin models of the Trinity are quite independent from theological heritage of the Early and Medieval Church. Very few contemporary philosophers have used arguments from the tradition in their own reasoning about the Trinity. Even those who have incorporated some of the historical material into their theories usually treat the tradition uncritically, either as a convenient example of a kindred spirit in the past, or as an authoritative point of reference. McCall's ideal of the retrieval theology requires critical examination of the traditional Trinitarian models. Such a retrieval of the historical models is a promising area of research in itself, and it would be of great value for the contemporary analytic debates about models of the Trinity. If we are to embark on a quest to retrieve the traditional Trinitarian models, what exactly should we be looking for? What is a Trinitarian model? I take it that the minimal requirements for a conception to qualify as a Trinitarian model consist of addressing the following questions: 1. What are "the three" in the Trinity, and what is "one" about them? The very idea of the "Tri-nity" implies that there are things to count, things of the same ilk; so the question is, what are those entities that we count ending up with the number 3? And what is this entity that we count as one in connection with those three? 2. How is there unity in plurality, and plurality in unity? In other words, what is responsible, or what accounts for the three being one, and what accounts for the one being three? To my knowledge, this is the question which contemporary analytic Trinitarian theology finds to 1 T.H. MCCALL, An Invitation to Analytic Christian Theology, Downers Grove, IL, InterVarsity Press, 2015, pp. 85-87. 2 be most appealing, since the majority of the debates are about some proper mixture of unity and plurality. 3. How each of the three is distinguished from the others? Answering this question is necessary for a Trinitarian model to be exhaustive. Unfortunately, most of the contemporary analytic models of the Trinity do not even attempt addressing it. As I see it, this is a major deficiency of the contemporary models, and this is where the retrieval of the traditional models could be of great value. I guess, I should have added yet another question: Why is the number 3 not accidental to the Trinity? But that would be unfair. There are so few models that address this question, not only in our time but also in the tradition, that adding this requirement would be too much of a burden. So, if we want to retrieve different Trinitarian models from the tradition, we should look there for answers to those three questions. What are those traditional answers? 1. As for the first question, there is only one orthodox answer. Initially, there was a variety of opinions, but the synod of Alexandria in 362 A.D. validated only one conventional formula: that which is one in the Godhead is essence, and those which are three are hypostases, or persons. 2. There is also a remarkable unanimity among the Church fathers in their answers to the second question: the foundation of unity is the divine essence, and the foundation of plurality are the intra-Trinitarian relations. Why relations? In the early 3 rd century Christian theologians came up with the idea that the names "Father" and "Son" indicate relations, and relations indicate plurality 2 . But the real breakthrough occurred somewhere in the middle of the 4 th century. In the thick of the debates with the followers of Arius, some pro-Nicene theologians happily stumbled upon a convenient philosophical idea: the Aristotelian category of relation is the only category that is not predicated to the essence. This maneuver was immediately taken up and transformed into an argument against the Arians. While the Arians argued that any plurality endangers the unity of the divine essence, the pro-Nicene theologians answered that since relation says nothing about the essence, then the relative distinctions in the Godhead do not violate the unity of the divine essence; therefore the distinctions in the Trinity must be according to the category of 2 L. TURCESCU, Gregory of Nyssa and the Concept of Divine Persons, Oxford, Oxford University Press, 2005, p. 81; L. AYRES, Nicaea and its Legacy. An Approach to Fourth-Century Trinitarian Theology, Oxford, Oxford University Press, 2006, pp. 43, 201-202. 3 relation. From then onward it became the standard way of treating plurality in the Godhead in Catholic theology 3 . 3. At this point, however, the patristic consensus has reached its end. There was no unanimity about a proper way of distinguishing the divine persons. While the Church fathers agreed that we should somehow apply relations to the distinctions in the Trinity, they did not have the same understanding of what the intra-Trinitarian relations really are. Unlike the widespread Aristotelian and Stoic lists of categories, which involved a category of relation, there was no conventional metaphysical theory of relations at the time. Different theologians came up with different ideas about the nature of relations, and that resulted in different ways of distinguishing one divine person from another. The only patristic consensus here was about the general rule that the distinction between the persons must be described according to their relations, but how one should interpret that rule was a matter of individual metaphysical preferences. II. HOW TO RETRIEVE A TRINITARIAN MODEL? Since the answers to the first two questions from our list are standard and well-known, our quest for patristic Trinitarian models should be focused only on the third one. We should also keep in mind that the only distinction between the persons that was approved by the Church Fathers is the difference in their mutual relations. Therefore, we have to narrow down our question for the patristic writers. Formulated in a more technical way, our main question (henceforth: "our main question") should look like this: "What is the relational internal structure of the Godhead, and how does it allow identifying the Father, the Son, and the Holy Spirit?" 4 . Looking for answers to our main question in the patristic writings would be more efficient if we could equip ourselves with up-to-date tools of analytic metaphysics. Unfortunately, as in the patristic era, the contemporary metaphysics of relations is "still in its infancy" 5 . Nevertheless, in spite of its infancy, it is already capable of providing some apparatus for the analysis of the patristic relational models. I suggest using the taxonomy of relations that is widely applied in mathematics and analytic philosophy. We will need such categories as the degree of relations, the symmetry, and the externality. 3 AYRES, Nicaea, (n. 2), p. 201; C.A. BEELEY, Gregory of Nazianzus on the Trinity and the Knowledge of God, New York, NY, Oxford University Press, 2008, pp. 161, 208, 312. 4 I borrow the phrase "internal structure of the Godhead" from Tertullian's concept of dispensatio, or οἰκονομία in the One God (Adv. Prax. 2.1). 5 P. SIMONS, Relations and Truthmaking, in Proceedings of the Aristotelian Society Supplementary Volume 84 (2010), 199-213, p. 199. 4 The degree of relation (also known as adicity or arity) is the number of things that are involved in the relation. Thus, a "two-place" relation (a.k.a. dyadic or binary) has the degree of 2, a "three-place" relation (triadic or ternary) has the degree of 3, and so on. If the relation has a definite degree (for example, it is always binary, or always ternary), then it is a unigrade relation. If it does not have a definite degree, i.e. it can be either binary, or ternary, or something else, it is called a multigrade relation. We will also use a distinction between symmetric and asymmetric relations. By definition, if x has a symmetric relation to y, then y has the same relation to x. And, by definition, if x has an asymmetric relation to y, then y does not have that same relation to x. Finally, we will need the distinction between external and internal relations. This distinction is not entirely clear and there are ongoing debates about its proper criteria 6 . Nevertheless, the basic idea is that a relation is internal if it is necessitated by the intrinsic properties of the related objects, otherwise it is external. Having equipped ourselves with this taxonomy of relations, we are ready to proceed with our quest for retrieval of traditional Trinitarian models. Due to the limits of this paper I will mention only a few models – those of Basil, Gregory Nazianzen, and Boethius. In addition I will examine a medieval attempt to combine the patristic ideas – the Trinitarian model of Aquinas. III. PATRISTIC TRINITARIAN MODELS 1. Pre-Cappadocian Trinitarian relations The earliest complete answers to our main question in the history of Christian theology are given by the Great Cappadocians, namely, Basil of Caesarea, Gregory Nazianzen, and Gregory of Nyssa. But before we proceed to their relational Trinitarian models, we should take a quick look at the earlier tradition. From the time of Tertullian and Origen 7 , there was a persistent theological line of reasoning that the name "Father" indicates that there is an eternal relation of fatherhood in God, and that, in turn, implies that there must be an eternal relation of sonship in God, which does not belong to the Father. This was not, however, a complete Trinitarian model, because the pre-Cappadocian theology did not address relations with the Holy Spirit. Since it fails to identify the third person of the Trinity, it does not provide a satisfactory answer to our main question. The incomplete model includes only two relations – fatherhood and sonship, which are binary, asymmetric, and internal (Figure 1). 6 Ibid., pp. 203-206. 7 TERTULLIAN, Adv. Prax. 4.4; ORIGEN, De Princ. I.2.2-3. See also AYRES, Nicaea, (n. 2), p. 22, BEELEY, Gregory, (n. 3), p. 312, n. 245. 5 Persons: F = Father, S = Son, HS = Holy Spirit. Relations: R1 = "fatherhood", R2 = "sonship". Figure 1. Pre-Cappadocian relational model Why bring it up if this was not yet an exhaustive model? There are two reasons for that. First, it was a meaningful step towards later fully developed relational models, and it would be worthwhile to compare this early idea with its future developments. The second reason has to do with the fact that the later Church fathers considered this reasoning to be a part of their authoritative tradition. They would often reproduce this discourse even if their own treatment of Trinitarian relations was quite different. In other words, not every statement which comes from the mouth of a Church father is an integral part of his own characteristic doctrine. And we have to be aware of those extraneous elements while retrieving original Trinitarian models. 2. Basil of Caesarea The first complete Trinitarian model comes from Basil of Caesarea. His writings on the Trinity are not entirely consistent, and his ideas are vulnerable to many criticisms; nevertheless, Basil provides the necessary elements of an exhaustive Trinitarian model. Before introducing his own ideas, Basil repeats the traditional discourse about the names "Father" and "Son" that indicate mutual relations 8 . Afterwards, he claims that divine persons can be distinguished by their peculiar properties (ἰδιώματα) – "fatherhood", "sonship", and "sanctifying power" 9 . Since those properties are distinctive for the persons, they must be relations (Figure 2). Relations: R1 = "fatherhood", R2 = "sonship", R3 = "sanctifying power". Figure 2. Trinitarian model of Basil of Caesarea 8 BASIL, Adv. Eun. II, 22. 9 BASIL, Ep. 214.4. 6 Basil's Trinitarian relations differ from the traditional ones. While his predecessors taught that "fatherhood" is that which distinguishes the Father from the Son, Basil's idea implies that "fatherhood" is not a mutual relation, but it is simply a property which defines the Father. In other words, for the predecessors, "fatherhood" was a binary relation, but in Basil's model it becomes unary. Thus, Basil's model can be described as containing three different unary relations, and each of the three relations pertains to only one of the divine persons. As for their symmetry and externality, unary relations are, obviously, internal, and symmetry does not apply to them. 3. Gregory Nazianzen The next model we will address belongs to Basil's younger friend, Gregory Nazianzen. It would be misleading to assume that the Cappadocians must have a common Trinitarian theology 10 . Gregory's model and his relational terminology are unique 11 . It is not easy, however, to extract his original model from his writings. While talking about the Father and the Son, he does not hesitate to repeat and even build upon the traditional binary fatherhood/sonship approach. Moreover, he also pays his respects to his senior friend's idea of personal distinctive properties, simply changing Basil's terminology of unary "fatherhood, sonship, sanctifying power" into "ungenerated, generated, proceeding". It is only when he addresses our main question, i.e. attempts to identify each of the three persons (especially the Holy Spirit), we can see his own original ideas. Gregory introduces two Trinitarian relations – "generation" for the Father and the Son, and "procession" for the Father and the Spirit (Figure 3). Relations: R1 = "generation", R2 = "procession". Figure 3. Trinitarian model of Gregory Nazianzen 10 I agree with Andrew Radde-Gallwitz that Gregory Nazianzen has significantly different Trinitarian views from the two brothers – Basil and Gregory of Nyssa (A. RADDE-GALLWITZ, Basil of Caesarea, Gregory of Nyssa, and the Transformation of Divine Simplicity, Oxford, Oxford University Press, 2009. p.87, n.1). I disagree with him, however, that the two brothers are "sufficiently like-minded", because their Trinitarian models have nothing in common. While Basil builds his Trinity upon three different unary relations, Gregory of Nyssa suffices with only one multigrade symmetric external relation of "communion" (TURCESCU, Gregory, (n. 2), pp. 58, 59, 117). 11 For Nazianzen, the technical term σχέσις, which generally denoted "relation" in Stoic and later Aristotelian philosophy, pre-Cappadocian theologians, and the other two Cappadocians, surprisingly has a different meaning of mutual disposition or position in a relational scheme (P. BUTAKOV, Dispositions and Relations in Gregory Nazianzen [in Russian], in Schole. Ancient Philosophy and the Classical Tradition 9 (2015), no. 2, 363-372). 7 For his predecessors, a relation pertains to only one of the persons; but for Gregory, relations pertain to pairs of persons 12 . Thus, the Spirit is identified as the one who does not participate in "generation", and the Son is the one who is not in "procession". This relational model is complete and fully functional, and it successfully answers our main question. It consists of two different binary relations, which are symmetric and external. 4. Boethius Our next model is of the Western origin. It has its roots in Augustine 13 , and it was brought to completion by Boethius. Boethius claims that there is only one relation that obtains in the simple divine essence, and that is the relation of identity or sameness. But, strangely enough, this relation of identity is not symmetric – it is directed from the Father to the Son, and from both of them to the Holy Spirit (see Figure 4) 14 . Relation R = "identity" (or "procession"). Figure 4. Trinitarian model of Boethius Boethius allows likening this relation of identity to the creedal term "procession". The Son proceeds from the Father, and the Spirit proceeds from the Father and the Son 15 . This elegant solution allows answering our main question: he, who the relation is from, is the Father; he, who the relation is to and from, is the Son; he, who the relation is to, is the Holy Spirit. Thus, Boethius manages to produce an exhaustive Trinitarian model by utilizing only one relation, which is multigrade, asymmetric, and internal. Let us stop here for a moment and compare the three Trinitarian models (Figure 5). It is obvious that they are completely different and incompatible. Each one of them has its own set of 12 Gregory's peculiar approach to relations as referring to pairs of persons becomes obvious when he says that "Father" is the name of the "mutual disposition and relation of the Father to the Son or of the Son to the Father" (Or. 29.16). I provide a more substantiated account of Gregory's Trinitarian model in P. BUTAKOV, Relations in the Trinitarian Reality: Two Approaches, in Schole. Ancient Philosophy and the Classical Tradition 8 (2014), no. 2, 505-519, pp. 507-509. 13 AUGUSTINE, De Trinitate, books V, VII (e.g. V.5.6, VII.1.2). While being considered as typically Western, Augustine can also be seen as a successor of the Trinitarian ideas of Gregory of Nyssa (AYRES, Nicaea, (n. 2), p. 366). 14 BOETHIUS, De Trinitate, 6.20-22. 15 Ibid., 5.46-48. 8 relations, uses different types of relations, and identifies the divine persons in its own unique way. Each one of them, however, is an exhaustive and viable model, and each one conforms to the Catholic doctrine of the Trinity. Author Number of relations Degree of relations Symmetry Externality Basil of Caesarea 3 1 n/a internal Gregory Nazianzen 2 2 symmetric external Boethius 1 multigrade asymmetric internal Figure 5. Patristic Trinitarian relations Will it be worthwhile to bring them all together, as if they were just fragments of a greater picture? Should we consolidate them into one extensive Trinitarian model? I am certain that we ought not to do that. Each of them already is a complete picture and does not require any enhancement. There was, however, a theologian who attempted to produce an all-embracing Trinitarian model – St. Thomas Aquinas. 5. Thomas Aquinas The model of Aquinas is a complex arrangement of several types of Trinitarian relations (see Figure 6). Subsistent relations: R1 = "fatherhood", R2 = "sonship", R3 = "procession". Relations of origin: opposite: R4 = "fatherhood", R5 = "sonship"; non-opposite: R6 = "spiration", R7 = "procession". Figure 6. Trinitarian model of Thomas Aquinas The first type is the subsistent relations 16 : fatherhood, sonship, and procession 17 . The three subsistent relations are the personal properties, which constitute the divine persons. These three relations are unary, and they function in the same way as Basil's relations: each divine person is identified with a certain relation. In addition to the subsistent relations, Aquinas introduces 16 AQUINAS, Summa Theologiae, I, 29, 4. 17 Ibid., I, 30, 2, ad 1. 9 another type – relations of origin 18 . There are four of them: fatherhood, sonship, spiration, and procession. Moreover, there is a further subdivision: two of the four relations of origin – fatherhood and sonship – are opposite relations, and two – spiration and procession – are not, because spiration belongs not to one, but to two persons – the Father and the Son 19 . Fatherhood and sonship are similar to the pre-Cappadocian relations, spiration resembles the procession of the Spirit in the model of Boethius, and the division of the relations of origin into two types – towards the Son, and towards the Spirit – follows the idea of Gregory. Aquinas claims that the persons can be distinguished only through opposite relations of origin 20 . Thus, the Father and the Son are distinguished through the opposite relations of fatherhood and sonship. It is not entirely clear, however, how Aquinas's model identifies the person of the Holy Spirit, since there is no opposite relation of origin for the Spirit's procession. All of the relations of origin are asymmetric and internal, while the opposite ones are binary, and the non-opposite are ternary. Type of relations Number of relations Degree of relations Symmetry Externality Subsistent relations 3 1 n/a internal Opposite relations of origin 2 2 asymmetric internal Non-opposite relations of origin 2 3 asymmetric internal Figure 7. Trinitarian relations in the model of Aquinas The combined model of Aquinas was hardly a success. Apparently, it has no advantage over the models of his predecessors and does not allow achieving more than they already did. It is cumbersome, excessively complex, and it still fails to properly distinguish the person of the Holy Spirit. It utilizes seven different relations of three different types (see Figure 7), which does not sit well with Aquinas's ideal of divine simplicity. I do not imply that one could do a better job of combining the traditional models – I believe that they are mutually exclusive, and the very project of their unification is doomed to failure. 18 Ibid., I, 28, 4. 19 Ibid., I, 30, 2. 20 Ibid. 10 IV. A BONUS: THE FILIOQUE Instead of trying to mix the incompatible ingredients together, I suggest dealing with the traditional models as they are. We should remember, however, that those models are not the sacred doctrine. Albeit being authoritative, they are, nevertheless, negotiable metaphysical theories. If we want to retrieve those traditional models for our contemporary needs, we ought to examine and critically evaluate them, preferably by using the tools provided by analytic philosophy 21 . I hope that this approach has the potential for going beyond the confines of armchair philosophy into the area of systematic theology. For example, it can offer a new solution to the embarrassing problem of the filioque 22 . A closer look at the relational language of the Eastern and Western Trinitarian theologies shows that the fight over the filioque, at its core, is an opposition between metaphysical models. The Western church generally follows the model of Boethius. In that model there is only one relation in the Trinity – the relation of procession, which is from the Father to the Son, and from both of them to the Holy Spirit. In order for the Western Trinitarian model to be functional, there has to be the relation of the Son to the Spirit, otherwise the two persons would be indistinguishable (see Figure 8). Thus, within the framework of the Boethius's model, the Spirit must proceed from the Father and the Son. Figure 8. The filioque in the Western model 21 Such an analysis, for example, is made by John Lamont, who, using the tools of contemporary analytic metaphysics, reveals incoherence in Aquinas's concept of subsistent relations (J. LAMONT, Aquinas on Subsistent Relation, in Recherches de Théologie et Philosophie Médiévales 71 (2004), no. 2, 260-279). Also elsewhere I question the tenability of introduction of external relations into the Godhead by Gregory Nazianzen (BUTAKOV, Relations, (n. 12), pp. 509, 512). 22 I do not suggest that in order to overcome the division over the filioque we should invent yet another relational model à la Nikk Effingham's latest Trinity in N. EFFINGHAM, The Philosophy of Filioque, in Religious Studies 54 (2018), no. 3, 297-312. We should rather sort out the mess that is already on our hands. 11 The Eastern theology operates within the framework of Gregory Nazianzen's model 23 . This model has two different Trinitarian relations – "generation", which is between the Father and the Son, and "procession", which is between the Father and the Holy Spirit. If one would add an additional "procession" between the Son and the Spirit, then the model would fail to distinguish between the Father and the Son (see Figure 9). Therefore, within the Nazianzen's relational model, the Spirit must proceed only from the Father. Figure 9. The filioque in the Eastern model The relation of procession of the Spirit from the Son – the filioque – neither should be forced into the Eastern model, nor should be taken away from the Western model. The Western "procession" is nothing like the Eastern "procession". For the West, "procession" is the name of the only relation in the Trinity, which is multigrade, asymmetric, and internal. For the East, "procession" designates one of the two Trinitarian relations; it is binary, symmetric, and external. Arguing about the filioque without acknowledging the difference in the meaning of "procession" is simply talking past each other. Instead, analytic theologians of the East and the West ought to address the source of the disagreement – their metaphysical models, with unwavering open-mindedness and humility. 23 It was Gregory Nazianzen, and not the other two Cappadocians, who became the definitive theologian for the Eastern church (hence, his title: "Gregory the Theologian"). "Byzantine Christianity, in a real sense, was Gregory's mind-child and masterpiece" (J.A. MCGUCKIN, St. Gregory of Nazianzus: an intellectual biography. Crestwood, NY, St. Vladimir's Seminary Press, 2001, p. xxiv). The great systematician of Eastern theology John of Damascus in his magnum opus teaches about the Trinity following the model of Gregory Nazianzen (DAMASCENE, De Fid. Orth., I.8).